Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.48.0-wmf.3 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk Event Event talk 0 119778 2844819 2843448 2026-11-07T17:17:02Z Young1lim 21186 /* Non-linear Equations */ 2844819 wikitext text/x-wiki == Calculus == === Numerical Differentiation === * Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]]) * Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20241021.pdf |pdf]]) * Discrete Function Differentiation ([[Media:NM.Diff.1Discrete.20241116.pdf |pdf]]) * Forward, Backward, Central Divided Difference * High Accuracy Differentiation * Richardson Extrapolation * Unequal Spaced Data Differentiation * Numerical Differentiation with Octave </br> === Non-linear Equations === * Bisection Method ([[Media:NM.NLE.1Bisection.20241130.pdf |pdf]]) * Newton-Raphson Method ([[Media:NM.NLE.2Newton.20261102.pdf |pdf]]) * Secant Method * False-Position Method </br> === Numerical Integration === * Trapezoidal Rule * Simpson's 1/3 Rule * Romberg Rule * Gauss-Quadrature Rule * Adaptive Quadrature </br> === Roots of a Nonlinear Equation === </br> === Optimization === </br> </br> == Matrix Algebra == === Simultaneous Linear Equations === * A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]]) </br> === Gaussian Elimination === </br> === LU Decomposition === </br> === Cholesky Decomposition === </br> === LDL Decomposition === </br> === Gauss-Seidel method === </br> === Adequacy of Solutions === </br> === Eigenvalue and Singular Value === </br> === QRD === </br> === SVD === </br> === Iterative methods === </br> </br> == Regression == === Linear Regression === </br> === Non-linear Regression === </br> === Linear Least Squares === </br> </br> == Interpolation == === Polynomial Interpolation === </br> === Linear Splines === </br> === Piecewise Interpolation === </br> </br> == Ordinary Differential Equation == </br> == Partial Differential Equation == </br> == FEM (Finite Element Method) == </br> </br> </br> == Using Symbolic Package in Octave == * Visit http://octave.sourceforge.net/index.html * Download symbolic-1.0.9.tar.gz * In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed. * After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps. ./configure ./make ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 * While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu. == Read some tutorials about symbolic computation == * Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf) * Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf) [[Category:Numerical methods]] == Using SymPy ( a Python library for symbolic mathematics) == </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] ke75opb72xveukukfgnavl5p9u25ldp 2844821 2844819 2026-11-07T17:24:10Z Young1lim 21186 /* Non-linear Equations */ 2844821 wikitext text/x-wiki == Calculus == === Numerical Differentiation === * Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]]) * Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20241021.pdf |pdf]]) * Discrete Function Differentiation ([[Media:NM.Diff.1Discrete.20241116.pdf |pdf]]) * Forward, Backward, Central Divided Difference * High Accuracy Differentiation * Richardson Extrapolation * Unequal Spaced Data Differentiation * Numerical Differentiation with Octave </br> === Non-linear Equations === * Bisection Method ([[Media:NM.NLE.1Bisection.20241130.pdf |pdf]]) * Newton-Raphson Method ([[Media:NM.NLE.2Newton.20261103.pdf |pdf]]) * Secant Method * False-Position Method </br> === Numerical Integration === * Trapezoidal Rule * Simpson's 1/3 Rule * Romberg Rule * Gauss-Quadrature Rule * Adaptive Quadrature </br> === Roots of a Nonlinear Equation === </br> === Optimization === </br> </br> == Matrix Algebra == === Simultaneous Linear Equations === * A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]]) </br> === Gaussian Elimination === </br> === LU Decomposition === </br> === Cholesky Decomposition === </br> === LDL Decomposition === </br> === Gauss-Seidel method === </br> === Adequacy of Solutions === </br> === Eigenvalue and Singular Value === </br> === QRD === </br> === SVD === </br> === Iterative methods === </br> </br> == Regression == === Linear Regression === </br> === Non-linear Regression === </br> === Linear Least Squares === </br> </br> == Interpolation == === Polynomial Interpolation === </br> === Linear Splines === </br> === Piecewise Interpolation === </br> </br> == Ordinary Differential Equation == </br> == Partial Differential Equation == </br> == FEM (Finite Element Method) == </br> </br> </br> == Using Symbolic Package in Octave == * Visit http://octave.sourceforge.net/index.html * Download symbolic-1.0.9.tar.gz * In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed. * After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps. ./configure ./make ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 * While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu. == Read some tutorials about symbolic computation == * Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf) * Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf) [[Category:Numerical methods]] == Using SymPy ( a Python library for symbolic mathematics) == </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] e1qmr6eb9k5czyjhqemutihmv4fybwp 0 215163 2844862 2843386 2026-11-08T10:06:48Z CommonsDelinker 9184 Replacing Toby_Fox_mask_(cropped_2).jpg with [[File:Toby_Fox_2017_(cropped_2).jpg]] (by [[:c:User:CommonsDelinker|CommonsDelinker]] because: [[:c:COM:FR|File renamed]]: [[:c:COM:FR#FR4|Criterion 4]] (harmonizing names of file set) · Consistency with other 2844862 wikitext text/x-wiki {{Digital Media Concepts|Toby Fox}} {{Infobox | title = '''Toby Fox''' | image = [[File:Toby Fox 2017 (cropped 2).jpg|200px]] | headerstyle = background:#ccf;{{Text color default}}; | labelstyle = background:#ddf;{{Text color default}}; | label2 = Nationality | data2 = {{{item_one|American}}} | label3 = Born | data3 = {{{item_two|October 11, 1991}}} | label4 = Known For | data4 = {{{item_three| ''Undertale'' and ''Deltarune''}}} | label5 = Birth Place | data5 = {{{item_Four|Manchester, New Hampshire}}} }} Toby Fox (born October 11, 1991) is a video game developer, composer, and musician most known for developing and composing the soundtrack for the critically acclaimed roleplaying game ''Undertale and Deltarune''. == History == Fox was a fan of the game ''EarthBound'' and began as a forum member on its fansite, Starmen.net, under the username Radiation. He became a musician in 2008-2009 and made soundtracks for popular games like Pokemon Scarlet and Violet and Sword and Shield He would be an active member on the site and managed one of the site's forums up until 2011.<ref>{{cite web |url=https://forum.starmen.net/members/473|title= Starmen.net}}</ref> Before starting work on ''Undertale'', he had little experience in actual game development except for the incomplete games he often made with his three brothers using the proprietary game engine RPG Maker 2000. He has made 2 different games and helped by making music in 5 others. He is a self-taught musician and ghool game developer. He graduated from Northeastern University with a Bachelor’s Degree. He was deeply inspired by EarthBound, which influenced his approach to game design and storytelling from a young age. <ref>{{cite web |url=https://seagaia.wordpress.com/2013/05/25/toby-foxs-undertale-dev-2-dev-interview-1/|title= Seagaia}}</ref> For a while, Fox developed ''Undertale'' in the basement of webcomic artist Andrew Hussie, known for creating the popular comic ''Homestuck'', for which Fox also composed tracks for. He has won a NAVGTR Award for Original Role Playing Game, a Japan Game Awards: Award for Excellence, and the SXSW Gaming Matthew Crump Cultural Innovation Award, alongside numerous nominations and accolades from publications like The Escapist, Ars Technica, and Giant Bomb for his groundbreaking work in indie game development and music. He was also named to Forbes' 30 Under 30 list for his impact on gaming. He is known to support the LGBTQ+ community.<ref>{{cite web |url=https://www.kickstarter.com/projects/14293468/homestuck-adventure-game/posts/1453119|title= Homestuck Kickstarter}}</ref><ref>{{cite web |url=http://www.gameinformer.com/themes/blogs/generic/post.aspx?WeblogApp=podcasts&y=2015&m=10&d=15&WeblogPostName=gi-show-_1320_-yoshis-woolly-world_2c00_-star-wars_3a00_-battlefront_2c00_-undertale-toby-fox&GroupKeys=|title= Game Informer}}</ref> == Games == === ''Undertale'' === ''Undertale'' was the first major game completely developed by Toby. He worked on the project independently, with only artwork and sprites being supplied by other creators, mainly freelance artist Temmie Chang.<ref>{{cite web |url=https://www.kickstarter.com/projects/1002143342/undertale/description|title= Undertale Kickstarter}}</ref> Fox began creating ''Undertale'' after already making a battle system using the engine GameMaker: Studio.<ref>{{cite web |url=http://existentialgamer.com/interview-toby-fox-undertale|title= Existential Gamer}}</ref> The original game was meant to be released in 2014 but production was delayed. ''Undertale'' was praised for its writing, for which Fox claims he was inspired by internet culture, comedy shows such as ''Mr. Bean'' and the game ''EarthBound''.<ref>{{cite web |url=http://www.gameinformer.com/themes/blogs/generic/post.aspx?WeblogApp=podcasts&y=2015&m=10&d=15&WeblogPostName=gi-show-_1320_-yoshis-woolly-world_2c00_-star-wars_3a00_-battlefront_2c00_-undertale-toby-fox&GroupKeys=|title= Game Informer}}</ref> When it came to developing the game itself Fox said he wanted to develop a role-playing game that was non-traditional, had "interesting characters", and that "utilizes the medium as a storytelling device ... instead of having the story and gameplay abstractions be completely separate".<ref>{{cite web |url=https://seagaia.wordpress.com/2013/05/25/toby-foxs-undertale-dev-2-dev-interview-1/|title= Seagaia}}</ref>''Undertale'' took 2.7 years to completely develop and was financed through a crowdfunding effort on Kickstarter.<ref>{{cite web |url=http://www.gameinformer.com/themes/blogs/generic/post.aspx?WeblogApp=podcasts&y=2015&m=10&d=15&WeblogPostName=gi-show-_1320_-yoshis-woolly-world_2c00_-star-wars_3a00_-battlefront_2c00_-undertale-toby-fox&GroupKeys=|title= Game Informer}}</ref> The game was released on September 15, 2015 for Windows and OS X, and July 17, 2016 for Linux. === ''Deltarune'' === ''Deltarune'' is another of the major games released by Toby. Chapter 1 of the game was released October 31, 2018, Chapter 2 was released September 17, 2021, and Chapters 3 and 4 came out most recently and released June 4, 2025. ''Deltarune'' Chapters 1-4, by Toby Fox, build an immersive RPG world with familiar ''Undertale'' characters in an alternate universe, following silent protagonist Kris, the delinquent Susie, and the prince Ralsei on quests through "Dark Worlds" to seal fountains, battling foes with unique action RPG mechanics and dodge-bullets, all while weaving deeper mysteries, character depth (like Noelle in Chapter 2 and Tenna in Chapter 3), unique themes (cards, internet, TV), and a surprisingly dark, impactful story that subverts expectations and explores themes of identity, loneliness, and control, setting up a potential masterpiece even as an incomplete game. * '''The Fun Gang:''' You control Kris (silent protagonist), Susie (lizard-like delinquent), and Ralsei (gentle prince) in a party-based combat system. * '''Dodge-Bullet Battles:''' Combat mixes traditional RPG choices (Attack/Act/Spare) with bullet-hell dodging, requiring strategic party health management. * '''Dark Worlds:''' Each chapter introduces a fantastical "Dark World" based on a real-world location (closet, computer), sealed by sealing a "Dark Fountain". * '''Mystery & Control:''' Kris removes their soul at chapter ends, suggesting the player controls the soul, not Kris, raising questions about free will. ** '''Chapter 1: The Beginning (Cards)''': Introduces Kris and Susie, their first trip to the Dark World, and meeting Ralsei, establishing the core quest. ** '''Chapter 2: A Cyber's World (Internet)''': Adds Noelle to the party, introduces the memorable Spamton, and deepens lore with secrets like the "Weird Route". ** '''Chapter 3: Late Night (TV/Game Show)''': Shifts focus to a game show format with Tenna, adding rhythm, quizzes, and darker themes. ** '''Chapter 4: Prophecy (Church/Dark Sanctuary)''': A surprisingly mature chapter with religious themes, moral choices, a rescue mission, and a significant "Dark Sanctuary". *** '''Character Depth:''' Explores loneliness and self-worth for Kris, Susie, and Ralsei. *** '''Humor & Darkness:''' Balances quirky humor with surprisingly serious, adult themes and dark consequences. *** '''Meta-Narrative:''' The vessel creation and soul-removal mechanics hint at greater control and player choices. *** '''World Building:''' Expands ''Undertale''<nowiki/>'s universe with unique worlds (Cyber World, TV World, Dark Sanctuary). **** '''Incomplete Game:''' Chapters 1-4 are a substantial, free experience, but the full story requires future releases. **** '''Secrets:''' Features numerous secrets, missable items (like the TopCake), and alternate paths (like the Weird Route). **** '''Exceptional Quality:''' Praised for its music, unique gameplay, character writing, and ambition, building anticipation for the finale. ==Musical Contributions== Fox is a self-taught musician and has composed soundtracks for many games and comics including ''Midnight Crew: Drawing Dead'', ''Pokémon Sword/Pokémon Shield'', Animal Crossing: New Horizons, ''Alternia'' and ''Homestuck''. He composed all of the soundtrack for ''Undertale'' as well. When it comes to his influences for producing music, Fox states that he tries to be inspired by everything he listens to, especially tracks in video games.<ref>{{cite web |url=http://www.themarysue.com/interview-undertale-game-creator-toby-fox/|title= The Mary Sue}}</ref> ==Discography== {| class="wikitable collapsible collapsed" style="width:100%;" |- style="background:#ccc;{{Text color default}}; text-align:center;" ! colspan="2" style="background: LightSteelBlue;{{Text color default}};" | Discography |- style="background:#ccc;{{Text color default}}; text-align:center;" ! Album ! Tracks Composed |- | Midnight Crew: Drawing Dead (February 4, 2010) <ref name="MC: DD">{{cite web |url=https://homestuck.bandcamp.com/album/midnight-crew-drawing-dead-2 |title = Midnight Crew: Drawing Dead}}</ref> | "Liquid Negrocity", "The Ballad of Jack Noir" (Original Version) |- | Homestuck Vol. 4 (April 13, 2010) <ref name="Homestuck 4">{{cite web |url=https://homestuck.bandcamp.com/album/homestuck-vol-1-4| title= Homestuck Vol. 4}}</ref> | "John Sleeps / Skaian Magicant", "Carefree Victory", "Atomyk Ebonpyre", "Black" |- |Homestuck Vol. 5 (June 13, 2010) <ref name="Homestuck 5">{{cite web |url=https://homestuck.bandcamp.com/album/homestuck-vol-5| title= Homestuck Vol. 5}}</ref> | "Skaian Skirmish", "Savior of the Waking World", "Happy Cat Song!", "Hardchorale", "White", "Octoroon Rangoon", "Lotus Land Story", "Versus", "Dupliblaze COMAGMA", "Moonshatter", "Sunsetter", "Get Up", "Vertical Motion", "Amphibious Subterrain", "Snow Pollen", "Descend" |- | Alternia (July 18, 2010) <ref name="Alternia">{{cite web |url=https://homestuck.bandcamp.com/album/alternia| title= Alternia}}</ref> | "Crustacean", "Showdown", "mIrAcLeS", "The Lemonsnout Turnabout", "Phaze and Blood", "psych0ruins", "Walls Covered In Blood", "dESPERADO ROCKET CHAIRS,", "Death of the Lusii", "Virgin Orb", "The La2t Frontiier", "Skaian Summoning", "Spider's Claw (Bonus)", "Staring (Bonus)", "Keepers (Bonus)" |- | Squiddles! (August 26, 2010) <ref name="Squiddles">{{cite web |url=https://homestuck.bandcamp.com/album/squiddles| title = Squiddles!}}</ref> | "Squiddles the Movie Trailer - The Day the Unicorns Couldn't Play" |- | The Baby Is You (October 13, 2010) | "THROGUH SONG", "IM HAVING A BABY, AND THE BABY IS YOU", "bootes", "ROSE PRAGNET (feat. ????)", "the rose rap (feat. von fawn)", "uh oh", "vs. bros", "A BABY IS BORN (feat. artemis251 as luigi, chorus singer, kid, and hella jeff)" |- | The Felt (December 2, 2010) <ref name="The Felt">{{cite web |url=https://homestuck.bandcamp.com/album/the-felt| title= The Felt}}</ref> | "Humphrey's Lullaby", "English" |- | Homestuck for the Holidays (December 25, 2010) <ref name="Homestuck Holidays">{{cite web |url=https://homestuckgaiden.bandcamp.com/album/homestuck-for-the-holidays-unofficial-album| title = Homestuck for the Holidays }}</ref> | "Carefree Perigee" |- | Homestuck Vol. 6: Heir Transparent (January 5, 2011) <ref name="Homestuck 6">{{cite web |url=https://homestuck.bandcamp.com/album/homestuck-vol-6-heir-transparent| title = Homestuck Vol. 6: Heir Transparent}}</ref> | "Umbral Ultimatum", "MeGaLoVania", "Gaia Queen", "Wacky Antics", "Nic Cage Song", "A Tender Moment" |- | AlterniaBound (March 14, 2011) <ref name="AB">{{cite web |url=https://homestuck.bandcamp.com/album/alterniabound| title= AlterniaBound}}</ref> | "Karkat's Theme", "Terezi's Theme", "Vriska's Theme", "FIDUSPAWN, GO!", "Darling Kanaya", "Eridan's Theme", "Nautical Nightmare", "Nepeta's Theme", "Killed by BR8K Spider!!!!!!!!", "Catapult Capuchin", "Science Seahorse", "A Fairy Battle", "The Blind Prophet", "AlterniaBound", "You Won A Combat", "Rest A While" |- | Homestuck Vol. 7: At the Price of Oblivion (May 31, 2011) <ref name="Homestuck 7">{{cite web |url=https://homestuck.bandcamp.com/album/homestuck-vol-7-at-the-price-of-oblivion| title= Homestuck Vol. 7: At the Price of Oblivion}}</ref> | "Terezi Owns", "Rumble at the Rink", "Earthsea Borealis" |- | The Wanderers (July 14, 2011) <ref name="Wanderers">{{cite web |url=https://homestuck.bandcamp.com/album/the-wanderers| title= The Wanderers}}</ref> | "Mayor Maynot", "Riches to Ruins Movements I & II", "Tomahawk Head" |- | Homestuck Vol. 8 (October 25, 2011) <ref name="Homestuck 8">{{cite web |url=https://homestuck.bandcamp.com/album/homestuck-vol-8| title= Homestuck Vol. 8}}</ref> | "Love You (Feferi's Theme)", "Davesprite", "Frostbite", "The Lost Child", "Judgement Day", "Penumbra Phantasm" (featured in the third part of "Cascade") |- | Improvised Touhou Music with Annoying Commentary (November 29, 2011) <ref name="ITM">{{cite web |url=http://fwugradiation.tumblr.com/post/13528293577/improvised-touhou-music-with-annoying-commentary |title= Improvised Touhou Music with Annoying Commentary}}</ref> | "Girl's Pretty Dress Dress, Do Your Best Now", "Magical Hopalong Cassidy Station", "An Apple Disaster!" |- | I Miss You - EarthBound 2012 (January 1, 2012) <ref name="E 2012">{{cite web |url=https://sleepytimejesse.bandcamp.com/album/i-miss-you-earthbound-2012|title= I Miss You - EarthBound 2012}}</ref> | "Fallen Down", "A New Line", "Megalo Strike Back", "Checkerboard Memories" |- | coloUrs and mayhem: Universe A (April 2, 2012) <ref name="CAMA">{{cite web |url=https://homestuck.bandcamp.com/album/colours-and-mayhem-universe-a| title= coloUrs and mayhem: Universe A}}</ref> | "~~SIDE 1~~", "~~SIDE 2~~", "~~ADDITIONAL MAYHEM~~" |- | coloUrs and mayhem: Universe B (April 13, 2012) <ref name="CAMB">{{cite web |url=https://homestuck.bandcamp.com/album/colours-and-mayhem-universe-b| title= coloUrs and mayhem: Universe B}}</ref> | "~~SIDE 1~~", "~~SIDE 2~~", "~~ADDITIONAL MAYHEM~~" |- | Cherubim (March 14, 2013) <ref name="Cherubim">{{cite web |url=https://homestuck.bandcamp.com/album/cherubim|title= Cherubim}}</ref> | "The Lordling" |- | Undertale Demo OST (May 21, 2013) | "Once Upon a Time", "Menu", "Your Best Friend", "Fallen Down", "Ruins", "Anticipation", "Unnecessary Tension", "Enemy Approaching", "Ghost Fight", "Determination", "Home", "Heartache", "End", "Nyeh Heh Heh!", "Home (Music Box)", "Empty House" |- |UNDERTALE Soundtrack (September 15, 2015) | "Once Upon a Time", "Start Menu", 'Your Best Friend", "Fallen Down", "Ruins", "Uwa!! So Temperate♫", "Anticipation", "Unnecessary Tension", "Enemy Approaching", "Ghost Fight", "Determination", "Home", "Home (Music Box)", "Heartache", "sans.", "Nyeh Heh Heh!", "Snowy", "Uwa!! So Holiday♫", "Dogbass", "Mysterious Place", "Dogsong", "Snowdin Town", "Shop", "Bonetrousle", "Dating Start!", "Dating Tense!", "Dating Fight!", "Premonition", "Danger Mystery", "Undyne", "Waterfall", "Run!", "Quiet Water", "Memory", "Bird That Carries You Over A Disproportionately Small Gap", "Dummy!", "Pathetic House", "Spooktune", "Spookwave", "Ghouliday", "Chill", "Thundersnail", "Temmie Village", "Tem Shop", "NGAHHH!!", "Spear of Justice", "Ooo", "Alphys", "It's Showtime!", "Metal Crusher", "Another Medium", "Uwa!! So HEATS!!♫", "Stronger Monsters", "Hotel", "Can You Really Call This A Hotel, I Didn't Receive A Mint On My Pillow Or Anything", "Confession", "Live Report", "Death Report", "Spider Dance", "Wrong Enemy !?", "Oh! One True Love", "Oh! Dungeon", "It's Raining Somewhere Else", "CORE Approach", "CORE (Soundtrack)", "Last Episode!", "Oh My...", "Death by Glamour", "For The Fans", "Long Elevator", "Undertale", "Song That Might Play When You Fight Sans", "The Choice", "Small Shock", "Barrier", "Bergentrückung", "ASGORE", "You Idiot", "Your Best Nightmare", "Finale", "An Ending", "She's Playing Piano", "Here We Are", "Amalgam", "Fallen Down (Reprise)", "Don't Give Up", "Hopes and Dreams", "Burn in Despair!", "SAVE the World", "His Theme", "Final Power", "Reunited", "Menu (Full)", "Respite", "Bring It In, Guys!", "Last Goodbye", "But the Earth Refused to Die", "Battle Against a True Hero", "Power of "NEO"", "MEGALOVANIA", "Good Night" |- | [S] Collide. (April 6, 2016) <ref name="S Collide">{{cite web |url=https://homestuck.bandcamp.com/album/s-collide|title= [S] Collide.}}</ref> | "Oppa Toby Style" |} ==Awards and Nominations== ===Reception=== ''Undertale'' was released to rave reviews by many magazines and publications. The game and Toby Fox was nominated for and won many awards such as Game of the Year, Best Debut, and Best Game Ever. As for Fox's reaction to the massive success of his own game he stated that it overwhelmed him and caused a lot of stress, as he did not want the game to be tiring or spoiled for anyone. He also stated that he is perfectly comfortable if he never makes a game as successful again.<ref>{{cite web |url=http://undertale.tumblr.com/post/150397346860/retrospective-on-undertales-popularity|title= Undertale Blog}}</ref> {| class="wikitable collapsible collapsed" style="width:100%;" ! List of awards and nominations for ''Undertale'' |- | style="padding:0; border:none;"| {| class="wikitable sortable plainrowheaders" style="border:none; margin:0; width:100%;" |- ! scope="col"| Date !! scope="col"| Award !! scope="col"| Category !! scope="col"| Recipient(s) and Nominee(s) !! scope="col"| Result !! scope="col" class="unsortable" | Ref. |- | align="center"| October 30, 2015 ! scope="row"| ''Rock, Paper, Shotgun'' Game of the Month: October | Game of the Month | ''Undertale'' | Won | align="center"| <ref name="RPS GOTM">{{cite web |url=https://www.rockpapershotgun.com/2015/10/13/undertale-game-of-the-month/ |title=Game of the Month: October – Undertale |website=[[Rock, Paper, Shotgun]] |date=October 30, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egCag9iE |archivedate=January 20, 2016 }}</ref> |- | align="center"| November 27, 2015 ! scope="row"| Global Game Awards 2015 | Best Indie | ''Undertale'' | Runner-Up | align="center"| <ref name="Global Game Awards">{{cite web |url=http://www.game-debate.com/awards/2015 |title=Global Game Awards 2015 |website=Game-Debate |date=November 27, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6eaF8iirs |archivedate=January 16, 2016 }}</ref> |- | align="center"| December 1, 2015 ! scope="row"| ''Time's Top 10 Video Games'' | Best Game | ''Undertale'' | Ninth | align="center"| <ref name="Time">{{cite web |url=http://time.com/4106659/top-10-video-games/ |title=Top 10 Video Games |last=Peckham |first=Matt |website=[[Time (magazine)|Time]] |publisher=[[Time Inc.]] |date=December 1, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egtDVkOF |archivedate=December 20, 2016 }}</ref> |- | align="center"| December 3, 2015 ! scope="row"| The Game Awards 2015 | Best Independent Game | ''Undertale'' | Nominated | align="center"| <ref name="The Game Awards">{{cite web |url=https://www.vg247.com/2015/12/04/the-game-awards-2015-winners/ |title=The Game Awards 2015 – Game of the Year goes to The Witcher 3 |last=Nunneley |first=Stephany |website=[[VG247]] |publisher=[[Videogaming247]] |date=December 4, 2015 |accessdate=January 15, 2016 |archiveurl=http://www.webcitation.org/6eYOBjjTo |archivedate=January 15, 2016}}</ref> |- | align="center"| December 3, 2015 ! scope="row"| The Game Awards 2015 | Games for Change | ''Undertale'' | Nominated | align="center"| <ref name="The Game Awards" /> |- | align="center"| December 3, 2015 ! scope="row"| The Game Awards 2015 | Best Role-Playing Game | ''Undertale'' | Nominated | align="center"| <ref name="The Game Awards" /> |- | align="center"| December 4, 2015 ! scope="row"| ''Vice's Best 20 Video Games of 2015'' | Best Game | ''Undertale'' | Eighth | align="center"| <ref name="Vice Best">{{cite web |url=http://www.vice.com/en_ca/read/the-top-20-video-games-of-2015-according-to-vice-999 |title=The Best 20 Video Games of 2015 |last=Diver |first=Mike |website=[[Vice (magazine)|Vice]] |publisher=[[Vice Media]] |date=December 4, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6eaDGw7q0 |archivedate=January 16, 2016 }}</ref> |- | align="center"| December 15, 2015 ! scope="row"| ''Rock, Paper, Shotgun's'' Best PC Games of 2015 | Funniest Game on PC | ''Undertale'' | Won | align="center"| <ref name="rps funniest">{{cite web |url=https://www.rockpapershotgun.com/2015/12/16/funniest-pc-game-2015/ |title=The RPS Advent Calendar, Dec 16th: Undertale |date=December 16, 2015 |website=[[Rock, Paper, Shotgun]] |accessdate=May 16, 2016 |archive-url=https://web.archive.org/web/20151226135527/http://www.rockpapershotgun.com/2015/12/16/funniest-pc-game-2015/ |archivedate=December 26, 2015 }}</ref> |- | align="center"| December 15, 2015 ! scope="row"| ''Good Game'' Awards 2015 | Game of the Year | ''Undertale'' | Nominated | align="center"| <ref name="Good Game Awards">{{cite web |url=http://www.abc.net.au/tv/goodgame/stories/s4371946.htm |title=Game of the Year - Part 1 |last1=O'Donnell |first=Steven |authorlink1=Steven O'Donnell (Australian actor) |last2=Bendixsen |first2=Stephanie |authorlink2=Stephanie Bendixsen |website=[[Australian Broadcasting Corporation]] |date=December 15, 2015 |accessdate=January 17, 2016 |archiveurl=http://www.webcitation.org/6ea5CWKoh |archivedate=January 16, 2016}}</ref> |- | align="center"| December 16, 2015 ! scope="row"| GameFAQs' Best Game Ever | Best Game Ever | ''Undertale'' | Won | align="center"| <ref name="GameFAQs">{{cite web |url=http://www.polygon.com/2015/12/16/10323192/undertale-gamefaqs-best-game-ever |title=Undertale wins GameFAQs' Best Game Ever contest |last=Frank |first=Allegra |website=[[Polygon (website)|Polygon]] |publisher=[[Vox Media]] |date=December 16, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egsbSNsX |archivedate=January 20, 2016 }}</ref> |- | align="center"| December 18, 2015 ! scope="row"| GameSpot Game of the Year | Game of the Year | ''Undertale'' | Nineteenth | align="center"| <ref name="GameSpot GOTY">{{cite web |url=http://www.gamespot.com/articles/game-of-the-year-2015-countdown-20-16/1100-6432501/ |title=Game of the Year 2015 Countdown: #20 - #16 |website=[[GameSpot]] |publisher=[[CBS Interactive]] |date=December 18, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egsAMSDq |archivedate=January 20, 2016 }}</ref> |- | align="center"| December 21, 2015 ! scope="row"| ''The Jimquisition'' Game of the Year Awards 2015 | Game of the Year | ''Undertale'' | Won | align="center"| <ref name="Jimquisition Awards">{{cite web |url=http://www.thejimquisition.com/2015/12/the-jimquisition-game-of-the-year-awards-2015/ |title=The Jimquisition Game of the Year Awards 2015 |last=Sterling |first=Jim |authorlink=Jim Sterling |website=[[The Jimquisition]] |date=December 21, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egFRv1KT |archivedate=January 20, 2016 }}</ref> |- | align="center"| December 22, 2015 ! scope="row"| Destructoid Game of the Year | Best PC Game | ''Undertale'' | Won | align="center"| <ref name="Destructoid Award">{{cite web |url=http://www.destructoid.com/destructoid-s-award-for-best-pc-game-of-2015-goes-to--328410.phtml |title=Destructoid's award for Best PC Game of 2015 goes to... |last=Hansen |first=Steven |website=[[Destructoid]] |publisher=[[ModernMethod]] |date=December 22, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egF81TT0 |archivedate=January 20, 2016 }}</ref> |- | align="center"| December 25, 2015 ! scope="row"| ''The Escapist's'' Best Games of 2015 | Best Game | ''Undertale'' | Nominated | align="center"| <ref name="Escapist Best Game">{{cite web |url=http://www.escapistmagazine.com/articles/view/video-games/features/15167-Best-Games-of-2015.3 |title=The Escapist's Best Games of 2015 |page=3 |website=[[The Escapist (magazine)|The Escapist]] |publisher=[[Defy Media]] |date=December 25, 2015 |accessdate=February 17, 2016 |archiveurl=http://www.webcitation.org/6fMQCMr0P |archivedate=February 17, 2016 }}</ref> |- | align="center"| December 28, 2015 ! scope="row"| Ars Technica best video games of 2015 | Best Game | ''Undertale'' | Fifth | align="center"| <ref name="Ars Technica 2015">{{cite web |url=http://arstechnica.com/gaming/2015/12/the-best-video-games-of-2015-as-picked-by-the-ars-editors/4/ |title=The best video games of 2015, as picked by the Ars editor |page=4 |last=Orland |first=Kyle |website=[[Ars Technica]] |publisher=[[Condé Nast]] |date=December 28, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egDgThLD |archivedate=January 20, 2016 }}</ref> |- | align="center"| December 28, 2015 ! scope="row"| Giant Bomb's 2015 Game of the Year Awards | Best Surprise | ''Undertale'' | Runner-Up | align="center"| <ref name="Giant Bomb 1">{{cite web |url=http://www.giantbomb.com/articles/giant-bombs-2015-game-of-the-year-awards-day-one-t/1100-5316/ |title=Giant Bomb's 2015 Game of the Year Awards: Day One Text Recap |website=[[Giant Bomb]] |publisher=[[CBS Interactive]] |date=December 28, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egFb7Yri |archivedate=January 20, 2016 }}</ref> |- | align="center"| December 30, 2015 ! scope="row"| Giant Bomb's 2015 Game of the Year Awards | Best Debut | Toby Fox | Runner-Up | align="center"| <ref name="Giant Bomb 3">{{cite web |url=http://www.giantbomb.com/articles/giant-bombs-2015-game-of-the-year-awards-day-three/1100-5318/ |title=Giant Bomb's 2015 Game of the Year Awards: Day Three Text Recap |website=[[Giant Bomb]] |publisher=[[CBS Interactive]] |date=December 30, 2015 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egFkFhrG |archivedate=January 20, 2016 }}</ref> |- | align="center"| January 1, 2016 ! scope="row"| Giant Bomb's 2015 Game of the Year Awards | Game of the Year | ''Undertale'' | Seventh | align="center"| <ref name="Giant Bomb 5">{{cite web |url=http://www.giantbomb.com/articles/giant-bombs-2015-game-of-the-year-awards-day-five-/1100-5320/ |title=Giant Bomb's 2015 Game of the Year Awards: Day Five Text Recap |website=[[Giant Bomb]] |publisher=[[CBS Interactive]] |date=January 1, 2016 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egFsYZfi |archivedate=January 20, 2016 }}</ref> |- | align="center"| January 7, 2016 ! scope="row"| ''Zero Punctuation'' Top 5 Games of 2015 | Game of the Year | ''Undertale'' | Won | align="center"| <ref name="Zero Punctuation">{{cite web |url=http://www.escapistmagazine.com/videos/view/zero-punctuation/116617-Top-5-Best-and-Worst-Games-of-2015 |title=Top 5 Games of 2015 |website=[[The Escapist (magazine)|The Escapist]] |publisher=[[Defy Media]] |date=January 7, 2016 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egG6ajZK |archivedate=January 20, 2016 }}</ref> |- | align="center"| January 12, 2016 ! scope="row"| IGN's Best of 2015 | PC Game of the Year | ''Undertale'' | Won | align="center"| <ref name="IGN PC">{{cite web |url=http://ign.com/wikis/best-of-2015/PC_Game_of_the_Year |title=PC Game of the Year |website=[[IGN]] |publisher=[[IGN Entertainment]] |date=January 12, 2016 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6egGeCTFF |archivedate=January 20, 2016 }}</ref> |- | align="center"| January 12, 2016 ! scope="row"| IGN's Best of 2015 | Best Story | ''Undertale'' | Won | align="center"| <ref name="IGN Story">{{cite web |url=http://au.ign.com/wikis/best-of-2015/Best_Story |title=Best Story |website=[[IGN]] |publisher=[[IGN Entertainment]] |date=January 12, 2016 |accessdate=February 17, 2016 |archiveurl=http://www.webcitation.org/6fMKuWJ4e |archivedate=February 17, 2016 }}</ref> |- | align="center"| February 18, 2016 ! scope="row"| 19th Annual DICE Awards | Outstanding Achievement in Game Direction | ''Undertale'' | Nominated | align="center"| <ref name="DICE">{{cite web |url=http://www.polygon.com/2016/1/13/10760412/dice-awards-2016-nominees |title=DICE Awards finalists include Fallout 4, Witcher 3, Life is Strange and more |last=Frank |first=Allegra |website=[[Polygon (website)|Polygon]] |publisher=[[Vox Media]] |date=January 13, 2016 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6eaEctq4U |archivedate=January 16, 2016 }}</ref> |- | align="center"| February 18, 2016 ! scope="row"| 19th Annual DICE Awards | DICE Sprite Award | ''Undertale'' | Nominated | align="center"| <ref name="DICE" /> |- | align="center"| February 18, 2016 ! scope="row"| 19th Annual DICE Awards | Role-Playing/Massive Multiplayer Game of the Year | ''Undertale'' | Nominated | align="center"| <ref name="DICE" /> |- | align="center"| March 16, 2016 ! scope="row"| 2016 Game Developers Choice Awards | Innovation Award | ''Undertale'' | Nominated | align="center"| <ref name="GDC">{{cite web |url=http://www.vg247.com/2016/01/08/the-witcher-3-metal-gear-solid-5-lead-nominees-for-2016-game-developers-choice-awards/ |title=The Witcher 3, Metal Gear Solid 5 lead nominees for GDC 2016 Awards |last=Nunneley |first=Stephany |website=[[VG247]] |publisher=[[Videogaming247]] |date=January 8, 2016 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6eYOOuRrZ |archivedate=January 15, 2016 }}</ref> |- | align="center"| March 16, 2016 ! scope="row"| 2016 Game Developers Choice Awards | Best Debut | {{sort|Fox|Toby Fox}} | Nominated | align="center"| <ref name="GDC" /> |- | align="center"| March 16, 2016 ! scope="row"| 2016 Game Developers Choice Awards | Best Narrative | ''Undertale'' | Nominated | align="center"| <ref name="GDC" /> |- | align="center"| March 16, 2016 ! scope="row"| 2016 Independent Games Festival Awards | Seumas McNally Grand Prize | ''Undertale'' | Nominated | align="center"| <ref name="IGF">{{cite web |url=http://www.vg247.com/2016/01/06/her-story-2016-igf-awards/ |title=Her Story, Undertale, Darkest Dungeon receive multiple 2016 IGF Award nominations |last=Nunneley |first=Stephany |website=[[VG247]] |publisher=[[Videogaming247]] |date=January 6, 2016 |accessdate=January 21, 2016 |archiveurl=http://www.webcitation.org/6eYOWqOA1 |archivedate=January 15, 2016 }}</ref> |- | align="center"| March 16, 2016 ! scope="row"| 2016 Independent Games Festival Awards | Excellence in Audio | ''Undertale'' | Nominated | align="center"| <ref name="IGF" /> |- | align="center"| March 16, 2016 ! scope="row"| 2016 Independent Games Festival Awards | Excellence in Narrative | ''Undertale'' | Nominated | align="center"| <ref name="IGF" /> |- | align="center"| March 16, 2016 ! scope="row"| 2016 Independent Games Festival Awards | Audience Award | ''Undertale'' | Won | align="center"| <ref name="IGFwinners">{{cite web |url=http://www.gamasutra.com/view/news/268277/Her_Story_takes_home_top_honors_at_the_18th_annual_IGF_Awards.php |title=Her Story takes home top honors at the 18th annual IGF Awards |website=[[Gamasutra]] |publisher=[[UBM TechWeb]] |date=March 16, 2016 |accessdate=March 16, 2016 |archive-url=https://web.archive.org/web/20160411213833/http://www.gamasutra.com/view/news/268277/Her_Story_takes_home_top_honors_at_the_18th_annual_IGF_Awards.php |archive-date=April 11, 2016 }}</ref> |- | align="center"| March 19, 2016 ! scope="row"| South by Southwest Gaming Awards | Game of the Year | ''Undertale'' | Nominated | align="center"| <ref name="SXSW nom">{{cite web |url=http://www.polygon.com/2016/1/25/10830286/sxsw-gaming-award-nominees-2016 |title=Bloodborne, Metal Gear Solid 5 among SXSW Gaming Award nominees |last=Frank |first=Allegra |website=[[Polygon (website)|Polygon]] |publisher=[[Vox Media]] |date=January 25, 2016 |accessdate=February 17, 2016 |archiveurl=http://www.webcitation.org/6eoMvq8Nt |archivedate=January 25, 2016 }}</ref> |- | align="center"| March 19, 2016 ! scope="row"| South by Southwest Gaming Awards | Excellence in Gameplay | ''Undertale'' | Nominated | align="center"| <ref name="SXSW nom" /> |- | align="center"| March 19, 2016 ! scope="row"| South by Southwest Gaming Awards | Most Fulfilling Crowdfunded Game | ''Undertale'' | Won | align="center"| <ref name="SXSW">{{cite web |url=http://www.polygon.com/2016/3/21/11277046/sxsw-gaming-awards-winners-2016 |title=The Witcher 3 takes top honors at yet another award show, the SXSW Gaming Awards |last=Sarkar |first=Samit |work=[[Polygon (website)|Polygon]] |publisher=[[Vox Media]] |date=March 21, 2016 |accessdate=June 5, 2016 |archiveurl=http://www.webcitation.org/6gZ6BMatY |archivedate=April 6, 2016 }}</ref> |- | align="center"| March 19, 2016 ! scope="row"| South by Southwest Gaming Awards | Most Promising New Intellectual Property | ''Undertale'' | Nominated | align="center"| <ref name="SXSW nom" /> |- | align="center"| March 19, 2016 ! scope="row"| South by Southwest Gaming Awards | Matthew Crump Cultural Innovation Award | ''Undertale'' | Won | align="center"| <ref name="SXSW" /> |- | align="center"| April 7, 2016 ! scope="row"| British Academy Games Awards | Story | ''Undertale'' | Nominated | align="center"| <ref name="bafta noms">{{cite web | url = http://www.vg247.com/2016/03/10/rocket-league-the-witcher-3-fallout-4-others-up-for-bafta-best-game-award/ | title = Rocket League, The Witcher 3, Fallout 4, others up for BAFTA Best Game Award | website = [[VG247]] | first = Stephany | last = Nunnely | date = March 10, 2016 | accessdate = March 10, 2016 | publisher = [[Videogaming247]] |archive-url=http://www.webcitation.org/6hCnIWJHb |archive-date=May 2, 2016 }}</ref><ref>{{cite web | url = http://www.gamesindustry.biz/articles/2016-04-07-fallout-4-wins-best-game-at-baftas |website = [[GamesIndustry.biz]] | first = Rachel | last = Weber | title = Fallout 4 wins best game at BAFTAs | date = April 7, 2016 | accessdate = April 7, 2016 | publisher = [[Gamer Network]] |archive-url=http://www.webcitation.org/6hCmxLahf |archive-date=May 2, 2016 }}</ref> |} |} == References == {{reflist}} [[Category:Digital art]] c9mwubhd1gkac6jgf80vans0efkrjfz 0 264724 2844823 2844498 2026-11-07T17:44:51Z Scogdill 1331941 2844823 wikitext text/x-wiki {{Short description|Dress worn by Queen Victoria at her wedding to Prince Albert in 1840}} = Sandbox = Page to draft revisions for Wikipedia articles. For Gwladys Robinson, see Gwladys Lowther Robinson, [[Social Victorians/People/Ripon|Marchioness of Ripon]] and, earlier, [[Social Victorians/People/Lowther|Countess of Lonsdale]] ==References== {{reflist|2}} [[Category:1840 works]] [[Category:Royal wedding dresses|Victoria Queen]] [[Category:1840s fashion]] [[Category:British royal attire]] [[Category:Dresses in the Royal Collection of the United Kingdom|Victoria, Wedding]] [[Category:Diamond Jubilee of Queen Victoria]] = Victorian fashion = == Notes and Quotes == * Women followed Paris fashion in Europe and America, but London tailors led the way for men’s fashion. The Industrial Revolution actually impacted men’s fashion more than women’s. * Sewing machines in factories began mass producing cheap clothing for the largest group in the population, working class men. * Ready-made clothing affected the social structure, the economy, and gender differentiation. * Paper patterns, introduced in fashion magazines that targeted women, along with domestic sewing machines had more impact on women’s fashion than men’s. Haute couture was still bespoke (being individually constructed by tailors or dressmakers or fashion houses like Maison Worth). Sewing Machines and Clothes Before the industrial revolution wealthy people paid others to sew their clothes by hand and those who were of much lower economic status did all the manual labor necessary to feed and clothe the rich minority. The working class had to make all their own clothes. Sewing, however, came at the end of the process.  They began with raw wool cut from the backs of sheep or gathering flax. Only the wealthy could afford to buy fabric. They followed processes for cleaning and spinning the wool into thread and the processes of soaking and pulling out the fibrous strips to make into thread for linen fabric. After they had thread, it was tied to a loom so it could be woven into cloth. Then it had to be cut or torn into pieces. For many families scissors were a luxury. And the last step is sewing the pieces together to create a garment. Machines could not only sew, they could process the raw materials into thread and weave it into fabric much  quicker. Regarding clothing, working class men and their families benefitted greatly from ready-made clothes. Manufacturers marketed to them because they were the largest class. For example,<blockquote>–Men’s shirts, made by machine, take 3 hours and 10 minutes each to do; by hand, 15 hours and 20 minutes; a lady’s dress, by machine, takes 12 hours 4 minutes; by hand 20 hours 35 minutes; . . . a common frock-coat, by the machine occupies 17 hours 20 minutes; by the hand, 27 hours and 40 minutes: a linen vest, by machine, 3 hours 44 minutes; by hand 7 hours 18 minutes; a fine overcoat, by machine, 28 hours 13 minutes; by hand 31 hours 20 minutes; . . . <ref>Mitchell, Rebecca, ed. "22. 'Progress of the Sewing Machine,' ''Bow Bells'' (19 April 1865), p. 283." Section 6: Production and Industry. ''Fashioning the Victorians: A Critical Sourcebook''. Bloomsbury Visual Arts, 2018.</ref></blockquote> === Industrial Revolution and Technological Advancements === * the railroad * mass production of fabrics for working-class men's clothing ** Jacquard looms * sewing machines * aniline dyes, including black === Expanding Middle Class === * gender roles getting more clearly defined and rigid (referring back to page overview) === French Revolution === Sarah Gharmallah Alzahrani and Safia Abdelaziz Saroukh (https://www.researchgate.net/profile/Safia-Saroukh/publication/385099194_The_Semiotic_Dimension_of_Men's_Fashion_in_Modern_Eras/links/671686fbd796f96b8ec4f90e/The-Semiotic-Dimension-of-Mens-Fashion-in-Modern-Eras.pdf):<blockquote>The 19th century started with a fashion landscape that was changing dramatically and rapidly from the styles of a generation earlier. The French Revolution brought fashions that had been emerging since the 1780s to the forefront. Neoclassicism now defined fashion as both men and women taking inspiration from classical antiquity. For women, the high-waisted silhouette in lightweight muslin was the dominant style, while fashionable men looked to the tailors of Britain for a new, refined look [17]. [17]  Franklin, H. (Aug 18, 2020). Published on Jun 25, 2020, Retrieved: <nowiki>https://fashionhistory.fitnyc.edu/1800-1809/</nowiki> 11/11/2023. Edited. ...</blockquote>Brent Shannon:<blockquote>"Costume," wrote Max Beerbohm in 1896, "enables us to classify any 'professional man' at a glance, be he lawyer, leech or who not" (24–25). A man's profession and class were read by his jacket, his hat, what he rode in, and how he carried himself. "Perhaps there is a tendency among Englishmen to judge a man too much by the shape of his hat or the kind of collar he wears," conduct author John Wanamaker confessed; "But one must remember that in England if you ''wear'' the wrong thing, you will probably ''do'' the wrong thing, and generally ''be'' the wrong thing" (1).¹¹ Such assertions were predicated on the powerful Victorian conviction that outward appearance reflected inner qualities.<ref>{{Cite book|title=The Cut of His Coat: Men, Dress, and Consumer Culture in Britain, 1860–1914|last=Shannon|first=Brent Alan|publisher=Ohio University Press|year=2006|location=Athens, Ohio}}</ref> (148)</blockquote> ==Women's fashion== == Men's fashion == (Two intros: one to Victorian Fashion, giving background for both women's and men's fashions; two to the decades for men's fashion) Among the influences on men's styles: * differentiation of genders (domestic ideology, ideology of the spheres) * the "Great Male Renunciation," the French Revolution and English tailoring * industrial revolution: mass production of fabrics and articles of clothing, especially for working-class men * sports and country clothing * Albert Edward, Prince of Wales, later King Edward VII, influence went beyond England; tailors led by him led fashion for the upper classes * then later, cult of youth * military uniforms * comfort and convenience * evolving definitions of gender, both femininity and masculinity evolved as concepts. The changing definitions of masculinity affected men's clothing. For the growing and rising middle classes, gender roles became more and more rigid around the concept of the separate spheres, the public for men and the private sphere for women. Cultural sources for men's clothing and men's fashion: industrial revolution; expanding middle class; technological advancements; an association in the culture between outward appearance and inward nature; French Revolution; Albert Edward, Prince of Wales Citation for Victorian Hell: <ref name=":29">{{Cite web|url=https://victorianhell.substack.com/p/victorian-mens-fashion-history-and|title=Victorian Men’s Fashion History and Clothing Guide|last="It's Monty, Actually"|date=31 October 2025|website=Victorian Hell|access-date=7 September 2026}}</ref> === Waistcoats === *c. 1830, dark brown or black w faces, gold buttons, standing collar: File:Waistcoat MET 38.68 F.jpg * c. 1830, beige and white woven fabric with rose buds stamped or embroidered??: File:Waistcoat MET 19.181.4 F.jpg * 1830–1835, dotted and floral stamped fabric, brown and tan: File:Waistcoat MET 1976.254.1.jpg * * c. 1840, flowered fabric: File:Waistcoat MET 1979.346.45 F.jpg * c. 1840, red, jacquard-like, double-breasted: File:Waistcoat MET 1979.346.47 F.jpg * 1840s, white brocade: File:Waistcoat MET 1980.132.8 F.jpg * 1840s, dark blue, red, green? stamped?: File:Waistcoat MET 1976.254.1.jpg * Mid 1840s, brown, embroidered: File:Waistcoat MET 24.160.3 F.jpg * late 1840s, embossed white with hash thingies: File:Waistcoat MET 1978.88.9 F.jpg * 1845 waistcoat made from blue Chinese silk damask: File:1845 waistcoat made from blue Chinese silk damask.jpg * 1845–1855, white brocade wedding waistcoat, piping on the edges: File:Waistcoat MET 1986.373.3 F.jpg * '''1849–1860''', black w gold lining, ribbon: File:Waistcoat MET 1978.477.25 F.jpg * * 1850, print of St. James's Park: File:Print (BM 1880,1113.2351).jpg * 1850s, white and blue, w blue floral design stamped on white-and-grey stamped on white fabric: File:Waistcoat MET 1978.477.28 F.jpg *c. 1853, brown and tan plaid, with red squares: File:Waistcoat MET 1984.90.2 F.jpg *1854: Fashion plates, groups of ppl: File:Paris, New York & Philadelphia fashions for spring and summer 1854, published & sold by F. Mahan, no. 211 Chestnut Street, Philadelphia. LCCN2003655770.jpg *c. 1855, French fashion plate, frock coats, waistcoats, etc.: File:Album z ilustracjami do czasopism z moda francuska, niemiecka i angielska. ca 1855 (9109644).jpg * 1857, cream, printed flowers on check, watch pocket: File:Waistcoat MET 1978.88.8 F.jpg * * c. 1860, dark floral? fabric with machine embroidery?: File:Waistcoat MET 1983.479.13 F.jpg * * late 1870s–early 1880s, gold, woven: File:Waistcoat MET 1979.34.1 F.jpg === Frock coats === * Apostol Mănescu, politician, wearing a frock coat, butterfly tie, black waistcoat with button chain and light coloured pants, drainpipe type. Circa 1866. Photo by Franz Duschek.jpg (1866)[[File:Apostol Mănescu, politician, wearing a frock coat, butterfly tie, black waistcoat with button chain and light coloured pants, drainpipe type. Circa 1866. Photo by Franz Duschek.jpg|thumb|Romanian (?) Politician, c. 1866, ill-fitting but probably handmade suit|center]] Full-length portrait of two young men wearing frock coats with sashes and pistols at their waists LCCN2006689564.tif (right)[[File:Full-length portrait of two young men wearing frock coats with sashes and pistols at their waists LCCN2006689564.jpg|thumb|1860, American, young men with frock coats, performers??|center]] * George Augustus Henry Sala.jpg (Mathew Brady, 1855–1865) * [[File:George Augustus Henry Sala.jpg|center|thumb|George Augustus Sala, 1855–1865, LoC]] ==== Dress and Conduct Manuals, Histories, Victorian Theory, Catalogs ==== # [Baker, William Henry.]  ''Clothes Dictionary''. Chicago, Ill.: Cahn, Wampold, 1901. https://commons.wikimedia.org/wiki/File:Clothes_dictionary;_(IA_clothesdictionar00bake).pdf. # [[c:File:Hint's_about_men's_dress,_right_principles_economically_applied_(IA_hintsaboutmensdr00barr).pdf|Hint's about men's dress, right principles economically applied (IA hintsaboutmensdr00barr).pdf]] (book, conduct manual, American, 1888) #[https://upload.wikimedia.org/wikipedia/commons/6/69/Fashion-_the_power_that_influences_the_world_%28IA_fashionpowerthat00foxg%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original Fashion- the power that influences the world (IA fashionpowerthat00foxg).pdf] (1871) (American, incl court dress, Victorian fashion theory, livery, "White, as it is the color of day, is expressive to us of the cheerfulness or gaiety which the return of day brings." [145], "Gentlemen's Furnishing and Goods," "Head and Foot Covering," Index) # [https://upload.wikimedia.org/wikipedia/commons/a/ae/How_to_behave_and_how_to_amuse._A_handy_manual_of_etiquette_and_parlor_games_%28IA_howtobehavehowto00sand%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original How to behave and how to amuse. A handy manual of etiquette and parlor games (IA howtobehavehowto00sand).pdf] (1895; American; Men's Dress, p. 23; besides conduct and dress, it has parlor games) # [https://upload.wikimedia.org/wikipedia/commons/8/8e/The_etiquette_of_men%27s_dress_%28IA_etiquetteofmensd00cluc%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original The etiquette of men's dress (IA etiquetteofmensd00cluc).pdf] (1888; American; some ads; anthology of individually written articles; lots of sports, outdoor events; search for "frock" — cutaway vs Prince Albert) #[https://upload.wikimedia.org/wikipedia/commons/e/e9/S.W._Silver_%26_Co.%27s_handbook_for_transatlantic_travellers_.._%28IA_swsilvercoshandb00silv%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original S.W. Silver & Co.'s handbook for transatlantic travellers .. (IA swsilvercoshandb00silv).pdf] (1883; American; lots of ads from SW Silver, with prices; has blank pages where ppl can write "Introductions" and "Engagements," but this is not a conduct book, it's travel guide / catalog to London) #[https://upload.wikimedia.org/wikipedia/commons/f/f6/How_we_go_to_those_who_cannot_come_to_us.._%28IA_howwegotothosewh00roge%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original How we go to those who cannot come to us.. (IA howwegotothosewh00roge).pdf] (Roger, Peet & Co.; American; catalog, spring 1891; pp. 11, clerical frock; 7 "Prince Alberts" double-breasted frocks; p. 23 shirts as underwear; has a thing on fitting and mail order; bathing suits, collars and cuffs; tennis shoes) == Victorian Men's Fashion (Intro to the Men's Fashion Section) == Museums and other historical sites have plenty of women’s clothes from the nineteenth century. There is great variety in both outer wear and underwear. “Men’s garments of the Victorian period have survived in far less quantity than women’s.” Buck p. 185 More waistcoats have survived than any other garment. The hardest garment to find are trousers. Very few survived the nineteenth century. Buck p. 185 By 1850 trousers dominated the fashion for men; the trouser straps under the shoe had disappeared; and a fly front had replaced the fall-front. Buck 185 It took most of the nineteenth century for men’s fashion to evolve into the coat, trousers and vest (waistcoat) that dominated the twentieth century and appears to be unchanging in the twenty-first century. “Men’s clothing, like women’s, was specific to each occasion and type of activity during the late nineteenth century.” Payne2, p. 518 For example, formal wear for social events was different from the casual, everyday wear for upper middle class and aristocratic men. Victorians also dressed in ensembles for hunting and riding (included knickerbockers–breeches that had a fuller cut). Casual and looser clothing was worn when participating in sports. Many different cuts of coats were available, like the Norfolk jacket, the morning coat, or the sack coat. “Tailored wool garments , originally inspired by the clothing of English country gentry, formed the backbone of men’s wardrobes in the early nineteenth century.” Men’s clothing began to change from styles that were colorful and flamboyant in the eighteenth century to styles that emphasized cut over color. By the end of the century men’s clothing had settled into a kind of uniform with coats and trousers usually made of the same fabric, often with a vest or waistcoat of the same fabric. The uniform included a shirt with a stiff collar, a necktie and very little jewelry. It took the entire nineteenth century to change to a rather static style that is still worn today. Ready-made clothing affected the social structure, the economy, and the gender differentiation. David Kutcha traces the origin of the 3-piece men's suit to King Charles II of England, who may be said to be wearing a coat, pants and a waistcoat, but otherwise is not wearing a "suit" we — or the Victorians — would recognize as such: <blockquote>... since 1666, male gentility has been associated with modesty and plainness in dress. Eschewing fashion as an increasingly feminized realm Charles II's vest inaugurated a new and essentially modern era of masculine aesthetics, one that reversed a long-held association between elaborate display and high social status. Manly thrift now displayed elite status.<ref>{{Cite book|title=The Three-Piece Suit and Modern Masculinity, England 1550–1850|last=Kutcha|first=David|publisher=University of California Press|year=2002|location=Berkeley and Los Angeles}}</ref> (2)</blockquote>So it's really Cromwell who should get credit?? The French Revolution caused both men and women to change stylistic direction radically. For one generation, stylish women wore simple white muslin dresses without foundation garments underneath. The changes in men's fashion was more lasting: men turned away from the ornamentation and ruffles of the ''ancien régime'', choosing instead understated and subtle tailoring to indicate good taste and wealth. Poole "comfort and convenience" — trousers, sack coats, collars and cuffs without a shirt, wool rather than silks and satins; knee breeches constantly riding up men as leaders of fashion, in spite of our sense that men didn't do fashion in the way that women did, were more serious than that === Dandy Stuff === Beau Brummell: "Men began to aspire to fine cutting, tailoring, and perfect fit in their clothes, flawless grooming and manners in themselves. The Englishman George Bryan (Beau) Brummell deserves much credit for the ideal of meticulous masculine appearance."<ref name=":25">{{Cite book|title=The History of Costume: From Ancient Mesopotamia Through the Twentieth Century|last=Payne|first=Blanche|last2=Winakor|first2=Geitel|last3=Farrell-Beck|first3=Jane|publisher=Addison-Wesley Longman|year=1992|isbn=0-06-047141-7|edition=2nd|location=New York, New York}}</ref> (458) "From 1796 to 1816, the Beau set the pattern for cleanliness and liberal use of starch." (459) === Gender Ideologies === '''Victorian gender ideologies''' relegated men to the "public sphere" and women to the "domestic sphere." (??) More than that “the cult of youth . . . the secularization of sport and the influence of modern warfare in generating men’s fashions, the tendency to prefer modern ideas of comfort and convenience, and the transformation of fashion knowledge and fashion urbanism from print to hyperreality”<ref name=":26">McNeil, Peter. "Men's Fashion: 1800–2022." Chapter 22. ''The Routledge History of Fashion and Dress, 1800 to the Present''. Routledge, 2024. https://opus.lib.uts.edu.au/bitstream/10453/182707/2/Men%27s%20Fashion%20200822_24_12_20_09_29_44.pdf DOI: 10.4324/9780429295607-27.</ref> (McNeil 1 or 411) changed the perceptions of masculinity and femininity. === Class === The growing middle class involved among other things more and more jobs and careers for young men as clerks, office workers, they were junior, subordinate, and they were commuting on the railroads from suburbs. Carolyn Kirby:<blockquote>In western Europe the fashion for plain dark suits coincided with the rise of the affluent middle-classes in a world where the pace of industrialisation and the globalisation of trade was accelerating as never before. The sharp, dark business suit became the last word in male power-dressing. And so it remains to this day.<ref name=":27">{{Cite web|url=https://historiamag.com/invent-masculine-fashion/|title=The invention of masculine fashion|last=Kirby|first=Carolyn|date=3 December 2025|website=Historia: Magazine of the Historical Writers' Association|access-date=25 August 2026}}</ref></blockquote> === Bertie === Albert Edward, Prince of Wales was very concerned with fashion and authoritative about it, with a very specific eye to small details. He was increasingly influential in men's fashion from the last third of the 19th and into the 20th century, and many noticed what he did and copied him.<blockquote>When that great lover of pleasure, Edward VII, visited Marienbad incognito as the Duke of Lancaster, he was followed by tailors from Paris, Budapest, Vienna, and Berlin who photographed him and took notes about his clothes. Edward VII introduced many [423–424] novelties into men’s fashion. ... He is also credited with making fashionable the creased trouser in 1909 (his groom dried them with a board weight after heavy rain, resulting in the line), turned-up cuff trouser (after hitching his trouser bottoms at a dirty racing track) and, as his girth grew, undoing the bottom button of his waistcoat."<ref name=":26" /> (424)</blockquote>Cowles<blockquote>The Prince was not just ‘a swell’. In the jargon of the day he was ‘a heavy swell’, and apparently there was a world of difference between the two terms. A swell was a rich young aristocrat who lived in extreme comfort; but a heavy swell added showmanship to the comfort and lived in a stylish luxury that even the French were obliged to envy. And of course the heavy swell was the acme of sartorial elegance. The Prince did not mind changing his dress half a dozen times a day. He loved clothes, and since whatever he chose to wear became the prevailing fashion overnight, he soon was regarded as an expert on the subject. His tailor-in-chief made a fortune. For many years he patronised a Mr. Poole. He discovered this gentleman by accident. He went to the theatre one night to see a well-known actor by the name of Fecher playing ‘Robert Macaire’. As an impecunious adventurer [129–130] Fechter was obliged to wear a coat that was torn and dirty, but Bertie’s expert eye noticed the elegant cut. At the end of the performance he asked Fechter for the name of his tailor, and Mr. Poole’s future was assured. The Prince had so many clothes he could never travel with less than two valets; and two more valets were left at home cleaning, brushing and pressing his vast wardrobe. There were suits and coats for every variation of every climate the world over. There were over a hundred pieces of headgear; and since Bertie was an honorary admiral and an honorary general of most of the countries of Europe, there was an entire room devoted to uniforms, sashes, epaulettes, belts, buckles, swords, feathers and other regalia. ... Men’s clothes became of such importance that new [130–131] shops sprang up like mushrooms in Savile Row, Clifford Street and Bond Street. Most of the Prince’s innovations were inspired by comfort and convenience. He altered the cut of the evening dress waistcoat, he shortened the tails on the tail coat, he left his frock coat open (due to an increasing girth), he introduced the black homburg, and he attended race meetings, not in the frock coat hitherto ''de regueur'' but in tweeds. He tried having his trousers creased down the sides rather than the front and back, in order to hide his bandy legs, but this idea did not catch on, and he soon discarded it himself. But the prince was not the only arbiter of men’s fashions. The band of  "heavy swells" who followed his lead gave him plenty of competition. Lord Raglan and Lord Petersham invented coats which are still named after them. Lord Dupplin the dinner jacket and Lord Cardigan the button-up sweater. But Lord Hardwicke made the most spectacular contribution. Men’s silk hats were made of beaver which was left in its original rough, shaggy state. Lord Hardwicke polished his hat until he could see his face in it, and consequently was known as "Glossy Top". He is responsible for the top hat as we know it today.<ref name=":28">{{Cite book|title=Gay monarch, the life and pleasures of Edward VII|last=Cowles|first=Virginia|publisher=Harper|year=1956|location=New York, New York|archive-url=https://archive.org/details/gaymonarchlifepl0000cowl/}}</ref> (129–131)</blockquote> === Men’s Clothing 1830–1900 (Intro to the Decades) === * “Tailored wool garments , originally inspired by the clothing of English country gentry, formed the backbone of men’s wardrobes in the early nineteenth century.”<ref name=":25" /> (458) Men’s clothing began to change from styles that were colorful and flamboyant in the eighteenth century to styles that emphasized cut over color. By the end of the century men’s clothing had settled into a kind of uniform with coats and trousers usually made of the same fabric, often with a vest or waistcoat of the same fabric. The uniform included a shirt with a stiff collar, a necktie and very little jewelry. It took the entire nineteenth century to change to a rather static style that is still worn today. (this is middle-class men for day wear?) * The silhouette for men sometimes followed the same line as women’s clothing on the top half of their bodies. For example, as women’s sleeves grew into the huge leg-of-mutton fullness, the shoulders of men’s coats also had added fabric to make a pouf at the shoulder, thus emphasizing a broad shouldered look across the front. Men’s silhouettes changed subtly without the exaggerated fullness of women’s skirts or the raising and lowering of the neckline. Once men began to wear trousers, they did not go back to formal knee breeches (except in European courts or for court wear for Victoria). * The line of men’s garments changed in smaller increments than women’s. Coats and trousers might fit tighter in some decades and looser in others. They were slim, then boxy, flared, then straight and evolved into the contemporary line we see on men today. * Men's fashions in the 19th century have been less researched than women's fashions, in part because of fewer artifacts of what men wore were saved in museums for study. * Photography, the first century that we have actual images (rather than artists' interpretations) of what people wore. ==== Court and Formal Dress ==== * Livery, working class * Formal dress was separate attire, used for specified occasions, varies by decade ==== Shirts ==== * Shirts and collars separated: "by 1827 detachable collars became available."<ref name=":25" /> (477) Shirts were considered more like underwear early in the century but by the end of the 1800s, they were becoming the outside garments popular in the twentieth and twenty-first centuries. * Neck treatments (and shirt cuffs) * Shirts were treated as underwear early in the century but by the end of the 1800s, they were becoming the outside garments popular in the twentieth and twenty-first centuries. ==== Coats and Jackets ==== The 1901 ''Clothes Dictionary'' says coats were "The principal garment of men's attire."<ref name=":30" />{{rp|10}} Several styles of coats were available to fashion-conscious aristocratic and upper-middle-class men. Men’s suits in this period were tailor made, fitted to one specific man. The factories, however, knew that the vast majority of men were working class and began to manufacture and sell ready-made shirts, coats and trousers. More clothes were available for working men and they cost less. The cheaper work clothes enabled upper-working-class men to own more than one set of clothes and to have more formal clothes for church or other events. Ready-made shirts were also available in generic sizes, small, medium and large. Generic sizing speeded up the mass production process and, since little of the shirts could be seen, they did not need custom fitting. Almost all of the coats Victorian men wore could be single or double breasted, with a couple of exceptions like morning coats and Norfolk jackets. On more formal occasions upper-class men wore a '''cutaway morning coat''' with light trousers during the daytime, and a dark '''tail coat''' and trousers in the evening. (define these terms) Morning coats was a general term for the jacket part of "full dress" or formal daytime wear, distinguished from formal evening wear. Most morning coats were cutaways, but the shape or cut is not the distinguishing feature: the bottom was curved or tailed, so the coat was short in front, it did not have a waist seam, single-breasted. Worn over a waistcoat and shirt. * According to Payne, "During the early 1820s tailcoats were the most popular type of coat."<ref name=":25" />{{rp|474}} * "Tailcoats gave way to skirted frock coats by the 1840s."<ref name=":25" /> (491) Tailcoats came down as far as the waist and then had tails (or "claw hammer" tails) attached at the waist in the back. Single-breasted, could be worn buttoned or unbuttoned in the front, over a waistcoat and shirt. * Nowadays, the only tailcoats are tuxedos, a term not in use until the 1880s, and named for Tuxedo Park, a village in New York populated by the elite. Originally only the white coat, ''tuxedo'' gradually came to mean the entire suit. ==== Frock Coats ==== [[File:Frock coat MET CI38.23.39 F.jpeg|alt=Old-fashioned coat hanging on a mannequin|thumb|Frock coat, 1840, American]] * Frock coats were introduced in the 1820s and worn throughout the nineteenth century with only minor changes to the line or fit. Sleeves were full at the top and waists were tight, creating an hourglass form. Initially frock coats were tightly fitted and closed with buttons. The more tailored frock coats had a waist seam and a flared skirt almost to the knees. The rate of fashion change notable in women's fashion was true for men's clothing as well. The frock coat persisted for a century, but it was in a state of constant (but subtle) evolution, with collars and lapels, coat length, the waist seam, the fullness of the coat itself as well as the sleeve, color, patterns like stripes or plaids. * A Prince Albert is a double-breasted, very well-tailored, form-fitting frock coat.<ref name=":30">[Baker, William Henry.] ''Clothes Dictionary''. Chicago, Ill.: Cahn, Wampold, 1901. https://commons.wikimedia.org/wiki/File:Clothes_dictionary;_(IA_clothesdictionar00bake).pdf.</ref>{{rp|33}} * Gentlemen, clergy, military * Men around the world and especially in the British Empire wore frock coats: images and descriptions exist of men wearing frock coats in India<ref>Woodyatt, Nigel Gresley. ''Under Ten Viceroys; The Reminiscences of a Gurkha''. London: H. Jenkins Limited, 1922. Pp. 31, 107, 1774.</ref>, Iran (Persia at that time)<ref>Sparroy, Wilfrid. ''Persian children of the royal family; the narrative of an English tutor at the court of H. I. H. Zillus-Sultán, G.C.S.I''. London and New York, J. Lane, 1902. Pp. 11, 29, 30.[https://upload.wikimedia.org/wikipedia/commons/d/d1/Persian_children_of_the_royal_family%3B_the_narrative_of_an_English_tutor_at_the_court_of_H._I._H._Zillus-Sult%C3%A1n%2C_G._C._S._I_%28IA_persianchildreno00sparrich%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original https://upload.wikimedia.org/wikipedia/commons/d/d1/Persian_children_of_the_royal_family%3B_the_narrative_of_an_English_tutor_at_the_court_of_H._I._H._Zillus-Sult%C3%A1n%2C_G._C._S._I_%28IA_persianchildreno00sparrich%29.pdf].</ref>, Japan<ref>Watson, W. Petrie. ''Japan, Aspects and Destinies''. New York, Dutton: 1904. P. 7, 19, 31.</ref>, Egypt and Turkey<ref>Butler, Alfred Joshua. ''Court Life in Egypt''. London: Chapman and Hall, 1887. P. 7.</ref>, ... * Payne: "In the 1720s, Englishmen adopted another coat [than the redingote]: a straighter, functional style that originated among the working classes. Made of plain woollen cloth in practical colors such as brown, it had no pleats, narrow sleeves, a small flat collar, and a minimum of decoration. This became known as the frock coat and was useful for riding, hunting, and overseeing one's lands." (402) ==== Trousers ==== In 1872, in analyzing men's clothing as evolutionary behavior — like coloration for mating among birds in the natural world — George Darwin (Charles's son) says, of trousers:<blockquote>... a form yields to a succeeding form, which is better adapted to the then surrounding conditions; thus, when it ceased to be requisite that men in active life should be ready to ride at any moment, and when riding had for some time ceased to be the ordinary method of travelling, knee breeches and boots yielded to trousers.<ref name=":33" /> (125 of 565)</blockquote> * Working-class men had been wearing trousers (or "trowsers") increasingly since the 16th century in Europe,('''citation''') but after the French revolution the middle and upper classes adopted them because "the safest dress was that of the working man, ... who did not wear knee breeches, but rather trousers."<ref name=":26" /> (416) * Lewandowski: "First worn by the early horse-riding steppe people, introduced to Western world by Italians in 16th century. They were accepted as informal dress in the Directoire (1790–1815 C.E.). They became a part of semi-formal dress around 1815 and became worn commonly after 1830."<ref name=":31">{{Cite book|title=The Complete Costume Dictionary|last=Lewandowski|first=Elizabeth J.|publisher=Scarecrow Press|year=2011}}</ref> (29) * Breeches: Men’s bifurcated garment that ended just below the knee * Trousers (or long pants): men’s bifurcated garment that went down to the ankles or foot * The most sweeping change in men’s fashion before 1820 was in the length of their pants. Trousers that went from waist to foot were so much more comfortable and popular than knee breeches that they replaced what had dominated men’s wear since the sixteenth century. And trousers have been worn for over two centuries now. * They were originally tailored but began to be mass produced. Although the aristocracy were required to wear knee breeches at court, they wore trousers more than they wore breeches, and they could afford to have their suits and shirts hand sewn and individually. Working class men had to contend with small, medium, and large from mass production. * This bifurcated garment was modified in specific places, like the length, the fullness over the hips or the width of the leg. In summer trousers were lighter in color — "grayish blue, aqua and pearl gray." (Payne 2, 505) In winter trousers mixed darker colors like "steel gray and brown, black and brown, and black and green." (Payne 505) More on summer colors, winter colors? * [Find quote about QV's men's court dress and the men being so cold] ==== Waistcoats ==== For most of the century, the waist-length sleeveless coat that men wore over their shirt and under their suit coat was called a waistcoat. By the 1880s, everyday waistcoats were called vests, and what was called a waistcoat was worn with formal, evening attire like tailcoats and tuxedos. Necklines rose and fell and collars and lapels came and went over the century, but by the end of the century, formal waistcoats had low necklines and lapels.<ref name=":25" /> (528) Many more waistcoats exist as artifacts in collections than vests, perhaps because they were special and thus were saved.[[File:Waistcoat MET CI60.22.55 F.jpg|thumb|Men's waistcoat, 1850s]] Over the course of the century the waistcoat evolved from ornate and decorative to something simpler, whose fabric matched the suit coat and trousers — the vest, in fact. Victorian men put their creativity, color and specialty fabrics into their waistcoats. At the beginning of the century men's waistcoats were made from specialty fabrics, like velvet or brocade or a patterned silk. Early in the century, stylish men wore two vivid waistcoats at the same time.<ref name=":25" /> (474) An elaborate waistcoat might have a colorful, patterned base fabric as well as a floral ribbon embellishment (for example, see right). Long after coats and trousers were made from the same dark wool, waistcoats continued to be colorful, making them the focus of the ensemble. By the end of the 19th century, the plain style came to dominate men’s fashion (and continues to dominate it to this day). When waistcoats became vests, they became part of the plain style ==== Overcoats ==== As their name suggests, overcoats or surcoats were coats worn for warmth and for protection from rain and snow on top of the other articles of clothing, including suit coats and frock coats. Overcoats became a significant fashion element, and many styles were seen throughout the century. [Top coat] Victorians used the terms ''overcoat'' and ''great coat''., and sometimes perhaps ''surtout''. A great coat was a "large overcoat, commonly made of wool."<ref name=":31" /> (124) In his 1901 ''Clothes Dictionary'', Baker says a surtout is "An overcoat cut in the style of a frock coat."<ref name=":30" /> (39) Lewandowski says something more generic — "term referring to any man's long cloak or coat."<ref name=":31" /> (282) Victorians also specified which of the many kinds of overcoat: redingote, Chesterfield coat, Inverness coat, macintosh (or mackintosh), paletot, Ulster coat, Norfolk jacket [[File:Dandies of 1831.jpg|thumb|Redingote on figure in back, 1831]] ===== Redingote ===== A redingote was a type of a "full-length overcoat, usually open at the front and belted, popular in varying designs through the eighteenth and nineteenth centuries."<ref name=":32">Mitchell, Rebecca, ed. ''Fashioning the Victorians: A Critical Sourcebook''. Bloomsbury Visual Arts, 2018.</ref> (527 or 565) Because the redingote was popular for so long, it existed in various forms through the two centuries. Generally, it was single- or double-breasted, with a split skirt or box pleats in back (or both) and with a high standing collar, a rolled collar or a double collar. Derived "from riding coat," (Payne 402) it was fitted at the waist and reached mid-calf, with sleeves that were full at the shoulders and upper arm and narrow from the elbow to the wrist, sporting a wide cuff. The length varied over time between knee- and ankle-length. Also, women wore redingotes — in France (1865–1890) — that were shaped to cover the bustle.<ref name=":31" /> (247–248) Redingotes continued to develop, eventually evolving "into an overcoat ..., but the overcoat lacked the pleats and large cuffs of the redingote,"<ref name=":25" /> (402) as well as, possibly, the waist seam.[[File:George Stanhope, 7th Earl of Chesterfield.jpg|thumb|George Stanhope, 7th Earl of Chesterfield, wearing a Chesterfield coat, 1860]] ===== Chesterfield Coat ===== * "Chesterfield coats were single-breasted, with fly fronts [regular buttons and button holes, as opposed to fall front, in which a panel of cloth covers the button holes and the placket covers the closure completely] and velvet collars."<ref name=":25" />  Payne2 p. 519 * They were one kind of overcoat, named for George Stanhope, 6th Earl of Chesterfield. 1840s. * Signature velvet collar. * "Man's fitted overcoat with hidden buttons and velvet collar"<ref name=":31" /> (62) * "fitted men’s knee-length overcoat, narrower than the frock coat and without a waist seam, popular from the end of the nineteenth century."<ref name=":32" /> (519 of 565) ===== Ulster Coat ===== In 1872, in analyzing men's clothing as evolutionary behavior — like coloration for mating among birds in the natural world — George Darwin (Charles's son) says, of Ulster coats:<blockquote>... a form yields to a succeeding form, which is better adapted to the then surrounding conditions .... The "Ulster Coat", now so much in vogue, is evidently largely fostered by railway travelling, and could hardly have flourished in the last century, when men either rode or travelled in coaches, where there was no spare room for any very bulky garment.<ref name=":33">Mitchell, Rebecca, ed. "3. 'George H. Darwin, ‘Development in Dress', ''Macmillan’s Magazine'' 26 (September 1872), pp. 410–16." Section 1: Fashion Theory in the Nineteenth Century. ''Fashioning the Victorians: A Critical Sourcebook''. Bloomsbury Visual Arts, 2018.</ref> (125 of 565)</blockquote> * "men’s overcoat with attached waist-length cape, popular in the nineteenth century."<ref name=":32" /> (530 of 565) * ulster overcoat for travel. * "Man's single- or double-breasted overcoat with waist belt. Initially had hood, but by 1870s was detachable. In 1875, the ticket pocket was added on the left sleeve above the cuff."<ref name=":31" /> (304) * "Travel called for an ulster — a long, loose, heavy overcoat — or for an Inverness coat with attached cape."<ref name=":25" /> (527) * "Heavy tweed coats for travel such as the ulster had half-belts and box pleating in back."<ref name=":25" /> (551) * Ulster may have had a shorter cape than the Inverness * Can we find a source linking John McGee (of McGee & Co.) with the invention of the Ulster coat in 1866? (per Wikipedia)? [[File:The man wot drove the sovereign to the last stage trying it on the next. (BM 1868,0808.9200).jpg|thumb|Duke of Wellington, 1830, wearing a coachman's coat, or Inverness coat]] ===== Inverness Coat ===== * "men’s overcoat, with long, full, open sleeves, giving a cape-like appearance from the front; worn from the mid-nineteenth century to the early twentieth century as formal wear."<ref name=":32" /> (523 of 565) * an Inverness coat with up to five cape collars and a high curved collar. * Lewandowski: "(1840–1865 C.E.) to 20th century. Worn after 1858, man's large, loose, knee-length overcoat with fitted collar and long cape."<ref name=":31" /> (143) * An Inverness coat had a high standing collar as well as up to 5 capes over a knee-length, loose overcoat.<ref name=":31" /> (143) * Caricature of the Duke of Wellington in a "coachman's caped great-coat,"<ref>{{Cite web|url=https://www.britishmuseum.org/collection/object/P_1868-0808-9200|title=Duke of Wellington in Coachman's coat. print; satirical print {{!}} British Museum|website=www.britishmuseum.org|language=en|access-date=2026-11-04}}</ref> or Inverness, 1830 * In the 1880s, the Inverness was sometimes sleeveless, so the capes were not merely decorative. * both formal and informal styles exist; also called a coachman's cape. [[File:Carson, Pirie, Scott & Co. Macintosh, 1893.jpg|thumb|360x360px|Gentleman's Macintosh, 1893]] ===== Mackintosh ===== * "Introduced in 1836, short loose overcoat made of Mackintosh's [sic] patent India-rubber cloth. Came in drab or dark green."<ref name=":31" /> (181) * "waterproofed overcoat, named after its inventor [Charles Macintosh]; now used generically to refer to raincoat."<ref name=":32" /> (524 of 565) * [according to Wikipedia, the spelling ''Mackintosh'' is now standard.] ===== Paletot ===== * "short, loose overcoat for men or women."<ref name=":32" /> (526 of 565) * "The pilot coat, or paletot, was the original of all the loosely cut garments which appeared from the 1830's onwards and which inspired the more casual coats and sportswear of the end of the century.<ref name=":34">{{Cite book|title=The Cut of Men’s Clothes: 1600-1900|last=Waugh|first=Norah|publisher=Theatre Arts Books|year=1987|isbn=978-0878300259}}</ref> (1533 of 2116) ===== Norfolk Jacket ===== * "A single breasted sack coat having two or three box plaits [pleats] in back, two in front and a belt of material. Most used for hunting and outdoor sports."<ref name=":30" /> (28) * "A variation 'suitable for any kind of outdoor exercise', was the 'Norfolk jacket' which appeared in the 1870's. It also was a two-seamed jacket but was cut full and the fullness arranged in box pleats, two in the front and two in the back. It had a belt and was worn with 'knickerbockers'-knee breeches with legs cut loose and gathered into a knee-band."<ref name=":34" /> (1547 of 2116) <ref name=":24" />Kay, Fiona and Neil R. Storey, ''Victorian Fashions for Women'', Pen & Sword History, Yorkshire - Philadelphia, 2022 [[File:Homosexualitywilde.jpg|thumb|Oscar Wilde and Bosie Douglas, straw boater and derby, 1894]] ==== Hats ==== The upper-class continued to wear top hats, and [[bowler hats]] (known in America as a derby) were worn by the working class. 1830s This class of men also wore round cloth caps, often seen on male children. The straw boater was the most popular hat by the end of the century and was worn by all of the classes. Men wore [[top hats]], with wide brims in sunny weather. 1830s - 1900 Top hats briefly became the very tall "stovepipe" shape, but a variety of other hat shapes were popular. Homburgs, deerstalkers and “Trilbies” were also popular. Buck, p. 198-199 (George de Maurier novel ''Trilby'') Hats were ''de rigueur'' for all Victorians, all classes, all ages, all genders. ==== Shoes ==== [[File:Men's fashion silhouette of 1837.jpg|thumb|Men's coats, 1837]] [[File:Lev Wittgenstein by F. Kruger.JPG|thumb|Lev Wittgenstein by F. Kruger, 1836, wearing a surtout]] === 1830s and 1840s === For men's fashion, the 1830s and 1840s were dominated by a defined waist, lean limbs and tall hats. Working-class men had been wearing trousers for some time, but by the 1830s and '40s, middle- and upper-class men generally wore frock coats and trousers for casual or less formal attire in the city. In the country, what they wore depended on what they were doing — hunting, riding, shooting and so onen[[File:Man's Frock Coat LACMA M.2007.211.61 (1 of 4).jpg|alt=Male mannequin wearing a light-colored thigh-length coat similar to a suit jacket and a top hat|thumb|Men's frock coat, c. 1845]] [[File:Stockholms mode-journal- Tidskrift för den eleganta werlden 1847, illustration nr 2.jpg|thumb|Stockholm's fashion magazine, 1847]]Some men wore corsets during this time, so the waist was nipped in and the skirt of the frock coat flared out. The sleeves of their coats and jackets were slightly puffed at the shoulders. The trouser legs were straight with a strap under the instep. The figure on the left in the fashion plate from ''Modes de Paris Journal des Tailleurs'' (right) illustrates this silhouette very clearly as well as the frock coat, the strap under the instep, and the puffed shoulders. ==== Coats and Jackets ==== Frock coats had become fashionable for day wear in the 1820s<ref name=":25" />{{rp|474}} and were worn throughout the century. In the 1830s frock coats were tightly fitted and closed with buttons. The more tailored frock coats had a waist seam and a flared skirt almost to the knees. The main changes in frock coats in these two decades were in the colors and the neck treatments (collar and lapels). Initially frock coats were not necessarily black. They could be colorful — like "plum, mulberry, brown, bright blue, and bottle green" — with "contrasting velvet collars."<ref name=":25" />{{rp|474}} The truly bright, saturated colors made possible by synthetic dyes, however, were a couple of decades away still and were never used for frock coats. Middle- and upper-class men limited their use of tailcoats to evening wear and more formal occasions. (In the 1847 Stockholm fashion magazine, below right, the figure in the center is wearing a tailcoat.) A cutaway morning coat was worn with light trousers for formal events during the daytime, and a dark tail coat and trousers were worn in the evening. ==== Shirts ==== Shirts were made of linen or cotton with low collars, occasionally turned down, and were worn with wide [[cravats]] or neck ties. Before they were mass produced, shirts made of finer linen or cotton were tailored for upper and wealthy middle-class men. Depending on occupation, working-class men's shirts were made from a rougher, home-woven linen or cotton, often shaped loosely like a smock and sometimes without a front closure. Shirts were sometimes as long as knee-length. ==== Trousers ==== Men had adopted trousers over knee breeches for semi-formal dress "around 1815"<ref name=":31" /> (298) beginning after the French Revolution.<ref name=":26" /> (416) They were wearing trousers both for formal and semi-formal dress by the 1830s. Initially trousers "fit quite snugly ..., but in the 1840s they became looser."<ref name=":25" /> (477) Upper-class and aristocratic men still wore knee breeches at court and loose-fitting breeches (in the form of knickerbockers) for country wear and some sports, like riding and golf. Generally, however, they wore trousers more than they wore breeches. Men flocked to them once trousers became a stylish option because the looser fit was warmer in cold weather and more comfortable than the tight-fitting knee breeches from earlier in the century. Ready-made men's clothing was available in the US early, but by the 1840s ready-made suits were making an impact in Europe and the UK,<ref name=":26" /> (419–420) especially outside the upper classes. Aristocrats and upper middle class could afford the well-tailored cut and fit of individually hand-sewn trousers and coats. ==== Waistcoats ==== Waistcoats were both single- or double-breasted, with shawl or notched collars, and might be finished in double points at the lowered waist. Collars gradually lowered over the course of the two decades. Often the colorful vests were decorated with fur or velvet collars. “Waistcoats remained colorful, decorative items in men’s wardrobes after the rest of their costumes had become plain.” (Payne 2 460-462) <nowiki>:</nowiki> "During the 1820s and 1830s, men sometimes wore two waistcoats, in combinations like white velvet over rose-and-gold brocade."<ref name=":25" /> (474) ==== "Overcoats ==== Men wore a variety of topcoats or overcoats. Surtouts were overcoats built like long frock coats, like the one worn by Lev Wittgenstein in the portrait (above right). The redingote was most popular in the 1830s and 1840s. ==== Original Text ==== During the [[1840s in fashion|1840s]], men wore tight-fitting, calf length [[frock coat]]s and a [[waistcoat]] or vest. Sleeves were full at the top and waists were tight, creating an hourglass form. For more formal occasions, a cutaway morning coat was worn with light trousers during the daytime, and a dark tail coat and trousers was worn in the evening. Shirts were made of linen or cotton with low collars, occasionally turned down, and were worn with wide [[Cravat (early)|cravat]]s or neck ties. Men wore [[top hat]]s, with wide brims in sunny weather. === 1850s === The 1850s revealed several industrial inventions that significantly impacted clothing. First, the Industrial Revolution began (and still does today) with machines to weave fabric and machines to sew fabrics. Manufacturers quickly learned that the majority of the population was working class. Theirs were the simplest, least trimmed garments made in the nineteenth century. Second, mass production of shirts, trousers and coats changed how most people shopped for clothes. The aristocracy and upper middle class folks could still have their clothes made to specifically fit their bodies. Manufacturers knew that they could not mass produce clothing for each individual’s body. They invented generic sizing in small, medium, and large. They could, therefore, produce many more items of clothing with generic sizing. Third, Isaac Singer patented and began to manufacture home or domestic sewing machines (treadle machines) enabling more form-fitted '''dresses''' to be constructed for an individual’s specific shape and size. The fourth item to impact fashion and clothing was the invention of the paper pattern. These were introduced in fashion magazines targeting women. Almost all women were taught to sew by hand, whether they were aristocrats or working class. Sewing machines enormously speeded up the '''process of constructing from hours to minutes'''. Finally, aniline dyes made colors brighter and longer lasting. Prints and stripes, checks and plaids, fabrics had much more vibrant color with aniline dyes. The Industrial Revolution impacted the working class and changed their lives the most. children's clothes? Women made men's clothing too According to Judith Flanders, working-class men's clothes could be colorful. For example drivers of hansom cabs () dressed more up-scale, and drivers of hackneys () did not.<blockquote>While hackney drivers were also considered to be stereotypically shabby, hansom-cab drivers were generally represented as smartly dressed. A print in 1850 showed a driver in a snappy brown coat instead of the coachman’s heavy multiple-caped outfit, pale green striped trousers, short boots and top hat, the [167–168] reins held daintily in his gloved hands. Both cab and coach drivers wore top hats, but cabbies of a sporting bent later switched to bowlers, and in summer donned bright checked outfits.<ref name=":23">{{Cite book|title=The Victorian City: Everyday Life in Dickens' London|last=Flanders|first=Judith|publisher=Thomas Dunne Books|year=2012|location=New York, New York}}</ref> (167–168 [of 972])</blockquote> A variety of silhouettes was seen in the 1850s. Trousers were long and slim with a strap under the instep of the shoe. ==== Coats and Jackets ==== "Although the frock coat was worn throughout the century, it lost its dominant position in the 1850s, when the morning coat began to replace it."<ref name=":29" /> A jacket shorter than the frock coat or morning coat that had visible pockets began to be worn in about 1850. Cutaway tail coats were still reserved for formal occasions. All of these coats could be single or double breasted. They were called “ditto suits” by those who wore them because the coat, trousers, and waistcoat were all made from the same fabric. There were morning coats and cutaway morning coats; there were Norfolk jackets and ditto suits. The most formal were the cutaway tail coats for evening wear and balls; and the least formal were the boxy shaped sack coats. By the 1860s, it had become the most popular casual coat. ==== Shirts ==== During the [[1850s in fashion|1850s]], men started wearing shirts with high upstanding or turnover [[collar (clothing)|collars]] and [[necktie#Four-in-hand|four-in-hand necktie]]s tied in a bow, or tied in a knot with the pointed ends sticking out like "wings." ==== Trousers ==== Trousers had fly fronts and breeches were used for formal functions and knickers (short pants fuller cut than breeches) for horseback riding. Men's choice to wear trousers is an instance of the importance of comfort and convenience outweighing style and presentation, a value that increased in importance through the 20th century. ==== Waistcoats ==== Waistcoats remained the one garment that could be brightly colored and copiously trimmed on exotic fabrics. Waistcoats show that men were concerned with decorative elements in their ensemble. ==== Notes & Quotes ==== * transition from frock coats to ditto suits, 1850s (Payne, 463) ==== Hats ==== The upper-class continued to wear top hats, and [[bowler hat]]s were worn by the working class. Caps ==== Overcoats ==== Overcoats were cut fuller with wider sleeves and no extra fullness at the shoulder. Unlike the redingote, the overcoats had straight seams to the knee length. Many had wide lapels that reached below the waist. Working class men and their families benefitted more from the industrial revolution in regards to clothing.  Manufacturers marketed to them because because they were the largest class. [[File:Gazette of Fashion, February 1865, RP-P-2009-2675.jpg|thumb|1865, Frock coats, etc. (Paris)]] [[File:Gazette of Fashion, October 1864, RP-P-2009-2673.jpg|thumb|1864, Frock coats, etc., Paris]] [[File:Broadway fashions, New York LCCN2003677917.jpg|thumb|Butterick, Spring-Summer 1866, Broadway Fashions]] [[File:Four young men wearing frock coats - DPLA - 4706a21c9267c45034d51c8fc5309251 (page 1).jpg|thumb|1860s, working class?, ill fitting, frock coats, trousers, shirts, vest, derby hats]] === 1860s === [[File:Corporal frock coat 1862 med.jpg|thumb|Corporal frock coat 1862, 9-botton military]]The 1860s saw fewer inventions that influenced or changed the way people were acquiring clothes. But the changes begun by mass production continued with the working class. Little changed for the higher classes, except maybe paper patterns and sewing machines. The different shape and size in clothing continued to provide slightly different silhouettes for men in the upper and middle classes. As women's clothes grew more complex in cut and style, men's clothes became simpler in cut and style. ==== Coats and Jackets ==== Individualized fittings continued for upper class and wealthy middle class clients. (Working class as well as middle and upper class.) Working class was well over 60% of the population. For the largest class, ready-made garments were ideal for men and women who were working class. For the two upper classes morning coats still led the way but frock coats were still in demand and worn in business and more casual situations. Leisure wear like knickers and ditto suits became more popular in the 1860s. Haute couture wanted every occasion or event to have special clothing. In some ways men dressed more alike (coat, trousers, waistcoat) and in some ways there was more variety in the cut of their coats and in the manufactured clothing they could buy. Many upper class men still had their shirts custom made. Frock coats were shortened to knee-length and were worn for business, while the mid-thigh length [[sack coat]] slowly displaced the frock coat for less-formal occasions, with the overall effect of a looser silhouette. The Prince of Wales: "For the countryside such as at Sandringham, he permitted an informal dress code. The Henry Poole ledger marked as 'HRH 1865' is for an evening coat without tails, the first 'dinner jacket.'"<ref name=":26" /> (424) ==== Shirts ==== Ready-made shirts rarely were seen since shirts were more underwear than outerwear. Factories began to make and sell detachable collars and cuffs. It was more convenient to replace collars and cuffs each day than the time it took a servant (working class) to wash and starch enough to look like the celluloid many of those collars were made of. ==== Trousers ==== Trousers were cut full and boxy during most of the 1850s and 1860s. The strap under the shoe disappeared and trouser legs reached the back of the heel in length. Knickers were still worn for hunting or riding and breeches were still ''de rigueur'' at court. ==== Waistcoats ==== Waistcoats remained decorative and worn with most of the coats that were popular. The young “dandies” wore the most colorful and decorated waistcoats. These “dandies” gave their highest priority to their appearance. They were the avant garde of haute couture for men. ==== Necks Treatments ==== In the [[1860s in fashion|1860s]], men started wearing wider neckties that were tied in a bow or looped into a loose knot and fastened with a stickpin. ==== Hats ==== Top hats briefly became the very tall "stovepipe" shape, but a variety of other hat shapes were popular. ==== Overcoats ==== The single-breasted redingote continued in popularity among the aristocracy and upper middle-class.  These coats were often “in colors such as plum, mulberry, brown, bright blue, and bottle green . . . [with] contrasting velvet collars.” Payne2 p. 474 [[File:Mens Coats 1872 Fashion Plate.jpg|thumb|upright|Drawing of Victorian men 1870s]] [[File:Ashurst frock coat.jpg|thumb|Ashurst Frock coat]] [[File:Grand Duke Alexis Alexandrovich of Russia Wearing a Frock Coat; Standing (fbc266c2feca43f6ad5b44e031635a8d).tif|alt=Old photograph of a man wearing a dark thigh-length coat similar to a suit coat with light-colored trousers|thumb|Grand Duke Alexis Alexandrovich of Russia Wearing a Frock Coat, c. 1872]] [[File:Caillebotte Hugot.jpg|thumb|Portrait of Paul Hugot, 1878]] [[File:Oscar Wilde (1854-1900), by Hills & Saunders, Rugby & Oxford 3 april 1876.jpg|thumb|Oscar Wilde, 1876, ditto suit]] [[File:FrockCoat.jpg|thumb|English frock coat, 1870s]] === 1870s === To correct and prevent errors being made in court dress, in 1875 the Lord Chamberlain published ''Dress Worn by Gentleman at Her Majesty's Court'', "a summary of regulations for court uniform and dress."<ref>{{Cite book|url=https://www.google.com/books/edition/Dress_worn_by_Gentlemen_at_Her_Majesty_s/pvrbQCXq0MEC?hl=en|title=Dress worn by Gentlemen at Her Majesty's Court|last=Britain)|first=Victoria (Queen of Great|date=1875|language=en}}</ref> This is the kind of thing Bertie really cared about. Define court dress. A portly, boxy silhouette was sought for most of the 1870s. Older men whose stomachs had spread outward and thus looked prosperous to the Victorians were the ideal for men’s high fashion. Sack coats and trousers were cut a little wider in the legs. Corduroy for trousers and muslin for shirts was often used in working class clothing. ==== Coats and Jackets ==== There were minor changes to some of the coats Victorian men wore. Frock coats were shortened to the knee. Sack coats (or ditto coats — the forerunner of the suits worn by men in the western cultures of the twentieth and twenty-first centuries) were found to be so comfortable that most men of the upper and middle classes had a ditto suit. Men still wore morning coats and the aristocracy still wore cutaway coats with trousers to parties and balls but cutaway coats with knee breeches at court. ==== Shirts ==== Although ready-made shirts were available, the upper and middle classes still wore bespoke clothing hand-made, with better fabric and an excellent fit but stitched on machines. The suits and shirts made for the working class were of cheaper fabrics. ==== Trousers ==== Most men were wearing trousers  all of the time (except at court) and have worn them ever since. Trousers had button flies by the 1870s which most men found to be much more convenient than laces. Trousers did not “ride up” the leg in the way that knee breeches did when dancing or sitting. If a man did not have fashionable legs, they could be obscured behind trousers. ==== Waistcoats ==== White waistcoats began to be worn by men. Black were also worn when mourning. Changes in the waistcoat could be seen but were very subtle. For example, collars were lowered as the neckline grew deeper and deeper in front, revealing more of the fancy vest. ==== Overcoats ==== A longer version of the standard overcoat, “sometimes with fur collar, cuffs, and lining” was often worn for warmth. Payne2 p. 519 ==== Original Text ==== During the [[1870s in fashion|1870s]], three-piece suits grew in popularity along with patterned fabrics for shirts. Neckties were the four-in-hand and, later, the [[Ascot tie]]s. A narrow ribbon tie was an alternative for tropical climates, especially in the Americas. Both frock coats and sack coats became shorter and more form fitting. Flat straw boaters were worn when boating. [[File:Elliott & Fry10a.jpg|thumb|William Gladstone, 1887, morning coat]] [[File:British politicians gambling at Ascot Wellcome V0050378.jpg|thumb|British Politicians Gambling at Ascot, 1884]] [[File:Scribner's magazine (1887) (14595087238).jpg|thumb|1887, types of American servants]] === 1880s === The silhouette narrowed and straightened. That is, the line went straight down without the flare of skirts on the coats. This smooth line had few decorations. Men wore hardly any jewelry. They might have a boutonniere or a ring.  Suits were not  decorated. All coats were straighter and shorter. Depending on the time of day, the Prince of Wales might change his clothes (thus, his silhouette) up to six times per day,<ref name=":28" /> (129) and some aristocrats and upper-class men would follow his lead. ==== Coats and Jackets ==== Although the frock coat was worn throughout the nineteenth century, the single fabric sack suit was worn for casual wear and was beginning to be seen as a businessman’s suit.  Morning coats were still in use for some events as well as casual occasions. The modern tuxedo or Cowes jacket appeared and was worn for formal occasions. The tuxedo is still worn as formal dress today. ==== Shirts ==== Shirts were still custom made for the rich and the working class bought ready-made shirts. The shirt remained basically the same but it could handle the different neck treatments.  Even mass produced shirts could have buttons or button holes for detachable collars and cuffs. ==== Trousers ==== Trouser legs began to decrease in width as the coat became narrower and emphasized strong vertical lines. ==== Waistcoats ==== During the 1880s waistcoats were called vests [is it regional?] and much of their bold trim and colorful fabric disappeared and vests were constructed from the same fabric as the coat and trousers. The business suit for men developed in the 1880s and was firmly established in the 1890s. ==== Overcoats ==== Versions of topcoats increased, adding an ulster overcoat for travel and an Inverness coat with up to five cape collars and a high curved collar. Double breasted topcoats were popular and some were knee-length and some calf-length. ==== Original Text ==== During the [[1880s in fashion|1880s]], formal evening dress remained a dark tail coat and trousers with a dark waistcoat, a white bow tie, and a shirt with a winged collar. In mid-decade, the dinner jacket or [[tuxedo]], was used in more relaxed formal occasions. The [[Norfolk jacket]] and tweed or woolen breeches were used for rugged outdoor pursuits such as shooting. Knee-length topcoats, often with contrasting velvet or fur collars, and calf-length overcoats were worn in winter. Men's shoes had higher heels and a narrow toe. [[File:American fashions - The Jno. J. Mitchell Co. Litho., New York. LCCN2006676665.jpg|thumb|Fashion plate from the Jno. J. Mitchell Co., New York, 1899]] [[File:Alfred Milner Vanity Fair 1897-04-15.jpg|thumb|Alfred Milner, 1897, Leslie Ward ("Spy"), for Vanity Fair]] [[File:Nobl-08.jpg|thumb|Sherlock Holmes, 1892, Sidney Paget]] [[File:PUK1894page380rector poor.jpg|thumb|Rector and Drinker, 1894]] === 1890s === The dominant silhouette for men became the sack suit in the 1890s and while changes in the sack have been subtle, it remains the dominant silhouette today. ==== Coats and Jackets ==== “Sacks became ''the'' favored style of suit coat,”(Payne2, p. 532) especially among the younger men. Frock coats were associated with older men along with the cutaway coat. There were many more choices for sports wear and leisure wear than ever before. Norfolk jackets were often worn while hunting. Most informal styles could be purchased ready made. The rich still had their clothing custom made by tailors but even working class men could purchase most ready-made versions of the coats, trousers, and vests. ==== Shirts ==== Shirts could be made of patterned fabric as well as solid colors and white.  Shirts were beginning to be acceptable as outer wear especially when worn as sporting clothing. ==== Trousers ==== Early in the 1890s, “slim, straight trousers were news.” (Payne 2, p. 532) Trousers could be plaid or checked as well as the same fabric as the coat and vest. ==== Waistcoats ==== Fancy fabrics and bold trim were not seen much as the more subdued vest dominated the fashion scene. ==== Neck Treatments ==== In the 1860s, men started wearing wider neckties that were tied in a bow or looped into a loose knot and fastened with a stickpin. ==== Overcoats ==== “Topcoats included fingertip-length styles made of twill covert cloth. Single-breasted, fly-front overcoats were fashionable too. Roomy overcoats with fur linings and collars warmed the wealthy. Inverness overcoats remained in vogue.” Payne2, p.532 ==== Original Text ==== Starting from the [[1890s in fashion|1890s]], the [[blazer]] was introduced, and was worn for sports, sailing, and other casual activities.<ref>{{cite web|last=Landow|first=George|url=http://www.victorianweb.org/art/costume/90s/2.html|title=Men's informal sporting dress, late 1880s and '90s}}</ref> Throughout much of the Victorian era most men wore fairly short hair. This was often accompanied by various forms of facial hair including moustaches, side-burns, and full beards. A clean-shaven face did not come back into fashion until the end of the 1880s and early 1890s.<ref>{{cite web|url=http://www.victorianweb.org/art/costume/nunn21.html|title=Victorian Men's Fashions, 1850–1900: Hair}}</ref> Distinguishing what men really wore from what was marketed to them in periodicals and advertisements is difficult, as reliable records do not exist.<ref name="shannon597">{{cite journal|last=Shannon|first=Brent|title=Refashioning Men: Fashion, Masculinity, and the Cultivation of the Male Consumer in Britain, 1860–1914|journal=Victorian Studies|year=2004|volume=46|issue=4|pages=597–630|doi=10.1353/vic.2005.0022}}</ref> === Notes === *Men's suits buttoned higher up than today (Payne, 467) * Norfolk jackets and sack suits (Payne, 471) * formal attire, tuxedos with tails, cutaways (Payne, 469) * Keith Middlemas (https://archive.org/details/storyoffiesta00huxf/page/200/mode/2up?q=fashion) *Brent Shannon. "Refashioning Men: Fashion, Masculinity, and the Cultivation of the Male Consumer in Britain, 1860–1914." Victorian Studies 46, no. 4 (Summer 2004): 597–630. == Hats and headwear == [[File:Ford.madox.brown.last.emma.study.jpg|thumb|''Emma Hill'' by [[Ford Madox Brown]] (1853), a woman wearing a later version of the [[poke bonnet]]]] [[File:Hoed,_objectnr_KA_1237.tif|left|thumb|Perched bonnet style of the early 1870s.]] Hats were crucial to a respectable appearance for both men and women. === Men's Hats === The top hat, for example, was standard formal wear for upper- and middle-class men.[Payne] According to Blanche Payne, "The high top hat, usually black or dark gray, had reached its characteristic shape by 1798 and dominated the entire nineteenth century." (457–58) Although top hats were the dominant hat in the 19th century, other hats became popular for working classes and lower income middle class. “The style of an individual’s hat varied, depending on fashion and their social position, as well as their profession or chosen activity..” ''Goodman 53 of 460'' Other hats that became necessary and popular include the Derby, the straw Boater, and a flat cap with a short brim. In many cases the class, work activity and income could be determined by what kind of hat was on the head of the wearer. For some men, a hat supporting a particular sport or team was important. The Derby or Bowler hat was designed by William and Thomas Bowler, brother shopkeepers in 1849. ''(Goodman 55 of 460)'' It cost less than a top hat but  lasted longer and was soon worn by middle class bankers and clerks. Straw boaters were worn by the aristocracy for casual events and working class factory workers and agricultural laborers. By 1901 working class men had changed their preference to the flat caps which became the most popular hat for the workers. Headdress for men was an essential part of dress for the entire period of the Victorian age, from the 1830s through the end of the century. Judith Flanders describes the hats worn by men in London, <blockquote>It is difficult to bear in mind the importance of hats as not only markers of class and income, but also as indicators of respectability. [509–519] [George Augustus] Sala commented that "every" man throughout the history of the world "must, necessarily and habitually, wear some kind of covering to his head". Postmen wore hats, small children wore hats, field labourers and market gardeners wore hats, cricketers, skaters — all sportsmen — wore hats. It was, self-evidently, impossible to go outdoors without one. ... Those in professional occupations wore pot hats, as did clerks and all those with pretensions to middle-class status. Even doctors' delivery boys wore battered hand-me-down pot hats: "the nap rusty, the band a mournful strip of tarnished lace; but still a Hat", which "stamps him as being associated, in however slender a manner, with a learned profession". Cloth caps were for labourers, for costers and for boys. ... Artisans wore caps made out of paper, which they folded [510–511] themselves and so could easily replace as they became dirty.<ref name=":23" /> (509–511 [of 972]) </blockquote>A pot-hat is a kind of derby or bowler in men's hats. (Lewandowski, 237) ==== Original Text ==== Hats were crucial to a respectable appearance for both men and women. The top hat, for example, was standard formal wear for upper- and middle-class men.<ref name=":4">{{Cite book |last=Steele |first=Valerie |url=https://archive.org/details/fashioneroticism0000stee |title=Victorian Fashion. Fashion and Eroticism: Ideals of Feminine Beauty from the Victorian Era to the Jazz Age |publisher=Oxford University Press |year=1985 |isbn=978-0-19-503530-8 |pages=[https://archive.org/details/fashioneroticism0000stee/page/51 51]–84 |url-access=registration}}</ref> For women, the styles of hats changed over time and were designed to match their outfits. === Women's Hats === For a discussion of the history of plumes and feathers, see [[Social Victorians/Victorian Things#Ostrich Plumes and Prince of Wales's Feathers|Ostrich Plumes and Prince of Wales's Feathers in ''Victorian Things'']]. ==== Original Wikipedia Text ==== During the early Victorian decades, hats were modest in size and design, straw and fabric bonnets being the popular choice. [[Poke bonnet]]s, which had been worn during the late [[Regency period]], had high, small crowns and brims that grew larger until the 1830s, when the face of a woman wearing a poke bonnet could only be seen directly from the front. They had rounded brims, echoing the rounded form of the bell-shaped hoop skirts. Bonnets shrunk at the end of the 1860s and moved to a perched position in the early 1870s as hairstyles grew in scale and intricacy. This led to the popularization of hats, which became the headwear of choice for the remainder of the Victorian era.<ref name="g4223">{{cite book |last=Cunnington |first=Cecil Willett |title=English Women's Clothing in the Nineteenth Century |date=1990-05-01 |publisher=Courier Corporation |isbn=0-486-26323-1 |publication-place=New York |page=}}</ref> [[File:The_London_and_Paris_ladies'_magazine_(Apr_1885)_03.png|thumb|Flower pot style hat of 1885.]] The 1880s saw a hat inspired by the top hat for women known as the flowerpot hat, and the 1890s saw the popularity of the boater. The hats of the late Victorian era were covered with elaborate creations of silk flowers, ribbons, and above all, exotic plumes; hats sometimes included entire exotic birds that had been stuffed. Many of these plumes came from birds in the Florida everglades, which were nearly made entirely extinct by overhunting. By 1899, early environmentalists like [[Adeline Knapp]] were engaged in efforts to curtail the hunting for plumes. By 1900, more than five million birds a year were being slaughtered, and nearly 95 per cent of Florida's shore birds had been killed by [[Plume hunting|plume hunter]]s.<ref>{{cite web|title=Everglades National Park|url=https://www.pbs.org/nationalparks/parks/everglades/|archive-url=https://web.archive.org/web/20090927085907/http://www.pbs.org/nationalparks/parks/everglades/|url-status=dead|archive-date=27 September 2009|publisher=PBS|access-date=7 November 2011}}</ref> == Shoes == The women's shoes of the early Victorian period were narrow and heelless, in black or white satin. By 1850s and 1860s, they were slightly broader with a low heel and made of leather or cloth. Ankle-length laced or buttoned boots were also popular. From the 1870s to the twentieth century, heels grew higher and toes more pointed. Low-cut pumps were worn for the evening.<ref name=":4" /> == Cosmetics == [[Victorian-era cosmetics]] were typically less obvious than ours. However, small amounts of pale face powder or powdered blush were widely used.<ref>{{Cite book |last=Goodman |first=Ruth |title=How to be a Victorian |date=2014 |publisher=Penguin Books |isbn=978-0-670-92136-2 |location=London}}</ref> Tints were sometimes added to face creams. Some cosmetics contained toxic or caustic ingredients like lead, mercury, ammonia, and arsenic {{Citation needed|date=October 2025}}. Hair color ==Mourning black== {{See also |Mourning stationery}} [[File:The royal children in mourning Mar 1862.jpg|thumb|Victoria's five daughters (Alice, Helena, Beatrice, Victoria and Louise), photographed wearing mourning black beneath a bust of their late father, Prince Albert (1862)]] [[File:Mourning dress MET 50.40.3a-b front CP4.jpg|alt=Black Victorian mourning dress|thumb|Mourning Dress, 1894–95]] In Britain, black is the colour traditionally associated with mourning for the dead. The customs and etiquette expected of men, and especially women, were rigid but evolving during much of the Victorian era. The expectations depended on a complex hierarchy of close or distant relationship with the deceased. (Davidoff) The closer the relationship, the longer the mourning period and the wearing of black. The wearing of full black was known as First Mourning, which had its own expected attire, including fabrics, and an expected duration of 4 to 18 months. Following the initial period of First Mourning, the mourner would progress to Second Mourning, a transition period of wearing less black, which was followed by Ordinary Mourning, and then Half-mourning. Some of these stages of mourning were shortened or skipped completely if the mourner's relationship to the deceased was more distant. Half-mourning was a transition period when black was replaced by acceptable colours such as lavender and mauve, possibly considered acceptable transition colours because of the tradition of [[Church of England]] (and [[Catholic Church|Catholic]]) clergy wearing lavender or mauve [[Stole (vestment)|stoles]] for funeral services, to represent the [[Passion (Christianity)|Passion of Christ]].<ref>{{cite web|title=The Colors of the Church Year|url=http://fullhomelydivinity.org/articles/colors.htm|publisher=Consortium of Country Churches|access-date=6 November 2011|archive-date=13 November 2011|archive-url=https://web.archive.org/web/20111113075214/http://fullhomelydivinity.org/articles/colors.htm|url-status=dead}}</ref> The mourning dress worn by Queen Victoria (below, right) "shows the traditional touches of mourning attire, which she wore from the death of her husband, Prince Albert (1819–1861), until her own death."<ref>{{Cite web|url=https://www.metmuseum.org/art/collection/search/155839?&searchField=All&sortBy=Relevance&deptids=8&ft=queen+victoria&offset=0&rpp=20&amp;pos=2|title=Mourning Dress, 1894–95|last=The Metropolitan Museum of Art|date=7 September 2019|website=The Metropolitan Museum of Art|access-date=7 September 2019}}</ref> Dating from 1894–95, Queen Victoria wore this dress as a result of the death of the eldest son of the Prince and Princess of Wales, Eddy, in line to the throne. === Norms for mourning=== ''Manners and Rules of Good Society, or, Solecisms to be Avoided'' (London, Frederick Warne & Co., 1887) gives clear instructions, such as the following:<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–83}}</ref> {| class="wikitable" |- ! Relationship to deceased !! First mourning !! Second mourning !! Ordinary mourning !! Half-mourning |- | Wife for husband || 1-year, 1-month; [[bombazine]] fabric covered with [[Crape|crepe]]; [[widow's cap]], [[lawn cuff]]s, collars || 6 months: less crepe || 6 months: no crepe, silk or wool replaces bombazine; in last 3 months jet jewellery and ribbons can be added || 6 months: colours permitted are grey, lavender, mauve, and black-and-grey |- | Daughter for parent || 6 months: black with black or white crepe (for young girls); no linen cuffs and collars; no jewellery for first 2 months || 4 months: less crepe || – || 2 months as above |- | Wife for husband's parents || 18 months in black bombazine with crepe || – || 3 months in black || 3 months as above |- | Parent for son- or daughter-in-law's parent || – Black armband in representation of someone lost || – || 1-month black || – |- | Second wife for parent of a first wife || – || – || 3 months black || – |} The complexity of these etiquette rules extends to specific mourning periods and attire for siblings, step-parents, aunts and uncles distinguished by blood and by marriage, nieces, nephews, first and second cousins, children, infants, and "connections" (who were entitled to ordinary mourning for a period of "1–3 weeks, depending on level of intimacy"). Men were expected to wear mourning black to a lesser extent than women, and for a shorter mourning period. After the mid-19th century, men would wear a black hatband and black suit, but for only half the prescribed period of mourning expected of women. Widowers were expected to mourn for a mere three months, whereas the proper mourning period expected for widows was up to four years.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–9}}</ref> Women who mourned in black for longer periods were accorded great respect in public for their devotion to the departed, the most prominent example being Queen Victoria herself. It was not uncommon for a widow who did not remarry to wear half-mourning for the rest of her life, except when another death necessitated full mourning. For example, Alexandra, Princess of Wales wore half-mourning for the rest of her life after her eldest son Eddy died in 1894. Empress Elisabeth of Austria did the same, as did Empress Eugénie of France. They reverted to full mourning when appropriate, but they never wore less than half-mourning after their sons' deaths. Women with lesser financial means tried to keep up with the example being set by the middle and upper classes by dyeing their daily dress. Dyers made most of their income during the Victorian period by dyeing clothes black for mourning.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|page=341}}</ref> == Technological advancement == The technological changes that affected the manufacture and consumption of clothing in the Victorian age included the following: * the mass production of fabrics — for example, "by the early 1850s there were thousands of steam-powered looms churning out millions of miles of fabric every year"  [62] * the invention of aniline dyes, which were much more vibrantly colored and resistant to fading than the natural dyes that had been used. — . Invented by chemist [[William Henry Perkin]] in 1856, the first aniline dye mauveine (or mauve) "wash[ed] the fashionable landscape in a haze of purple."<ref name=":22">{{Cite book|title=The Dress Diary: Secrets from a Victorian Woman's Wardrobe|last=Strasdin|first=Kate|publisher=Pegasus Books|year=2023|location=New York, New York}}</ref> (247) Other intense and, to the Victorians, intensely exciting colors followed, but the new synthetic additions to fabric sometimes included chemicals harmful to their wearers. For example, a "bright-magenta hue was achieved by adding arsenical-based chemicals to existing aniline dyes, brightening the already luminous shades – but these left residues themselves, along with a toxic labour trail in their wake."<ref name=":22" /> (255) Perhaps the most famous of these is arsenic green, used on fabrics, wallpapers, and trim: "The craze for artificial foliage to adorn the heads and dresses of women of fashion in the mid-nineteenth century had seen the proliferation of flower workshops, where young women in their hundreds laboured to produce the lifelike green leaves and blooms that would make a fetching headdress or would trail becomingly across the bodice of a gown. The lushness of the green was achieved by the application of a powder, a pigment that was created by mixing copper and the highly toxic chemical, arsenic trioxide. The physical effects of working with this poisonous compound were horrific. Contemporary medical drawings depict the green hue of the skin and dreadful open lesions on the hands of the maker, whilst the daily gradual ingestion of the powder by the flower girls was eventually fatal."<ref name=":22" /> (255) * the invention of a sewing machine that could be used in the home. Although sewing machines were already in use in the clothing industry, in 1858 Isaac Merritt Singer began to sell "lightweight domestic machines" for home sewing, radically increasing women's control over their own dress.<ref name=":24">{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|last2=Storey|first2=Neil R.|publisher=Pen & Sword History|year=2022|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=}}</ref> (91 [of 298]) * the spread of journalism for women and fashion journalism * the Jacquard loom: "French inventor Joseph-Marie Jacquard’s loom attachment mechanized the weaving of figured fabrics by 1804."<ref name=":25" /> (454) Perhaps not at the same scale as these but as important in 1850s designs was a technology that turned iron into steel, which could then be drawn into fine wires.<ref name=":3">{{Cite book|title=The Culture of Fashion|last=Breward|first=Christopher|publisher=Manchester University Press|year=1995|pages=145–180}}</ref> Steel was refined to a malleable state so that thin blades could be curved into concentric circles (called hoops) and connected with wires to form the cage. Technological advancements not only influenced the economy but brought a major change in the fashion styles worn by men and women. As the Victorian era was based on the principles of gender, race and class.<ref>{{cite journal|last1=Graham|first1=P|title=The Victorian Era|url=https://archive.org/details/in.ernet.dli.2015.261548|journal=Digital Library of India}}</ref> Much advancement was in favor of the upper class as they were the ones who could afford the latest technology and change their fashion styles accordingly. In 1830s there was introduction of horse hair crinoline that became a symbol of status and wealth as only the upper-class women could wear it. In 1850s there were more fashion technological advancements hence 1850s could rightly be called a revolution in the Victorian fashion industry such as the innovation of artificial cage crinoline that gave women an artificial hourglass silhouette without layers of petticoats, which was lighter and more hygienic.<ref>{{cite book|last1=Shrimpton|first1=J|title=Victorian Fashion|publisher=Bloomsbury Shire Publications}}</ref> Synthetic dyes, such as [[mauveine]] (aniline purple), were introduced in 1856, adding bright colours to garments. In 1855's ''[[Haute couture]]'' was introduced as tailoring became more mainstream in years to follow.<ref>{{cite book|last1=Aspelund|first1=Karl|title=Fashioning Society|publisher=Fairchild Books}}</ref> Charles Frederick Worth, a prominent English designer, became popular amongst the upper class though its city of destiny always is Paris. Haute couture became popular at the same time that sewing machines were invented.<ref name="Haute Couture">{{cite book|last1=Martin|first1=Richard|last2=Koda|first2=Harold|title=Haute Couture|publisher=The Metropolitan Museum of Art}}</ref> Princess [[Eugénie de Montijo|Eugenie]] of France wore the Englishman dressmaker, Charles Frederick Worth's couture and he instantly became famous in France though he had just arrived in Paris a few years ago. In 1855, Queen Victoria and Prince Albert of Britain welcomed [[Napoleon III]] and Eugenie of France to a full state visit to England. Eugenie was considered a fashion icon in France. Queen Victoria, who had been the fashion icon for European high fashion, was inspired by Eugenie's style and the fashions she wore.{{Citation needed|date=October 2025}} Later, Queen Victoria also appointed Charles Frederick Worth as her dress maker and he became a prominent designer amongst the European upper class. Charles Frederick Worth is known as the father of the haute couture as later the concept of labels were also invented in the late 19th century as custom, made to fit tailoring became mainstream.<ref>{{cite book|last1=Saillard|first1=Olivier|last2=Zazzo|first2=Anne|title=Paris Haute Couture|publisher=Skira Flammarion}}</ref> By the 1860s, when made-to-fit tailoring was popular in Europe, crinolines were considered impractical. In the 1870s, women preferred more slimmer silhouettes, hence bodices grew longer and the polonaise, a skirt and bodice made together, was introduced. In 1870s the Cuirass Bodice, a piece of armour that covers the torso and functions like a corset, was invented. Towards the end of Victoria's reign, dresses were flared naturally as crinolines were rejected by middle-class women. Designers such as Charles Frederick Worth were also against them. All these inventions and changes in fashion led to women's liberation as tailored looks improved posture and were more practical.<ref name="Haute Couture"/> dressmakers, couturiers, modistes == Home decor == {{main|Victorian decorative arts}} Home decor started spare, veered into the elaborately draped and decorated style we today regard as Victorian, then embraced the retro-chic of [[William Morris]] as well as pseudo-[[Japonaiserie]]. == Myths and Oversimplifications == === Modesty === {{main|Victorian morality}} {{Original research|section|date=May 2008}} [[File:1868-skirt-lengths-girl-ages-Harpers-Bazar.gif|thumb|upright|"The proper length for little girls' skirts at various ages", from ''[[Harper's Bazaar]]'', showing a 1900 idea of how the hemline should descend towards the ankle as a girl got older]]Many myths and exaggerations about the period persist to the modern day. Examples include the idea of men's clothing is seen as formal and stiff, women's as elaborate and over-done; clothing covered the entire body, and even the glimpse of an ankle was scandalous. Critics contend that [[corset]]s constricted women's bodies and lives. Homes are described as gloomy, dark, cluttered with massive and over-ornate furniture and proliferating [[bric-a-brac]]. Myth has it that even piano legs were scandalous, and covered with tiny [[pantalette]]s. === Tight Lacing === Tight-lacing, which was not possible until the development of the grommet in 1828, was famously controversial in the Victorian age, generating many column inches of profitable newspaper copy, in part because it was (and still is) fetishistic and subversive in that adolescent girls used it as a means of rebellion and upper-working- or lower-middle-class shop girls saw it as a means of upward mobility.<ref name=":21">{{Cite book|title=Fashion and Fetishism: Corsets, Tight-Lacing and Other Forms of Body-sculpture|last=Kunzle|first=David|publisher=History Press|year=2013|isbn=978 0 7524 9545 3|location=Stroud, Gloucestershire|pages=}}</ref> (71 [of 1182]) No evidence exists that tight lacing was widespread or particularly dangerous.<ref name=":21" /> () In truth, men's formal clothing may have been less colourful than it was in the previous century, but brilliant [[waistcoat]]s and [[cummerbund]]s provided a touch of colour, and [[smoking jacket]]s and [[robe|dressing gown]]s were often of rich Oriental [[brocade]]s. This phenomenon was the result of the growing textile manufacturing sector, developing mass production processes, and increasing attempts to market fashion to men.<ref name="shannon597"/> Corsets stressed a woman's sexuality, exaggerating hips and bust by contrast with a tiny waist. Women's [[evening gown]]s bared the shoulders and the tops of the breasts. The [[jersey dress]]es of the 1880s may have covered the body, but the stretchy novel fabric fit the body like a glove.<ref>{{cite book |last=Gernsheim |first=Alison |title=Victorian & Edwardian Fashion: A Photographic Survey |year=1981 |publisher=Dover Publications |location=New York |page=65|edition=New |isbn=0-486-24205-6}}</ref> Home furnishing was not necessarily ornate or overstuffed. However, those who could afford lavish draperies and expensive ornaments, and wanted to display their wealth, would often do so. Since the Victorian era was one of increased social mobility, there were ever more ''[[nouveaux riches]]'' making a rich show. The items used in decoration may also have been darker and heavier than those used today, simply as a matter of practicality. London was noisy and its air was full of [[soot]] from countless coal fires. Hence those who could afford it draped their windows in heavy, sound-muffling curtains, and chose colours that didn't show soot quickly. When all washing was done by hand, curtains were not washed as frequently as they might be today. There is no actual evidence that piano legs were considered scandalous. Pianos and tables were often draped with [[shawl]]s or cloths—but if the shawls hid anything, it was the cheapness of the furniture. There are references to lower-middle-class families covering up their [[pine]] tables rather than show that they couldn't afford [[mahogany]]. The piano leg story seems to have originated in the 1839 book, ''A Diary in America'' written by Captain [[Frederick Marryat]], as a satirical comment on American prissiness.<ref>{{cite book |last1=Marryat |first1=C.B. |title=A Diary in America: With Remarks on Its Institutions |date=1839 |publisher=Longman, Orme, Brown, Green, and Longmans |location=London, England |volume=2 |pages=246–247 |url=https://books.google.com/books?id=2-VEAAAAIAAJ&pg=PA246}} From pp. 246-247: "I was requested by a lady to escort her to a seminary for young ladies, and on being ushered into the reception-room, conceive my astonishment at beholding a square piano-forte with four ''limbs''. However, that the ladies who visited their daughters, might feel in its full force the extreme delicacy of the mistress of the establishment, and her care to preserve in their utmost purity the ideas of the young ladies under her charge, she had dressed all these four limbs in modest little trousers, with frills at the bottom of them!"</ref> Victorian manners may have been as strict as imagined—on the surface. One simply did not speak publicly about sex, childbirth, and such matters, at least in the respectable middle and upper classes. However, as is well known, discretion covered a multitude of sins. Prostitution flourished. Upper-class men and women indulged in [[adultery|adulterous]] liaisons. == Gallery == {{gallery |2=A mid-Victorian interior: ''Hide and Seek'' by [[James Tissot]], c. 1877 Image:Winterhalter Elisabeth.jpg|3=Dress designed by [[Charles Frederick Worth]] for [[Elisabeth of Bavaria|Elisabeth of Austria]] painted by [[Franz Xaver Winterhalter]].|4=File:Frith A Private View detail.jpg|5=[[William Powell Frith]]'s painting of 1883 contrasts women's [[Aesthetic dress]] (left and right) with fashionable attire (center).|6=File:Tissot lilacs 1875.jpg|7=Day dress, c. 1875 [[James Tissot]] painting.|8=File:James Abbot McNeill Whistler 011.jpg|9=[[James McNeill Whistler|Whistler]]'s [[Portrait of Lady Meux]], 1882 Image:Jeanna_Samary-Renoir.png|10=[[Pierre-Auguste Renoir|Renoir]]'s portrait of [[Jeanne Samary]] in an [[evening gown]], 1878|11=File:Melville_-_Queen_Victoria.jpg|12=Portrait by [[Alexander Melville (artist)|Alexander Melville]] of [[Victoria of the United Kingdom|Queen Victoria]], 1845|13=File:Henry Treffry Dunn Rossetti and Dunton at 16 Cheyne Walk.jpg|14=An artistic interior: [[Dante Gabriel Rossetti]] reading to [[Theodore Watts-Dunton]] in the drawing room at No. 16 [[Cheyne Walk]], 1882|15=File:Punch - Masculine beauty retouched1.png|16=Men's swimwear: Cartoon from ''[[Punch (magazine)|Punch]]'' by [[George du Maurier]]}} == See also == * [[Emily Clapham]] * [[Victorian decorative arts]] * [[Victorian dress reform]] * [[Victorian morality]] * [[Victoriana]] * [[Women in the Victorian Era]] * [[Charles Frederick Worth]] === Time periods === * [[1830s in fashion]] * [[1840s in fashion]] * [[1850s in fashion]] * [[1860s in fashion]] * [[1870s in fashion]] * [[1880s in fashion]] * [[1890s in fashion]] === Women's clothing === * [[Corset]] * [[Corset controversy]] * [[Tightlacing]] * [[Bloomers (clothing)|Bloomers]] * [[Bodice]] === Contemporary interpretations === * [[Steampunk]] * [[Neo-Victorian]] * [[Lolita Fashion|Lolita]] == References == {{Reflist}} == Further reading == *{{cite book |author=Phipps, Elena| title= ''From Queen to Empress: Victorian dress 1837-1877'' | location=New York | publisher=The Metropolitan Museum of Art | year=1988 | isbn=0870995340| url= http://libmma.contentdm.oclc.org/cdm/compoundobject/collection/p15324coll10/id/69547/rec/235 | display-authors=etal}} * Sweet, Matthew – ''Inventing the Victorians'', St. Martin's Press, 2001 {{ISBN|0-312-28326-1}} == External links == * [http://www.victorians.co.uk/victorian-fashion Victorian Fashion] {{Webarchive|url=https://web.archive.org/web/20180407223711/http://www.victorians.co.uk/victorian-fashion |date=7 April 2018 }} * [https://www.victorianvoices.net/topics/fashion/index.shtml VictorianVoices.net] – Fashion articles and illustrations from Victorian periodicals; extensive fashion image gallery * [http://www.cracked.com/article_19575_5-ridiculous-sex-myths-from-history-you-probably-believe.html Victorian myths] * [http://www.victorianstation.com/lifestylemenu.htm Victorian fashion, etiquette, and sports] {{Webarchive|url=https://web.archive.org/web/20180103162620/http://www.victorianstation.com/lifestylemenu.htm |date=3 January 2018 }} * [http://www.thesmartset.com/article/article12180701.aspx Background on "A Diary in America"] * [http://www.mccord-museum.qc.ca/en/keys/webtours/VQ_P2_17_EN.html Form and Fashion] — the evolution of women's dress during the 19th century (many photographs) * [http://www.mccord-museum.qc.ca/en/keys/games/jeu2/ Educational Game: Mix and Match] — build a 19th-century dress using a virtual mannequin * {{cite web |publisher= [[Victoria and Albert Museum]] |url= http://www.vam.ac.uk/content/articles/v/victorian-dress-at-v-and-a/ |title= Victorian Dress |work= Fashion, Jewellery & Accessories |date= 14 January 2011 |access-date= 2011-04-03}} *[http://cv.vic.gov.au/stories/creative-life/fashion-detective-fashion-fiction-and-forensics/ Fashion detective: Fashion, Fiction and Forensics in nineteenth century Australian fashion] on Culture Victoria {{Timeline of clothing and fashion|state=collapsed}}{{Victorian era|state=collapsed}} [[Category:Victorian fashion| ]] [[Category:19th-century fashion|*]] [[Category:1900s fashion]] [[Category:History of Western fashion]] [[Category:19th century in the arts]] =From ''Women in the Victorian era''= ===Victorian women's fashion=== {{Multiple issues|{{tone|date=March 2023}} {{more footnotes needed|date=March 2023}}|section=y}}{{Further|Victorian fashion}} The ideal Victorian woman was pure, chaste, refined, and modest. This ideal was supported by etiquette and manners. The etiquette extended to the pretension of never acknowledging the use of undergarments (sometimes generically referred to as "unmentionables"). The discussion of such a topic, it was feared, would gravitate towards unhealthy attention on anatomical details. As one Victorian lady expressed it: "[those] are not things, my dear, that we speak of; indeed, we try not even to think of them", in contrast to current norms.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=20}}</ref> The pretence of avoiding acknowledgement of anatomical realities met with embarrassing failure on occasion. In 1859, the Hon. Eleanor Stanley wrote about an incident where the [[Louisa Cavendish, Duchess of Devonshire|Duchess of Manchester]] moved too quickly while manoeuvring over a [[stile]], tripping over her large [[hoop skirt]]: {{blockquote|[the Duchess] caught a hoop of her cage in it and went regularly head over heels lighting on her feet with her cage and whole petticoats above, above her head. They say there was never such a thing seen – and the other ladies hardly knew whether to be thankful or not that a part of her undergarments consisted in a pair of scarlet tartan [[knickerbockers (clothing)|knickerbockers]] (the things Charlie shoots in) which were revealed to the view of all the world in general and the [[Aimable Pélissier|Duc de Malakoff]] in particular".<ref>{{cite book|last=Cunnington|first=C. Willett|title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations|year=1990|publisher=Dover Publications|isbn=978-0-486-26323-6|pages=20–1}}</ref>}} However, despite the fact that Victorians considered the mention of women's undergarments in mixed company unacceptable, men's entertainment made great comedic material out of the topic of ladies' [[bloomers (clothing)|bloomers]], including men's magazines and music hall skits.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=22}}</ref> Victorian women's clothing followed trends that emphasised elaborate dresses, skirts with wide volume created by the use of layered material such as [[crinoline]]s, hoop skirt frames, and heavy fabrics. Because of the impracticality and health impact of the era's fashions, a [[Victorian dress reform|dress reform movement]] began among women. The ideal silhouette of the time demanded a narrow waist, which was accomplished by constricting the abdomen with a laced [[corset]]. While the silhouette was striking, and the dresses themselves were often exquisitely detailed creations, the fashions were cumbersome. At best, they restricted women's movements and at worst, they had a harmful effect on women's health. Physicians turned their attention to the use of corsets and determined that they caused several medical problems: compression of the thorax, restricted breathing, organ displacement, poor circulation, and prolapsed uterus.<ref name="O'Connor"/> Articles advocating the reform of women's clothing by the British National Health Society, the Ladies' Dress Association, and the [[Rational Dress Society]] were reprinted in ''The Canada Lancet'', Canada's medical journal. In 1884, Dr J. Algernon Temple of Toronto even voiced concern that the fashions were having a negative impact on the health of young women from the working classes. He pointed out that a young working-class woman was likely to spend a large part of her earnings on fine hats and shawls, while "her feet are improperly protected, and she wears no flannel petticoat or woollen stockings".<ref name="O'Connor"/> [[File:Bloomers.jpg|thumb|1850s illustration of a woman wearing [[bloomers]]]] [[Florence Pomeroy]], Lady Haberton, was president of the Rational Dress movement in Britain. At a National Health Society exhibition held in 1882, Viscountess Haliburton presented her invention of a "[[divided skirt]]", which was a long skirt that cleared the ground, with separate halves at the bottom made with material attached to the bottom of the skirt. She hoped that her invention would become popular by supporting women's freedom of physical movement, but the British public was not impressed by the invention, perhaps because of the negative "unwomanly" association of the style with the American [[Bloomers]] movement.<ref>{{cite book|last=Murray|first=Janet Horowitz|title=Strong-Minded Women and Other Lost Voices from 19th Century England|year=1982|publisher=Pantheon Books|location=New York|isbn=0-394-71044-4|pages=[https://archive.org/details/strongmindedwome00jane/page/68 68–70]|url=https://archive.org/details/strongmindedwome00jane/page/68}}</ref> [[Amelia Jenks Bloomer]] had encouraged the wearing of visible bloomers by feminists to assert their right to wear comfortable and practical clothing, but it was no more than a passing fashion itself among radical feminists. The movement to reform women's dress would persist and have long-term success, however; by the 1920s, [[Coco Chanel]] was successful at selling a progressive, far less restrictive silhouette that abandoned the corset and raised hemlines. The new silhouette symbolised modernism for trendy young women and became the 20th century standard. Other Paris designers continued reintroducing pants for women and the trend was gradually adopted over the next century. Fashion trends, in one sense, travelled "full circle" over the course of the Victorian era. The popular women's styles during the [[Georgian era]], and at the very beginning of Victoria's reign, emphasized a simple style influenced by flowing gowns worn by women in [[Ancient Greek clothing|Ancient Greece]] and [[Clothing in ancient Rome|Rome]]. The [[Empire waist]] silhouette was replaced by a trend towards ornate styles and an artificial silhouette, with the restrictiveness of women's clothing reaching its low point during the mid-century passion for narrow corseted waists and hoop skirts. The iconic wide-brimmed women's hats of the later Victorian era also followed the trend towards ostentatious display. Hats began the Victorian era as simple [[Bonnet (headgear)|bonnets]]. By the 1880s, milliners were tested by the competition among women to top their outfits with the most creative (and extravagant) hats, designed with expensive materials such as silk flowers and exotic plumes such as ostrich and peacock. As the Victorian era drew to a close, however, fashions were showing indications of a popular backlash against excessive styles. Model, actress and socialite [[Lillie Langtry]] took London by storm in the 1870s, attracting notice for wearing simple black dresses to social events. Combined with her natural beauty, the style appeared dramatic. Fashions followed her example (as well as Queen Victoria's wearing of mourning black later in her reign). According to [[Harold Koda]], the former Curator-in-chief of the [[Costume Institute at The Met|Metropolitan Museum of Art's Costume Institute]],<ref>{{cite web|url=http://www.metmuseum.org/about-the-museum/press-room/exhibitions/2014/death-becomes-her|title=Death Becomes Her: A Century of Mourning Attire : October 21, 2014-February 1, 2015|website=Metmuseuim.org|access-date=7 November 2021}}</ref> "The predominantly black palette of [[mourning]] dramatizes the evolution of period silhouettes and the increasing absorption of fashion ideals into this most codified of etiquettes," said Koda, "The veiled widow could elicit sympathy as well as predatory male advances. As a woman of sexual experience without marital constraints, she was often imagined as a potential threat to the social order." ====Evolution of Victorian women's fashion==== <gallery> File:Fashion plate December 1844.jpg|Ladies' December Fashions (1844). Hand-coloured steel engraving from a women's magazine. File:Thegalleryofhmscalcutta james tissot 1876.jpg|''[[The Gallery of HMS Calcutta]]'' by [[James Tissot]] (1876). [[Bustle]]s were fashionable in the 1870s and 1880s. File:Mrs lillie langtry george frederic watts 1880.jpg|''Mrs. Lillie Langtry'' by [[George Frederic Watts]] (1880). File:Five-women-on-queenslander-steps-r.jpg|Fashionable women in [[Queensland]], Australia around 1900. </gallery> {{Short description|Irish writer (born 1963)}} {{Use Irish English|date=August 2025}} {{Use dmy dates|date=August 2025}} {{Infobox writer | name = Darach Ó Scolaí | image = Darach Ó Scolaí.JPG | alt = Man holding prize-winning book | caption = Ó Scolaí in 2019 | birth_name = Darach Ó Scolaí | birth_date = {{Birth date and age|1963|df=y}} | birth_place = [[County Galway]], The Republic of Ireland | death_date = | death_place = | occupation = Writer, artist, publisher | alma_mater = [[University of Galway]] | years_active = 1998–present | genre = Novel, retelling, translation, play, screenplay, illustrated book for children and adults | other_names = | spouse = | children = 3 | awards = [[Awards and Honors received by Darach Ó Scolaí|Awards and Honors]] | signature = | website = }}[[File:Darach Ó Scolaí.JPG|thumb|Darach Ó Scolaí, holding ''Oileán an Órchiste'' (his translation of Robert Louis Stevenson's ''Treasure Island'')]] == Darach Ó Scolaí == Darach Ó Scolaí (<small>Irish:</small> [/ˈda.rax/ /oː/ /sˠkˠoː/l̪ˠəi/]; born 1963<ref>{{Cite web|url=https://portraidi.ie/en/darach-o-scolai/|title=Darach Ó Scolaí|date=20 October 2017|website=Portráidí (Portraits of Irish-Language Writers)|access-date=1 August 2025}}</ref>) is an Irish author who works in a number of genres, from novels, plays and screenplays to illustrated books for children and adults. He began his literary career in 1998 writing screenplays, stage plays, retellings and translations; he began to publish novels in 2008. Ó Scolaí is widely recognized as a leading figure in contemporary Irish literature, known as “one of the most important Irish language writers of his generation”<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=2022|title=? Suil an Daill: Constant Tensions and Shifting Allegiances|url=https://booksirelandmagazine.com/suil-an-daill-constant-tensions-and-shifting-allegiances/|journal=Books Ireland}}</ref> and "one of the great Irish language novelists [duine d’úrscéalaithe móra na Gaeilge]."<ref name=":17" /> His writing has been called “the high literature of the Irish language.”<ref>Ó Coimín, Maitiú. ''Nós'' 2 February 2018). Qtd. in "Táin Bó Cuailnge." ''Leabhar Breac''. Retrieved 25 August 2025.</ref> Much of his fiction is based on a knowledge of traditional Irish tales and narrative practices as well as Irish history. He specializes in literary and [[wikipedia:Historical_fiction|historical fiction]], or as novelist Alan Titley says, Ó Scolaí’s “peak (for now), or at least his greatest imaginative interest, is the historical novel [tá an chuma air gurb é a bhuaic (go fóill), nó ar a laghad, a mhórspéis samhlaíochta, an t-úrscéal staire].”<ref name=":11">{{Cite journal|last=Titley|first=Alan|date=Fall 2020|title=An Stíl Go Deo!: Soather Dharach Uí Scolaí (The style would be forever!: Worker Darach Ó Scolaí)|url=https://www.jstor.org/stable/27046090|journal=Comhar|volume=80, No. 10|pages=27|via=JSTOR}}</ref> His retellings of old stories and tales from their original Middle and Early-Modern Irish into Modern Irish ([[wikipedia:Irish_language|Gaeilge]]) are respected for their accessibility to students and language learners as well as for their artistry. Ó Scolaí also regularly reviews books and lectures and writes on literature and culture. Beyond his writing, Ó Scolaí is a publisher and has co-produced a number of film, television shows and stage plays. == Life == Ó Scolaí was born in Dublin and raised in the Galway [[wikipedia:Gaeltacht#Galway Gaeltacht|Gaeltacht]] (Irish-speaking) regions of Cois Fharraige on the north shore of Galway Bay, in the Republic of Ireland, where he lives now with his wife and children in Lochán Beag (Indreabhán).<ref name=":7">{{Cite journal|date=30 October 2024|title=Duais don úrscéal liteartha is fearr buaite ag Darach Ó Scolaí ag Oireachtas na Samhna|url=https://tuairisc.ie/duais-don-ursceal-liteartha-is-fearr-buaite-ag-darach-o-scolai-ag-oireachtas-na-samhna/|journal=Tuairisc}}</ref><ref>{{Cite journal|last=Ní Scolaí|first=Aifric|date=2024|title=Darach Ó Scolaí|url=https://www.taiscecf.ie/ealaiontoiri?category=Scr%C3%ADbhneoir|journal=Taisce Chois Fharraige}}</ref> He graduated the [[wikipedia:University_of_Galway|University of Galway]] (then University College Galway) with a B.A. in 1983.<ref>{{Cite web|url=https://www.linkedin.com/in/darach-ó-scolaí-20026920/|title=Darach Ó Scolaí|last=Ó Scolaí|first=Darach|date=August 2025|website=LinkedIn}}</ref> === Writing and Publishing === Ó Scolaí writes in Irish ([[wikipedia:Irish_language|Gaeilge]]), his native language, and lives in an area defined for the predominant presence of Irish as the vernacular language, the language spoken at home. Irish was the language of his parents' home and is the language of children as well. He is fluent in Irish and English and conversant in French. None of his works has been translated into English. ==== Leabhar Breac ==== In 1995 Darach Ó Scolaí and his brother Caomhán Ó Scolaí — a [[wikipedia:Typography|typographer]] and designer — founded the publishing house Leabhar Breac at Indreabhán (Inverin), County Galway. Their father “Séamas Ó Scolaí was an editor at An Gúm and worked on the Irish-English dictionary team [bhí a n-athair Séamas Ó Scolaí ina eagarthóir sa Ghúm agus d’oibrigh sé ar fhoireann an fhoclóra Gaeilge-Béarla].”<ref name=":0">{{Cite web|url=https://leabharbreac.com/en/about-us/|title=About Us|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> Darach Ó Scolaí has been publisher and literary editor at Leabhar Breac since its founding. Named for [[wikipedia:An_Leabhar_Breac|An Leabhar Breac (The Speckled Book)]], Leabhar Breac publishing house has more than 140 books in print.<ref name=":0" /> Leabhar Breac aims to publish Irish-language books that meet “a high literary and artistic standard.”<ref name=":0" /> Besides the content, Leabhar Breac is known for the typically "superb [thar cionn]" quality of the design and production of the "physical book [leabhar fisiciúil]."<ref name=":8">{{Cite journal|last=Ní Mhuilneoir|first=Gráinne|date=30 July 2024|title=‘Bláthnaid’ – leabhar álainn i sraithín álainn faoi mhná|url=https://tuairisc.ie/blathnaid-leabhar-alainn-i-sraithin-alainn-faoi-mhna/|journal=Tuairisc}}</ref> Its books regularly win awards for literary and artistic quality. Leabhar Breac also publishes translations for children and adults from various early versions of Irish as well as from French and English (and has published translations of books for young readers from Spanish, Catalan, and Italian as well). Leabhar Breac prints its books in Ireland. === Stage and Screen === ==== Rosg ==== In 1998 along with Ciarán Ó Cofaigh,<ref name=":1">{{Cite web|url=http://www.rosg.ie/en/about/History_6/|title=About Us: History|date=July 2025|website=Rosg|access-date=1 August 2025}}</ref> Ó Scolaí co-founded the film and television production company [http://www.rosg.ie/en/ Rosg] and was co-director until 2006. Rosg produced Ó ScolaÍ’s films ''Cosa Nite'' (1999), ''An Leabhar'' (2001) and ''Na Cloigne'' (2010). He left Rosg in 2006 to devote his time to other artistic activities. ==== Ealaín ar Oileán ==== In 2004, along with Val Balance, Ó Scolaí co-founded the annual artists' symposium Ealaín ar Oileán (trans., Art on an Island). The Irish-language symposium was held annually in the Áras Éanna arts and cultural center on Inis Oírr ([[wikipedia:Inisheer|Inisheer]], the smallest of the [[wikipedia:Aran_Islands|Aran Islands]]) from 2004 to 2013. Ó Scolaí was its co-director from its founding<ref>{{Cite web|url=https://ga.wikipedia.org/wiki/Darach_Ó_Scolaí.|title=Darach Ó Scolaí|date=3 February 2024|website=Vicipéid|access-date=1 July 2025}}</ref> until 2013. Besides being its co-director, Ó Scolaí has taken part in this conference as an artist<ref>{{Cite journal|date=16 January 2005|title=Darach Ó Scolaí|url=https://web.archive.org/web/20050116163252/http://bliainiris.com/authors/darach_oscolai.html|journal=Bliainiris}}</ref> and writer<ref name=":2">{{Cite web|url=http://ealainaroilean.ie/ealainaroilean.html|title=The Conference|date=7 September 2013|website=Ealaín ar Oileán|archive-url=https://web.archive.org/web/20130907083744/http://ealainaroilean.ie/ealainaroilean.html|archive-date=7 September 2013|access-date=1 August 2025}}</ref>. ==== Salamandar ==== In 2006 Ó Scolaí founded the stage production company Salamandar and directed his own play ''An Braon Aníos''. His plays ''An tSeanbhróg'' (2009) and ''Craos'' (2008) were also produced by Salamandar.<ref name=":19">{{Cite web|url=https://leabharbreac.com/en/product-category/darach-o-scolai/|title=Darach Ó Scolaí|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> == Works == === Novels === * [[wikipedia:An_Cléireach|''An Cléireach'' (trans., ''The Clerk'')]], Leabhar Breac, 2007. The Oireachtas Prize for Literary Fiction, 2007; The Ó Súilleabháin Award (Book of the Year) in 2008, and "named as ‘the best novel since the turn of the Century’ by Comhar."<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-cleireach/|title=An Cléireach - Leabhar Breac - Irish language novel|website=Leabhar Breac|language=en-US|access-date=2025-10-24}}</ref> * ''Na Comharthaí'' (trans., ''The Signs''), Leabhar Breac, 2014. * ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. The Oireachtas Prize for Literary Fiction, 2019.<ref name=":4">{{Cite web|url=https://leabharbreac.com/en/shop/fiction/suil-an-daill/|title=Súil an Daill|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Bódléar'', Leabhar Breac, 2024. The Oireachtas Prize for Literary Fiction, 2024<ref name=":7" />; The Ó Súilleabháin Award (Book of the Year) in 2025; featured in the 2025 Listen-Up Irish Summer Challenge for students of the Irish language.<ref>{{Cite news|url=https://connachttribune.ie/novel-approach-helps-people-learn-irish-in-a-creative-way/|title=Novel approach helps people learn Irish in a creative way|last=Murphy|first=Judy|date=3 October 2025|work=Connaught Tribune|access-date=24 October 2025}}</ref> === Retellings, Translations and Editions === The retellings and translations are into modern Irish. * ''Feis Tigh Chonáin'' (trans., ''The Feast of Conán's House''), Leabhar Breac, 2000; a retelling of a 15^th-century tale from the [[wikipedia:Fenian_Cycle|Fenian Cycle]].<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/feis-tigh-chonain/|title=Feis Tigh Chonáin|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''An Ceithearnach Caolriabhach'' (trans., ''The Narrow-Striped Kern''), Leabhar Breac, 2002; a retelling from c. 1500, also illustrated by Darach Ó ScolaÍ.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-ceithearnach-caolriabhach/|title=An Ceithearnach Caolriabhach|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), Leabhar Breac, 2017, both a modern edition of an 11th-century epic and an annotated edition.<ref name=":3">{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/tain-bo-cuailnge-2-2/|title=Táin Bó Cuailnge|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> "''Táin Bó Cuailnge'' won the Aodán Mac Poilín Memorial Prize 2017."<ref name=":19" /> * ''Deirdre'', Leabhar Breac, 2023, a “picture book for adults” with artist Anastasia Melnykova.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/deirdre/|title=Deirdre|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Part of the [[wikipedia:Ulster_Cycle|Ulster Cycle]], ''Deirdre'' is a retelling of the story of possibly the most widely known Irish figure from the early tales and sagas.<ref>{{Cite book|title=A Dictionary of Celtic Mythology|last=MacKillop|first=James|publisher=Oxford University Press|year=2004|isbn=9780198609674|pages=181}}</ref> * ''Bláthnaid'', Leabhar Breac, 2024, a “picture book for adults” with artist Anastasia Melnykova; “one of the great stories of the [[wikipedia:Ulster_Cycle|Ulster Cycle]].”<ref name=":4" /> * ''Sadhbh,'' Leabhar Breac, 2025, a picture book for adult readers, illustrated by Alé Mercado; a retelling of the medieval tale ''Ceasacht Inghine Ghuile (''trans., ''The Complaint of Guile's Daughter'').<ref name=":5">{{Cite web|url=https://leabharbreac.com/en/tales-of-wonder/|title=Tales of Wonder|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Eoghan Béal'', Leabhar Breac, 2025, a picture book for adult readers illustrated by Alé Mercado<ref name=":5" />; a retelling of the medieval tale ''[https://ga.wikipedia.org/wiki/Caithr%C3%A9im_Cellaig Cathréim Ceallaigh]'' from ''The Yellow Book of Leacan.''<ref name=":5" /> === For Young Readers === Ó Scolaí has written illustrated books for young readers (8–10 years old) in two series, the Fionn Series and the Scéalta Staire series, and translated a large number of classics and popular books for children of all ages. The number of these written and translated works suggests a commitment to children and their literacy in Irish. The Fionn Series “is a retelling ... of the great legends of the Fianna for the young Irish readers of today.”<ref name=":6">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/doiteoir-na-samhna/|title=Dóiteoir na Samhna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> [[wikipedia:The_Boyhood_Deeds_of_Fionn|Macgnímartha Finn (The Boyhood Deeds of Fionn)]] is a medieval story in the [[wikipedia:Fenian_Cycle|Fenian Cycle]]. * ''An Bradán Feasa'' (trans., ''The Salmon of Knowledge''), Leabhar Breac, 2010, “shortlisted for the Réics Carlo award 2010.”<ref name=":9">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/an-bradan-feasa/|title=An Bradán Feasa|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Dóiteoir na Samhna'' (trans., ''The Halloween Burner''), 2010.<ref name=":6" /> * ''Bodach an Chóta Lachna'' (trans., ''The Churl in the Dun Coat''), 2011.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/|title=Bodach an Chóta Lachna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> The Scéalta Staire (Historical Stories) series<ref name=":9" /> * ''Mánas Ó Dónaill'', 2000. * ''Seán Ó Néill'', Leabhar Breac, 2000. * ''Gráinne Mhaol Ní Mháille'', Leabhar Breac, 2003. * ''Tadhg Dall Ó hUiginn'', Leabhar Breac, 2003. ==== Translations ==== * Robert Louis Stevenson, ''Oileán an Órchiste'' (trans. of ''Treasure Island''), Leabhar Breac, 2014.<ref>{{Cite journal|date=2025-06-19|title=Oireachtas na Gaeilge|url=https://en.wikipedia.org/w/index.php?title=Oireachtas_na_Gaeilge&oldid=1296394643|journal=Wikipedia|language=en}}</ref> * Robert Louis Stevenson, ''An Fuadach'' (trans. of ''Kidnapped''), Leabhar Breac, 2016. * Clement Clarke Moore, ''Cuairt San Nioclás'' (trans. of ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas"), Leabhar Breac, 2022. '''''The Corto Maltese Graphic Novels''''' Written in Italian by Hugo Pratt and translated by Ó Scolaí, both adults and teenagers read this series of Italian adventure graphic novels.<ref>{{Cite journal|date=2025-07-01|title=Corto Maltese|url=https://en.wikipedia.org/w/index.php?title=Corto_Maltese&oldid=1298285365|journal=Wikipedia|language=en}}</ref> Ó Scolaí's '''translation of ''Corto Maltese''''' was listed in 2017 among "The 30 Irish books that Irish people love."<ref>{{Cite journal|last=Ó Murchú|first=Eoin P.|date=09/06/2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil [The 30 Irish books that Irish people love]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * Hugo Pratt, ''Corto: Port na Farraige Goirt'', Leabhar Breac, 2013. * Hugo Pratt, ''Corto: The Golden House in Samarkand'', 2014. * Hugo Pratt, ''Corto: Na Liopard-Fhir ó Rufiji'' (trans. of ''Corto: The Leopard Men of Rufiji''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: In Ainm Dé Uilthrócairigh'' (trans. of ''Corto: In the Name of God All-Merciful''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Tóraíocht Eile'' (trans. of ''Corto: Another Quest''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Sa tSibéir'' (trans. of ''Corto: In Siberia''), Leabhar Breac, 2016. '''''Other Translations for Children''''' Ó Scolaí has translated into Irish six books from the ''Le Pavillon Noir'' (trans., ''Jolly Roger'') series by Alain Surget; four books from the ''Catalan First Steps'' series by Enric Lluch Girbés and the ''Caitlín & Cormac'' series by Joan Carles; three books from the ''Louisette le Taupe'' series by Bruno Heitz, and three books from the ''Loup'' series by Orianne Lallemand. === Plays and Screenplays === ==== Stage Plays ==== Ó Scolaí was writer and director of the original productions of two plays in the ''Trí Bhraon'' (trans., ''Three Drops'') trilogy; ''Coinneáil Orainn'' was directed by Darach Mac Con Iomaire and staged by An Taibhdhearc. All three plays have been published in book form by Leabhar Breac. * ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32553|title=Coinneáil Orainn|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> The first play in the ''Trí Bhraon'' (''Three Drops'') trilogy. [[wikipedia:Taibhdhearc_na_Gaillimhe|An Taibhdhearc]], the national Irish-language theatre of Ireland, toured the country in 2005 with ''Coinneáil Orainn''.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/coinneail-orainn/|title=Coinneáil Orainn|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Walter Macken Prize, 2005; BBC Stewart Parker Award, 2006.<ref>{{Cite web|url=https://irishplayography.com/person/darach-scola|title=Darach Ó Scolaí|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> * ''Branwen'', 2006, by Darach Ó Scolaí and Ifor ap Glyn, in Irish, Welsh and English, co-produced by Project Arts Centre and Llwyfan Gogledd Cymru, toured the Republic of Ireland and Wales.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32418|title=Branwen|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An Braon'' Aníos (trans., ''Rising Damp''), 2006, directed by Ó Scolaí.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32461|title=An Braon Aníos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The second play in the ''Trí Bhraon'' (''Three Drops'') trilogy. “The Salamandar company toured the country in 2006-07 with this play, and Salamandar also produced a radio version of the play for RTÉ Raidió na Gaeltachta in 2009.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/an-braon-anios/|title=An Braon Aníos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Craos'' (trans., ''Gluttony''), 2008, directed by Ó Scolaí.<ref name=":13">{{Cite web|url=https://irishplayography.com/play?playid=32867|title=Craos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The third play in the ''Trí Bhraon'' (''Three Drops'') trilogy, it toured to Cork and Belfast.<ref name=":13" /> A review of the 2008 Salamander performance in the ''Irish Times'' says, “a humorous play which offers plenty to think about, fine acting, and sparklingly witty dialogue.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/craos-2/|title=Craos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''A+E'', 2008, by Ríonach Ní Néill and Darach Ó Scolaí, "dance and music drama," co-produced by Ciotóg and Salamandar.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32962|title=A+E|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An tSeanbhróg'' (trans., ''The Old Shoe''), 2009, produced by Salamander<ref>{{Cite web|url=https://irishplayography.com/play?playid=33042|title=An tSeanbhróg|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> and staged in the Axis Arts Centre, Dublin, and the Letterkenny Arts Centre. * '''In ''Mhuir Fhíondorcha/The Wine-Dark Sea: The Homer Project'', Ó Scolaí's translation of Homer's Cyclops story, performed at the 2019 IMRAM festival'''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/books/imram-a-festival-celebrating-the-irish-language-1.4047610|title=Imram: a festival celebrating the Irish language. Liam Carson reveals the myths and legends appearing in this year’s programme|last=Carson|first=Liam|date=11 October 2019|work=The Irish Times|access-date=15 October 2025}}</ref> ==== Screenplays ==== * ''Cosa Nite'' (trans., ''Washed Feet''), short film, 1998 (dir. Dearbhla Walsh, prod. Ciarán Ó Cofaigh, Rosg); "a prose version of ''Cosa Nite'' was published (Rosg 2000)."<ref name=":9" /> Nominated for an Irish Film and Television Award.<ref>{{Citation|title=Cosa Nite (Short 1998) - Awards - IMDb|url=https://www.imdb.com/title/tt0191917/awards/|accessdate=2025-08-25|language=en-US}}</ref> * ''Na Glúnta'' (trans., ''The Generations''), 2001<ref>{{Cite web|url=https://www.iftn.ie/production/production_companies/production_sub/feature/?act1=record&aid=70&rid=3917&tpl=filmography_dets&only=1&force=1|title=Na Glúnta {{!}} The Irish Film & Television Network|website=www.iftn.ie|access-date=2025-08-25}}</ref>, co-directors Ciarán Ó Cofaigh & Darach Ó Scolaí, prod. Ciarán Ó Cofaigh, Rosg. * ''An Leabhar'' (trans., ''The Book''), short film, 2000, (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg) Rosg, 2000.<ref>{{Citation|title=An Leabhar|url=https://www.imdb.com/title/tt0963767/|publisher=Bord Scannán na hÉireann / The Irish Film Board, ROSG|accessdate=2025-08-25|first=Robert|last=Quinn|others=Colm O&apos;Maonlai, Peadar O&apos;Treasaigh, Diarmuid Mac an Adhastair}}</ref> * ''Na Cloigne'' [trans., The Heads], 3-episide series, 2010 (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg), TG4.<ref>{{Cite web|url=https://www.imdb.com/title/tt1607924/|title=Na cloigne|date=2010|website=IMDb|access-date=25 August 2025}}</ref> === Nonfiction === Ó Scolaí's essays and lectures are published and his interviews are broadcast regularly, making for a large body of nonfiction critical and analytical work. Here are a few, almost all published in [https://comhar.ie/iris/scribhneoiri/darach-o-scolai/ Comhar]: * “Ceol Ciúin na nÉagmaise” (trans., “The Silent Music of Absence ['''the Fall?''']”), an essay on the 2014 Nobel Prize winner for literature, [[wikipedia:Patrick_Modiano|Patrick Modiano]], ''Comhar'', December 2014. * The Ó Cadhain Lecture: [https://leachtaiuichadhain.clo.ie/leachtai/2014 “Cuimhne agus Díchuimhne (trans., “Memory & Forgetfulness"]), 2014. * “Rithim agus Réim” ("Rhythm and Register"), a public lecture in the University College Dublin lecture series “Ó Thrácht go Twitter” (trans., "From Talk to Twitter"), 2014. * Review of Pádraig Ó Cíobháin’s ''Dréachta Chrích Fodla'', '''Comhar?, ??'''. * “Na Geilt i mBun an Tí” (trans., "The Madmen in Charge"), a talk at the Merriman Winter School, Comhar April 2012.<ref name=":18">{{Cite web|url=http://darachoscolai.ie/beathaisneis.html|title=Darach Ó Scolaí: Beathaisnéis|website=darachoscolai.ie|access-date=2025-09-26}}</ref> * The EFACIS podcast: Síle Ní Choincheannain talks to Darach Ó Scolaí about the historical novel. == Critical Reception == Ó Scolaí’s style has been called “crisp and elegant, and rich in language while being highly readable,”<ref>{{Cite journal|last=Heussaf|first=Anna|date=Summer 2025|title=Bláthnaid—A tale of love, violence and sorcery retold for readers today|url=https://booksirelandmagazine.com/blathnaid-a-tale-of-love-violence-and-sorcery/|journal=Books Ireland}}</ref> with “an unsurpassed richness and precision of language.”<ref name=":12">{{Cite journal|last=Ó Cróinín|first=Breandán|date=Summer 2025|title=unknown|journal=The Limerick Leader}}</ref> “Whimsical, hilarious, and subtly learned” is how Éilis Ní Dhuibhne described his writing.<ref name=":20" /> === Original Works === Ó Scolaí’s first novel, the 2007 ''An Cléireach'' (''The Clerk'') won two prizes and was described as “one of the great historical novels in the Irish language and among the best books written in the language since the beginning of this century.”<ref name=":12" /> Novelist Alan Titley says, “In ''An Cléireach'' Ó Scolaí creates the Ireland of war in the 17th century more fully than any other Irish writer on the subject of war since ''L’Attaque'' Eoghain Ó Thuairisc around 1798 [In ''An Cléireach'' cruthaíonn Ó Scolaí Éire an chogaidh san 17ú haois níos iomláine ná mar a dhein aon scríbhneoir Gaeilge eile ar ábhar cogaidh ó ''L’Attaque'' Eoghain Uí Thuairisc timpeall ar 1798].”<ref name=":11" />{{rp|25, Col. 1a}} Not all the reviews of this first novel were so positive, however; Proinsias O' Drisceoil says for the Irish Times says,<blockquote>This then is a novel in search of a plot, a story that attempts to attain a significance that eludes it.<ref>{{Cite news|url=https://www.irishtimes.com/news/a-disaffected-clerk-in-the-confederates-1.943070|title=A disaffected clerk in the confederates|last=O' Drisceoil|first=Proinsias|date=5 July 2008|work=The Irish Times|access-date=16 October 2025}}</ref></blockquote> In the ''Oxford Handbook of Modern Irish Fiction'' Pádraig Ó Siadhail analyzes rather than reviews ''An Cléireach'': <blockquote>In ''An Cléireach'', Ó Scolaí revisits the trauma of Cromwellian Ireland. The primary narrative device is once again the first-hand account, in this case by Tadhg Ó Dúbháin, a clerk and quartermaster in the Confederate Army in 1650. We sample the hardships, the friendships, the tensions, the rivalries, and the petty jealousies amongst comrades in arms, including remnants of the Gaelic literary class, as the Confederate soldiers, increasingly a rabble more than a cohesive unit, retreat in advance of Cromwell’s forces. ''An Cléireach'' concludes with the narrator and his family in exile in continental Europe. But along the retreat route, and central to the novel, members of the Confederate army camp, rest up, and tell versions of a story about the keeper of the treasured manuscript "Saltair an Easpaig" (The Bishop’s Psalter). Their versions raise issues about memory construction, the limitations of individual perspectives, personal agendas, and how minor changes in the telling of a story can alter our understanding of history, Thus, ''An Cléireach'' complements ''Fontenoy'' in moving beyond more realistic recreation of a historical event or period to interrogate the notion of history as construct.<ref>{{Cite book|title=The Oxford Handbook of Modern Irish Fiction|last=Ó Siadhail|first=Pádraig|publisher=Oxford University Press|year=2020|isbn=9780198754893|editor-last=Harte|editor-first=Liam|pages=598–99|chapter=Contemporary Irish Fiction}}</ref> </blockquote> Of ''Súil an Daill,'' in ''Nós'', Cathal Seoighe says, "The book deserves a significant place among the collection of high-quality books published in recent years that would make you feel sorry for someone who does not speak Irish [Tá áit shuntasach ag dul don leabhar i measc an chnuasaigh leabhair ar ardchaighdeán a foilsíodh le roinnt blianta anuas a d’fhágfadh trua agat don té atá gan Ghaeilge]."<ref>{{Cite journal|last=Seoighe|first=Cathal|date=09/26/2022|title=‘Dar leathmhagairle an diabhail, is leabhar den scoth é seo!’ ['According to the devil’s half-wit, this is a great book!’]|url=https://nos.ie/cultur/leabhair/dar-leathmhagairle-an-diabhail-is-leabhar-den-scoth-e-seo/|journal=Nós}}</ref> ''Bódléar'', Ó Scolaí's most recent book, is a “beautiful novel. There is magic and craftsmanship in it. A small miracle of a book and it is highly recommended.”<ref>{{Cite web|url=https://leabharbreac.com/bodlear-mioruilt-bheag-de-leabhar/|title=Bódléar: Míorúilt bheag de leabhar (Bódléar: A Small Miracle of a Book)|last=Ní Ghairbhí|first=Róisín|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Éilis Ní Dhuibhne in the ''Irish Times'' says,<blockquote>what a gem! An affectionately gentle satire of the Irish poetic scene during one creatively fluid 19th-century year, the story focuses on a Maigue poet and schoolteacher who goes on a trip to France and returns with camembert, a cafetiere, ‘Fleurs du Mal’, and a mission to convert the local traditionalists to la modernité. Whimsical, hilarious, and subtly learned, it’s absolutely delightful!<ref name=":20">{{Cite journal|last=Ní Dhuibhne|first=Éilis|date=30 June 2025|title=Éilís Ní Dhuibhne on the best Irish language books of 2025 so far: Including a history of the Gaeltacht Civil Rights Movements, a gem of a novel by Darach Ó Scolaí and Joe McHugh’s entertaining account of learning Irish|url=https://www.irishtimes.com/culture/books/review/2025/06/30/eilis-ni-dhuibhne-on-the-best-irish-language-books-of-2025-so-far/|journal=The Irish Times|pages=22}}</ref></blockquote> === Retellings and Translations === ==== ''Táin Bó Cuailnge'' ==== ''Táin Bó Cuailnge'' [''The Cattle Raid of Cooley''] is a modern edition of an 11th-century epic into modern Irish.<ref name=":3" /> Gearóid Denvir reviewed ''Táin Bó Cuailnge'' for ''Comhar'':<blockquote>Darach Ó Scolaí has ​​achieved a feat in this challenging reworking. He has found a high level of the Irish language to tell his story – as he has done before in his groundbreaking novel An Cléireach (2007, Leabhar Breac) and in his other prose works. This book is a decoration of the language, literature and culture of the Irish language, following the path of the old storytellers and writers and presenting material from the tradition to his own generation according to the understandings of his own time. The book will be a classic that will be of great interest to all readers of the Irish language, both ordinary readers, students, scholars and writers, and there should be a copy in every home in the country. [Tá éacht déanta ag Darach Ó Scolaí san athleagan dúshlánach seo. Tá réim ard den teanga Ghaeilge aimsithe aige lena scéal a inseacht – mar a rinne sé cheana ina úrscéal ceannródaíoch An Cléireach (2007, Leabhar Breac) agus i saothair eile phróis dá chuid. Is maisiú ar an teanga agus ar litríocht agus cultúr na Gaeilge an leabhar seo a leanas conair na seanscéalaithe agus na seanscríobhaithe agus ábhar de chuid an traidisiúin á chur i láthair a ghlúine féin aige de réir thuiscintí a linne féin. Clasaic a bheas sa leabhar a gcuirfidh léitheoirí uilig na Gaeilge, idir ghnáthléitheoirí, mhic léinn, scoláirí agus scríbhneoirí spéis thar na bearta ann, agus ba cheart cóip a bheith i chuile theach sa tír.]<ref name=":15">{{Cite journal|last=Denvir|first=Gearóid|date=April 2018|title=Táin Bó Cuailgne|url=https://comhar.ie/iris/78/4/leirmheas/|journal=Comhar|via=JSTOR}}</ref> </blockquote>Cathal Poirtéir says, "The freshness and richness of Ó Scolaí’s version are a joy …. The author delights us with the linguistic and stylistic richness of the ancient epic in a modern-Irish version that reflects the original’s spirit and language."<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=May/June 2018|title=Leabhair Idir Lámha|url=https://www.jstor.org/stable/26564180|journal=Books Ireland|pages=46–47|via=JSTOR}}</ref>{{rp|47}} Novelist and academic Alan Titley calls Ó Scolaí's "a wonderful gutsy telling" of ''Táin Bó Cuailnge''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/2023/03/11/the-tain-retold-maeve-and-ailills-spat-could-be-out-of-a-soap-opera/|title=The Táin retold: ‘Maeve and Ailill’s spat could be out of a soap opera’|last=Titley|first=Alan|date=11 March 2023|work=The Irish Times|access-date=16 October 2025}}</ref> ==== ''Deirdre'' ==== Marie Whelton, in "Léann Teanga" ("Language Studies"), in the 2024 ''An Reiviú'' says,<blockquote>this version [of ''Deirdre''] by Darach Ó Scolaí succeeds in skillfully capturing and portraying the complexity of gender and power issues in the ‘Deirdre’ tradition [éiríonn leis an leagan seo le Darach Ó Scolaí castacht cheisteanna na hinscne agus na cumhachta i dtraidisiún scéal Dheirdre a ghabháil agus a léiriú go sciliúil]. … There is no doubt that this new version greatly contributes to the legacy of the story and that it revives that legacy thoughtfully and artistically [Níl amhras faoi ach go gcuireann an leagan úr seo go mór le hoidhreacht an scéil agus go ndéanann sé an oidhreacht sin a athbheochan go tuisceanach agus go healaíonta.].<ref name=":16">{{Cite web|url=https://www.tara.tcd.ie/tara8/server/api/core/bitstreams/3c20175a-7631-44b2-8b0f-f454edd712b4/content|title=An Artistic Retelling of Deirdre's Tale and the Defeat of Conor Review of Deirdre or the Ship of Mac Uisnigh by Darach Ó Scolaí [Athinsint Ealaíonta ar Oidhe Dheirdre agus ar Ansmacht Chonchúir Léirmheas ar Deirdre nó Loingeas Mhac Uisnigh le Darach Ó Scolaí]|last=Whelton|first=Marie|date=2024|website=The Review [An Reiviú], Language Studies [Léann Teanga]|access-date=25 September 2025}}</ref></blockquote> === Works for Young Readers === Meadhbh Ní Eadhra said of ''Bodach an Chóta Lachna'' that it was "Beautiful Irish, but easy to understand for young readers."<ref>Ní Eadhra, Meadhbh. In ''Gaelscéal'', qtd. in "Bodach an Chóta Lachna" https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/.</ref> == Awards and Honors == Ó Scolaí's works are regularly nominated and make the short list for prizes, an honor in itself, but they are generally not listed here unless they are named as the first-place winner in their category. === Oireachtas Prize === The Oireachtas Prize is the literary prize awarded by [[wikipedia:Oireachtas_na_Gaeilge|Oireachtas na Gaeilge]], the annual arts festival dedicated to Irish language, arts and culture. Darach Ó Scolaí has won the Oireachtas Prize for Literary Fiction three times, once for ''An Cléireach'' (''The Clerk'') in 2007, for ''Súil an Daill'' (''The Eye of the Blind'') in 2021 and for ''Bódléar'' in 2024. * 2007, for ''An Cléireach'' (trans., ''The Clerk'') — “(a special prize commemorating the 400th anniversary of the foundation of Coláiste na nGael in Louvain, awarded under the auspices of the Franciscan Province of Ireland). The prize of €10,000 was the largest prize ever awarded to an Irish language novel [(duais speisialta chomórtha 400 bliain bhunú Choláiste na nGael i Lobháin a bronnadh faoi urraíocht Phroibhinse Phroinsiasach na hÉireann). Ba é an duais €10,000 sin an duais ba mhó a bronnadh riamh ar úrscéal Gaeilge].”<ref name=":18" /> * 2021, for ''Súil an Daill'' (''The Eye of the Blind'') * 2024, for ''Bódléar'' === Ó Shúilleabháin Award, Irish language “Book of the Year” === The first prize of this award includes €5,000 to the publisher and €2,500 to the author of the winning work.<ref name=":10">{{Cite journal|date=15 August 2023|title=20 saothar san iomaíocht do ‘Leabhair Ghaeilge na Bliana 2023’|url=https://tuairisc.ie/20-saothar-san-iomaiocht-do-leabhair-ghaeilge-na-bliana-2023/|journal=Tuairisc}}</ref> * ''An Cléireach'' (''The Clerk'').<ref>{{Cite web|url=http:/www.gaelport.com/uploads/documents/edition19.html|title=Eagrán / Edition 19 - 04 11 2008|date=4/11/2008|website=Internet Archive|archive-url=https://web.archive.org/web/20130525011340/http:/www.gaelport.com/uploads/documents/edition19.html|archive-date=25 May 2013|access-date=25 August 2025}}</ref> * ''Táin Bó Cuailnge'', 2018. * ''Bódléar'', 2025. ==== De Bhaldraithe Award ==== The Gradam de Bhaldraithe is awarded to the best work in translation.<ref name=":10" /> * ''Cuairt San Nioclás,'' a translation of Clement Clarke Moore's ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas."<ref name=":10" /> ==== Other ==== * Walter Macken Prize, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005 * Bháiteir Uí Mhaicín Memorial Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005<ref>{{Cite news|url=https://www.irishtimes.com/gaeilge/tuarascail/duais-oireachtais-1.501571|title=Oireachtas Prize: Over €50,000 was awarded to writers in the Oireachtas Literary Competitions at an event in Dublin last night. Winners… [Duais Oireachtais: Bronnadh breis agus €50,000 ar scríbhneoirí i gComórtais Liteartha an Oireachtais ar ócáid i mBaile Átha Cliath aréir. Bhuaigh…]|work=5 October 2005|access-date=15 October 2025}}</ref> * BBC Stewart Parker Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2006 * The Aodán Mac Póilín Commemorative Prize, for ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), 2017 == External Links == * Leabhar Breac website: https://leabharbreac.com/en/ * Leabhar Breac Facebook pages: * Rosg website: [http://www.rosg.ie/en/ <nowiki>http://ww</nowiki>w.rosg.ie/en/] * Art on the Island (Ealaín ar Oileán) website, archived at the Wayback Machine: https://web.archive.org/web/20130601000520/http://ealainaroilean.ie/ 31 March 2012, 1 June 2013 and 8 January 2014 * Darach Ó Scolaí's website Archived 25 September 2015 at the Wayback Machine: https://web.archive.org/web/20150925103456/http://darachoscolai.ie/ * Youtube video of [https://www.youtube.com/watch?v=OlP2AmSBzXc Breandán Ó Cróinin introducing Deirdre at the book launch] in the pub Tigh Mholly (Molly’s House). == Primordial Ooze == * Known for his sensitivity to language and voices. * Finish scanning through JSTOR * Scan through Irish Times, 56 hits * Check Goodreads * Check YouTube (In the spring of 2013, the arts programme Imeall interviewed the author on TG4.) * Check both Wikipedias for pages on the origins of the retold tales (like Deirdre) and link to this article * Propose link from University of Galway page once Darach’s is up * Write Irish National Biography (<nowiki>https://www.dib.ie</nowiki>) to propose an article about Darach once the Wikip article is done? See what they say. * Link to Ó Scolaí from the Wikipedia * Make sure links '''to''' Wikipedia in the actual encyclopedia work right === Not Placed Yet === * "So here are the books that Irish people love the most! [Mar sin seo iad na leabhair is gile leis na Gaeil!]" — "32. An Cléireach – Darach Ó Scolaí (2)" [18 books got 2 votes, and then they're alphabetized by author's last name, so the 32 of 34 doesn't signify the specificity it seems to]<ref name=":14">{{Cite journal|last=Ó Murchú|first=Eoin P.|date=9 June 2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil. [The 30 best Irish books for Irish people]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * "Below is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers.Here is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers [Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí.Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí]." "Corto Maltese – Hugo Pratt (aistrithe ag Darach Ó Scolaí)"<ref name=":14" /> * "Ceann eile de bhuaicphointí na hÉigse a bheidh sa seisiún le Darach Ó Scolaí, duine d’úrscéalaithe móra na Gaeilge, agus duine de chomhbhunaitheoirí teach foilsitheoireachta Leabhar Breac. [Another highlight of the Éigse will be the session with Darach Ó Scolaí, one of the great Irish language novelists, and one of the co-founders of the publishing house Leabhar Breac.]"<ref name=":17">{{Cite journal|last=Nós|date=4 May 2023|title=Éigse na Bruiséile le filleadh i mí na Bealtaine. [Éigse na Bruséile to return in May]|url=https://nos.ie/cultur/eigse-na-bruiseile-le-filleadh-i-mi-na-bealtaine/|journal=Nós}}</ref> === Things Taken Out for Now === “’The play is a comedy about language, lies, bureaucracy and Gaeltacht grants, in the tradition of Myles na Gcopaleen,’ according to Norma-Jean Kenny in the ''Galway Advertizer'', ‘in which the author comments and criticizes the institutions of the Irish language in Ireland without ceasing.’" Supposedly a quotation by Gearóid Denvir reviewing ''Táin Bó Cuailnge'' for ''Comhar'' (but I don't find it in the article): This book has long been needed by Irish language readers and there is no doubt that it will become a classic in time and surpass Thomas Kinsella’s English version. This version remains faithful to the language of the original while at the same time finding an appropriate language in today’s Irish. Ó Scolaí masterfully overcomes the difficulties of the original’s rhetorical difficulties and the versions of the original poetic texts are extremely effective.[supposedly <ref name=":15" />] “The biggest prize ever awarded for a novel in Irish was presented at a special ceremony in the National Concert Hall in Dublin, today (Thursday, 4 October 2007). Darach Ó Scolaí, writer, artist & playwright from Casla, Co. Galway, was awarded €10,000 for his literary novel, ‘An Ardscoil’. This work, under the new title ‘An Cléireach’, will be launched at Oireachtas na Samhna in Westport in November. This is the first novel from his pen, a story set in the late seventeenth century. This competition was sponsored by the Franciscan Province of Ireland.” (archive, Oireachtas na Gaeilge site, 04 October, 2007) ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. number 2 in ''Comhar'' literary magazine’s list of best books of 2021. '''{6}.''' *William Shakespeare, ''Romeo agus Juliet'' (trans. of ''Romeo and Juliet''), Leabhar Breac, 2016. *Jonathan Swift, ''Camchuairt Ghuilivéir'' (trans. of ''Gulliver's Travels''), Leabhar Breac, 2016. *Hugo Pratt, ''Corto Maltese'' '''''Flag of Bones (Bratach na gCnámh) Series''''' Leabhar Breac published the Bratach na gCnámh series of books for young readers. Written in French by Alain Surget, illustrated by Annette Marnat and translated by Darach Ó Scolaí, this series uses the history of Caribbean Sea pirates<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/alain-surget/|title=Alain Surget Archives|website=Leabhar Breac|language=en-US|access-date=2025-09-30}}</ref>: *Alain Surget, ''Éalú as Páras'' (''Escape from Paris''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Oilean na Siorcanna'' (''Shark Island''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Long na dTaibhsi'' (''Ship of the Ghosts''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''San Ochtapas Dubh'' (''In the Black Octopus''), Annette Marnat (Illustr.), Leabhar Breac, 2013. * Alain Surget, ''San Ionsai ar Veracruz'' (''The Attack on Veracruz''), Annette Marnat (Illustr.), Leabhar Breac, 2013. '''''For "First Readers" (children to 6 years old or so)''''' These books were written originally in Catalan by Spanish author Enric Lluch Girbés and translated into Irish by Ó ScolaÍ: *Enric Lluch, ''Ag Péinteáil an Tí'' (''Painting the House''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Colúr Bacach'' (''The Lazy Dove''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Phluais'' (''The Cave''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Madra Dhaideo'' (''Grandpa's Dog''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Fiacail Mháire'' (''Mary's Tooth''), Anna Clariana (Illustr.), Leabhar Breac, 2017. '''''Bruno Heitz''''' Leabhar Breac published a series of 3 Heitz books for small children. Published originally in French, this series of three comic books is about a blind mole named Cáitín Chaoch in Irish (and ''Louisette la taupe'' in French).<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/bruno-heitz-en/|title=Bruno Heitz Archives|website=Leabhar Breac|language=en-US|access-date=2025-10-02}}</ref> Ó Scolaí translated these: *Bruno Heitz (author and illustr.), ''Práinneach'' (''Urgent''), Leabhar Breac, 2020 *Bruno Heitz (author and illustr.), ''Preab san Aer'' (''Bounce in the Air''), Leabhar Breac, 2020. '''''Books for Toddlers''''' Leabhar Breac has published 14 books written by French author Orianne Lallemand's and illustrated by Eleonore Thuillier, about Lallemmand's popular character Loup, Wolf. These are translated by Ó Scolaí: *Orianne Lallemand, ''An Mac Tire a Raibh Faitios an Domhain Air'' (trans. of ''The Son Who Saw the World in His Eyes''), Eleonore Thuillier  Illustr.), Leabhar Breac, 2018. *Orianne Lallemand, ''Macan agus an Goban'' (trans. of ''Macan and the Goblin''), Eleonore Thuillier (Illustr.), Leabhar Breac, 2018. * Orianne Lallemand, ''A Mac Tíre a Chuaigh go Tóin na Farraige'' (trans. of ''The Wolf Who Went to the Bottom of the Sea''), Éléanore Thuillier  (Illustr.), Leabhar Breac, 2019. '''''Board Books (for babies)''''' J. C. (Joan Carles) Girbés Aparisi is a Catalan author and editor. These books were written in Catalan and translated by Ó Scolai. *J. C. Girbés, ''An Phicnic'' (''The Picnic''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. * J. C. Girbés, ''An Chóisir'' (''The Party''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. *J. C. Girbés, ''Lá Mór Fada'' (''A Long Day''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. *J. C. Girbés, ''Tabhair Leat do Leabhar'' (''Bring Your Book''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. ==== Gradam Réics Carló ==== The Réics Carló prize is awarded for the best book in the Irish language for young readers. It is named for one of the characters of 20th-century writer [[wikipedia:Cathal_Ó_Sándair|Cathal Ó Sándair (Charles Saunders)]]. * ''An Bradán Feasa'' was “shortlisted for the Réics Carlo award 2010.”<ref name=":9" /> == References == {{reflist}} 9bzrnvpvkt47j8ogzyda2srirpee6iv 2844824 2844823 2026-11-07T17:48:23Z Scogdill 1331941 /* Redingote */ 2844824 wikitext text/x-wiki {{Short description|Dress worn by Queen Victoria at her wedding to Prince Albert in 1840}} = Sandbox = Page to draft revisions for Wikipedia articles. For Gwladys Robinson, see Gwladys Lowther Robinson, [[Social Victorians/People/Ripon|Marchioness of Ripon]] and, earlier, [[Social Victorians/People/Lowther|Countess of Lonsdale]] ==References== {{reflist|2}} [[Category:1840 works]] [[Category:Royal wedding dresses|Victoria Queen]] [[Category:1840s fashion]] [[Category:British royal attire]] [[Category:Dresses in the Royal Collection of the United Kingdom|Victoria, Wedding]] [[Category:Diamond Jubilee of Queen Victoria]] = Victorian fashion = == Notes and Quotes == * Women followed Paris fashion in Europe and America, but London tailors led the way for men’s fashion. The Industrial Revolution actually impacted men’s fashion more than women’s. * Sewing machines in factories began mass producing cheap clothing for the largest group in the population, working class men. * Ready-made clothing affected the social structure, the economy, and gender differentiation. * Paper patterns, introduced in fashion magazines that targeted women, along with domestic sewing machines had more impact on women’s fashion than men’s. Haute couture was still bespoke (being individually constructed by tailors or dressmakers or fashion houses like Maison Worth). Sewing Machines and Clothes Before the industrial revolution wealthy people paid others to sew their clothes by hand and those who were of much lower economic status did all the manual labor necessary to feed and clothe the rich minority. The working class had to make all their own clothes. Sewing, however, came at the end of the process.  They began with raw wool cut from the backs of sheep or gathering flax. Only the wealthy could afford to buy fabric. They followed processes for cleaning and spinning the wool into thread and the processes of soaking and pulling out the fibrous strips to make into thread for linen fabric. After they had thread, it was tied to a loom so it could be woven into cloth. Then it had to be cut or torn into pieces. For many families scissors were a luxury. And the last step is sewing the pieces together to create a garment. Machines could not only sew, they could process the raw materials into thread and weave it into fabric much  quicker. Regarding clothing, working class men and their families benefitted greatly from ready-made clothes. Manufacturers marketed to them because they were the largest class. For example,<blockquote>–Men’s shirts, made by machine, take 3 hours and 10 minutes each to do; by hand, 15 hours and 20 minutes; a lady’s dress, by machine, takes 12 hours 4 minutes; by hand 20 hours 35 minutes; . . . a common frock-coat, by the machine occupies 17 hours 20 minutes; by the hand, 27 hours and 40 minutes: a linen vest, by machine, 3 hours 44 minutes; by hand 7 hours 18 minutes; a fine overcoat, by machine, 28 hours 13 minutes; by hand 31 hours 20 minutes; . . . <ref>Mitchell, Rebecca, ed. "22. 'Progress of the Sewing Machine,' ''Bow Bells'' (19 April 1865), p. 283." Section 6: Production and Industry. ''Fashioning the Victorians: A Critical Sourcebook''. Bloomsbury Visual Arts, 2018.</ref></blockquote> === Industrial Revolution and Technological Advancements === * the railroad * mass production of fabrics for working-class men's clothing ** Jacquard looms * sewing machines * aniline dyes, including black === Expanding Middle Class === * gender roles getting more clearly defined and rigid (referring back to page overview) === French Revolution === Sarah Gharmallah Alzahrani and Safia Abdelaziz Saroukh (https://www.researchgate.net/profile/Safia-Saroukh/publication/385099194_The_Semiotic_Dimension_of_Men's_Fashion_in_Modern_Eras/links/671686fbd796f96b8ec4f90e/The-Semiotic-Dimension-of-Mens-Fashion-in-Modern-Eras.pdf):<blockquote>The 19th century started with a fashion landscape that was changing dramatically and rapidly from the styles of a generation earlier. The French Revolution brought fashions that had been emerging since the 1780s to the forefront. Neoclassicism now defined fashion as both men and women taking inspiration from classical antiquity. For women, the high-waisted silhouette in lightweight muslin was the dominant style, while fashionable men looked to the tailors of Britain for a new, refined look [17]. [17]  Franklin, H. (Aug 18, 2020). Published on Jun 25, 2020, Retrieved: <nowiki>https://fashionhistory.fitnyc.edu/1800-1809/</nowiki> 11/11/2023. Edited. ...</blockquote>Brent Shannon:<blockquote>"Costume," wrote Max Beerbohm in 1896, "enables us to classify any 'professional man' at a glance, be he lawyer, leech or who not" (24–25). A man's profession and class were read by his jacket, his hat, what he rode in, and how he carried himself. "Perhaps there is a tendency among Englishmen to judge a man too much by the shape of his hat or the kind of collar he wears," conduct author John Wanamaker confessed; "But one must remember that in England if you ''wear'' the wrong thing, you will probably ''do'' the wrong thing, and generally ''be'' the wrong thing" (1).¹¹ Such assertions were predicated on the powerful Victorian conviction that outward appearance reflected inner qualities.<ref>{{Cite book|title=The Cut of His Coat: Men, Dress, and Consumer Culture in Britain, 1860–1914|last=Shannon|first=Brent Alan|publisher=Ohio University Press|year=2006|location=Athens, Ohio}}</ref> (148)</blockquote> ==Women's fashion== == Men's fashion == (Two intros: one to Victorian Fashion, giving background for both women's and men's fashions; two to the decades for men's fashion) Among the influences on men's styles: * differentiation of genders (domestic ideology, ideology of the spheres) * the "Great Male Renunciation," the French Revolution and English tailoring * industrial revolution: mass production of fabrics and articles of clothing, especially for working-class men * sports and country clothing * Albert Edward, Prince of Wales, later King Edward VII, influence went beyond England; tailors led by him led fashion for the upper classes * then later, cult of youth * military uniforms * comfort and convenience * evolving definitions of gender, both femininity and masculinity evolved as concepts. The changing definitions of masculinity affected men's clothing. For the growing and rising middle classes, gender roles became more and more rigid around the concept of the separate spheres, the public for men and the private sphere for women. Cultural sources for men's clothing and men's fashion: industrial revolution; expanding middle class; technological advancements; an association in the culture between outward appearance and inward nature; French Revolution; Albert Edward, Prince of Wales Citation for Victorian Hell: <ref name=":29">{{Cite web|url=https://victorianhell.substack.com/p/victorian-mens-fashion-history-and|title=Victorian Men’s Fashion History and Clothing Guide|last="It's Monty, Actually"|date=31 October 2025|website=Victorian Hell|access-date=7 September 2026}}</ref> === Waistcoats === *c. 1830, dark brown or black w faces, gold buttons, standing collar: File:Waistcoat MET 38.68 F.jpg * c. 1830, beige and white woven fabric with rose buds stamped or embroidered??: File:Waistcoat MET 19.181.4 F.jpg * 1830–1835, dotted and floral stamped fabric, brown and tan: File:Waistcoat MET 1976.254.1.jpg * * c. 1840, flowered fabric: File:Waistcoat MET 1979.346.45 F.jpg * c. 1840, red, jacquard-like, double-breasted: File:Waistcoat MET 1979.346.47 F.jpg * 1840s, white brocade: File:Waistcoat MET 1980.132.8 F.jpg * 1840s, dark blue, red, green? stamped?: File:Waistcoat MET 1976.254.1.jpg * Mid 1840s, brown, embroidered: File:Waistcoat MET 24.160.3 F.jpg * late 1840s, embossed white with hash thingies: File:Waistcoat MET 1978.88.9 F.jpg * 1845 waistcoat made from blue Chinese silk damask: File:1845 waistcoat made from blue Chinese silk damask.jpg * 1845–1855, white brocade wedding waistcoat, piping on the edges: File:Waistcoat MET 1986.373.3 F.jpg * '''1849–1860''', black w gold lining, ribbon: File:Waistcoat MET 1978.477.25 F.jpg * * 1850, print of St. James's Park: File:Print (BM 1880,1113.2351).jpg * 1850s, white and blue, w blue floral design stamped on white-and-grey stamped on white fabric: File:Waistcoat MET 1978.477.28 F.jpg *c. 1853, brown and tan plaid, with red squares: File:Waistcoat MET 1984.90.2 F.jpg *1854: Fashion plates, groups of ppl: File:Paris, New York & Philadelphia fashions for spring and summer 1854, published & sold by F. Mahan, no. 211 Chestnut Street, Philadelphia. LCCN2003655770.jpg *c. 1855, French fashion plate, frock coats, waistcoats, etc.: File:Album z ilustracjami do czasopism z moda francuska, niemiecka i angielska. ca 1855 (9109644).jpg * 1857, cream, printed flowers on check, watch pocket: File:Waistcoat MET 1978.88.8 F.jpg * * c. 1860, dark floral? fabric with machine embroidery?: File:Waistcoat MET 1983.479.13 F.jpg * * late 1870s–early 1880s, gold, woven: File:Waistcoat MET 1979.34.1 F.jpg === Frock coats === * Apostol Mănescu, politician, wearing a frock coat, butterfly tie, black waistcoat with button chain and light coloured pants, drainpipe type. Circa 1866. Photo by Franz Duschek.jpg (1866)[[File:Apostol Mănescu, politician, wearing a frock coat, butterfly tie, black waistcoat with button chain and light coloured pants, drainpipe type. Circa 1866. Photo by Franz Duschek.jpg|thumb|Romanian (?) Politician, c. 1866, ill-fitting but probably handmade suit|center]] Full-length portrait of two young men wearing frock coats with sashes and pistols at their waists LCCN2006689564.tif (right)[[File:Full-length portrait of two young men wearing frock coats with sashes and pistols at their waists LCCN2006689564.jpg|thumb|1860, American, young men with frock coats, performers??|center]] * George Augustus Henry Sala.jpg (Mathew Brady, 1855–1865) * [[File:George Augustus Henry Sala.jpg|center|thumb|George Augustus Sala, 1855–1865, LoC]] ==== Dress and Conduct Manuals, Histories, Victorian Theory, Catalogs ==== # [Baker, William Henry.]  ''Clothes Dictionary''. Chicago, Ill.: Cahn, Wampold, 1901. https://commons.wikimedia.org/wiki/File:Clothes_dictionary;_(IA_clothesdictionar00bake).pdf. # [[c:File:Hint's_about_men's_dress,_right_principles_economically_applied_(IA_hintsaboutmensdr00barr).pdf|Hint's about men's dress, right principles economically applied (IA hintsaboutmensdr00barr).pdf]] (book, conduct manual, American, 1888) #[https://upload.wikimedia.org/wikipedia/commons/6/69/Fashion-_the_power_that_influences_the_world_%28IA_fashionpowerthat00foxg%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original Fashion- the power that influences the world (IA fashionpowerthat00foxg).pdf] (1871) (American, incl court dress, Victorian fashion theory, livery, "White, as it is the color of day, is expressive to us of the cheerfulness or gaiety which the return of day brings." [145], "Gentlemen's Furnishing and Goods," "Head and Foot Covering," Index) # [https://upload.wikimedia.org/wikipedia/commons/a/ae/How_to_behave_and_how_to_amuse._A_handy_manual_of_etiquette_and_parlor_games_%28IA_howtobehavehowto00sand%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original How to behave and how to amuse. A handy manual of etiquette and parlor games (IA howtobehavehowto00sand).pdf] (1895; American; Men's Dress, p. 23; besides conduct and dress, it has parlor games) # [https://upload.wikimedia.org/wikipedia/commons/8/8e/The_etiquette_of_men%27s_dress_%28IA_etiquetteofmensd00cluc%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original The etiquette of men's dress (IA etiquetteofmensd00cluc).pdf] (1888; American; some ads; anthology of individually written articles; lots of sports, outdoor events; search for "frock" — cutaway vs Prince Albert) #[https://upload.wikimedia.org/wikipedia/commons/e/e9/S.W._Silver_%26_Co.%27s_handbook_for_transatlantic_travellers_.._%28IA_swsilvercoshandb00silv%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original S.W. Silver & Co.'s handbook for transatlantic travellers .. (IA swsilvercoshandb00silv).pdf] (1883; American; lots of ads from SW Silver, with prices; has blank pages where ppl can write "Introductions" and "Engagements," but this is not a conduct book, it's travel guide / catalog to London) #[https://upload.wikimedia.org/wikipedia/commons/f/f6/How_we_go_to_those_who_cannot_come_to_us.._%28IA_howwegotothosewh00roge%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original How we go to those who cannot come to us.. (IA howwegotothosewh00roge).pdf] (Roger, Peet & Co.; American; catalog, spring 1891; pp. 11, clerical frock; 7 "Prince Alberts" double-breasted frocks; p. 23 shirts as underwear; has a thing on fitting and mail order; bathing suits, collars and cuffs; tennis shoes) == Victorian Men's Fashion (Intro to the Men's Fashion Section) == Museums and other historical sites have plenty of women’s clothes from the nineteenth century. There is great variety in both outer wear and underwear. “Men’s garments of the Victorian period have survived in far less quantity than women’s.” Buck p. 185 More waistcoats have survived than any other garment. The hardest garment to find are trousers. Very few survived the nineteenth century. Buck p. 185 By 1850 trousers dominated the fashion for men; the trouser straps under the shoe had disappeared; and a fly front had replaced the fall-front. Buck 185 It took most of the nineteenth century for men’s fashion to evolve into the coat, trousers and vest (waistcoat) that dominated the twentieth century and appears to be unchanging in the twenty-first century. “Men’s clothing, like women’s, was specific to each occasion and type of activity during the late nineteenth century.” Payne2, p. 518 For example, formal wear for social events was different from the casual, everyday wear for upper middle class and aristocratic men. Victorians also dressed in ensembles for hunting and riding (included knickerbockers–breeches that had a fuller cut). Casual and looser clothing was worn when participating in sports. Many different cuts of coats were available, like the Norfolk jacket, the morning coat, or the sack coat. “Tailored wool garments , originally inspired by the clothing of English country gentry, formed the backbone of men’s wardrobes in the early nineteenth century.” Men’s clothing began to change from styles that were colorful and flamboyant in the eighteenth century to styles that emphasized cut over color. By the end of the century men’s clothing had settled into a kind of uniform with coats and trousers usually made of the same fabric, often with a vest or waistcoat of the same fabric. The uniform included a shirt with a stiff collar, a necktie and very little jewelry. It took the entire nineteenth century to change to a rather static style that is still worn today. Ready-made clothing affected the social structure, the economy, and the gender differentiation. David Kutcha traces the origin of the 3-piece men's suit to King Charles II of England, who may be said to be wearing a coat, pants and a waistcoat, but otherwise is not wearing a "suit" we — or the Victorians — would recognize as such: <blockquote>... since 1666, male gentility has been associated with modesty and plainness in dress. Eschewing fashion as an increasingly feminized realm Charles II's vest inaugurated a new and essentially modern era of masculine aesthetics, one that reversed a long-held association between elaborate display and high social status. Manly thrift now displayed elite status.<ref>{{Cite book|title=The Three-Piece Suit and Modern Masculinity, England 1550–1850|last=Kutcha|first=David|publisher=University of California Press|year=2002|location=Berkeley and Los Angeles}}</ref> (2)</blockquote>So it's really Cromwell who should get credit?? The French Revolution caused both men and women to change stylistic direction radically. For one generation, stylish women wore simple white muslin dresses without foundation garments underneath. The changes in men's fashion was more lasting: men turned away from the ornamentation and ruffles of the ''ancien régime'', choosing instead understated and subtle tailoring to indicate good taste and wealth. Poole "comfort and convenience" — trousers, sack coats, collars and cuffs without a shirt, wool rather than silks and satins; knee breeches constantly riding up men as leaders of fashion, in spite of our sense that men didn't do fashion in the way that women did, were more serious than that === Dandy Stuff === Beau Brummell: "Men began to aspire to fine cutting, tailoring, and perfect fit in their clothes, flawless grooming and manners in themselves. The Englishman George Bryan (Beau) Brummell deserves much credit for the ideal of meticulous masculine appearance."<ref name=":25">{{Cite book|title=The History of Costume: From Ancient Mesopotamia Through the Twentieth Century|last=Payne|first=Blanche|last2=Winakor|first2=Geitel|last3=Farrell-Beck|first3=Jane|publisher=Addison-Wesley Longman|year=1992|isbn=0-06-047141-7|edition=2nd|location=New York, New York}}</ref> (458) "From 1796 to 1816, the Beau set the pattern for cleanliness and liberal use of starch." (459) === Gender Ideologies === '''Victorian gender ideologies''' relegated men to the "public sphere" and women to the "domestic sphere." (??) More than that “the cult of youth . . . the secularization of sport and the influence of modern warfare in generating men’s fashions, the tendency to prefer modern ideas of comfort and convenience, and the transformation of fashion knowledge and fashion urbanism from print to hyperreality”<ref name=":26">McNeil, Peter. "Men's Fashion: 1800–2022." Chapter 22. ''The Routledge History of Fashion and Dress, 1800 to the Present''. Routledge, 2024. https://opus.lib.uts.edu.au/bitstream/10453/182707/2/Men%27s%20Fashion%20200822_24_12_20_09_29_44.pdf DOI: 10.4324/9780429295607-27.</ref> (McNeil 1 or 411) changed the perceptions of masculinity and femininity. === Class === The growing middle class involved among other things more and more jobs and careers for young men as clerks, office workers, they were junior, subordinate, and they were commuting on the railroads from suburbs. Carolyn Kirby:<blockquote>In western Europe the fashion for plain dark suits coincided with the rise of the affluent middle-classes in a world where the pace of industrialisation and the globalisation of trade was accelerating as never before. The sharp, dark business suit became the last word in male power-dressing. And so it remains to this day.<ref name=":27">{{Cite web|url=https://historiamag.com/invent-masculine-fashion/|title=The invention of masculine fashion|last=Kirby|first=Carolyn|date=3 December 2025|website=Historia: Magazine of the Historical Writers' Association|access-date=25 August 2026}}</ref></blockquote> === Bertie === Albert Edward, Prince of Wales was very concerned with fashion and authoritative about it, with a very specific eye to small details. He was increasingly influential in men's fashion from the last third of the 19th and into the 20th century, and many noticed what he did and copied him.<blockquote>When that great lover of pleasure, Edward VII, visited Marienbad incognito as the Duke of Lancaster, he was followed by tailors from Paris, Budapest, Vienna, and Berlin who photographed him and took notes about his clothes. Edward VII introduced many [423–424] novelties into men’s fashion. ... He is also credited with making fashionable the creased trouser in 1909 (his groom dried them with a board weight after heavy rain, resulting in the line), turned-up cuff trouser (after hitching his trouser bottoms at a dirty racing track) and, as his girth grew, undoing the bottom button of his waistcoat."<ref name=":26" /> (424)</blockquote>Cowles<blockquote>The Prince was not just ‘a swell’. In the jargon of the day he was ‘a heavy swell’, and apparently there was a world of difference between the two terms. A swell was a rich young aristocrat who lived in extreme comfort; but a heavy swell added showmanship to the comfort and lived in a stylish luxury that even the French were obliged to envy. And of course the heavy swell was the acme of sartorial elegance. The Prince did not mind changing his dress half a dozen times a day. He loved clothes, and since whatever he chose to wear became the prevailing fashion overnight, he soon was regarded as an expert on the subject. His tailor-in-chief made a fortune. For many years he patronised a Mr. Poole. He discovered this gentleman by accident. He went to the theatre one night to see a well-known actor by the name of Fecher playing ‘Robert Macaire’. As an impecunious adventurer [129–130] Fechter was obliged to wear a coat that was torn and dirty, but Bertie’s expert eye noticed the elegant cut. At the end of the performance he asked Fechter for the name of his tailor, and Mr. Poole’s future was assured. The Prince had so many clothes he could never travel with less than two valets; and two more valets were left at home cleaning, brushing and pressing his vast wardrobe. There were suits and coats for every variation of every climate the world over. There were over a hundred pieces of headgear; and since Bertie was an honorary admiral and an honorary general of most of the countries of Europe, there was an entire room devoted to uniforms, sashes, epaulettes, belts, buckles, swords, feathers and other regalia. ... Men’s clothes became of such importance that new [130–131] shops sprang up like mushrooms in Savile Row, Clifford Street and Bond Street. Most of the Prince’s innovations were inspired by comfort and convenience. He altered the cut of the evening dress waistcoat, he shortened the tails on the tail coat, he left his frock coat open (due to an increasing girth), he introduced the black homburg, and he attended race meetings, not in the frock coat hitherto ''de regueur'' but in tweeds. He tried having his trousers creased down the sides rather than the front and back, in order to hide his bandy legs, but this idea did not catch on, and he soon discarded it himself. But the prince was not the only arbiter of men’s fashions. The band of  "heavy swells" who followed his lead gave him plenty of competition. Lord Raglan and Lord Petersham invented coats which are still named after them. Lord Dupplin the dinner jacket and Lord Cardigan the button-up sweater. But Lord Hardwicke made the most spectacular contribution. Men’s silk hats were made of beaver which was left in its original rough, shaggy state. Lord Hardwicke polished his hat until he could see his face in it, and consequently was known as "Glossy Top". He is responsible for the top hat as we know it today.<ref name=":28">{{Cite book|title=Gay monarch, the life and pleasures of Edward VII|last=Cowles|first=Virginia|publisher=Harper|year=1956|location=New York, New York|archive-url=https://archive.org/details/gaymonarchlifepl0000cowl/}}</ref> (129–131)</blockquote> === Men’s Clothing 1830–1900 (Intro to the Decades) === * “Tailored wool garments , originally inspired by the clothing of English country gentry, formed the backbone of men’s wardrobes in the early nineteenth century.”<ref name=":25" /> (458) Men’s clothing began to change from styles that were colorful and flamboyant in the eighteenth century to styles that emphasized cut over color. By the end of the century men’s clothing had settled into a kind of uniform with coats and trousers usually made of the same fabric, often with a vest or waistcoat of the same fabric. The uniform included a shirt with a stiff collar, a necktie and very little jewelry. It took the entire nineteenth century to change to a rather static style that is still worn today. (this is middle-class men for day wear?) * The silhouette for men sometimes followed the same line as women’s clothing on the top half of their bodies. For example, as women’s sleeves grew into the huge leg-of-mutton fullness, the shoulders of men’s coats also had added fabric to make a pouf at the shoulder, thus emphasizing a broad shouldered look across the front. Men’s silhouettes changed subtly without the exaggerated fullness of women’s skirts or the raising and lowering of the neckline. Once men began to wear trousers, they did not go back to formal knee breeches (except in European courts or for court wear for Victoria). * The line of men’s garments changed in smaller increments than women’s. Coats and trousers might fit tighter in some decades and looser in others. They were slim, then boxy, flared, then straight and evolved into the contemporary line we see on men today. * Men's fashions in the 19th century have been less researched than women's fashions, in part because of fewer artifacts of what men wore were saved in museums for study. * Photography, the first century that we have actual images (rather than artists' interpretations) of what people wore. ==== Court and Formal Dress ==== * Livery, working class * Formal dress was separate attire, used for specified occasions, varies by decade ==== Shirts ==== * Shirts and collars separated: "by 1827 detachable collars became available."<ref name=":25" /> (477) Shirts were considered more like underwear early in the century but by the end of the 1800s, they were becoming the outside garments popular in the twentieth and twenty-first centuries. * Neck treatments (and shirt cuffs) * Shirts were treated as underwear early in the century but by the end of the 1800s, they were becoming the outside garments popular in the twentieth and twenty-first centuries. ==== Coats and Jackets ==== The 1901 ''Clothes Dictionary'' says coats were "The principal garment of men's attire."<ref name=":30" />{{rp|10}} Several styles of coats were available to fashion-conscious aristocratic and upper-middle-class men. Men’s suits in this period were tailor made, fitted to one specific man. The factories, however, knew that the vast majority of men were working class and began to manufacture and sell ready-made shirts, coats and trousers. More clothes were available for working men and they cost less. The cheaper work clothes enabled upper-working-class men to own more than one set of clothes and to have more formal clothes for church or other events. Ready-made shirts were also available in generic sizes, small, medium and large. Generic sizing speeded up the mass production process and, since little of the shirts could be seen, they did not need custom fitting. Almost all of the coats Victorian men wore could be single or double breasted, with a couple of exceptions like morning coats and Norfolk jackets. On more formal occasions upper-class men wore a '''cutaway morning coat''' with light trousers during the daytime, and a dark '''tail coat''' and trousers in the evening. (define these terms) Morning coats was a general term for the jacket part of "full dress" or formal daytime wear, distinguished from formal evening wear. Most morning coats were cutaways, but the shape or cut is not the distinguishing feature: the bottom was curved or tailed, so the coat was short in front, it did not have a waist seam, single-breasted. Worn over a waistcoat and shirt. * According to Payne, "During the early 1820s tailcoats were the most popular type of coat."<ref name=":25" />{{rp|474}} * "Tailcoats gave way to skirted frock coats by the 1840s."<ref name=":25" /> (491) Tailcoats came down as far as the waist and then had tails (or "claw hammer" tails) attached at the waist in the back. Single-breasted, could be worn buttoned or unbuttoned in the front, over a waistcoat and shirt. * Nowadays, the only tailcoats are tuxedos, a term not in use until the 1880s, and named for Tuxedo Park, a village in New York populated by the elite. Originally only the white coat, ''tuxedo'' gradually came to mean the entire suit. ==== Frock Coats ==== [[File:Frock coat MET CI38.23.39 F.jpeg|alt=Old-fashioned coat hanging on a mannequin|thumb|Frock coat, 1840, American]] * Frock coats were introduced in the 1820s and worn throughout the nineteenth century with only minor changes to the line or fit. Sleeves were full at the top and waists were tight, creating an hourglass form. Initially frock coats were tightly fitted and closed with buttons. The more tailored frock coats had a waist seam and a flared skirt almost to the knees. The rate of fashion change notable in women's fashion was true for men's clothing as well. The frock coat persisted for a century, but it was in a state of constant (but subtle) evolution, with collars and lapels, coat length, the waist seam, the fullness of the coat itself as well as the sleeve, color, patterns like stripes or plaids. * A Prince Albert is a double-breasted, very well-tailored, form-fitting frock coat.<ref name=":30">[Baker, William Henry.] ''Clothes Dictionary''. Chicago, Ill.: Cahn, Wampold, 1901. https://commons.wikimedia.org/wiki/File:Clothes_dictionary;_(IA_clothesdictionar00bake).pdf.</ref>{{rp|33}} * Gentlemen, clergy, military * Men around the world and especially in the British Empire wore frock coats: images and descriptions exist of men wearing frock coats in India<ref>Woodyatt, Nigel Gresley. ''Under Ten Viceroys; The Reminiscences of a Gurkha''. London: H. Jenkins Limited, 1922. Pp. 31, 107, 1774.</ref>, Iran (Persia at that time)<ref>Sparroy, Wilfrid. ''Persian children of the royal family; the narrative of an English tutor at the court of H. I. H. Zillus-Sultán, G.C.S.I''. London and New York, J. Lane, 1902. Pp. 11, 29, 30.[https://upload.wikimedia.org/wikipedia/commons/d/d1/Persian_children_of_the_royal_family%3B_the_narrative_of_an_English_tutor_at_the_court_of_H._I._H._Zillus-Sult%C3%A1n%2C_G._C._S._I_%28IA_persianchildreno00sparrich%29.pdf?utm_source=commons.wikimedia.org&utm_campaign=index&utm_content=original https://upload.wikimedia.org/wikipedia/commons/d/d1/Persian_children_of_the_royal_family%3B_the_narrative_of_an_English_tutor_at_the_court_of_H._I._H._Zillus-Sult%C3%A1n%2C_G._C._S._I_%28IA_persianchildreno00sparrich%29.pdf].</ref>, Japan<ref>Watson, W. Petrie. ''Japan, Aspects and Destinies''. New York, Dutton: 1904. P. 7, 19, 31.</ref>, Egypt and Turkey<ref>Butler, Alfred Joshua. ''Court Life in Egypt''. London: Chapman and Hall, 1887. P. 7.</ref>, ... * Payne: "In the 1720s, Englishmen adopted another coat [than the redingote]: a straighter, functional style that originated among the working classes. Made of plain woollen cloth in practical colors such as brown, it had no pleats, narrow sleeves, a small flat collar, and a minimum of decoration. This became known as the frock coat and was useful for riding, hunting, and overseeing one's lands." (402) ==== Trousers ==== In 1872, in analyzing men's clothing as evolutionary behavior — like coloration for mating among birds in the natural world — George Darwin (Charles's son) says, of trousers:<blockquote>... a form yields to a succeeding form, which is better adapted to the then surrounding conditions; thus, when it ceased to be requisite that men in active life should be ready to ride at any moment, and when riding had for some time ceased to be the ordinary method of travelling, knee breeches and boots yielded to trousers.<ref name=":33" /> (125 of 565)</blockquote> * Working-class men had been wearing trousers (or "trowsers") increasingly since the 16th century in Europe,('''citation''') but after the French revolution the middle and upper classes adopted them because "the safest dress was that of the working man, ... who did not wear knee breeches, but rather trousers."<ref name=":26" /> (416) * Lewandowski: "First worn by the early horse-riding steppe people, introduced to Western world by Italians in 16th century. They were accepted as informal dress in the Directoire (1790–1815 C.E.). They became a part of semi-formal dress around 1815 and became worn commonly after 1830."<ref name=":31">{{Cite book|title=The Complete Costume Dictionary|last=Lewandowski|first=Elizabeth J.|publisher=Scarecrow Press|year=2011}}</ref> (29) * Breeches: Men’s bifurcated garment that ended just below the knee * Trousers (or long pants): men’s bifurcated garment that went down to the ankles or foot * The most sweeping change in men’s fashion before 1820 was in the length of their pants. Trousers that went from waist to foot were so much more comfortable and popular than knee breeches that they replaced what had dominated men’s wear since the sixteenth century. And trousers have been worn for over two centuries now. * They were originally tailored but began to be mass produced. Although the aristocracy were required to wear knee breeches at court, they wore trousers more than they wore breeches, and they could afford to have their suits and shirts hand sewn and individually. Working class men had to contend with small, medium, and large from mass production. * This bifurcated garment was modified in specific places, like the length, the fullness over the hips or the width of the leg. In summer trousers were lighter in color — "grayish blue, aqua and pearl gray." (Payne 2, 505) In winter trousers mixed darker colors like "steel gray and brown, black and brown, and black and green." (Payne 505) More on summer colors, winter colors? * [Find quote about QV's men's court dress and the men being so cold] ==== Waistcoats ==== For most of the century, the waist-length sleeveless coat that men wore over their shirt and under their suit coat was called a waistcoat. By the 1880s, everyday waistcoats were called vests, and what was called a waistcoat was worn with formal, evening attire like tailcoats and tuxedos. Necklines rose and fell and collars and lapels came and went over the century, but by the end of the century, formal waistcoats had low necklines and lapels.<ref name=":25" /> (528) Many more waistcoats exist as artifacts in collections than vests, perhaps because they were special and thus were saved.[[File:Waistcoat MET CI60.22.55 F.jpg|thumb|Men's waistcoat, 1850s]] Over the course of the century the waistcoat evolved from ornate and decorative to something simpler, whose fabric matched the suit coat and trousers — the vest, in fact. Victorian men put their creativity, color and specialty fabrics into their waistcoats. At the beginning of the century men's waistcoats were made from specialty fabrics, like velvet or brocade or a patterned silk. Early in the century, stylish men wore two vivid waistcoats at the same time.<ref name=":25" /> (474) An elaborate waistcoat might have a colorful, patterned base fabric as well as a floral ribbon embellishment (for example, see right). Long after coats and trousers were made from the same dark wool, waistcoats continued to be colorful, making them the focus of the ensemble. By the end of the 19th century, the plain style came to dominate men’s fashion (and continues to dominate it to this day). When waistcoats became vests, they became part of the plain style ==== Overcoats ==== As their name suggests, overcoats or surcoats were coats worn for warmth and for protection from rain and snow on top of the other articles of clothing, including suit coats and frock coats. Overcoats became a significant fashion element, and many styles were seen throughout the century. [Top coat] Victorians used the terms ''overcoat'' and ''great coat''., and sometimes perhaps ''surtout''. A great coat was a "large overcoat, commonly made of wool."<ref name=":31" /> (124) In his 1901 ''Clothes Dictionary'', Baker says a surtout is "An overcoat cut in the style of a frock coat."<ref name=":30" /> (39) Lewandowski says something more generic — "term referring to any man's long cloak or coat."<ref name=":31" /> (282) Victorians also specified which of the many kinds of overcoat: redingote, Chesterfield coat, Inverness coat, macintosh (or mackintosh), paletot, Ulster coat, Norfolk jacket [[File:Dandies of 1831.jpg|thumb|Redingote on figure in back, 1831]] ===== Redingote ===== A redingote was a type of a "full-length overcoat, usually open at the front and belted, popular in varying designs through the eighteenth and nineteenth centuries."<ref name=":32">Mitchell, Rebecca, ed. ''Fashioning the Victorians: A Critical Sourcebook''. Bloomsbury Visual Arts, 2018.</ref> (527 or 565) (The figure in the back in the fashion plate, right, shows a redingote from 1831.) Because the redingote was popular for so long, it existed in various forms through the two centuries. Generally, it was single- or double-breasted, with a split skirt or box pleats in back (or both) and with a high standing collar, a rolled collar or a double collar. Derived "from riding coat," (Payne 402) it was fitted at the waist and reached mid-calf, with sleeves that were full at the shoulders and upper arm and narrow from the elbow to the wrist, sporting a wide cuff. The length varied over time between knee- and ankle-length. Also, women wore redingotes — in France (1865–1890) — that were shaped to cover the bustle.<ref name=":31" /> (247–248) Redingotes continued to develop, eventually evolving "into an overcoat ..., but the overcoat lacked the pleats and large cuffs of the redingote,"<ref name=":25" /> (402) as well as, possibly, the waist seam.[[File:George Stanhope, 7th Earl of Chesterfield.jpg|thumb|George Stanhope, 7th Earl of Chesterfield, wearing a Chesterfield coat, 1860]] ===== Chesterfield Coat ===== * "Chesterfield coats were single-breasted, with fly fronts [regular buttons and button holes, as opposed to fall front, in which a panel of cloth covers the button holes and the placket covers the closure completely] and velvet collars."<ref name=":25" />  Payne2 p. 519 * They were one kind of overcoat, named for George Stanhope, 6th Earl of Chesterfield. 1840s. * Signature velvet collar. * "Man's fitted overcoat with hidden buttons and velvet collar"<ref name=":31" /> (62) * "fitted men’s knee-length overcoat, narrower than the frock coat and without a waist seam, popular from the end of the nineteenth century."<ref name=":32" /> (519 of 565) ===== Ulster Coat ===== In 1872, in analyzing men's clothing as evolutionary behavior — like coloration for mating among birds in the natural world — George Darwin (Charles's son) says, of Ulster coats:<blockquote>... a form yields to a succeeding form, which is better adapted to the then surrounding conditions .... The "Ulster Coat", now so much in vogue, is evidently largely fostered by railway travelling, and could hardly have flourished in the last century, when men either rode or travelled in coaches, where there was no spare room for any very bulky garment.<ref name=":33">Mitchell, Rebecca, ed. "3. 'George H. Darwin, ‘Development in Dress', ''Macmillan’s Magazine'' 26 (September 1872), pp. 410–16." Section 1: Fashion Theory in the Nineteenth Century. ''Fashioning the Victorians: A Critical Sourcebook''. Bloomsbury Visual Arts, 2018.</ref> (125 of 565)</blockquote> * "men’s overcoat with attached waist-length cape, popular in the nineteenth century."<ref name=":32" /> (530 of 565) * ulster overcoat for travel. * "Man's single- or double-breasted overcoat with waist belt. Initially had hood, but by 1870s was detachable. In 1875, the ticket pocket was added on the left sleeve above the cuff."<ref name=":31" /> (304) * "Travel called for an ulster — a long, loose, heavy overcoat — or for an Inverness coat with attached cape."<ref name=":25" /> (527) * "Heavy tweed coats for travel such as the ulster had half-belts and box pleating in back."<ref name=":25" /> (551) * Ulster may have had a shorter cape than the Inverness * Can we find a source linking John McGee (of McGee & Co.) with the invention of the Ulster coat in 1866? (per Wikipedia)? [[File:The man wot drove the sovereign to the last stage trying it on the next. (BM 1868,0808.9200).jpg|thumb|Duke of Wellington, 1830, wearing a coachman's coat, or Inverness coat]] ===== Inverness Coat ===== * "men’s overcoat, with long, full, open sleeves, giving a cape-like appearance from the front; worn from the mid-nineteenth century to the early twentieth century as formal wear."<ref name=":32" /> (523 of 565) * an Inverness coat with up to five cape collars and a high curved collar. * Lewandowski: "(1840–1865 C.E.) to 20th century. Worn after 1858, man's large, loose, knee-length overcoat with fitted collar and long cape."<ref name=":31" /> (143) * An Inverness coat had a high standing collar as well as up to 5 capes over a knee-length, loose overcoat.<ref name=":31" /> (143) * Caricature of the Duke of Wellington in a "coachman's caped great-coat,"<ref>{{Cite web|url=https://www.britishmuseum.org/collection/object/P_1868-0808-9200|title=Duke of Wellington in Coachman's coat. print; satirical print {{!}} British Museum|website=www.britishmuseum.org|language=en|access-date=2026-11-04}}</ref> or Inverness, 1830 * In the 1880s, the Inverness was sometimes sleeveless, so the capes were not merely decorative. * both formal and informal styles exist; also called a coachman's cape. [[File:Carson, Pirie, Scott & Co. Macintosh, 1893.jpg|thumb|360x360px|Gentleman's Macintosh, 1893]] ===== Mackintosh ===== * "Introduced in 1836, short loose overcoat made of Mackintosh's [sic] patent India-rubber cloth. Came in drab or dark green."<ref name=":31" /> (181) * "waterproofed overcoat, named after its inventor [Charles Macintosh]; now used generically to refer to raincoat."<ref name=":32" /> (524 of 565) * [according to Wikipedia, the spelling ''Mackintosh'' is now standard.] ===== Paletot ===== * "short, loose overcoat for men or women."<ref name=":32" /> (526 of 565) * "The pilot coat, or paletot, was the original of all the loosely cut garments which appeared from the 1830's onwards and which inspired the more casual coats and sportswear of the end of the century.<ref name=":34">{{Cite book|title=The Cut of Men’s Clothes: 1600-1900|last=Waugh|first=Norah|publisher=Theatre Arts Books|year=1987|isbn=978-0878300259}}</ref> (1533 of 2116) ===== Norfolk Jacket ===== * "A single breasted sack coat having two or three box plaits [pleats] in back, two in front and a belt of material. Most used for hunting and outdoor sports."<ref name=":30" /> (28) * "A variation 'suitable for any kind of outdoor exercise', was the 'Norfolk jacket' which appeared in the 1870's. It also was a two-seamed jacket but was cut full and the fullness arranged in box pleats, two in the front and two in the back. It had a belt and was worn with 'knickerbockers'-knee breeches with legs cut loose and gathered into a knee-band."<ref name=":34" /> (1547 of 2116) <ref name=":24" />Kay, Fiona and Neil R. Storey, ''Victorian Fashions for Women'', Pen & Sword History, Yorkshire - Philadelphia, 2022 [[File:Homosexualitywilde.jpg|thumb|Oscar Wilde and Bosie Douglas, straw boater and derby, 1894]] ==== Hats ==== The upper-class continued to wear top hats, and [[bowler hats]] (known in America as a derby) were worn by the working class. 1830s This class of men also wore round cloth caps, often seen on male children. The straw boater was the most popular hat by the end of the century and was worn by all of the classes. Men wore [[top hats]], with wide brims in sunny weather. 1830s - 1900 Top hats briefly became the very tall "stovepipe" shape, but a variety of other hat shapes were popular. Homburgs, deerstalkers and “Trilbies” were also popular. Buck, p. 198-199 (George de Maurier novel ''Trilby'') Hats were ''de rigueur'' for all Victorians, all classes, all ages, all genders. ==== Shoes ==== [[File:Men's fashion silhouette of 1837.jpg|thumb|Men's coats, 1837]] [[File:Lev Wittgenstein by F. Kruger.JPG|thumb|Lev Wittgenstein by F. Kruger, 1836, wearing a surtout]] === 1830s and 1840s === For men's fashion, the 1830s and 1840s were dominated by a defined waist, lean limbs and tall hats. Working-class men had been wearing trousers for some time, but by the 1830s and '40s, middle- and upper-class men generally wore frock coats and trousers for casual or less formal attire in the city. In the country, what they wore depended on what they were doing — hunting, riding, shooting and so onen[[File:Man's Frock Coat LACMA M.2007.211.61 (1 of 4).jpg|alt=Male mannequin wearing a light-colored thigh-length coat similar to a suit jacket and a top hat|thumb|Men's frock coat, c. 1845]] [[File:Stockholms mode-journal- Tidskrift för den eleganta werlden 1847, illustration nr 2.jpg|thumb|Stockholm's fashion magazine, 1847]]Some men wore corsets during this time, so the waist was nipped in and the skirt of the frock coat flared out. The sleeves of their coats and jackets were slightly puffed at the shoulders. The trouser legs were straight with a strap under the instep. The figure on the left in the fashion plate from ''Modes de Paris Journal des Tailleurs'' (right) illustrates this silhouette very clearly as well as the frock coat, the strap under the instep, and the puffed shoulders. ==== Coats and Jackets ==== Frock coats had become fashionable for day wear in the 1820s<ref name=":25" />{{rp|474}} and were worn throughout the century. In the 1830s frock coats were tightly fitted and closed with buttons. The more tailored frock coats had a waist seam and a flared skirt almost to the knees. The main changes in frock coats in these two decades were in the colors and the neck treatments (collar and lapels). Initially frock coats were not necessarily black. They could be colorful — like "plum, mulberry, brown, bright blue, and bottle green" — with "contrasting velvet collars."<ref name=":25" />{{rp|474}} The truly bright, saturated colors made possible by synthetic dyes, however, were a couple of decades away still and were never used for frock coats. Middle- and upper-class men limited their use of tailcoats to evening wear and more formal occasions. (In the 1847 Stockholm fashion magazine, below right, the figure in the center is wearing a tailcoat.) A cutaway morning coat was worn with light trousers for formal events during the daytime, and a dark tail coat and trousers were worn in the evening. ==== Shirts ==== Shirts were made of linen or cotton with low collars, occasionally turned down, and were worn with wide [[cravats]] or neck ties. Before they were mass produced, shirts made of finer linen or cotton were tailored for upper and wealthy middle-class men. Depending on occupation, working-class men's shirts were made from a rougher, home-woven linen or cotton, often shaped loosely like a smock and sometimes without a front closure. Shirts were sometimes as long as knee-length. ==== Trousers ==== Men had adopted trousers over knee breeches for semi-formal dress "around 1815"<ref name=":31" /> (298) beginning after the French Revolution.<ref name=":26" /> (416) They were wearing trousers both for formal and semi-formal dress by the 1830s. Initially trousers "fit quite snugly ..., but in the 1840s they became looser."<ref name=":25" /> (477) Upper-class and aristocratic men still wore knee breeches at court and loose-fitting breeches (in the form of knickerbockers) for country wear and some sports, like riding and golf. Generally, however, they wore trousers more than they wore breeches. Men flocked to them once trousers became a stylish option because the looser fit was warmer in cold weather and more comfortable than the tight-fitting knee breeches from earlier in the century. Ready-made men's clothing was available in the US early, but by the 1840s ready-made suits were making an impact in Europe and the UK,<ref name=":26" /> (419–420) especially outside the upper classes. Aristocrats and upper middle class could afford the well-tailored cut and fit of individually hand-sewn trousers and coats. ==== Waistcoats ==== Waistcoats were both single- or double-breasted, with shawl or notched collars, and might be finished in double points at the lowered waist. Collars gradually lowered over the course of the two decades. Often the colorful vests were decorated with fur or velvet collars. “Waistcoats remained colorful, decorative items in men’s wardrobes after the rest of their costumes had become plain.” (Payne 2 460-462) <nowiki>:</nowiki> "During the 1820s and 1830s, men sometimes wore two waistcoats, in combinations like white velvet over rose-and-gold brocade."<ref name=":25" /> (474) ==== "Overcoats ==== Men wore a variety of topcoats or overcoats. Surtouts were overcoats built like long frock coats, like the one worn by Lev Wittgenstein in the portrait (above right). The redingote was most popular in the 1830s and 1840s. ==== Original Text ==== During the [[1840s in fashion|1840s]], men wore tight-fitting, calf length [[frock coat]]s and a [[waistcoat]] or vest. Sleeves were full at the top and waists were tight, creating an hourglass form. For more formal occasions, a cutaway morning coat was worn with light trousers during the daytime, and a dark tail coat and trousers was worn in the evening. Shirts were made of linen or cotton with low collars, occasionally turned down, and were worn with wide [[Cravat (early)|cravat]]s or neck ties. Men wore [[top hat]]s, with wide brims in sunny weather. === 1850s === The 1850s revealed several industrial inventions that significantly impacted clothing. First, the Industrial Revolution began (and still does today) with machines to weave fabric and machines to sew fabrics. Manufacturers quickly learned that the majority of the population was working class. Theirs were the simplest, least trimmed garments made in the nineteenth century. Second, mass production of shirts, trousers and coats changed how most people shopped for clothes. The aristocracy and upper middle class folks could still have their clothes made to specifically fit their bodies. Manufacturers knew that they could not mass produce clothing for each individual’s body. They invented generic sizing in small, medium, and large. They could, therefore, produce many more items of clothing with generic sizing. Third, Isaac Singer patented and began to manufacture home or domestic sewing machines (treadle machines) enabling more form-fitted '''dresses''' to be constructed for an individual’s specific shape and size. The fourth item to impact fashion and clothing was the invention of the paper pattern. These were introduced in fashion magazines targeting women. Almost all women were taught to sew by hand, whether they were aristocrats or working class. Sewing machines enormously speeded up the '''process of constructing from hours to minutes'''. Finally, aniline dyes made colors brighter and longer lasting. Prints and stripes, checks and plaids, fabrics had much more vibrant color with aniline dyes. The Industrial Revolution impacted the working class and changed their lives the most. children's clothes? Women made men's clothing too According to Judith Flanders, working-class men's clothes could be colorful. For example drivers of hansom cabs () dressed more up-scale, and drivers of hackneys () did not.<blockquote>While hackney drivers were also considered to be stereotypically shabby, hansom-cab drivers were generally represented as smartly dressed. A print in 1850 showed a driver in a snappy brown coat instead of the coachman’s heavy multiple-caped outfit, pale green striped trousers, short boots and top hat, the [167–168] reins held daintily in his gloved hands. Both cab and coach drivers wore top hats, but cabbies of a sporting bent later switched to bowlers, and in summer donned bright checked outfits.<ref name=":23">{{Cite book|title=The Victorian City: Everyday Life in Dickens' London|last=Flanders|first=Judith|publisher=Thomas Dunne Books|year=2012|location=New York, New York}}</ref> (167–168 [of 972])</blockquote> A variety of silhouettes was seen in the 1850s. Trousers were long and slim with a strap under the instep of the shoe. ==== Coats and Jackets ==== "Although the frock coat was worn throughout the century, it lost its dominant position in the 1850s, when the morning coat began to replace it."<ref name=":29" /> A jacket shorter than the frock coat or morning coat that had visible pockets began to be worn in about 1850. Cutaway tail coats were still reserved for formal occasions. All of these coats could be single or double breasted. They were called “ditto suits” by those who wore them because the coat, trousers, and waistcoat were all made from the same fabric. There were morning coats and cutaway morning coats; there were Norfolk jackets and ditto suits. The most formal were the cutaway tail coats for evening wear and balls; and the least formal were the boxy shaped sack coats. By the 1860s, it had become the most popular casual coat. ==== Shirts ==== During the [[1850s in fashion|1850s]], men started wearing shirts with high upstanding or turnover [[collar (clothing)|collars]] and [[necktie#Four-in-hand|four-in-hand necktie]]s tied in a bow, or tied in a knot with the pointed ends sticking out like "wings." ==== Trousers ==== Trousers had fly fronts and breeches were used for formal functions and knickers (short pants fuller cut than breeches) for horseback riding. Men's choice to wear trousers is an instance of the importance of comfort and convenience outweighing style and presentation, a value that increased in importance through the 20th century. ==== Waistcoats ==== Waistcoats remained the one garment that could be brightly colored and copiously trimmed on exotic fabrics. Waistcoats show that men were concerned with decorative elements in their ensemble. ==== Notes & Quotes ==== * transition from frock coats to ditto suits, 1850s (Payne, 463) ==== Hats ==== The upper-class continued to wear top hats, and [[bowler hat]]s were worn by the working class. Caps ==== Overcoats ==== Overcoats were cut fuller with wider sleeves and no extra fullness at the shoulder. Unlike the redingote, the overcoats had straight seams to the knee length. Many had wide lapels that reached below the waist. Working class men and their families benefitted more from the industrial revolution in regards to clothing.  Manufacturers marketed to them because because they were the largest class. [[File:Gazette of Fashion, February 1865, RP-P-2009-2675.jpg|thumb|1865, Frock coats, etc. (Paris)]] [[File:Gazette of Fashion, October 1864, RP-P-2009-2673.jpg|thumb|1864, Frock coats, etc., Paris]] [[File:Broadway fashions, New York LCCN2003677917.jpg|thumb|Butterick, Spring-Summer 1866, Broadway Fashions]] [[File:Four young men wearing frock coats - DPLA - 4706a21c9267c45034d51c8fc5309251 (page 1).jpg|thumb|1860s, working class?, ill fitting, frock coats, trousers, shirts, vest, derby hats]] === 1860s === [[File:Corporal frock coat 1862 med.jpg|thumb|Corporal frock coat 1862, 9-botton military]]The 1860s saw fewer inventions that influenced or changed the way people were acquiring clothes. But the changes begun by mass production continued with the working class. Little changed for the higher classes, except maybe paper patterns and sewing machines. The different shape and size in clothing continued to provide slightly different silhouettes for men in the upper and middle classes. As women's clothes grew more complex in cut and style, men's clothes became simpler in cut and style. ==== Coats and Jackets ==== Individualized fittings continued for upper class and wealthy middle class clients. (Working class as well as middle and upper class.) Working class was well over 60% of the population. For the largest class, ready-made garments were ideal for men and women who were working class. For the two upper classes morning coats still led the way but frock coats were still in demand and worn in business and more casual situations. Leisure wear like knickers and ditto suits became more popular in the 1860s. Haute couture wanted every occasion or event to have special clothing. In some ways men dressed more alike (coat, trousers, waistcoat) and in some ways there was more variety in the cut of their coats and in the manufactured clothing they could buy. Many upper class men still had their shirts custom made. Frock coats were shortened to knee-length and were worn for business, while the mid-thigh length [[sack coat]] slowly displaced the frock coat for less-formal occasions, with the overall effect of a looser silhouette. The Prince of Wales: "For the countryside such as at Sandringham, he permitted an informal dress code. The Henry Poole ledger marked as 'HRH 1865' is for an evening coat without tails, the first 'dinner jacket.'"<ref name=":26" /> (424) ==== Shirts ==== Ready-made shirts rarely were seen since shirts were more underwear than outerwear. Factories began to make and sell detachable collars and cuffs. It was more convenient to replace collars and cuffs each day than the time it took a servant (working class) to wash and starch enough to look like the celluloid many of those collars were made of. ==== Trousers ==== Trousers were cut full and boxy during most of the 1850s and 1860s. The strap under the shoe disappeared and trouser legs reached the back of the heel in length. Knickers were still worn for hunting or riding and breeches were still ''de rigueur'' at court. ==== Waistcoats ==== Waistcoats remained decorative and worn with most of the coats that were popular. The young “dandies” wore the most colorful and decorated waistcoats. These “dandies” gave their highest priority to their appearance. They were the avant garde of haute couture for men. ==== Necks Treatments ==== In the [[1860s in fashion|1860s]], men started wearing wider neckties that were tied in a bow or looped into a loose knot and fastened with a stickpin. ==== Hats ==== Top hats briefly became the very tall "stovepipe" shape, but a variety of other hat shapes were popular. ==== Overcoats ==== The single-breasted redingote continued in popularity among the aristocracy and upper middle-class.  These coats were often “in colors such as plum, mulberry, brown, bright blue, and bottle green . . . [with] contrasting velvet collars.” Payne2 p. 474 [[File:Mens Coats 1872 Fashion Plate.jpg|thumb|upright|Drawing of Victorian men 1870s]] [[File:Ashurst frock coat.jpg|thumb|Ashurst Frock coat]] [[File:Grand Duke Alexis Alexandrovich of Russia Wearing a Frock Coat; Standing (fbc266c2feca43f6ad5b44e031635a8d).tif|alt=Old photograph of a man wearing a dark thigh-length coat similar to a suit coat with light-colored trousers|thumb|Grand Duke Alexis Alexandrovich of Russia Wearing a Frock Coat, c. 1872]] [[File:Caillebotte Hugot.jpg|thumb|Portrait of Paul Hugot, 1878]] [[File:Oscar Wilde (1854-1900), by Hills & Saunders, Rugby & Oxford 3 april 1876.jpg|thumb|Oscar Wilde, 1876, ditto suit]] [[File:FrockCoat.jpg|thumb|English frock coat, 1870s]] === 1870s === To correct and prevent errors being made in court dress, in 1875 the Lord Chamberlain published ''Dress Worn by Gentleman at Her Majesty's Court'', "a summary of regulations for court uniform and dress."<ref>{{Cite book|url=https://www.google.com/books/edition/Dress_worn_by_Gentlemen_at_Her_Majesty_s/pvrbQCXq0MEC?hl=en|title=Dress worn by Gentlemen at Her Majesty's Court|last=Britain)|first=Victoria (Queen of Great|date=1875|language=en}}</ref> This is the kind of thing Bertie really cared about. Define court dress. A portly, boxy silhouette was sought for most of the 1870s. Older men whose stomachs had spread outward and thus looked prosperous to the Victorians were the ideal for men’s high fashion. Sack coats and trousers were cut a little wider in the legs. Corduroy for trousers and muslin for shirts was often used in working class clothing. ==== Coats and Jackets ==== There were minor changes to some of the coats Victorian men wore. Frock coats were shortened to the knee. Sack coats (or ditto coats — the forerunner of the suits worn by men in the western cultures of the twentieth and twenty-first centuries) were found to be so comfortable that most men of the upper and middle classes had a ditto suit. Men still wore morning coats and the aristocracy still wore cutaway coats with trousers to parties and balls but cutaway coats with knee breeches at court. ==== Shirts ==== Although ready-made shirts were available, the upper and middle classes still wore bespoke clothing hand-made, with better fabric and an excellent fit but stitched on machines. The suits and shirts made for the working class were of cheaper fabrics. ==== Trousers ==== Most men were wearing trousers  all of the time (except at court) and have worn them ever since. Trousers had button flies by the 1870s which most men found to be much more convenient than laces. Trousers did not “ride up” the leg in the way that knee breeches did when dancing or sitting. If a man did not have fashionable legs, they could be obscured behind trousers. ==== Waistcoats ==== White waistcoats began to be worn by men. Black were also worn when mourning. Changes in the waistcoat could be seen but were very subtle. For example, collars were lowered as the neckline grew deeper and deeper in front, revealing more of the fancy vest. ==== Overcoats ==== A longer version of the standard overcoat, “sometimes with fur collar, cuffs, and lining” was often worn for warmth. Payne2 p. 519 ==== Original Text ==== During the [[1870s in fashion|1870s]], three-piece suits grew in popularity along with patterned fabrics for shirts. Neckties were the four-in-hand and, later, the [[Ascot tie]]s. A narrow ribbon tie was an alternative for tropical climates, especially in the Americas. Both frock coats and sack coats became shorter and more form fitting. Flat straw boaters were worn when boating. [[File:Elliott & Fry10a.jpg|thumb|William Gladstone, 1887, morning coat]] [[File:British politicians gambling at Ascot Wellcome V0050378.jpg|thumb|British Politicians Gambling at Ascot, 1884]] [[File:Scribner's magazine (1887) (14595087238).jpg|thumb|1887, types of American servants]] === 1880s === The silhouette narrowed and straightened. That is, the line went straight down without the flare of skirts on the coats. This smooth line had few decorations. Men wore hardly any jewelry. They might have a boutonniere or a ring.  Suits were not  decorated. All coats were straighter and shorter. Depending on the time of day, the Prince of Wales might change his clothes (thus, his silhouette) up to six times per day,<ref name=":28" /> (129) and some aristocrats and upper-class men would follow his lead. ==== Coats and Jackets ==== Although the frock coat was worn throughout the nineteenth century, the single fabric sack suit was worn for casual wear and was beginning to be seen as a businessman’s suit.  Morning coats were still in use for some events as well as casual occasions. The modern tuxedo or Cowes jacket appeared and was worn for formal occasions. The tuxedo is still worn as formal dress today. ==== Shirts ==== Shirts were still custom made for the rich and the working class bought ready-made shirts. The shirt remained basically the same but it could handle the different neck treatments.  Even mass produced shirts could have buttons or button holes for detachable collars and cuffs. ==== Trousers ==== Trouser legs began to decrease in width as the coat became narrower and emphasized strong vertical lines. ==== Waistcoats ==== During the 1880s waistcoats were called vests [is it regional?] and much of their bold trim and colorful fabric disappeared and vests were constructed from the same fabric as the coat and trousers. The business suit for men developed in the 1880s and was firmly established in the 1890s. ==== Overcoats ==== Versions of topcoats increased, adding an ulster overcoat for travel and an Inverness coat with up to five cape collars and a high curved collar. Double breasted topcoats were popular and some were knee-length and some calf-length. ==== Original Text ==== During the [[1880s in fashion|1880s]], formal evening dress remained a dark tail coat and trousers with a dark waistcoat, a white bow tie, and a shirt with a winged collar. In mid-decade, the dinner jacket or [[tuxedo]], was used in more relaxed formal occasions. The [[Norfolk jacket]] and tweed or woolen breeches were used for rugged outdoor pursuits such as shooting. Knee-length topcoats, often with contrasting velvet or fur collars, and calf-length overcoats were worn in winter. Men's shoes had higher heels and a narrow toe. [[File:American fashions - The Jno. J. Mitchell Co. Litho., New York. LCCN2006676665.jpg|thumb|Fashion plate from the Jno. J. Mitchell Co., New York, 1899]] [[File:Alfred Milner Vanity Fair 1897-04-15.jpg|thumb|Alfred Milner, 1897, Leslie Ward ("Spy"), for Vanity Fair]] [[File:Nobl-08.jpg|thumb|Sherlock Holmes, 1892, Sidney Paget]] [[File:PUK1894page380rector poor.jpg|thumb|Rector and Drinker, 1894]] === 1890s === The dominant silhouette for men became the sack suit in the 1890s and while changes in the sack have been subtle, it remains the dominant silhouette today. ==== Coats and Jackets ==== “Sacks became ''the'' favored style of suit coat,”(Payne2, p. 532) especially among the younger men. Frock coats were associated with older men along with the cutaway coat. There were many more choices for sports wear and leisure wear than ever before. Norfolk jackets were often worn while hunting. Most informal styles could be purchased ready made. The rich still had their clothing custom made by tailors but even working class men could purchase most ready-made versions of the coats, trousers, and vests. ==== Shirts ==== Shirts could be made of patterned fabric as well as solid colors and white.  Shirts were beginning to be acceptable as outer wear especially when worn as sporting clothing. ==== Trousers ==== Early in the 1890s, “slim, straight trousers were news.” (Payne 2, p. 532) Trousers could be plaid or checked as well as the same fabric as the coat and vest. ==== Waistcoats ==== Fancy fabrics and bold trim were not seen much as the more subdued vest dominated the fashion scene. ==== Neck Treatments ==== In the 1860s, men started wearing wider neckties that were tied in a bow or looped into a loose knot and fastened with a stickpin. ==== Overcoats ==== “Topcoats included fingertip-length styles made of twill covert cloth. Single-breasted, fly-front overcoats were fashionable too. Roomy overcoats with fur linings and collars warmed the wealthy. Inverness overcoats remained in vogue.” Payne2, p.532 ==== Original Text ==== Starting from the [[1890s in fashion|1890s]], the [[blazer]] was introduced, and was worn for sports, sailing, and other casual activities.<ref>{{cite web|last=Landow|first=George|url=http://www.victorianweb.org/art/costume/90s/2.html|title=Men's informal sporting dress, late 1880s and '90s}}</ref> Throughout much of the Victorian era most men wore fairly short hair. This was often accompanied by various forms of facial hair including moustaches, side-burns, and full beards. A clean-shaven face did not come back into fashion until the end of the 1880s and early 1890s.<ref>{{cite web|url=http://www.victorianweb.org/art/costume/nunn21.html|title=Victorian Men's Fashions, 1850–1900: Hair}}</ref> Distinguishing what men really wore from what was marketed to them in periodicals and advertisements is difficult, as reliable records do not exist.<ref name="shannon597">{{cite journal|last=Shannon|first=Brent|title=Refashioning Men: Fashion, Masculinity, and the Cultivation of the Male Consumer in Britain, 1860–1914|journal=Victorian Studies|year=2004|volume=46|issue=4|pages=597–630|doi=10.1353/vic.2005.0022}}</ref> === Notes === *Men's suits buttoned higher up than today (Payne, 467) * Norfolk jackets and sack suits (Payne, 471) * formal attire, tuxedos with tails, cutaways (Payne, 469) * Keith Middlemas (https://archive.org/details/storyoffiesta00huxf/page/200/mode/2up?q=fashion) *Brent Shannon. "Refashioning Men: Fashion, Masculinity, and the Cultivation of the Male Consumer in Britain, 1860–1914." Victorian Studies 46, no. 4 (Summer 2004): 597–630. == Hats and headwear == [[File:Ford.madox.brown.last.emma.study.jpg|thumb|''Emma Hill'' by [[Ford Madox Brown]] (1853), a woman wearing a later version of the [[poke bonnet]]]] [[File:Hoed,_objectnr_KA_1237.tif|left|thumb|Perched bonnet style of the early 1870s.]] Hats were crucial to a respectable appearance for both men and women. === Men's Hats === The top hat, for example, was standard formal wear for upper- and middle-class men.[Payne] According to Blanche Payne, "The high top hat, usually black or dark gray, had reached its characteristic shape by 1798 and dominated the entire nineteenth century." (457–58) Although top hats were the dominant hat in the 19th century, other hats became popular for working classes and lower income middle class. “The style of an individual’s hat varied, depending on fashion and their social position, as well as their profession or chosen activity..” ''Goodman 53 of 460'' Other hats that became necessary and popular include the Derby, the straw Boater, and a flat cap with a short brim. In many cases the class, work activity and income could be determined by what kind of hat was on the head of the wearer. For some men, a hat supporting a particular sport or team was important. The Derby or Bowler hat was designed by William and Thomas Bowler, brother shopkeepers in 1849. ''(Goodman 55 of 460)'' It cost less than a top hat but  lasted longer and was soon worn by middle class bankers and clerks. Straw boaters were worn by the aristocracy for casual events and working class factory workers and agricultural laborers. By 1901 working class men had changed their preference to the flat caps which became the most popular hat for the workers. Headdress for men was an essential part of dress for the entire period of the Victorian age, from the 1830s through the end of the century. Judith Flanders describes the hats worn by men in London, <blockquote>It is difficult to bear in mind the importance of hats as not only markers of class and income, but also as indicators of respectability. [509–519] [George Augustus] Sala commented that "every" man throughout the history of the world "must, necessarily and habitually, wear some kind of covering to his head". Postmen wore hats, small children wore hats, field labourers and market gardeners wore hats, cricketers, skaters — all sportsmen — wore hats. It was, self-evidently, impossible to go outdoors without one. ... Those in professional occupations wore pot hats, as did clerks and all those with pretensions to middle-class status. Even doctors' delivery boys wore battered hand-me-down pot hats: "the nap rusty, the band a mournful strip of tarnished lace; but still a Hat", which "stamps him as being associated, in however slender a manner, with a learned profession". Cloth caps were for labourers, for costers and for boys. ... Artisans wore caps made out of paper, which they folded [510–511] themselves and so could easily replace as they became dirty.<ref name=":23" /> (509–511 [of 972]) </blockquote>A pot-hat is a kind of derby or bowler in men's hats. (Lewandowski, 237) ==== Original Text ==== Hats were crucial to a respectable appearance for both men and women. The top hat, for example, was standard formal wear for upper- and middle-class men.<ref name=":4">{{Cite book |last=Steele |first=Valerie |url=https://archive.org/details/fashioneroticism0000stee |title=Victorian Fashion. Fashion and Eroticism: Ideals of Feminine Beauty from the Victorian Era to the Jazz Age |publisher=Oxford University Press |year=1985 |isbn=978-0-19-503530-8 |pages=[https://archive.org/details/fashioneroticism0000stee/page/51 51]–84 |url-access=registration}}</ref> For women, the styles of hats changed over time and were designed to match their outfits. === Women's Hats === For a discussion of the history of plumes and feathers, see [[Social Victorians/Victorian Things#Ostrich Plumes and Prince of Wales's Feathers|Ostrich Plumes and Prince of Wales's Feathers in ''Victorian Things'']]. ==== Original Wikipedia Text ==== During the early Victorian decades, hats were modest in size and design, straw and fabric bonnets being the popular choice. [[Poke bonnet]]s, which had been worn during the late [[Regency period]], had high, small crowns and brims that grew larger until the 1830s, when the face of a woman wearing a poke bonnet could only be seen directly from the front. They had rounded brims, echoing the rounded form of the bell-shaped hoop skirts. Bonnets shrunk at the end of the 1860s and moved to a perched position in the early 1870s as hairstyles grew in scale and intricacy. This led to the popularization of hats, which became the headwear of choice for the remainder of the Victorian era.<ref name="g4223">{{cite book |last=Cunnington |first=Cecil Willett |title=English Women's Clothing in the Nineteenth Century |date=1990-05-01 |publisher=Courier Corporation |isbn=0-486-26323-1 |publication-place=New York |page=}}</ref> [[File:The_London_and_Paris_ladies'_magazine_(Apr_1885)_03.png|thumb|Flower pot style hat of 1885.]] The 1880s saw a hat inspired by the top hat for women known as the flowerpot hat, and the 1890s saw the popularity of the boater. The hats of the late Victorian era were covered with elaborate creations of silk flowers, ribbons, and above all, exotic plumes; hats sometimes included entire exotic birds that had been stuffed. Many of these plumes came from birds in the Florida everglades, which were nearly made entirely extinct by overhunting. By 1899, early environmentalists like [[Adeline Knapp]] were engaged in efforts to curtail the hunting for plumes. By 1900, more than five million birds a year were being slaughtered, and nearly 95 per cent of Florida's shore birds had been killed by [[Plume hunting|plume hunter]]s.<ref>{{cite web|title=Everglades National Park|url=https://www.pbs.org/nationalparks/parks/everglades/|archive-url=https://web.archive.org/web/20090927085907/http://www.pbs.org/nationalparks/parks/everglades/|url-status=dead|archive-date=27 September 2009|publisher=PBS|access-date=7 November 2011}}</ref> == Shoes == The women's shoes of the early Victorian period were narrow and heelless, in black or white satin. By 1850s and 1860s, they were slightly broader with a low heel and made of leather or cloth. Ankle-length laced or buttoned boots were also popular. From the 1870s to the twentieth century, heels grew higher and toes more pointed. Low-cut pumps were worn for the evening.<ref name=":4" /> == Cosmetics == [[Victorian-era cosmetics]] were typically less obvious than ours. However, small amounts of pale face powder or powdered blush were widely used.<ref>{{Cite book |last=Goodman |first=Ruth |title=How to be a Victorian |date=2014 |publisher=Penguin Books |isbn=978-0-670-92136-2 |location=London}}</ref> Tints were sometimes added to face creams. Some cosmetics contained toxic or caustic ingredients like lead, mercury, ammonia, and arsenic {{Citation needed|date=October 2025}}. Hair color ==Mourning black== {{See also |Mourning stationery}} [[File:The royal children in mourning Mar 1862.jpg|thumb|Victoria's five daughters (Alice, Helena, Beatrice, Victoria and Louise), photographed wearing mourning black beneath a bust of their late father, Prince Albert (1862)]] [[File:Mourning dress MET 50.40.3a-b front CP4.jpg|alt=Black Victorian mourning dress|thumb|Mourning Dress, 1894–95]] In Britain, black is the colour traditionally associated with mourning for the dead. The customs and etiquette expected of men, and especially women, were rigid but evolving during much of the Victorian era. The expectations depended on a complex hierarchy of close or distant relationship with the deceased. (Davidoff) The closer the relationship, the longer the mourning period and the wearing of black. The wearing of full black was known as First Mourning, which had its own expected attire, including fabrics, and an expected duration of 4 to 18 months. Following the initial period of First Mourning, the mourner would progress to Second Mourning, a transition period of wearing less black, which was followed by Ordinary Mourning, and then Half-mourning. Some of these stages of mourning were shortened or skipped completely if the mourner's relationship to the deceased was more distant. Half-mourning was a transition period when black was replaced by acceptable colours such as lavender and mauve, possibly considered acceptable transition colours because of the tradition of [[Church of England]] (and [[Catholic Church|Catholic]]) clergy wearing lavender or mauve [[Stole (vestment)|stoles]] for funeral services, to represent the [[Passion (Christianity)|Passion of Christ]].<ref>{{cite web|title=The Colors of the Church Year|url=http://fullhomelydivinity.org/articles/colors.htm|publisher=Consortium of Country Churches|access-date=6 November 2011|archive-date=13 November 2011|archive-url=https://web.archive.org/web/20111113075214/http://fullhomelydivinity.org/articles/colors.htm|url-status=dead}}</ref> The mourning dress worn by Queen Victoria (below, right) "shows the traditional touches of mourning attire, which she wore from the death of her husband, Prince Albert (1819–1861), until her own death."<ref>{{Cite web|url=https://www.metmuseum.org/art/collection/search/155839?&searchField=All&sortBy=Relevance&deptids=8&ft=queen+victoria&offset=0&rpp=20&amp;pos=2|title=Mourning Dress, 1894–95|last=The Metropolitan Museum of Art|date=7 September 2019|website=The Metropolitan Museum of Art|access-date=7 September 2019}}</ref> Dating from 1894–95, Queen Victoria wore this dress as a result of the death of the eldest son of the Prince and Princess of Wales, Eddy, in line to the throne. === Norms for mourning=== ''Manners and Rules of Good Society, or, Solecisms to be Avoided'' (London, Frederick Warne & Co., 1887) gives clear instructions, such as the following:<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–83}}</ref> {| class="wikitable" |- ! Relationship to deceased !! First mourning !! Second mourning !! Ordinary mourning !! Half-mourning |- | Wife for husband || 1-year, 1-month; [[bombazine]] fabric covered with [[Crape|crepe]]; [[widow's cap]], [[lawn cuff]]s, collars || 6 months: less crepe || 6 months: no crepe, silk or wool replaces bombazine; in last 3 months jet jewellery and ribbons can be added || 6 months: colours permitted are grey, lavender, mauve, and black-and-grey |- | Daughter for parent || 6 months: black with black or white crepe (for young girls); no linen cuffs and collars; no jewellery for first 2 months || 4 months: less crepe || – || 2 months as above |- | Wife for husband's parents || 18 months in black bombazine with crepe || – || 3 months in black || 3 months as above |- | Parent for son- or daughter-in-law's parent || – Black armband in representation of someone lost || – || 1-month black || – |- | Second wife for parent of a first wife || – || – || 3 months black || – |} The complexity of these etiquette rules extends to specific mourning periods and attire for siblings, step-parents, aunts and uncles distinguished by blood and by marriage, nieces, nephews, first and second cousins, children, infants, and "connections" (who were entitled to ordinary mourning for a period of "1–3 weeks, depending on level of intimacy"). Men were expected to wear mourning black to a lesser extent than women, and for a shorter mourning period. After the mid-19th century, men would wear a black hatband and black suit, but for only half the prescribed period of mourning expected of women. Widowers were expected to mourn for a mere three months, whereas the proper mourning period expected for widows was up to four years.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–9}}</ref> Women who mourned in black for longer periods were accorded great respect in public for their devotion to the departed, the most prominent example being Queen Victoria herself. It was not uncommon for a widow who did not remarry to wear half-mourning for the rest of her life, except when another death necessitated full mourning. For example, Alexandra, Princess of Wales wore half-mourning for the rest of her life after her eldest son Eddy died in 1894. Empress Elisabeth of Austria did the same, as did Empress Eugénie of France. They reverted to full mourning when appropriate, but they never wore less than half-mourning after their sons' deaths. Women with lesser financial means tried to keep up with the example being set by the middle and upper classes by dyeing their daily dress. Dyers made most of their income during the Victorian period by dyeing clothes black for mourning.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|page=341}}</ref> == Technological advancement == The technological changes that affected the manufacture and consumption of clothing in the Victorian age included the following: * the mass production of fabrics — for example, "by the early 1850s there were thousands of steam-powered looms churning out millions of miles of fabric every year"  [62] * the invention of aniline dyes, which were much more vibrantly colored and resistant to fading than the natural dyes that had been used. — . Invented by chemist [[William Henry Perkin]] in 1856, the first aniline dye mauveine (or mauve) "wash[ed] the fashionable landscape in a haze of purple."<ref name=":22">{{Cite book|title=The Dress Diary: Secrets from a Victorian Woman's Wardrobe|last=Strasdin|first=Kate|publisher=Pegasus Books|year=2023|location=New York, New York}}</ref> (247) Other intense and, to the Victorians, intensely exciting colors followed, but the new synthetic additions to fabric sometimes included chemicals harmful to their wearers. For example, a "bright-magenta hue was achieved by adding arsenical-based chemicals to existing aniline dyes, brightening the already luminous shades – but these left residues themselves, along with a toxic labour trail in their wake."<ref name=":22" /> (255) Perhaps the most famous of these is arsenic green, used on fabrics, wallpapers, and trim: "The craze for artificial foliage to adorn the heads and dresses of women of fashion in the mid-nineteenth century had seen the proliferation of flower workshops, where young women in their hundreds laboured to produce the lifelike green leaves and blooms that would make a fetching headdress or would trail becomingly across the bodice of a gown. The lushness of the green was achieved by the application of a powder, a pigment that was created by mixing copper and the highly toxic chemical, arsenic trioxide. The physical effects of working with this poisonous compound were horrific. Contemporary medical drawings depict the green hue of the skin and dreadful open lesions on the hands of the maker, whilst the daily gradual ingestion of the powder by the flower girls was eventually fatal."<ref name=":22" /> (255) * the invention of a sewing machine that could be used in the home. Although sewing machines were already in use in the clothing industry, in 1858 Isaac Merritt Singer began to sell "lightweight domestic machines" for home sewing, radically increasing women's control over their own dress.<ref name=":24">{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|last2=Storey|first2=Neil R.|publisher=Pen & Sword History|year=2022|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=}}</ref> (91 [of 298]) * the spread of journalism for women and fashion journalism * the Jacquard loom: "French inventor Joseph-Marie Jacquard’s loom attachment mechanized the weaving of figured fabrics by 1804."<ref name=":25" /> (454) Perhaps not at the same scale as these but as important in 1850s designs was a technology that turned iron into steel, which could then be drawn into fine wires.<ref name=":3">{{Cite book|title=The Culture of Fashion|last=Breward|first=Christopher|publisher=Manchester University Press|year=1995|pages=145–180}}</ref> Steel was refined to a malleable state so that thin blades could be curved into concentric circles (called hoops) and connected with wires to form the cage. Technological advancements not only influenced the economy but brought a major change in the fashion styles worn by men and women. As the Victorian era was based on the principles of gender, race and class.<ref>{{cite journal|last1=Graham|first1=P|title=The Victorian Era|url=https://archive.org/details/in.ernet.dli.2015.261548|journal=Digital Library of India}}</ref> Much advancement was in favor of the upper class as they were the ones who could afford the latest technology and change their fashion styles accordingly. In 1830s there was introduction of horse hair crinoline that became a symbol of status and wealth as only the upper-class women could wear it. In 1850s there were more fashion technological advancements hence 1850s could rightly be called a revolution in the Victorian fashion industry such as the innovation of artificial cage crinoline that gave women an artificial hourglass silhouette without layers of petticoats, which was lighter and more hygienic.<ref>{{cite book|last1=Shrimpton|first1=J|title=Victorian Fashion|publisher=Bloomsbury Shire Publications}}</ref> Synthetic dyes, such as [[mauveine]] (aniline purple), were introduced in 1856, adding bright colours to garments. In 1855's ''[[Haute couture]]'' was introduced as tailoring became more mainstream in years to follow.<ref>{{cite book|last1=Aspelund|first1=Karl|title=Fashioning Society|publisher=Fairchild Books}}</ref> Charles Frederick Worth, a prominent English designer, became popular amongst the upper class though its city of destiny always is Paris. Haute couture became popular at the same time that sewing machines were invented.<ref name="Haute Couture">{{cite book|last1=Martin|first1=Richard|last2=Koda|first2=Harold|title=Haute Couture|publisher=The Metropolitan Museum of Art}}</ref> Princess [[Eugénie de Montijo|Eugenie]] of France wore the Englishman dressmaker, Charles Frederick Worth's couture and he instantly became famous in France though he had just arrived in Paris a few years ago. In 1855, Queen Victoria and Prince Albert of Britain welcomed [[Napoleon III]] and Eugenie of France to a full state visit to England. Eugenie was considered a fashion icon in France. Queen Victoria, who had been the fashion icon for European high fashion, was inspired by Eugenie's style and the fashions she wore.{{Citation needed|date=October 2025}} Later, Queen Victoria also appointed Charles Frederick Worth as her dress maker and he became a prominent designer amongst the European upper class. Charles Frederick Worth is known as the father of the haute couture as later the concept of labels were also invented in the late 19th century as custom, made to fit tailoring became mainstream.<ref>{{cite book|last1=Saillard|first1=Olivier|last2=Zazzo|first2=Anne|title=Paris Haute Couture|publisher=Skira Flammarion}}</ref> By the 1860s, when made-to-fit tailoring was popular in Europe, crinolines were considered impractical. In the 1870s, women preferred more slimmer silhouettes, hence bodices grew longer and the polonaise, a skirt and bodice made together, was introduced. In 1870s the Cuirass Bodice, a piece of armour that covers the torso and functions like a corset, was invented. Towards the end of Victoria's reign, dresses were flared naturally as crinolines were rejected by middle-class women. Designers such as Charles Frederick Worth were also against them. All these inventions and changes in fashion led to women's liberation as tailored looks improved posture and were more practical.<ref name="Haute Couture"/> dressmakers, couturiers, modistes == Home decor == {{main|Victorian decorative arts}} Home decor started spare, veered into the elaborately draped and decorated style we today regard as Victorian, then embraced the retro-chic of [[William Morris]] as well as pseudo-[[Japonaiserie]]. == Myths and Oversimplifications == === Modesty === {{main|Victorian morality}} {{Original research|section|date=May 2008}} [[File:1868-skirt-lengths-girl-ages-Harpers-Bazar.gif|thumb|upright|"The proper length for little girls' skirts at various ages", from ''[[Harper's Bazaar]]'', showing a 1900 idea of how the hemline should descend towards the ankle as a girl got older]]Many myths and exaggerations about the period persist to the modern day. Examples include the idea of men's clothing is seen as formal and stiff, women's as elaborate and over-done; clothing covered the entire body, and even the glimpse of an ankle was scandalous. Critics contend that [[corset]]s constricted women's bodies and lives. Homes are described as gloomy, dark, cluttered with massive and over-ornate furniture and proliferating [[bric-a-brac]]. Myth has it that even piano legs were scandalous, and covered with tiny [[pantalette]]s. === Tight Lacing === Tight-lacing, which was not possible until the development of the grommet in 1828, was famously controversial in the Victorian age, generating many column inches of profitable newspaper copy, in part because it was (and still is) fetishistic and subversive in that adolescent girls used it as a means of rebellion and upper-working- or lower-middle-class shop girls saw it as a means of upward mobility.<ref name=":21">{{Cite book|title=Fashion and Fetishism: Corsets, Tight-Lacing and Other Forms of Body-sculpture|last=Kunzle|first=David|publisher=History Press|year=2013|isbn=978 0 7524 9545 3|location=Stroud, Gloucestershire|pages=}}</ref> (71 [of 1182]) No evidence exists that tight lacing was widespread or particularly dangerous.<ref name=":21" /> () In truth, men's formal clothing may have been less colourful than it was in the previous century, but brilliant [[waistcoat]]s and [[cummerbund]]s provided a touch of colour, and [[smoking jacket]]s and [[robe|dressing gown]]s were often of rich Oriental [[brocade]]s. This phenomenon was the result of the growing textile manufacturing sector, developing mass production processes, and increasing attempts to market fashion to men.<ref name="shannon597"/> Corsets stressed a woman's sexuality, exaggerating hips and bust by contrast with a tiny waist. Women's [[evening gown]]s bared the shoulders and the tops of the breasts. The [[jersey dress]]es of the 1880s may have covered the body, but the stretchy novel fabric fit the body like a glove.<ref>{{cite book |last=Gernsheim |first=Alison |title=Victorian & Edwardian Fashion: A Photographic Survey |year=1981 |publisher=Dover Publications |location=New York |page=65|edition=New |isbn=0-486-24205-6}}</ref> Home furnishing was not necessarily ornate or overstuffed. However, those who could afford lavish draperies and expensive ornaments, and wanted to display their wealth, would often do so. Since the Victorian era was one of increased social mobility, there were ever more ''[[nouveaux riches]]'' making a rich show. The items used in decoration may also have been darker and heavier than those used today, simply as a matter of practicality. London was noisy and its air was full of [[soot]] from countless coal fires. Hence those who could afford it draped their windows in heavy, sound-muffling curtains, and chose colours that didn't show soot quickly. When all washing was done by hand, curtains were not washed as frequently as they might be today. There is no actual evidence that piano legs were considered scandalous. Pianos and tables were often draped with [[shawl]]s or cloths—but if the shawls hid anything, it was the cheapness of the furniture. There are references to lower-middle-class families covering up their [[pine]] tables rather than show that they couldn't afford [[mahogany]]. The piano leg story seems to have originated in the 1839 book, ''A Diary in America'' written by Captain [[Frederick Marryat]], as a satirical comment on American prissiness.<ref>{{cite book |last1=Marryat |first1=C.B. |title=A Diary in America: With Remarks on Its Institutions |date=1839 |publisher=Longman, Orme, Brown, Green, and Longmans |location=London, England |volume=2 |pages=246–247 |url=https://books.google.com/books?id=2-VEAAAAIAAJ&pg=PA246}} From pp. 246-247: "I was requested by a lady to escort her to a seminary for young ladies, and on being ushered into the reception-room, conceive my astonishment at beholding a square piano-forte with four ''limbs''. However, that the ladies who visited their daughters, might feel in its full force the extreme delicacy of the mistress of the establishment, and her care to preserve in their utmost purity the ideas of the young ladies under her charge, she had dressed all these four limbs in modest little trousers, with frills at the bottom of them!"</ref> Victorian manners may have been as strict as imagined—on the surface. One simply did not speak publicly about sex, childbirth, and such matters, at least in the respectable middle and upper classes. However, as is well known, discretion covered a multitude of sins. Prostitution flourished. Upper-class men and women indulged in [[adultery|adulterous]] liaisons. == Gallery == {{gallery |2=A mid-Victorian interior: ''Hide and Seek'' by [[James Tissot]], c. 1877 Image:Winterhalter Elisabeth.jpg|3=Dress designed by [[Charles Frederick Worth]] for [[Elisabeth of Bavaria|Elisabeth of Austria]] painted by [[Franz Xaver Winterhalter]].|4=File:Frith A Private View detail.jpg|5=[[William Powell Frith]]'s painting of 1883 contrasts women's [[Aesthetic dress]] (left and right) with fashionable attire (center).|6=File:Tissot lilacs 1875.jpg|7=Day dress, c. 1875 [[James Tissot]] painting.|8=File:James Abbot McNeill Whistler 011.jpg|9=[[James McNeill Whistler|Whistler]]'s [[Portrait of Lady Meux]], 1882 Image:Jeanna_Samary-Renoir.png|10=[[Pierre-Auguste Renoir|Renoir]]'s portrait of [[Jeanne Samary]] in an [[evening gown]], 1878|11=File:Melville_-_Queen_Victoria.jpg|12=Portrait by [[Alexander Melville (artist)|Alexander Melville]] of [[Victoria of the United Kingdom|Queen Victoria]], 1845|13=File:Henry Treffry Dunn Rossetti and Dunton at 16 Cheyne Walk.jpg|14=An artistic interior: [[Dante Gabriel Rossetti]] reading to [[Theodore Watts-Dunton]] in the drawing room at No. 16 [[Cheyne Walk]], 1882|15=File:Punch - Masculine beauty retouched1.png|16=Men's swimwear: Cartoon from ''[[Punch (magazine)|Punch]]'' by [[George du Maurier]]}} == See also == * [[Emily Clapham]] * [[Victorian decorative arts]] * [[Victorian dress reform]] * [[Victorian morality]] * [[Victoriana]] * [[Women in the Victorian Era]] * [[Charles Frederick Worth]] === Time periods === * [[1830s in fashion]] * [[1840s in fashion]] * [[1850s in fashion]] * [[1860s in fashion]] * [[1870s in fashion]] * [[1880s in fashion]] * [[1890s in fashion]] === Women's clothing === * [[Corset]] * [[Corset controversy]] * [[Tightlacing]] * [[Bloomers (clothing)|Bloomers]] * [[Bodice]] === Contemporary interpretations === * [[Steampunk]] * [[Neo-Victorian]] * [[Lolita Fashion|Lolita]] == References == {{Reflist}} == Further reading == *{{cite book |author=Phipps, Elena| title= ''From Queen to Empress: Victorian dress 1837-1877'' | location=New York | publisher=The Metropolitan Museum of Art | year=1988 | isbn=0870995340| url= http://libmma.contentdm.oclc.org/cdm/compoundobject/collection/p15324coll10/id/69547/rec/235 | display-authors=etal}} * Sweet, Matthew – ''Inventing the Victorians'', St. Martin's Press, 2001 {{ISBN|0-312-28326-1}} == External links == * [http://www.victorians.co.uk/victorian-fashion Victorian Fashion] {{Webarchive|url=https://web.archive.org/web/20180407223711/http://www.victorians.co.uk/victorian-fashion |date=7 April 2018 }} * [https://www.victorianvoices.net/topics/fashion/index.shtml VictorianVoices.net] – Fashion articles and illustrations from Victorian periodicals; extensive fashion image gallery * [http://www.cracked.com/article_19575_5-ridiculous-sex-myths-from-history-you-probably-believe.html Victorian myths] * [http://www.victorianstation.com/lifestylemenu.htm Victorian fashion, etiquette, and sports] {{Webarchive|url=https://web.archive.org/web/20180103162620/http://www.victorianstation.com/lifestylemenu.htm |date=3 January 2018 }} * [http://www.thesmartset.com/article/article12180701.aspx Background on "A Diary in America"] * [http://www.mccord-museum.qc.ca/en/keys/webtours/VQ_P2_17_EN.html Form and Fashion] — the evolution of women's dress during the 19th century (many photographs) * [http://www.mccord-museum.qc.ca/en/keys/games/jeu2/ Educational Game: Mix and Match] — build a 19th-century dress using a virtual mannequin * {{cite web |publisher= [[Victoria and Albert Museum]] |url= http://www.vam.ac.uk/content/articles/v/victorian-dress-at-v-and-a/ |title= Victorian Dress |work= Fashion, Jewellery & Accessories |date= 14 January 2011 |access-date= 2011-04-03}} *[http://cv.vic.gov.au/stories/creative-life/fashion-detective-fashion-fiction-and-forensics/ Fashion detective: Fashion, Fiction and Forensics in nineteenth century Australian fashion] on Culture Victoria {{Timeline of clothing and fashion|state=collapsed}}{{Victorian era|state=collapsed}} [[Category:Victorian fashion| ]] [[Category:19th-century fashion|*]] [[Category:1900s fashion]] [[Category:History of Western fashion]] [[Category:19th century in the arts]] =From ''Women in the Victorian era''= ===Victorian women's fashion=== {{Multiple issues|{{tone|date=March 2023}} {{more footnotes needed|date=March 2023}}|section=y}}{{Further|Victorian fashion}} The ideal Victorian woman was pure, chaste, refined, and modest. This ideal was supported by etiquette and manners. The etiquette extended to the pretension of never acknowledging the use of undergarments (sometimes generically referred to as "unmentionables"). The discussion of such a topic, it was feared, would gravitate towards unhealthy attention on anatomical details. As one Victorian lady expressed it: "[those] are not things, my dear, that we speak of; indeed, we try not even to think of them", in contrast to current norms.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=20}}</ref> The pretence of avoiding acknowledgement of anatomical realities met with embarrassing failure on occasion. In 1859, the Hon. Eleanor Stanley wrote about an incident where the [[Louisa Cavendish, Duchess of Devonshire|Duchess of Manchester]] moved too quickly while manoeuvring over a [[stile]], tripping over her large [[hoop skirt]]: {{blockquote|[the Duchess] caught a hoop of her cage in it and went regularly head over heels lighting on her feet with her cage and whole petticoats above, above her head. They say there was never such a thing seen – and the other ladies hardly knew whether to be thankful or not that a part of her undergarments consisted in a pair of scarlet tartan [[knickerbockers (clothing)|knickerbockers]] (the things Charlie shoots in) which were revealed to the view of all the world in general and the [[Aimable Pélissier|Duc de Malakoff]] in particular".<ref>{{cite book|last=Cunnington|first=C. Willett|title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations|year=1990|publisher=Dover Publications|isbn=978-0-486-26323-6|pages=20–1}}</ref>}} However, despite the fact that Victorians considered the mention of women's undergarments in mixed company unacceptable, men's entertainment made great comedic material out of the topic of ladies' [[bloomers (clothing)|bloomers]], including men's magazines and music hall skits.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=22}}</ref> Victorian women's clothing followed trends that emphasised elaborate dresses, skirts with wide volume created by the use of layered material such as [[crinoline]]s, hoop skirt frames, and heavy fabrics. Because of the impracticality and health impact of the era's fashions, a [[Victorian dress reform|dress reform movement]] began among women. The ideal silhouette of the time demanded a narrow waist, which was accomplished by constricting the abdomen with a laced [[corset]]. While the silhouette was striking, and the dresses themselves were often exquisitely detailed creations, the fashions were cumbersome. At best, they restricted women's movements and at worst, they had a harmful effect on women's health. Physicians turned their attention to the use of corsets and determined that they caused several medical problems: compression of the thorax, restricted breathing, organ displacement, poor circulation, and prolapsed uterus.<ref name="O'Connor"/> Articles advocating the reform of women's clothing by the British National Health Society, the Ladies' Dress Association, and the [[Rational Dress Society]] were reprinted in ''The Canada Lancet'', Canada's medical journal. In 1884, Dr J. Algernon Temple of Toronto even voiced concern that the fashions were having a negative impact on the health of young women from the working classes. He pointed out that a young working-class woman was likely to spend a large part of her earnings on fine hats and shawls, while "her feet are improperly protected, and she wears no flannel petticoat or woollen stockings".<ref name="O'Connor"/> [[File:Bloomers.jpg|thumb|1850s illustration of a woman wearing [[bloomers]]]] [[Florence Pomeroy]], Lady Haberton, was president of the Rational Dress movement in Britain. At a National Health Society exhibition held in 1882, Viscountess Haliburton presented her invention of a "[[divided skirt]]", which was a long skirt that cleared the ground, with separate halves at the bottom made with material attached to the bottom of the skirt. She hoped that her invention would become popular by supporting women's freedom of physical movement, but the British public was not impressed by the invention, perhaps because of the negative "unwomanly" association of the style with the American [[Bloomers]] movement.<ref>{{cite book|last=Murray|first=Janet Horowitz|title=Strong-Minded Women and Other Lost Voices from 19th Century England|year=1982|publisher=Pantheon Books|location=New York|isbn=0-394-71044-4|pages=[https://archive.org/details/strongmindedwome00jane/page/68 68–70]|url=https://archive.org/details/strongmindedwome00jane/page/68}}</ref> [[Amelia Jenks Bloomer]] had encouraged the wearing of visible bloomers by feminists to assert their right to wear comfortable and practical clothing, but it was no more than a passing fashion itself among radical feminists. The movement to reform women's dress would persist and have long-term success, however; by the 1920s, [[Coco Chanel]] was successful at selling a progressive, far less restrictive silhouette that abandoned the corset and raised hemlines. The new silhouette symbolised modernism for trendy young women and became the 20th century standard. Other Paris designers continued reintroducing pants for women and the trend was gradually adopted over the next century. Fashion trends, in one sense, travelled "full circle" over the course of the Victorian era. The popular women's styles during the [[Georgian era]], and at the very beginning of Victoria's reign, emphasized a simple style influenced by flowing gowns worn by women in [[Ancient Greek clothing|Ancient Greece]] and [[Clothing in ancient Rome|Rome]]. The [[Empire waist]] silhouette was replaced by a trend towards ornate styles and an artificial silhouette, with the restrictiveness of women's clothing reaching its low point during the mid-century passion for narrow corseted waists and hoop skirts. The iconic wide-brimmed women's hats of the later Victorian era also followed the trend towards ostentatious display. Hats began the Victorian era as simple [[Bonnet (headgear)|bonnets]]. By the 1880s, milliners were tested by the competition among women to top their outfits with the most creative (and extravagant) hats, designed with expensive materials such as silk flowers and exotic plumes such as ostrich and peacock. As the Victorian era drew to a close, however, fashions were showing indications of a popular backlash against excessive styles. Model, actress and socialite [[Lillie Langtry]] took London by storm in the 1870s, attracting notice for wearing simple black dresses to social events. Combined with her natural beauty, the style appeared dramatic. Fashions followed her example (as well as Queen Victoria's wearing of mourning black later in her reign). According to [[Harold Koda]], the former Curator-in-chief of the [[Costume Institute at The Met|Metropolitan Museum of Art's Costume Institute]],<ref>{{cite web|url=http://www.metmuseum.org/about-the-museum/press-room/exhibitions/2014/death-becomes-her|title=Death Becomes Her: A Century of Mourning Attire : October 21, 2014-February 1, 2015|website=Metmuseuim.org|access-date=7 November 2021}}</ref> "The predominantly black palette of [[mourning]] dramatizes the evolution of period silhouettes and the increasing absorption of fashion ideals into this most codified of etiquettes," said Koda, "The veiled widow could elicit sympathy as well as predatory male advances. As a woman of sexual experience without marital constraints, she was often imagined as a potential threat to the social order." ====Evolution of Victorian women's fashion==== <gallery> File:Fashion plate December 1844.jpg|Ladies' December Fashions (1844). Hand-coloured steel engraving from a women's magazine. File:Thegalleryofhmscalcutta james tissot 1876.jpg|''[[The Gallery of HMS Calcutta]]'' by [[James Tissot]] (1876). [[Bustle]]s were fashionable in the 1870s and 1880s. File:Mrs lillie langtry george frederic watts 1880.jpg|''Mrs. Lillie Langtry'' by [[George Frederic Watts]] (1880). File:Five-women-on-queenslander-steps-r.jpg|Fashionable women in [[Queensland]], Australia around 1900. </gallery> {{Short description|Irish writer (born 1963)}} {{Use Irish English|date=August 2025}} {{Use dmy dates|date=August 2025}} {{Infobox writer | name = Darach Ó Scolaí | image = Darach Ó Scolaí.JPG | alt = Man holding prize-winning book | caption = Ó Scolaí in 2019 | birth_name = Darach Ó Scolaí | birth_date = {{Birth date and age|1963|df=y}} | birth_place = [[County Galway]], The Republic of Ireland | death_date = | death_place = | occupation = Writer, artist, publisher | alma_mater = [[University of Galway]] | years_active = 1998–present | genre = Novel, retelling, translation, play, screenplay, illustrated book for children and adults | other_names = | spouse = | children = 3 | awards = [[Awards and Honors received by Darach Ó Scolaí|Awards and Honors]] | signature = | website = }}[[File:Darach Ó Scolaí.JPG|thumb|Darach Ó Scolaí, holding ''Oileán an Órchiste'' (his translation of Robert Louis Stevenson's ''Treasure Island'')]] == Darach Ó Scolaí == Darach Ó Scolaí (<small>Irish:</small> [/ˈda.rax/ /oː/ /sˠkˠoː/l̪ˠəi/]; born 1963<ref>{{Cite web|url=https://portraidi.ie/en/darach-o-scolai/|title=Darach Ó Scolaí|date=20 October 2017|website=Portráidí (Portraits of Irish-Language Writers)|access-date=1 August 2025}}</ref>) is an Irish author who works in a number of genres, from novels, plays and screenplays to illustrated books for children and adults. He began his literary career in 1998 writing screenplays, stage plays, retellings and translations; he began to publish novels in 2008. Ó Scolaí is widely recognized as a leading figure in contemporary Irish literature, known as “one of the most important Irish language writers of his generation”<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=2022|title=? Suil an Daill: Constant Tensions and Shifting Allegiances|url=https://booksirelandmagazine.com/suil-an-daill-constant-tensions-and-shifting-allegiances/|journal=Books Ireland}}</ref> and "one of the great Irish language novelists [duine d’úrscéalaithe móra na Gaeilge]."<ref name=":17" /> His writing has been called “the high literature of the Irish language.”<ref>Ó Coimín, Maitiú. ''Nós'' 2 February 2018). Qtd. in "Táin Bó Cuailnge." ''Leabhar Breac''. Retrieved 25 August 2025.</ref> Much of his fiction is based on a knowledge of traditional Irish tales and narrative practices as well as Irish history. He specializes in literary and [[wikipedia:Historical_fiction|historical fiction]], or as novelist Alan Titley says, Ó Scolaí’s “peak (for now), or at least his greatest imaginative interest, is the historical novel [tá an chuma air gurb é a bhuaic (go fóill), nó ar a laghad, a mhórspéis samhlaíochta, an t-úrscéal staire].”<ref name=":11">{{Cite journal|last=Titley|first=Alan|date=Fall 2020|title=An Stíl Go Deo!: Soather Dharach Uí Scolaí (The style would be forever!: Worker Darach Ó Scolaí)|url=https://www.jstor.org/stable/27046090|journal=Comhar|volume=80, No. 10|pages=27|via=JSTOR}}</ref> His retellings of old stories and tales from their original Middle and Early-Modern Irish into Modern Irish ([[wikipedia:Irish_language|Gaeilge]]) are respected for their accessibility to students and language learners as well as for their artistry. Ó Scolaí also regularly reviews books and lectures and writes on literature and culture. Beyond his writing, Ó Scolaí is a publisher and has co-produced a number of film, television shows and stage plays. == Life == Ó Scolaí was born in Dublin and raised in the Galway [[wikipedia:Gaeltacht#Galway Gaeltacht|Gaeltacht]] (Irish-speaking) regions of Cois Fharraige on the north shore of Galway Bay, in the Republic of Ireland, where he lives now with his wife and children in Lochán Beag (Indreabhán).<ref name=":7">{{Cite journal|date=30 October 2024|title=Duais don úrscéal liteartha is fearr buaite ag Darach Ó Scolaí ag Oireachtas na Samhna|url=https://tuairisc.ie/duais-don-ursceal-liteartha-is-fearr-buaite-ag-darach-o-scolai-ag-oireachtas-na-samhna/|journal=Tuairisc}}</ref><ref>{{Cite journal|last=Ní Scolaí|first=Aifric|date=2024|title=Darach Ó Scolaí|url=https://www.taiscecf.ie/ealaiontoiri?category=Scr%C3%ADbhneoir|journal=Taisce Chois Fharraige}}</ref> He graduated the [[wikipedia:University_of_Galway|University of Galway]] (then University College Galway) with a B.A. in 1983.<ref>{{Cite web|url=https://www.linkedin.com/in/darach-ó-scolaí-20026920/|title=Darach Ó Scolaí|last=Ó Scolaí|first=Darach|date=August 2025|website=LinkedIn}}</ref> === Writing and Publishing === Ó Scolaí writes in Irish ([[wikipedia:Irish_language|Gaeilge]]), his native language, and lives in an area defined for the predominant presence of Irish as the vernacular language, the language spoken at home. Irish was the language of his parents' home and is the language of children as well. He is fluent in Irish and English and conversant in French. None of his works has been translated into English. ==== Leabhar Breac ==== In 1995 Darach Ó Scolaí and his brother Caomhán Ó Scolaí — a [[wikipedia:Typography|typographer]] and designer — founded the publishing house Leabhar Breac at Indreabhán (Inverin), County Galway. Their father “Séamas Ó Scolaí was an editor at An Gúm and worked on the Irish-English dictionary team [bhí a n-athair Séamas Ó Scolaí ina eagarthóir sa Ghúm agus d’oibrigh sé ar fhoireann an fhoclóra Gaeilge-Béarla].”<ref name=":0">{{Cite web|url=https://leabharbreac.com/en/about-us/|title=About Us|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> Darach Ó Scolaí has been publisher and literary editor at Leabhar Breac since its founding. Named for [[wikipedia:An_Leabhar_Breac|An Leabhar Breac (The Speckled Book)]], Leabhar Breac publishing house has more than 140 books in print.<ref name=":0" /> Leabhar Breac aims to publish Irish-language books that meet “a high literary and artistic standard.”<ref name=":0" /> Besides the content, Leabhar Breac is known for the typically "superb [thar cionn]" quality of the design and production of the "physical book [leabhar fisiciúil]."<ref name=":8">{{Cite journal|last=Ní Mhuilneoir|first=Gráinne|date=30 July 2024|title=‘Bláthnaid’ – leabhar álainn i sraithín álainn faoi mhná|url=https://tuairisc.ie/blathnaid-leabhar-alainn-i-sraithin-alainn-faoi-mhna/|journal=Tuairisc}}</ref> Its books regularly win awards for literary and artistic quality. Leabhar Breac also publishes translations for children and adults from various early versions of Irish as well as from French and English (and has published translations of books for young readers from Spanish, Catalan, and Italian as well). Leabhar Breac prints its books in Ireland. === Stage and Screen === ==== Rosg ==== In 1998 along with Ciarán Ó Cofaigh,<ref name=":1">{{Cite web|url=http://www.rosg.ie/en/about/History_6/|title=About Us: History|date=July 2025|website=Rosg|access-date=1 August 2025}}</ref> Ó Scolaí co-founded the film and television production company [http://www.rosg.ie/en/ Rosg] and was co-director until 2006. Rosg produced Ó ScolaÍ’s films ''Cosa Nite'' (1999), ''An Leabhar'' (2001) and ''Na Cloigne'' (2010). He left Rosg in 2006 to devote his time to other artistic activities. ==== Ealaín ar Oileán ==== In 2004, along with Val Balance, Ó Scolaí co-founded the annual artists' symposium Ealaín ar Oileán (trans., Art on an Island). The Irish-language symposium was held annually in the Áras Éanna arts and cultural center on Inis Oírr ([[wikipedia:Inisheer|Inisheer]], the smallest of the [[wikipedia:Aran_Islands|Aran Islands]]) from 2004 to 2013. Ó Scolaí was its co-director from its founding<ref>{{Cite web|url=https://ga.wikipedia.org/wiki/Darach_Ó_Scolaí.|title=Darach Ó Scolaí|date=3 February 2024|website=Vicipéid|access-date=1 July 2025}}</ref> until 2013. Besides being its co-director, Ó Scolaí has taken part in this conference as an artist<ref>{{Cite journal|date=16 January 2005|title=Darach Ó Scolaí|url=https://web.archive.org/web/20050116163252/http://bliainiris.com/authors/darach_oscolai.html|journal=Bliainiris}}</ref> and writer<ref name=":2">{{Cite web|url=http://ealainaroilean.ie/ealainaroilean.html|title=The Conference|date=7 September 2013|website=Ealaín ar Oileán|archive-url=https://web.archive.org/web/20130907083744/http://ealainaroilean.ie/ealainaroilean.html|archive-date=7 September 2013|access-date=1 August 2025}}</ref>. ==== Salamandar ==== In 2006 Ó Scolaí founded the stage production company Salamandar and directed his own play ''An Braon Aníos''. His plays ''An tSeanbhróg'' (2009) and ''Craos'' (2008) were also produced by Salamandar.<ref name=":19">{{Cite web|url=https://leabharbreac.com/en/product-category/darach-o-scolai/|title=Darach Ó Scolaí|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> == Works == === Novels === * [[wikipedia:An_Cléireach|''An Cléireach'' (trans., ''The Clerk'')]], Leabhar Breac, 2007. The Oireachtas Prize for Literary Fiction, 2007; The Ó Súilleabháin Award (Book of the Year) in 2008, and "named as ‘the best novel since the turn of the Century’ by Comhar."<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-cleireach/|title=An Cléireach - Leabhar Breac - Irish language novel|website=Leabhar Breac|language=en-US|access-date=2025-10-24}}</ref> * ''Na Comharthaí'' (trans., ''The Signs''), Leabhar Breac, 2014. * ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. The Oireachtas Prize for Literary Fiction, 2019.<ref name=":4">{{Cite web|url=https://leabharbreac.com/en/shop/fiction/suil-an-daill/|title=Súil an Daill|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Bódléar'', Leabhar Breac, 2024. The Oireachtas Prize for Literary Fiction, 2024<ref name=":7" />; The Ó Súilleabháin Award (Book of the Year) in 2025; featured in the 2025 Listen-Up Irish Summer Challenge for students of the Irish language.<ref>{{Cite news|url=https://connachttribune.ie/novel-approach-helps-people-learn-irish-in-a-creative-way/|title=Novel approach helps people learn Irish in a creative way|last=Murphy|first=Judy|date=3 October 2025|work=Connaught Tribune|access-date=24 October 2025}}</ref> === Retellings, Translations and Editions === The retellings and translations are into modern Irish. * ''Feis Tigh Chonáin'' (trans., ''The Feast of Conán's House''), Leabhar Breac, 2000; a retelling of a 15^th-century tale from the [[wikipedia:Fenian_Cycle|Fenian Cycle]].<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/feis-tigh-chonain/|title=Feis Tigh Chonáin|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''An Ceithearnach Caolriabhach'' (trans., ''The Narrow-Striped Kern''), Leabhar Breac, 2002; a retelling from c. 1500, also illustrated by Darach Ó ScolaÍ.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-ceithearnach-caolriabhach/|title=An Ceithearnach Caolriabhach|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), Leabhar Breac, 2017, both a modern edition of an 11th-century epic and an annotated edition.<ref name=":3">{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/tain-bo-cuailnge-2-2/|title=Táin Bó Cuailnge|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> "''Táin Bó Cuailnge'' won the Aodán Mac Poilín Memorial Prize 2017."<ref name=":19" /> * ''Deirdre'', Leabhar Breac, 2023, a “picture book for adults” with artist Anastasia Melnykova.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/deirdre/|title=Deirdre|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Part of the [[wikipedia:Ulster_Cycle|Ulster Cycle]], ''Deirdre'' is a retelling of the story of possibly the most widely known Irish figure from the early tales and sagas.<ref>{{Cite book|title=A Dictionary of Celtic Mythology|last=MacKillop|first=James|publisher=Oxford University Press|year=2004|isbn=9780198609674|pages=181}}</ref> * ''Bláthnaid'', Leabhar Breac, 2024, a “picture book for adults” with artist Anastasia Melnykova; “one of the great stories of the [[wikipedia:Ulster_Cycle|Ulster Cycle]].”<ref name=":4" /> * ''Sadhbh,'' Leabhar Breac, 2025, a picture book for adult readers, illustrated by Alé Mercado; a retelling of the medieval tale ''Ceasacht Inghine Ghuile (''trans., ''The Complaint of Guile's Daughter'').<ref name=":5">{{Cite web|url=https://leabharbreac.com/en/tales-of-wonder/|title=Tales of Wonder|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Eoghan Béal'', Leabhar Breac, 2025, a picture book for adult readers illustrated by Alé Mercado<ref name=":5" />; a retelling of the medieval tale ''[https://ga.wikipedia.org/wiki/Caithr%C3%A9im_Cellaig Cathréim Ceallaigh]'' from ''The Yellow Book of Leacan.''<ref name=":5" /> === For Young Readers === Ó Scolaí has written illustrated books for young readers (8–10 years old) in two series, the Fionn Series and the Scéalta Staire series, and translated a large number of classics and popular books for children of all ages. The number of these written and translated works suggests a commitment to children and their literacy in Irish. The Fionn Series “is a retelling ... of the great legends of the Fianna for the young Irish readers of today.”<ref name=":6">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/doiteoir-na-samhna/|title=Dóiteoir na Samhna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> [[wikipedia:The_Boyhood_Deeds_of_Fionn|Macgnímartha Finn (The Boyhood Deeds of Fionn)]] is a medieval story in the [[wikipedia:Fenian_Cycle|Fenian Cycle]]. * ''An Bradán Feasa'' (trans., ''The Salmon of Knowledge''), Leabhar Breac, 2010, “shortlisted for the Réics Carlo award 2010.”<ref name=":9">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/an-bradan-feasa/|title=An Bradán Feasa|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Dóiteoir na Samhna'' (trans., ''The Halloween Burner''), 2010.<ref name=":6" /> * ''Bodach an Chóta Lachna'' (trans., ''The Churl in the Dun Coat''), 2011.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/|title=Bodach an Chóta Lachna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> The Scéalta Staire (Historical Stories) series<ref name=":9" /> * ''Mánas Ó Dónaill'', 2000. * ''Seán Ó Néill'', Leabhar Breac, 2000. * ''Gráinne Mhaol Ní Mháille'', Leabhar Breac, 2003. * ''Tadhg Dall Ó hUiginn'', Leabhar Breac, 2003. ==== Translations ==== * Robert Louis Stevenson, ''Oileán an Órchiste'' (trans. of ''Treasure Island''), Leabhar Breac, 2014.<ref>{{Cite journal|date=2025-06-19|title=Oireachtas na Gaeilge|url=https://en.wikipedia.org/w/index.php?title=Oireachtas_na_Gaeilge&oldid=1296394643|journal=Wikipedia|language=en}}</ref> * Robert Louis Stevenson, ''An Fuadach'' (trans. of ''Kidnapped''), Leabhar Breac, 2016. * Clement Clarke Moore, ''Cuairt San Nioclás'' (trans. of ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas"), Leabhar Breac, 2022. '''''The Corto Maltese Graphic Novels''''' Written in Italian by Hugo Pratt and translated by Ó Scolaí, both adults and teenagers read this series of Italian adventure graphic novels.<ref>{{Cite journal|date=2025-07-01|title=Corto Maltese|url=https://en.wikipedia.org/w/index.php?title=Corto_Maltese&oldid=1298285365|journal=Wikipedia|language=en}}</ref> Ó Scolaí's '''translation of ''Corto Maltese''''' was listed in 2017 among "The 30 Irish books that Irish people love."<ref>{{Cite journal|last=Ó Murchú|first=Eoin P.|date=09/06/2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil [The 30 Irish books that Irish people love]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * Hugo Pratt, ''Corto: Port na Farraige Goirt'', Leabhar Breac, 2013. * Hugo Pratt, ''Corto: The Golden House in Samarkand'', 2014. * Hugo Pratt, ''Corto: Na Liopard-Fhir ó Rufiji'' (trans. of ''Corto: The Leopard Men of Rufiji''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: In Ainm Dé Uilthrócairigh'' (trans. of ''Corto: In the Name of God All-Merciful''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Tóraíocht Eile'' (trans. of ''Corto: Another Quest''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Sa tSibéir'' (trans. of ''Corto: In Siberia''), Leabhar Breac, 2016. '''''Other Translations for Children''''' Ó Scolaí has translated into Irish six books from the ''Le Pavillon Noir'' (trans., ''Jolly Roger'') series by Alain Surget; four books from the ''Catalan First Steps'' series by Enric Lluch Girbés and the ''Caitlín & Cormac'' series by Joan Carles; three books from the ''Louisette le Taupe'' series by Bruno Heitz, and three books from the ''Loup'' series by Orianne Lallemand. === Plays and Screenplays === ==== Stage Plays ==== Ó Scolaí was writer and director of the original productions of two plays in the ''Trí Bhraon'' (trans., ''Three Drops'') trilogy; ''Coinneáil Orainn'' was directed by Darach Mac Con Iomaire and staged by An Taibhdhearc. All three plays have been published in book form by Leabhar Breac. * ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32553|title=Coinneáil Orainn|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> The first play in the ''Trí Bhraon'' (''Three Drops'') trilogy. [[wikipedia:Taibhdhearc_na_Gaillimhe|An Taibhdhearc]], the national Irish-language theatre of Ireland, toured the country in 2005 with ''Coinneáil Orainn''.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/coinneail-orainn/|title=Coinneáil Orainn|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Walter Macken Prize, 2005; BBC Stewart Parker Award, 2006.<ref>{{Cite web|url=https://irishplayography.com/person/darach-scola|title=Darach Ó Scolaí|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> * ''Branwen'', 2006, by Darach Ó Scolaí and Ifor ap Glyn, in Irish, Welsh and English, co-produced by Project Arts Centre and Llwyfan Gogledd Cymru, toured the Republic of Ireland and Wales.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32418|title=Branwen|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An Braon'' Aníos (trans., ''Rising Damp''), 2006, directed by Ó Scolaí.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32461|title=An Braon Aníos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The second play in the ''Trí Bhraon'' (''Three Drops'') trilogy. “The Salamandar company toured the country in 2006-07 with this play, and Salamandar also produced a radio version of the play for RTÉ Raidió na Gaeltachta in 2009.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/an-braon-anios/|title=An Braon Aníos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Craos'' (trans., ''Gluttony''), 2008, directed by Ó Scolaí.<ref name=":13">{{Cite web|url=https://irishplayography.com/play?playid=32867|title=Craos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The third play in the ''Trí Bhraon'' (''Three Drops'') trilogy, it toured to Cork and Belfast.<ref name=":13" /> A review of the 2008 Salamander performance in the ''Irish Times'' says, “a humorous play which offers plenty to think about, fine acting, and sparklingly witty dialogue.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/craos-2/|title=Craos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''A+E'', 2008, by Ríonach Ní Néill and Darach Ó Scolaí, "dance and music drama," co-produced by Ciotóg and Salamandar.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32962|title=A+E|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An tSeanbhróg'' (trans., ''The Old Shoe''), 2009, produced by Salamander<ref>{{Cite web|url=https://irishplayography.com/play?playid=33042|title=An tSeanbhróg|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> and staged in the Axis Arts Centre, Dublin, and the Letterkenny Arts Centre. * '''In ''Mhuir Fhíondorcha/The Wine-Dark Sea: The Homer Project'', Ó Scolaí's translation of Homer's Cyclops story, performed at the 2019 IMRAM festival'''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/books/imram-a-festival-celebrating-the-irish-language-1.4047610|title=Imram: a festival celebrating the Irish language. Liam Carson reveals the myths and legends appearing in this year’s programme|last=Carson|first=Liam|date=11 October 2019|work=The Irish Times|access-date=15 October 2025}}</ref> ==== Screenplays ==== * ''Cosa Nite'' (trans., ''Washed Feet''), short film, 1998 (dir. Dearbhla Walsh, prod. Ciarán Ó Cofaigh, Rosg); "a prose version of ''Cosa Nite'' was published (Rosg 2000)."<ref name=":9" /> Nominated for an Irish Film and Television Award.<ref>{{Citation|title=Cosa Nite (Short 1998) - Awards - IMDb|url=https://www.imdb.com/title/tt0191917/awards/|accessdate=2025-08-25|language=en-US}}</ref> * ''Na Glúnta'' (trans., ''The Generations''), 2001<ref>{{Cite web|url=https://www.iftn.ie/production/production_companies/production_sub/feature/?act1=record&aid=70&rid=3917&tpl=filmography_dets&only=1&force=1|title=Na Glúnta {{!}} The Irish Film & Television Network|website=www.iftn.ie|access-date=2025-08-25}}</ref>, co-directors Ciarán Ó Cofaigh & Darach Ó Scolaí, prod. Ciarán Ó Cofaigh, Rosg. * ''An Leabhar'' (trans., ''The Book''), short film, 2000, (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg) Rosg, 2000.<ref>{{Citation|title=An Leabhar|url=https://www.imdb.com/title/tt0963767/|publisher=Bord Scannán na hÉireann / The Irish Film Board, ROSG|accessdate=2025-08-25|first=Robert|last=Quinn|others=Colm O&apos;Maonlai, Peadar O&apos;Treasaigh, Diarmuid Mac an Adhastair}}</ref> * ''Na Cloigne'' [trans., The Heads], 3-episide series, 2010 (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg), TG4.<ref>{{Cite web|url=https://www.imdb.com/title/tt1607924/|title=Na cloigne|date=2010|website=IMDb|access-date=25 August 2025}}</ref> === Nonfiction === Ó Scolaí's essays and lectures are published and his interviews are broadcast regularly, making for a large body of nonfiction critical and analytical work. Here are a few, almost all published in [https://comhar.ie/iris/scribhneoiri/darach-o-scolai/ Comhar]: * “Ceol Ciúin na nÉagmaise” (trans., “The Silent Music of Absence ['''the Fall?''']”), an essay on the 2014 Nobel Prize winner for literature, [[wikipedia:Patrick_Modiano|Patrick Modiano]], ''Comhar'', December 2014. * The Ó Cadhain Lecture: [https://leachtaiuichadhain.clo.ie/leachtai/2014 “Cuimhne agus Díchuimhne (trans., “Memory & Forgetfulness"]), 2014. * “Rithim agus Réim” ("Rhythm and Register"), a public lecture in the University College Dublin lecture series “Ó Thrácht go Twitter” (trans., "From Talk to Twitter"), 2014. * Review of Pádraig Ó Cíobháin’s ''Dréachta Chrích Fodla'', '''Comhar?, ??'''. * “Na Geilt i mBun an Tí” (trans., "The Madmen in Charge"), a talk at the Merriman Winter School, Comhar April 2012.<ref name=":18">{{Cite web|url=http://darachoscolai.ie/beathaisneis.html|title=Darach Ó Scolaí: Beathaisnéis|website=darachoscolai.ie|access-date=2025-09-26}}</ref> * The EFACIS podcast: Síle Ní Choincheannain talks to Darach Ó Scolaí about the historical novel. == Critical Reception == Ó Scolaí’s style has been called “crisp and elegant, and rich in language while being highly readable,”<ref>{{Cite journal|last=Heussaf|first=Anna|date=Summer 2025|title=Bláthnaid—A tale of love, violence and sorcery retold for readers today|url=https://booksirelandmagazine.com/blathnaid-a-tale-of-love-violence-and-sorcery/|journal=Books Ireland}}</ref> with “an unsurpassed richness and precision of language.”<ref name=":12">{{Cite journal|last=Ó Cróinín|first=Breandán|date=Summer 2025|title=unknown|journal=The Limerick Leader}}</ref> “Whimsical, hilarious, and subtly learned” is how Éilis Ní Dhuibhne described his writing.<ref name=":20" /> === Original Works === Ó Scolaí’s first novel, the 2007 ''An Cléireach'' (''The Clerk'') won two prizes and was described as “one of the great historical novels in the Irish language and among the best books written in the language since the beginning of this century.”<ref name=":12" /> Novelist Alan Titley says, “In ''An Cléireach'' Ó Scolaí creates the Ireland of war in the 17th century more fully than any other Irish writer on the subject of war since ''L’Attaque'' Eoghain Ó Thuairisc around 1798 [In ''An Cléireach'' cruthaíonn Ó Scolaí Éire an chogaidh san 17ú haois níos iomláine ná mar a dhein aon scríbhneoir Gaeilge eile ar ábhar cogaidh ó ''L’Attaque'' Eoghain Uí Thuairisc timpeall ar 1798].”<ref name=":11" />{{rp|25, Col. 1a}} Not all the reviews of this first novel were so positive, however; Proinsias O' Drisceoil says for the Irish Times says,<blockquote>This then is a novel in search of a plot, a story that attempts to attain a significance that eludes it.<ref>{{Cite news|url=https://www.irishtimes.com/news/a-disaffected-clerk-in-the-confederates-1.943070|title=A disaffected clerk in the confederates|last=O' Drisceoil|first=Proinsias|date=5 July 2008|work=The Irish Times|access-date=16 October 2025}}</ref></blockquote> In the ''Oxford Handbook of Modern Irish Fiction'' Pádraig Ó Siadhail analyzes rather than reviews ''An Cléireach'': <blockquote>In ''An Cléireach'', Ó Scolaí revisits the trauma of Cromwellian Ireland. The primary narrative device is once again the first-hand account, in this case by Tadhg Ó Dúbháin, a clerk and quartermaster in the Confederate Army in 1650. We sample the hardships, the friendships, the tensions, the rivalries, and the petty jealousies amongst comrades in arms, including remnants of the Gaelic literary class, as the Confederate soldiers, increasingly a rabble more than a cohesive unit, retreat in advance of Cromwell’s forces. ''An Cléireach'' concludes with the narrator and his family in exile in continental Europe. But along the retreat route, and central to the novel, members of the Confederate army camp, rest up, and tell versions of a story about the keeper of the treasured manuscript "Saltair an Easpaig" (The Bishop’s Psalter). Their versions raise issues about memory construction, the limitations of individual perspectives, personal agendas, and how minor changes in the telling of a story can alter our understanding of history, Thus, ''An Cléireach'' complements ''Fontenoy'' in moving beyond more realistic recreation of a historical event or period to interrogate the notion of history as construct.<ref>{{Cite book|title=The Oxford Handbook of Modern Irish Fiction|last=Ó Siadhail|first=Pádraig|publisher=Oxford University Press|year=2020|isbn=9780198754893|editor-last=Harte|editor-first=Liam|pages=598–99|chapter=Contemporary Irish Fiction}}</ref> </blockquote> Of ''Súil an Daill,'' in ''Nós'', Cathal Seoighe says, "The book deserves a significant place among the collection of high-quality books published in recent years that would make you feel sorry for someone who does not speak Irish [Tá áit shuntasach ag dul don leabhar i measc an chnuasaigh leabhair ar ardchaighdeán a foilsíodh le roinnt blianta anuas a d’fhágfadh trua agat don té atá gan Ghaeilge]."<ref>{{Cite journal|last=Seoighe|first=Cathal|date=09/26/2022|title=‘Dar leathmhagairle an diabhail, is leabhar den scoth é seo!’ ['According to the devil’s half-wit, this is a great book!’]|url=https://nos.ie/cultur/leabhair/dar-leathmhagairle-an-diabhail-is-leabhar-den-scoth-e-seo/|journal=Nós}}</ref> ''Bódléar'', Ó Scolaí's most recent book, is a “beautiful novel. There is magic and craftsmanship in it. A small miracle of a book and it is highly recommended.”<ref>{{Cite web|url=https://leabharbreac.com/bodlear-mioruilt-bheag-de-leabhar/|title=Bódléar: Míorúilt bheag de leabhar (Bódléar: A Small Miracle of a Book)|last=Ní Ghairbhí|first=Róisín|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Éilis Ní Dhuibhne in the ''Irish Times'' says,<blockquote>what a gem! An affectionately gentle satire of the Irish poetic scene during one creatively fluid 19th-century year, the story focuses on a Maigue poet and schoolteacher who goes on a trip to France and returns with camembert, a cafetiere, ‘Fleurs du Mal’, and a mission to convert the local traditionalists to la modernité. Whimsical, hilarious, and subtly learned, it’s absolutely delightful!<ref name=":20">{{Cite journal|last=Ní Dhuibhne|first=Éilis|date=30 June 2025|title=Éilís Ní Dhuibhne on the best Irish language books of 2025 so far: Including a history of the Gaeltacht Civil Rights Movements, a gem of a novel by Darach Ó Scolaí and Joe McHugh’s entertaining account of learning Irish|url=https://www.irishtimes.com/culture/books/review/2025/06/30/eilis-ni-dhuibhne-on-the-best-irish-language-books-of-2025-so-far/|journal=The Irish Times|pages=22}}</ref></blockquote> === Retellings and Translations === ==== ''Táin Bó Cuailnge'' ==== ''Táin Bó Cuailnge'' [''The Cattle Raid of Cooley''] is a modern edition of an 11th-century epic into modern Irish.<ref name=":3" /> Gearóid Denvir reviewed ''Táin Bó Cuailnge'' for ''Comhar'':<blockquote>Darach Ó Scolaí has ​​achieved a feat in this challenging reworking. He has found a high level of the Irish language to tell his story – as he has done before in his groundbreaking novel An Cléireach (2007, Leabhar Breac) and in his other prose works. This book is a decoration of the language, literature and culture of the Irish language, following the path of the old storytellers and writers and presenting material from the tradition to his own generation according to the understandings of his own time. The book will be a classic that will be of great interest to all readers of the Irish language, both ordinary readers, students, scholars and writers, and there should be a copy in every home in the country. [Tá éacht déanta ag Darach Ó Scolaí san athleagan dúshlánach seo. Tá réim ard den teanga Ghaeilge aimsithe aige lena scéal a inseacht – mar a rinne sé cheana ina úrscéal ceannródaíoch An Cléireach (2007, Leabhar Breac) agus i saothair eile phróis dá chuid. Is maisiú ar an teanga agus ar litríocht agus cultúr na Gaeilge an leabhar seo a leanas conair na seanscéalaithe agus na seanscríobhaithe agus ábhar de chuid an traidisiúin á chur i láthair a ghlúine féin aige de réir thuiscintí a linne féin. Clasaic a bheas sa leabhar a gcuirfidh léitheoirí uilig na Gaeilge, idir ghnáthléitheoirí, mhic léinn, scoláirí agus scríbhneoirí spéis thar na bearta ann, agus ba cheart cóip a bheith i chuile theach sa tír.]<ref name=":15">{{Cite journal|last=Denvir|first=Gearóid|date=April 2018|title=Táin Bó Cuailgne|url=https://comhar.ie/iris/78/4/leirmheas/|journal=Comhar|via=JSTOR}}</ref> </blockquote>Cathal Poirtéir says, "The freshness and richness of Ó Scolaí’s version are a joy …. The author delights us with the linguistic and stylistic richness of the ancient epic in a modern-Irish version that reflects the original’s spirit and language."<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=May/June 2018|title=Leabhair Idir Lámha|url=https://www.jstor.org/stable/26564180|journal=Books Ireland|pages=46–47|via=JSTOR}}</ref>{{rp|47}} Novelist and academic Alan Titley calls Ó Scolaí's "a wonderful gutsy telling" of ''Táin Bó Cuailnge''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/2023/03/11/the-tain-retold-maeve-and-ailills-spat-could-be-out-of-a-soap-opera/|title=The Táin retold: ‘Maeve and Ailill’s spat could be out of a soap opera’|last=Titley|first=Alan|date=11 March 2023|work=The Irish Times|access-date=16 October 2025}}</ref> ==== ''Deirdre'' ==== Marie Whelton, in "Léann Teanga" ("Language Studies"), in the 2024 ''An Reiviú'' says,<blockquote>this version [of ''Deirdre''] by Darach Ó Scolaí succeeds in skillfully capturing and portraying the complexity of gender and power issues in the ‘Deirdre’ tradition [éiríonn leis an leagan seo le Darach Ó Scolaí castacht cheisteanna na hinscne agus na cumhachta i dtraidisiún scéal Dheirdre a ghabháil agus a léiriú go sciliúil]. … There is no doubt that this new version greatly contributes to the legacy of the story and that it revives that legacy thoughtfully and artistically [Níl amhras faoi ach go gcuireann an leagan úr seo go mór le hoidhreacht an scéil agus go ndéanann sé an oidhreacht sin a athbheochan go tuisceanach agus go healaíonta.].<ref name=":16">{{Cite web|url=https://www.tara.tcd.ie/tara8/server/api/core/bitstreams/3c20175a-7631-44b2-8b0f-f454edd712b4/content|title=An Artistic Retelling of Deirdre's Tale and the Defeat of Conor Review of Deirdre or the Ship of Mac Uisnigh by Darach Ó Scolaí [Athinsint Ealaíonta ar Oidhe Dheirdre agus ar Ansmacht Chonchúir Léirmheas ar Deirdre nó Loingeas Mhac Uisnigh le Darach Ó Scolaí]|last=Whelton|first=Marie|date=2024|website=The Review [An Reiviú], Language Studies [Léann Teanga]|access-date=25 September 2025}}</ref></blockquote> === Works for Young Readers === Meadhbh Ní Eadhra said of ''Bodach an Chóta Lachna'' that it was "Beautiful Irish, but easy to understand for young readers."<ref>Ní Eadhra, Meadhbh. In ''Gaelscéal'', qtd. in "Bodach an Chóta Lachna" https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/.</ref> == Awards and Honors == Ó Scolaí's works are regularly nominated and make the short list for prizes, an honor in itself, but they are generally not listed here unless they are named as the first-place winner in their category. === Oireachtas Prize === The Oireachtas Prize is the literary prize awarded by [[wikipedia:Oireachtas_na_Gaeilge|Oireachtas na Gaeilge]], the annual arts festival dedicated to Irish language, arts and culture. Darach Ó Scolaí has won the Oireachtas Prize for Literary Fiction three times, once for ''An Cléireach'' (''The Clerk'') in 2007, for ''Súil an Daill'' (''The Eye of the Blind'') in 2021 and for ''Bódléar'' in 2024. * 2007, for ''An Cléireach'' (trans., ''The Clerk'') — “(a special prize commemorating the 400th anniversary of the foundation of Coláiste na nGael in Louvain, awarded under the auspices of the Franciscan Province of Ireland). The prize of €10,000 was the largest prize ever awarded to an Irish language novel [(duais speisialta chomórtha 400 bliain bhunú Choláiste na nGael i Lobháin a bronnadh faoi urraíocht Phroibhinse Phroinsiasach na hÉireann). Ba é an duais €10,000 sin an duais ba mhó a bronnadh riamh ar úrscéal Gaeilge].”<ref name=":18" /> * 2021, for ''Súil an Daill'' (''The Eye of the Blind'') * 2024, for ''Bódléar'' === Ó Shúilleabháin Award, Irish language “Book of the Year” === The first prize of this award includes €5,000 to the publisher and €2,500 to the author of the winning work.<ref name=":10">{{Cite journal|date=15 August 2023|title=20 saothar san iomaíocht do ‘Leabhair Ghaeilge na Bliana 2023’|url=https://tuairisc.ie/20-saothar-san-iomaiocht-do-leabhair-ghaeilge-na-bliana-2023/|journal=Tuairisc}}</ref> * ''An Cléireach'' (''The Clerk'').<ref>{{Cite web|url=http:/www.gaelport.com/uploads/documents/edition19.html|title=Eagrán / Edition 19 - 04 11 2008|date=4/11/2008|website=Internet Archive|archive-url=https://web.archive.org/web/20130525011340/http:/www.gaelport.com/uploads/documents/edition19.html|archive-date=25 May 2013|access-date=25 August 2025}}</ref> * ''Táin Bó Cuailnge'', 2018. * ''Bódléar'', 2025. ==== De Bhaldraithe Award ==== The Gradam de Bhaldraithe is awarded to the best work in translation.<ref name=":10" /> * ''Cuairt San Nioclás,'' a translation of Clement Clarke Moore's ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas."<ref name=":10" /> ==== Other ==== * Walter Macken Prize, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005 * Bháiteir Uí Mhaicín Memorial Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005<ref>{{Cite news|url=https://www.irishtimes.com/gaeilge/tuarascail/duais-oireachtais-1.501571|title=Oireachtas Prize: Over €50,000 was awarded to writers in the Oireachtas Literary Competitions at an event in Dublin last night. Winners… [Duais Oireachtais: Bronnadh breis agus €50,000 ar scríbhneoirí i gComórtais Liteartha an Oireachtais ar ócáid i mBaile Átha Cliath aréir. Bhuaigh…]|work=5 October 2005|access-date=15 October 2025}}</ref> * BBC Stewart Parker Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2006 * The Aodán Mac Póilín Commemorative Prize, for ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), 2017 == External Links == * Leabhar Breac website: https://leabharbreac.com/en/ * Leabhar Breac Facebook pages: * Rosg website: [http://www.rosg.ie/en/ <nowiki>http://ww</nowiki>w.rosg.ie/en/] * Art on the Island (Ealaín ar Oileán) website, archived at the Wayback Machine: https://web.archive.org/web/20130601000520/http://ealainaroilean.ie/ 31 March 2012, 1 June 2013 and 8 January 2014 * Darach Ó Scolaí's website Archived 25 September 2015 at the Wayback Machine: https://web.archive.org/web/20150925103456/http://darachoscolai.ie/ * Youtube video of [https://www.youtube.com/watch?v=OlP2AmSBzXc Breandán Ó Cróinin introducing Deirdre at the book launch] in the pub Tigh Mholly (Molly’s House). == Primordial Ooze == * Known for his sensitivity to language and voices. * Finish scanning through JSTOR * Scan through Irish Times, 56 hits * Check Goodreads * Check YouTube (In the spring of 2013, the arts programme Imeall interviewed the author on TG4.) * Check both Wikipedias for pages on the origins of the retold tales (like Deirdre) and link to this article * Propose link from University of Galway page once Darach’s is up * Write Irish National Biography (<nowiki>https://www.dib.ie</nowiki>) to propose an article about Darach once the Wikip article is done? See what they say. * Link to Ó Scolaí from the Wikipedia * Make sure links '''to''' Wikipedia in the actual encyclopedia work right === Not Placed Yet === * "So here are the books that Irish people love the most! [Mar sin seo iad na leabhair is gile leis na Gaeil!]" — "32. An Cléireach – Darach Ó Scolaí (2)" [18 books got 2 votes, and then they're alphabetized by author's last name, so the 32 of 34 doesn't signify the specificity it seems to]<ref name=":14">{{Cite journal|last=Ó Murchú|first=Eoin P.|date=9 June 2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil. [The 30 best Irish books for Irish people]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * "Below is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers.Here is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers [Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí.Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí]." "Corto Maltese – Hugo Pratt (aistrithe ag Darach Ó Scolaí)"<ref name=":14" /> * "Ceann eile de bhuaicphointí na hÉigse a bheidh sa seisiún le Darach Ó Scolaí, duine d’úrscéalaithe móra na Gaeilge, agus duine de chomhbhunaitheoirí teach foilsitheoireachta Leabhar Breac. [Another highlight of the Éigse will be the session with Darach Ó Scolaí, one of the great Irish language novelists, and one of the co-founders of the publishing house Leabhar Breac.]"<ref name=":17">{{Cite journal|last=Nós|date=4 May 2023|title=Éigse na Bruiséile le filleadh i mí na Bealtaine. [Éigse na Bruséile to return in May]|url=https://nos.ie/cultur/eigse-na-bruiseile-le-filleadh-i-mi-na-bealtaine/|journal=Nós}}</ref> === Things Taken Out for Now === “’The play is a comedy about language, lies, bureaucracy and Gaeltacht grants, in the tradition of Myles na Gcopaleen,’ according to Norma-Jean Kenny in the ''Galway Advertizer'', ‘in which the author comments and criticizes the institutions of the Irish language in Ireland without ceasing.’" Supposedly a quotation by Gearóid Denvir reviewing ''Táin Bó Cuailnge'' for ''Comhar'' (but I don't find it in the article): This book has long been needed by Irish language readers and there is no doubt that it will become a classic in time and surpass Thomas Kinsella’s English version. This version remains faithful to the language of the original while at the same time finding an appropriate language in today’s Irish. Ó Scolaí masterfully overcomes the difficulties of the original’s rhetorical difficulties and the versions of the original poetic texts are extremely effective.[supposedly <ref name=":15" />] “The biggest prize ever awarded for a novel in Irish was presented at a special ceremony in the National Concert Hall in Dublin, today (Thursday, 4 October 2007). Darach Ó Scolaí, writer, artist & playwright from Casla, Co. Galway, was awarded €10,000 for his literary novel, ‘An Ardscoil’. This work, under the new title ‘An Cléireach’, will be launched at Oireachtas na Samhna in Westport in November. This is the first novel from his pen, a story set in the late seventeenth century. This competition was sponsored by the Franciscan Province of Ireland.” (archive, Oireachtas na Gaeilge site, 04 October, 2007) ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. number 2 in ''Comhar'' literary magazine’s list of best books of 2021. '''{6}.''' *William Shakespeare, ''Romeo agus Juliet'' (trans. of ''Romeo and Juliet''), Leabhar Breac, 2016. *Jonathan Swift, ''Camchuairt Ghuilivéir'' (trans. of ''Gulliver's Travels''), Leabhar Breac, 2016. *Hugo Pratt, ''Corto Maltese'' '''''Flag of Bones (Bratach na gCnámh) Series''''' Leabhar Breac published the Bratach na gCnámh series of books for young readers. Written in French by Alain Surget, illustrated by Annette Marnat and translated by Darach Ó Scolaí, this series uses the history of Caribbean Sea pirates<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/alain-surget/|title=Alain Surget Archives|website=Leabhar Breac|language=en-US|access-date=2025-09-30}}</ref>: *Alain Surget, ''Éalú as Páras'' (''Escape from Paris''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Oilean na Siorcanna'' (''Shark Island''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Long na dTaibhsi'' (''Ship of the Ghosts''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''San Ochtapas Dubh'' (''In the Black Octopus''), Annette Marnat (Illustr.), Leabhar Breac, 2013. * Alain Surget, ''San Ionsai ar Veracruz'' (''The Attack on Veracruz''), Annette Marnat (Illustr.), Leabhar Breac, 2013. '''''For "First Readers" (children to 6 years old or so)''''' These books were written originally in Catalan by Spanish author Enric Lluch Girbés and translated into Irish by Ó ScolaÍ: *Enric Lluch, ''Ag Péinteáil an Tí'' (''Painting the House''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Colúr Bacach'' (''The Lazy Dove''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Phluais'' (''The Cave''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Madra Dhaideo'' (''Grandpa's Dog''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Fiacail Mháire'' (''Mary's Tooth''), Anna Clariana (Illustr.), Leabhar Breac, 2017. '''''Bruno Heitz''''' Leabhar Breac published a series of 3 Heitz books for small children. Published originally in French, this series of three comic books is about a blind mole named Cáitín Chaoch in Irish (and ''Louisette la taupe'' in French).<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/bruno-heitz-en/|title=Bruno Heitz Archives|website=Leabhar Breac|language=en-US|access-date=2025-10-02}}</ref> Ó Scolaí translated these: *Bruno Heitz (author and illustr.), ''Práinneach'' (''Urgent''), Leabhar Breac, 2020 *Bruno Heitz (author and illustr.), ''Preab san Aer'' (''Bounce in the Air''), Leabhar Breac, 2020. '''''Books for Toddlers''''' Leabhar Breac has published 14 books written by French author Orianne Lallemand's and illustrated by Eleonore Thuillier, about Lallemmand's popular character Loup, Wolf. These are translated by Ó Scolaí: *Orianne Lallemand, ''An Mac Tire a Raibh Faitios an Domhain Air'' (trans. of ''The Son Who Saw the World in His Eyes''), Eleonore Thuillier  Illustr.), Leabhar Breac, 2018. *Orianne Lallemand, ''Macan agus an Goban'' (trans. of ''Macan and the Goblin''), Eleonore Thuillier (Illustr.), Leabhar Breac, 2018. * Orianne Lallemand, ''A Mac Tíre a Chuaigh go Tóin na Farraige'' (trans. of ''The Wolf Who Went to the Bottom of the Sea''), Éléanore Thuillier  (Illustr.), Leabhar Breac, 2019. '''''Board Books (for babies)''''' J. C. (Joan Carles) Girbés Aparisi is a Catalan author and editor. These books were written in Catalan and translated by Ó Scolai. *J. C. Girbés, ''An Phicnic'' (''The Picnic''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. * J. C. Girbés, ''An Chóisir'' (''The Party''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. *J. C. Girbés, ''Lá Mór Fada'' (''A Long Day''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. *J. C. Girbés, ''Tabhair Leat do Leabhar'' (''Bring Your Book''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. ==== Gradam Réics Carló ==== The Réics Carló prize is awarded for the best book in the Irish language for young readers. It is named for one of the characters of 20th-century writer [[wikipedia:Cathal_Ó_Sándair|Cathal Ó Sándair (Charles Saunders)]]. * ''An Bradán Feasa'' was “shortlisted for the Réics Carlo award 2010.”<ref name=":9" /> == References == {{reflist}} 6e418v40rebuaiskerq8ap8ao9f3jx0 2 267624 2844818 2745010 2026-11-07T17:09:29Z Alandmanson 1669821 /* Functions of SOM */ 2844818 wikitext text/x-wiki == What is Soil Organic Matter? == Soil organic matter (SOM) is defined as “the organic matter component of soil, consisting of plant and animal residues at various stages of decomposition, cells and tissues of soil organisms, and substances synthesized by soil organisms” (Brady et al., 1999). It is made up of living biological biomass, fresh and partially decomposed residues, as well as well-decomposed organic material, sometimes known as humus, or humic supramolecular substances (Chen et al., 2004, cited by Manson, 2017). The living biomass includes microorganisms (archaea, bacteria, fungi, algae and protozoa), mesofauna (earthworms, termites, insects and mites) as well as plant roots. The fresh and partially decomposed residues are the decaying plant litter, roots and remains of other organisms in the soil. Carbohydrates, proteins, amino acids, enzymes, phenols, waste products such as faecal matter (manure), urine, root exudates, and microbial exudates also form part of the fresh and partially decomposed SOM. The well-decomposed SOM is understood to occur as a wide range of organic (or humic) substances. These substances may form complexes with positively charged substances such as enzymes or Al3+ in the soil matrix, and may also be adsorbed on the surfaces of clay minerals. A particularly stable fraction of SOM is biochar (charcoal), the result of pyrolysis (the incomplete oxidation of organic matter) in fires. (Jien et al., 2015, Fahramand et al., 2014, Pettit, 2004). Moreover, as SOM decomposes, the products eg. sugars and lignin decomposition products, tend to form supramolecular associations with humic substances, resulting in a form of organic matter that cannot be classified, as yet, as fresh, partially decomposed or well-decomposed SOM (Piccolo, 2005). Although SOM generally makes up 2 to 8% of the total topsoil mass, the amount of SOM in the soil depends on a variety of factors, which include land use, environmental factors and climatic conditions of that specific area. Topsoils or upper horizons in deserts normally contain less than 1% organic matter, while the SOM content of soils in low-lying, wet areas can be as high as 90% (peat). Soils containing greater than 12% SOC (20% SOM) are generally classified as organic soils (Troeh and Thompson, 2005). == Functions of SOM == Soil organic matter provides a source of nutrients for growth and development of plants and microbial populations living in the soil. Upon decomposition of fresh organic matter, nutrients such as nitrogen (N), phosphorus, (P), potassium, (K) and sulphur (S) are released as soluble, inorganic ions into the soil matrix, thereby becoming available for plant uptake. These nutrients are taken up through the plant-root system or microbial membrane for use within the cells and tissues. Soil organic matter provides a source of food for decomposers which may supress plant pathogens of (soil-borne diseases). Micronutrients such as magnesium (Mg) and calcium (Ca) can also be provided by SOM, depending on the quality of the organic matter. Soil organic matter is classified as of good quality when it is still fairly fresh, its C:N ration is below 30:1, and can provide (when mineralised) a wide range of nutrients at reasonable concentrations. Generally, with low quality SOM, the C:N ration is more than 30:1, and the mineralised N is quickly immobilised by microorganisms for metabolic purposes, resulting in the unavailability of this nutrient for plant uptake. Some fractions of SOM can form complexes (chelates) with micronutrients such as iron (Fe), copper (Cu), manganese (Mn), and zinc (Zn), preventing them from leaching, increasing their availability for biological uptake as well as reducing their toxicity as cations. Soil organic matter also serves as a source of cation exchange capacity. Humic substances can also stimulate root growth, proliferation and development, and shoot development. (Atiye, 2002, Pettit, 2004). Soil organic matter bonds soil particles together, forming stable aggregates. Soil organic matter increases water holding capacity this is particularly important in sandy soils. == Soil Life == Soil Biodiversity - https://www.youtube.com/watch?v=tUQtwwgU3r4 == Effect of land management practices on SOM == Land management practices can either increase or decrease organic matter in the soils. The decrease of SOM may result in decreased soil fertility, with loss of nutrient supplying capacity (especially N), pH buffering capacity (resistance to soil pH change), and cation storage capacity (ability to hold the exchangeable cations K+, NH4+, Ca2+, Mg2+). Loss of SOM also frequently results in lower aggregate stability, soil structure and tilth. However, increases in SOM content may reverse these losses, rehabilitating and conditioning the soil for sustainable production. Different land management practices have different impact on SOM. === Tillage/cropping systems === When land under natural vegetation is tilled, SOM declines. Its decline is rapid in the first 10 years, slows down with time, and comes to equilibrium after 20-60 years. Often a loss of 25-50% can occur over 30 years (Du Toit, 1994). This decline in SOM occurs because with conventional tillage systems, much of the produced biomass is removed, e.g. when maize is planted for silage or residue is used to supplement winter feed for livestock. This results in less plant residue being added to the soil as fresh SOM inputs, compared to the amount of biomass returned to soils in natural vegetation systems. Moreover, if cover crops or crop rotation practices are absent in these systems (annual crop lands), the land is usually fallow outside the growing season, hence there is no biomass being returned to the soil as SOM. During the fallow period, plant debris on the soil surface is usually susceptible to wind and water erosion. As the topsoil is eroded together with residues and SOM contained in the topsoil, SOM which is lighter than soil particles in mass, is preferentially eroded by wind and surface runoff. With the topsoil not being covered by residue, the velocity at which the rain-drops hit the soil surface is usually strong enough to break open soil aggregates, exposing SOM which was protected within the aggregates. The exposed organic matter is usually lost through erosion or decomposition by microorganisms. Cultivation however, results in many more aggregates being broken, exposing much of the protected SOM to erosion and decomposition, and CO2 emissions and the bioavailability of mineral nutrients may spike. In zero tillage or direct drilling tillage systems, however, seed is placed in a narrow slot in otherwise undisturbed soil, minimising the effect of cultivation on SOM. The surface crop residues or plant litter in these systems is not only a source of fresh SOM, it also minimises the impact of rain drops on aggregates, as well as protects soils from drying out, keeping life near the soil more active. However, it is worth noting that although minimum tillage systems may seem the ideal practice for increasing organic matter in soils, this SOM is only accumulated near the surface, rather than mixed with the whole plough layer. Near the surface, this SOM is still prone to be lost through sheet erosion, especially on steep slopes. === Pastures === Other land use systems such as perennial cultivated pastures also increase SOM content, especially if previously cultivated. This increase is due to high production of organic material, particularly when fertilizers have been used effectively, with adequate N inputs in the system. These N inputs may be supplied by mineral fertilizer or fixed by legumes incorporated into the system. Root biomass plays a major role in increasing SOM in these systems; much of the above-ground biomass is utilised by livestock, but grazing stimulates root production and turnover, thereby increasing organic-matter inputs. Grazing also recycles organic matter as dung. === Other beneficial practices === In all land use systems, appropriate fertilizer application (N, P, K and micronutrients) generally increases plant growth and dry matter production, therefore increasing return of organic residues to the soil (including roots). Higher row-crop yields have been observed to result in slower decline in SOM levels. Additions of organic material such as animal manures, composts, mulch of plant material, cover crops and green manures have also been observed to be beneficial in increasing SOM. Composted material has been observed to increase SOM content, while fresh organic matter tends to boosts microbial growth and aggregate stability, especially in cropping systems. === Strategies === To increase SOM in land management systems, the following strategies may be used: Elimination of fallows by practicing crop rotation and the use of cover crops and green manures may increase SOM inputs. The use of organic sources of plant nutrients as well as including a long-term (more than two years) pasture in the rotation may contribute positively in increasing SOM, among other benefits.  Reducing SOM losses by minimising erosion, tillage and retention of residue in cropping systems also has a significant impact in maintaining the systems SOM. == References == Atiyeh, R.M., Lee, S., Edwards, C.A., Arancon, N.Q. and Metzger, J.D., 2002. The influence of humic acids derived from earthworm-processed organic wastes on plant growth. Bioresource technology, 84(1), pp.7-14. <br> Brady, N.C., and Weil, R.R. 1999. The nature and properties of soils. Prentice Hall, Inc., Upper Saddle River, NJ.<br> Du Toit, M.E., Du Preez, C.C., Hensley, M. and Bennie, A.T.P., 1994. Effect of cultivation on the organic matter content of selected dryland soils in South Africa. South African Journal of Plant and Soil 11, pp.71-79 (In Afrikaans).<br> Fahramand, M., Moradi, H., Noori, M., Sobhkhizi, A., Adibian, M., Abdollahi, S. and Rigi, K., 2014. Influence of humic acid on increase yield of plants and soil properties. Intl J Farm & Alli Sci, 3, pp.339-341. <br> Piccolo, A., 2002. The supramolecular structure of humic substances: a novel understanding of humus chemistry and implications in soil science. Advances in agronomy, 75, pp.57-134.<br> Jien, S.H., Wang, C.C., Lee, C.H. and Lee, T.Y., 2015. Stabilization of Organic Matter by Biochar Application in Compost-amended Soils with Contrasting pH Values and Textures. Sustainability, 7(10), pp.13317-13333. http://www.mdpi.com/2071-1050/7/10/13317/htm<br> Troeh, F.R. and Thompson, L.M., 2005. Soils and soil fertility. 6th ed. Ames: Blackwell. == Some key aspects - Bibliography == === Microbial necromass contribution to soil organic matter === Alptekin, B., Hirsch, H., Kleven, B., King, L., McLimans, C., Daniels, D., Irving, T., Floss, D. and Ané, J.M. (2025). From glomalin to glomalose: unraveling the molecular identity of the MAb32B11 antigen. New Phytologist, 247: 2328-2341. https://doi.org/10.1111/nph.70253 <br> Summary: Glomalin, a substance produced by arbuscular mycorrhizal (AM) fungi, has well-documented benefits for plant and soil health, including water retention and soil aggregation. Glomalin quantification has been performed by enzyme-linked immunosorbent assay (ELISA) using a monoclonal antibody, MAb32B11, that has been described as targeting a heat shock protein 60 (RiHSP60). In this study, we re-examined the molecular nature of the antigen recognized by MAb32B11. MAb32B11 did not cross-react with the RiHSP60 polypeptide. Glomalin extracts of Rhizophagus irregularis showed strong and dose-dependent cross-reactivity with MAb32B11 even when protein levels were undetectable, raising doubts about the proteinaceous nature of the antigen. Protease treatments of glomalin extracts did not affect the ELISA signal. However, treatment with periodate, which degrades polysaccharides, significantly reduced the signal. A strong correlation between carbohydrate content and the ELISA signal was observed in glomalin extracts. These findings indicate that MAb32B11 recognizes a carbohydrate, likely originating from cell walls of AM fungi. Further analysis of glomalin extracts using size exclusion chromatography suggests that the epitope of MAb32B11 is a complex carbohydrate in the size range of 511–600 kDa. Understanding the true nature of glomalin will enhance our ability to quantify it accurately and leverage its agricultural benefits. Working model for glomalose and its multiple benefits We suggest a new working model for glomalose in light of our findings. We hypothesize that glomalose is an abundant polysaccharide specific to mycorrhizal fungi and resides in fungal hyphae and spores (Fig. 7). The specificity of glomalose to mycorrhizal fungi was already suggested by Dr. Wright (Wright et al., 1996), and our current data support this hypothesis (Fig. 6). Previous work suggested glomalose as a component of mycorrhizal hyphae and spore cell walls based on localization analysis using immuno-electron microscopy (Purin & Rillig, 2007). In agreement with findings from Driver et al. (2005), we hypothesize that glomalose is used for a physiological function in mycorrhizal fungi and is most likely released to the soil during fungal turnover. Although the actual structure of this cell wall polysaccharide remains to be determined, we hypothesize it is a water-soluble polysaccharide molecule due to its extraction procedure. Most of the studies on the cell wall of AM fungi focused on intraradical hyphae and arbuscules (Balestrini & Bonfante, 2014; Rich et al., 2014) so a more in-depth characterization of the cell wall from spores and extraradical hyphae will be necessary. Our current working model also fits well with the functional benefits attributed to glomalin/glomalose through years of research (Holátko et al., 2021; Irving et al., 2021; Fig. 7). Glomalose was named a super-glue for soils due to its contributions to soil aggregation and aggregate stability (Rillig, 2004; Holátko et al., 2021). Soil polysaccharides of bacterial and fungal origin have long been recognized as essential mediators of soil aggregation. Polysaccharides can often serve as a glue and help bind smaller soil particles, leading to aggregation. Soil polysaccharides can provide energy for other filamentous microorganisms supporting the aggregation process. The amount of polysaccharides in soils positively correlates with stable soil aggregates (Martins et al., 2012). Particularly, water-soluble polysaccharides extracted through autoclaving correlate better with aggregate stability than total soil polysaccharides (Puget et al., 1998). Hydrophilic polysaccharides help with soil water retention, another vital role of glomalose for soil function (Lowe, 1978). Glomalose was reported to contain a lot of iron (0.04–8.8%), and the fungal cell wall is an important iron store (Rillig et al., 2001; Nichols, 2003; Philpott, 2006). Furthermore, polysaccharides contribute substantially to long-term carbon storage, an essential soil function attributed to glomalose (Rillig et al., 2001; Wang et al., 2017). The alignment of these previous findings related to soil polysaccharides with the suggested functional role of glomalose further supports our current working model. While the benefits of glomalin/glomalose can yet only be correlated with the abundance of the MAb32B11 antigen rather than proven to originate from it, if the antigen is an abundant cell wall polymer, a causal link is more likely. <br> Angst, G., Mueller, C.W., Prater, I., Angst, Š., Frouz, J., Jílková, V., Peterse, F. and Nierop, K.G., 2019. '''Earthworms act as biochemical reactors to convert labile plant compounds into stabilized soil microbial necromass.''' Communications biology, 2(1), pp.1-7. [https://doi.org/10.1038/s42003-019-0684-z DOI]<br> Abstract: Earthworms co-determine whether soil, as the largest terrestrial carbon reservoir, acts as source or sink for photosynthetically fixed CO2. However, conclusive evidence for their role in stabilising or destabilising soil carbon has not been fully established. Here, we demonstrate that earthworms function like biochemical reactors by converting labile plant compounds into microbial necromass in stabilised carbon pools without altering bulk measures, such as the total carbon content. We show that much of this microbial carbon is not associated with mineral surfaces and emphasise the functional importance of particulate organic matter for long-term carbon sequestration. Our findings suggest that while earthworms do not necessarily affect soil organic carbon stocks, they do increase the resilience of soil carbon to natural and anthropogenic disturbances. Our results have implications for climate change mitigation and challenge the assumption that mineral-associated organic matter is the only relevant pool for soil carbon sequestration. Angst, G., Mueller, K.E., Nierop, K.G. and Simpson, M.J., 2021. '''Plant-or microbial-derived? A review on the molecular composition of stabilized soil organic matter.''' Soil Biology and Biochemistry, p.108189. [https://doi.org/10.1016/j.soilbio.2021.108189 DOI] [https://www.researchgate.net/profile/Gerrit-Angst/publication/349869158 PDF]<br> Highlights:<br> *Microbial necromass accounts for ~50% or less of the SOM in aggregates and mineral-associated organic matter (MAOM). *Plant compounds preferentially stabilized in aggregates & MAOM in some ecosystems. *Soil type, land use/cover, substrate quality explain variability in biomarker content. *Specifically, the effects of climate, soil fauna, soil depth require further study. Buckeridge, K.M., La Rosa, A.F., Mason, K.E., Jeanette, W., McNamara, N.P., Grant, H.K. and Nick, O., 2020. '''Sticky dead microbes: Rapid abiotic retention of microbial necromass in soil.''' Soil Biology and Biochemistry, p.107929. [https://doi.org/10.1016/j.soilbio.2020.107929 DOI] [https://www.sciencedirect.com/science/article/pii/S0038071720302261/pdfft?isDTMRedir=true&download=true PDF] <br> Abstract: Microbial necromass dominates soil organic matter. Recent research on necromass and soil carbon storage has focused on necromass production and stabilization mechanisms but not on the mechanisms of necromass retention. We present evidence from soil incubations with stable-isotope labeled necromass that abiotic adsorption may be more important than biotic immobilization for short-term necromass retention. We demonstrate that necromass adsorbs not only to mineral surfaces, but may also interact with other necromass. Furthermore, necromass cell chemistry alters necromass-necromass interaction, with more bacterial tracer retained when there is yeast necromass present. These findings suggest that the adsorption and abiotic interaction of microbial necromass and its functional properties, beyond chemical stability, deserve further investigation in the context of soil carbon sequestration. Creamer, C.A., Foster, A.L., Lawrence, C., McFarland, J., Schulz, M. and Waldrop, M.P., 2019. '''Mineralogy dictates the initial mechanism of microbial necromass association.''' Geochimica et Cosmochimica Acta, 260, pp.161-176. [10.1016/j.gca.2019.06.028 DOI] Abstract: Soil organic matter (SOM) improves soil fertility and mitigates disturbance related to climate and land use change. Microbial necromass (the accumulated cellular residues of microorganisms) comprises the majority of soil C, yet the formation and persistence of necromass in relation to mineralogy is poorly understood. We tested whether soil minerals had different microbial necromass association mechanisms. Specifically, we tested whether microbial necromass directly sorbed to mineral surfaces or was consumed by live microorganisms prior to mineral association. Applying Raman microspectroscopy with 13C enriched microbial necromass to quantify microbe-mineral interactions, we show that mineralogy alters the initial mechanism of microbial necromass association. In the presence of K-feldspar (lower abiotic C preservation potential), microbial necromass required assimilation by live microorganisms for mineral retention. In contrast, with amorphous aluminum hydroxide (higher abiotic C preservation potential) microbial necromass was retained predominately through abiotic sorption, and was subsequently protected from microbial decomposition. Despite different mechanisms, both minerals retained similar quantities of microbial necromass under biotic conditions. Mineralogy determined not only the quantity of mineral-associated C, but the distinct pathway of microbial necromass association. These findings show the utility of Raman microspectroscopy as a technique to study microbe-mineral interactions, and imply that heterogeneity in mineral-organic interactions could result in gradients of organic matter stability. Dwivedi, D., Tang, J., Bouskill, N., Georgiou, K., Chacon, S.S. and Riley, W.J., 2019. '''Abiotic and biotic controls on soil organo–mineral interactions: developing model structures to analyze why soil organic matter persists.''' Reviews in Mineralogy and Geochemistry, 85(1), pp.329-348. [https://doi.org/10.2138/rmg.2019.85.11 DOI] [https://www.researchgate.net/publication/338274058 PDF] <br> Summary: Soils store vast amounts of terrestrial organic carbon, more than the atmosphere and terrestrial vegetation combined. This carbon is vulnerable to release to the atmosphere under a changing climate. Although the mechanisms leading to the decomposition of SOM are well documented, uncertainties persist regarding the stability of SOM. To address this critical gap, a robust predictive understanding and modeling of SOM dynamics is essential for examining short- and long-term changes in soil carbon storage and feedbacks with climate. In this chapter, we reviewed recent research that improves emergent understanding of the important factors contributing to SOM stability. While there currently exists a suite of models representing SOM dynamics that span a range of complexity, some recent mechanistic models are more consistent with this emergent understanding of SOM persistence. Yet even those recent models do not represent several processes that can be important for SOM dynamics. We conclude that the next-generation models need to represent the full spectrum of quantitatively important mechanisms for determining SOM persistence—including rate-limited and equilibrium-based sorption, the formation of soil aggregates, representative soil minerals, microbial community dynamics, and vegetation interactions—to accurately predict short- and long-term SOM dynamics. Because this recommendation is obviously challenging, we have assembled an open-source, reactive-transport based SOM model that can be used to robustly integrate many of these processes (called BeTR-S; https://github.com/BeTR-biogeochemistry-modeling/sbetr) and invite the community to experiment with it (Riley et al. 2019). Overall, it is important to understand SOM dynamics because SOM decomposition gives rise to potential greenhouse gases. Microbial dynamics, MAOM, and the molecular structure of SOM compounds have implications for understanding and modeling the short- and long-term responses of soil carbon stocks under local and regional climatic perturbations. Finally, this chapter illustrates the need to evaluate SOM dynamics in a reactive transport modeling framework that includes ecosystem properties. Gerke, J., 2018. '''Concepts and misconceptions of humic substances as the stable part of soil organic matter: A review.''' Agronomy, 8(5), p.76.<br> Abstract: In the last three decades, the concept of soil humic substances has been questioned in two main directions. Misinterpretations of CP MAS13C NMR spectroscopy led to the conclusion that soil organic matter is mainly aliphatic, questioning the theory of polymerization of humic substances from phenolic molecules. Conversely, some critics of humic substances assume that a great proportion of aromatic soil organic carbon originates from fire-affected carbon, often termed as black carbon (BC). However, the determination of BC in soil by two widely applied methods, the benzene polycarboxylic acid marker method and the UV method, is not reliable and seems to strongly overestimate the BC content of soils. The concept of humic substances continues to be relevant today. The polymerization of phenolic molecules that originate from the degradation of lignin or synthesis by microorganisms may lead to humic substances which can incorporate a variety of organic and inorganic molecules and elements. The incorporation, e.g., of triazines or surfactants into the humic matrix, leading to bound residues, illustrates that humic substances are important to explain central reactions in soil. Humic substances are also important to understand the availability of plant nutrients in soil, including P, Fe, and Cu, and they may have a direct effect on the growth of higher plants in soil. Therefore, there are good reasons to reformulate or to further develop the concepts and models of humic substances introduced and developed by M. Schnitzer, W. Flaig, W. Ziechmann, and F.J. Stevenson. Kallenbach, C.M., Frey, S.D. and Grandy, A.S., 2016. '''Direct evidence for microbial-derived soil organic matter formation and its ecophysiological controls.''' Nature communications, 7, p.13630.<br> Abstract: Soil organic matter (SOM) and the carbon and nutrients therein drive fundamental submicron- to global-scale biogeochemical processes and influence carbon-climate feedbacks. Consensus is emerging that microbial materials are an important constituent of stable SOM, and new conceptual and quantitative SOM models are rapidly incorporating this view. However, direct evidence demonstrating that microbial residues account for the chemistry, stability and abundance of SOM is still lacking. Further, emerging models emphasize the stabilization of microbial-derived SOM by abiotic mechanisms, while the effects of microbial physiology on microbial residue production remain unclear. Here we provide the first direct evidence that soil microbes produce chemically diverse, stable SOM. We show that SOM accumulation is driven by distinct microbial communities more so than clay mineralogy, where microbial-derived SOM accumulation is greatest in soils with higher fungal abundances and more efficient microbial biomass production. Liang, C., Amelung, W., Lehmann, J. and Kästner, M., 2019. '''Quantitative assessment of microbial necromass contribution to soil organic matter.''' Global change biology, 25(11), pp.3578-3590. [https://doi.org/10.1111/gcb.14781 DOI] [https://www.researchgate.net/publication/334814209 PDF] <br> Abstract: Soil carbon transformation and sequestration have received significant interest in recent years due to a growing need for quantitating its role in mitigating climate change. Even though our understanding of the nature of soil organic matter has recently been substantially revised, fundamental uncertainty remains about the quantitative importance of microbial necromass as part of persistent organic matter. Addressing this uncertainty has been hampered by the absence of quantitative assessments whether microbial matter makes up the majority of the persistent carbon in soil. Direct quantitation of microbial necromass in soil is very challenging because of an overlapping molecular signature with nonmicrobial organic carbon. Here, we use a comprehensive analysis of existing biomarker amino sugar data published between 1996 and 2018, combined with novel appropriation using an ecological systems approach, elemental carbon–nitrogen stoichiometry, and biomarker scaling, to demonstrate a suit of strategies for quantitating the contribution of microbe‐derived carbon to the topsoil organic carbon reservoir in global temperate agricultural, grassland, and forest ecosystems. We show that microbial necromass can make up more than half of soil organic carbon. Hence, we suggest that next‐generation field management requires promoting microbial biomass formation and necromass preservation to maintain healthy soils, ecosystems, and climate. Our analyses have important implications for improving current climate and carbon models, and helping develop management practices and policies. Ritz, K., 2020. Special issue editorial: '''Microbial necromass on the rise in SOM: advances, challenges, and perspectives.''' [https://www.sciencedirect.com/journal/soil-biology-and-biochemistry/special-issue/100FJ7QM4MZ] <br> This special issue aims to bring together a number of studies that provide knowledge and perspectives, mechanistically and quantitatively, into microbial necromass and its contribution to soil organic matter (SOM) formation, transformation, and storage. Recent studies and conceptual models have persistently suggested that the incorporation of microbial biomass components into soils via microbial remnants is likely to be disproportionately large. This means that microbial inputs and microbial energetic processes play a far greater role in the sequestration of carbon and nitrogen into soils than traditionally considered, particularly when a significant portion of those inputs are more likely to be stabilized, rather than plant inputs. However, these inputs have rarely been reliably be determined, and thus the microbial anabolic controls of biomass formation, energy fluxes, and related SOM processes, as well as their interactions with other factors remains largely unknown. This special issue focusing on microbial necromass in soil aims to narrow-down the role of microbial anabolism in the creation and storage of SOM, as well as its resilience to disturbance or changing environmental conditions. We invite submissions on recent findings, methodological breakthroughs and challenges, and innovative concepts for inspiring discussions on microbial necromass in soils. We particularly call for the interactions of studies on soil microbial necromass from different disciplinary domains and the integrated system-related research. === Stoichiometry of soil organic matter === Cui, J., Zhu, Z., Xu, X., Liu, S., Jones, D.L., Kuzyakov, Y., Shibistova, O., Wu, J. and Ge, T., 2020. '''Carbon and nitrogen recycling from microbial necromass to cope with C: N stoichiometric imbalance by priming.''' Soil Biology and Biochemistry, 142, p.107720. [https://doi.org/10.1016/j.soilbio.2020.107720 DOI] [https://www.researchgate.net/publication/338666537 PDF] <br> Abstract: The impact of increasing amounts of labile C input on priming effects (PE) on soil organic matter (SOM) mineralization remains unclear, particularly under anoxic conditions and under high C input common in microbial hotspots. PE and their mechanisms were investigated by a 60-day incubation of three flooded paddy soils amended with13C-labeled glucose equivalent to 50–500% of microbial biomass C (MBC). PE (14–55% of unamended soil) peaked at moderate glucose addition rates (i.e., 50–300% of MBC). Glucose addition above 300% of MBC suppressed SOM mineralization but intensified microbial N acquisition, which contradicted the common PE mechanism of accelerating SOM decomposition for N-supply (frequently termed as “N mining”). Particularly at glucose input rate higher than 3 g kg−1 (i.e., 300–500% of MBC), mineral N content dropped on day 2 close to zero (1.1–2.5 mg N kg−1) because of microbial N immobilization. To cope with the N limitation, microorganisms greatly increased N-acetyl glucosaminidase and leucine aminopeptidase activities, while SOM decomposition decreased. Several discrete peaks of glucose-derived CO2 (contributing >80% to total CO2) were observed between days 13–30 under high glucose input (300–500% of MBC), concurrently with CH4 peaks. Such CO2 dynamics was distinct from the common exponential decay pattern, implicating the recycling and mineralization of 13C-enriched microbial necromass driven by glucose addition. Therefore, N recycling from necromass was hypothesized as a major mechanism to alleviate microbial N deficiency without SOM priming under excess labile C input. Compound-specific 13C-PLFA confirmed the redistribution of glucose-derived C among microbial groups, i.e., necromass recycling. Following glucose input, more than 4/5 of total 13C-PLFA was in the gram-negative and some non-specific bacteria, suggesting these microorganisms as r-strategists capable of rapidly utilizing the most labile C. However, their 13C-PLFA content decreased by 70% after 60 days, probably as a result of death of these r-strategists. On the contrary, the 13C-PLFA in gram-positive bacteria, actinomycetes and fungi (K-strategists) was initially minimal but increased by 0.5–5 folds between days 2 and 60. Consequently, the necromass of dead r-strategists provided a high-quality C–N source to the K-strategists. We conclude that under severe C excess, N recycling from necromass is a much more efficient microbial strategy to cover the acute N demand than N acquisition from the recalcitrant SOM. Kirkby, C.A., Richardson, A.E., Wade, L.J., Batten, G.D., Blanchard, C. and Kirkegaard, J.A., 2013. '''Carbon-nutrient stoichiometry to increase soil carbon sequestration.''' Soil Biology and Biochemistry, 60, pp.77-86. [https://doi.org/10.1016/j.soilbio.2013.01.011 DOI] [http://www.academia.edu/download/40387539/Carbon-nutrient_stoichiometry_to_increas20151125-22628-1ka223g.pdf PDF] <br> Abstract: The more stable fine fraction pool of soil organic matter (FF-SOM; <0.4 mm) has more nitrogen, phosphorus and sulphur (N, P, S) per unit of carbon (C) than the plant material from which it originates and has near constant ratios of C:N:P:S. Consequently, we hypothesised that the sequestration of C-rich crop residue material into the FF-SOM pool could be improved by adding supplementary nutrients to the residues based on these ratios. Here we report on the effect of N, P and S availability on the net humification efficiency (NHE), the change in the size of the FF-SOM pool (as estimated by fine fraction C (FF-C)), following incubation of soil with wheaten straw. Four diverse soils were subjected to seven consecutive incubation cycles, with wheaten straw (10 t ha−1 equivalent) added at the beginning of each cycle, with and without inorganic N, P, S addition (5 kg N, 2 kg P and 1.3 kg S per tonne of straw). This nutrient addition doubled the mean NHE in all soils (from 7% to 15%) and when applied at twice the rate increased NHE further (up to 29%) for the two soils that received this treatment. The FF-N, -P and -S levels increased in concert with FF-C levels in all soils in close agreement with published stoichiometric ratios (C:N:P:S = 10,000:833:200:143). Microbial biomass-C (MB-C) levels were estimated during one incubation cycle and found to increase in parallel with FF-C from 448 μg MB-C g−1 soil (no nutrient addition) to 727 μg MB-C g−1 soil (plus nutrients) and 947 μg MB-C g−1 soil (plus 2× nutrients). There was a significant relationship between MB-C and the change in FF-C during that incubation cycle, providing evidence of a close relationship between the microbial biomass and FF-SOM formation. The two to four-fold increases in NHE achieved with nutrient addition demonstrated that inorganic nutrient availability is critical to sequester C into the more stable FF-SOM pool irrespective of soil type and C input. This has important implications for strategies to build soil fertility or mitigate climate change via increased soil organic C, as the availability and value of these nutrients must be considered. Liang, C., Amelung, W., Lehmann, J. and Kästner, M., 2019. '''Quantitative assessment of microbial necromass contribution to soil organic matter.''' Global change biology, 25(11), pp.3578-3590. [https://doi.org/10.1111/gcb.14781 DOI] [https://www.researchgate.net/publication/334814209 PDF] <br> Abstract: Soil carbon transformation and sequestration have received significant interest in recent years due to a growing need for quantitating its role in mitigating climate change. Even though our understanding of the nature of soil organic matter has recently been substantially revised, fundamental uncertainty remains about the quantitative importance of microbial necromass as part of persistent organic matter. Addressing this uncertainty has been hampered by the absence of quantitative assessments whether microbial matter makes up the majority of the persistent carbon in soil. Direct quantitation of microbial necromass in soil is very challenging because of an overlapping molecular signature with nonmicrobial organic carbon. Here, we use a comprehensive analysis of existing biomarker amino sugar data published between 1996 and 2018, combined with novel appropriation using an ecological systems approach, elemental carbon–nitrogen stoichiometry, and biomarker scaling, to demonstrate a suit of strategies for quantitating the contribution of microbe‐derived carbon to the topsoil organic carbon reservoir in global temperate agricultural, grassland, and forest ecosystems. We show that microbial necromass can make up more than half of soil organic carbon. Hence, we suggest that next‐generation field management requires promoting microbial biomass formation and necromass preservation to maintain healthy soils, ecosystems, and climate. Our analyses have important implications for improving current climate and carbon models, and helping develop management practices and policies. Tipping, E., Somerville, C.J. and Luster, J., 2016. '''The C:N:P:S stoichiometry of soil organic matter.''' Biogeochemistry, 130(1-2), pp.117-131. [https://link.springer.com/content/pdf/10.1007/s10533-016-0247-z.pdf PDF]<br> Abstract: The formation and turnover of soil organic matter (SOM) includes the biogeochemical processing of the macronutrient elements nitrogen (N), phosphorus (P) and sulphur (S), which alters their stoichiometric relationships to carbon (C) and to each other. We sought patterns among soil organic C, N, P and S in data for c. 2000 globally distributed soil samples, covering all soil horizons. For non-peat soils, strong negative correlations (p < 0.001) were found between N:C, P:C and S:C ratios and % organic carbon (OC), showing that SOM of soils with low OC concentrations (high in mineral matter) is rich in N, P and S. The results can be described approximately with a simple mixing model in which nutrient-poor SOM (NPSOM) has N:C, P:C and S:C ratios of 0.039, 0.0011 and 0.0054, while nutrient-rich SOM (NRSOM) has corresponding ratios of 0.12, 0.016 and 0.016, so that P is especially enriched in NRSOM compared to NPSOM. The trends hold across a range of ecosystems, for topsoils, including O horizons, and subsoils, and across different soil classes. The major exception is that tropical soils tend to have low P:C ratios especially at low N:C. We suggest that NRSOM comprises compounds selected by their strong adsorption to mineral matter. The stoichiometric patterns established here offer a new quantitative framework for SOM classification and characterisation, and provide important constraints to dynamic soil and ecosystem models of carbon turnover and nutrient dynamics. Urbina, I., Grau, O., Sardans, J., Ninot, J.M. and Peñuelas, J., 2020. '''Encroachment of shrubs into subalpine grasslands in the Pyrenees changes the plant-soil stoichiometry spectrum.''' Plant and Soil, pp.1-17. [https://doi.org/10.1007/s11104-019-04420-3 DOI]<br> Abstract - Aims: Shrub encroachment has been reported over a large proportion of the subalpine grasslands across Europe and is expected to have an important impact on the biogeochemical cycle of these ecosystems. We investigated the stoichiometric changes in the plant-soil system along the succession (e.g. increase in encroachment from unencroached grassland to mature shrubland) at two contrasting sites in the Pyrenees. Methods: We analyzed the chemical composition (C, N,15N, P, K, Ca, Mg and Fe) in the soil and in the aboveground plant compartments (leaves, leaf-litter and stems) of the main herbaceous species and shrubs at three contrasting stages of the succession: unencroached grassland, young shrubland and mature shrubland. Results: The plant-soil stoichiometry spectrum differed between the successional stages. Shrub encroachment generally increased the concentration of C and Ca and the C:N ratio and often reduced to concentrations of N, P and K in the leaves and leaf-litter, while several soil nutrient concentrations (N, P, K Ca and Mg) decreased. The stocks of C, N, P, Ca, and Mg in the total aboveground biomass increased with encroachment. === Fractions of soil organic matter === Lavallee, J.M., Soong, J.L. and Cotrufo, M.F., 2020. '''Conceptualizing soil organic matter into particulate and mineral‐associated forms to address global change in the 21st century.''' Global Change Biology, 26(1), pp.261-273. [https://onlinelibrary.wiley.com/doi/full/10.1111/gcb.14859 PDF]<br> Abstract: Managing soil organic matter (SOM) stocks to address global change challenges requires well‐substantiated knowledge of SOM behavior that can be clearly communicated between scientists, management practitioners, and policy makers. However, SOM is incredibly complex and requires separation into multiple components with contrasting behavior in order to study and predict its ynamics. Numerous diverse SOM separation schemes are currently used, making cross‐study comparisons difficult and hindering broad‐scale generalizations. Here, we recommend separating SOM into particulate (POM) and mineral‐associated (MAOM) forms, two SOM components that are fundamentally different in terms of their formation, persistence, and functioning. We provide evidence of their highly contrasting physical and chemical properties, mean residence times in soil, and responses to land use change, plant litter inputs, warming, CO2 enrichment, and N fertilization. Conceptualizing SOM into POM versus MAOM is a feasible, well‐supported, and useful framework that will allow scientists to move beyond studies of bulk SOM, but also use a consistent separation scheme across studies. Ultimately, we propose the POM versus MAOM framework as the best way forward to understand and predict broad‐scale SOM dynamics in the context of global change challenges and provide necessary recommendations to managers and policy makers. Olk, D.C., Bloom, P.R., Perdue, E.M., McKnight, D.M., Chen, Y., Farenhorst, A., Senesi, N., Chin, Y.P., Schmitt-Kopplin, P., Hertkorn, N. and Harir, M., 2019. Environmental and agricultural relevance of humic fractions extracted by alkali from soils and natural waters. Journal of Environmental Quality, 48(2), pp.217-232. [https://doi.org/10.2134/jeq2019.02.0041 DOI] [https://www.researchgate.net/profile/Diane-Mcknight/publication/332642838 PDF]<br> Abstract: To study the structure and function of soil organic matter, soil scientists have performed alkali extractions for soil humic acid (HA) and fulvic acid (FA) fractions for more than 200 years. Over the last few decades aquatic scientists have used similar fractions of dissolved organic matter, extracted by resin adsorption followed by alkali desorption. Critics have claimed that alkaliextractable fractions are laboratory artifacts, hence unsuitable for studying natural organic matter structure and function in field conditions. In response, this review first addresses specific conceptual concerns about humic fractions. Then we discuss several case studies in which HA and FA were extracted from soils, waters, and organic materials to address meaningful problems across diverse research settings. Specifically, one case study demonstrated the importance of humic substances for understanding transport and bioavailability of persistent organic pollutants. An understanding of metal binding sites in FA and HA proved essential to accurately model metal ion behavior in soil and water. In landscape-based studies, pesticides were preferentially bound to HA, reducing their mobility. Compost maturity and acceptability of other organic waste for land application were well evaluated by properties of HA extracted from these materials. A young humic fraction helped understand N cycling in paddy rice (Oryza sativa L.) soils, leading to improved rice management. The HA and FA fractions accurately represent natural organic matter across multiple environments, source materials, and research objectives. Studying them can help resolve important scientific and practical issues.<br> Core Ideas: *Humic substances have long been extracted from soils, waters, and organic materials. *Their chemical composition has well represented that of natural organic matter. *Compost maturation and composition are well represented by their properties. *Soil humic studies elucidated metal and organic xenobiotic binding and nutrient cycling. *Their quantities and composition in soil respond to field treatments. === Carbon sequestration and soil organic matter === Alemu, A.W., Kröbel, R., McConkey, B.G. and Iwaasa, A.D., 2019. '''Effect of increasing species diversity and grazing management on pasture productivity, animal performance, and soil carbon sequestration of re-established pasture in Canadian Prairie.''' Animals, 9(4), p.127. [https://doi.org/10.3390/ani9040127 DOI] [https://www.mdpi.com/2076-2615/9/4/127/pdf PDF]<br> Simple Summary<br> Canadian grasslands are recognized for providing high quality forage for grazing livestock and wildlife. The study was conducted on a re-established pasture in aWestern Canadian semi-arid climate to investigate the effect of pasture species mixture and grazing management on pasture productivity, animal performance, and soil carbon sequestration. Pasture productivity and animal response were independent of pasture mixture but affected by grazing management. Average pasture dry matter productivity was greater with deferred-rotational grazing while pasture quality and animal gain were higher with continuous grazing. Soil carbon change varied with pasture seed mixture and grazing management interaction where pasture with 7-species mixture under continuous grazing had the lowest soil carbon gain. Yang, Y., Tilman, D., Furey, G. and Lehman, C., 2019. '''Soil carbon sequestration accelerated by restoration of grassland biodiversity.''' Nature communications, 10(1), pp.1-7. [https://doi.org/10.1038/s41467-019-08636-w DOI] [https://www.nature.com/articles/s41467-019-08636-w.pdf PDF]<br> Summary<br> Agriculturally degraded and abandoned lands can remove atmospheric CO2 and sequester it as soil organic matter during natural succession. However, this process may be slow, requiring a century or longer to re-attain pre-agricultural soil carbon levels. Here, we find that restoration of late-successional grassland plant diversity leads to accelerating annual carbon storage rates that, by the second period (years 13–22), are 200% greater in our highest diversity treatment than during succession at this site, and 70% greater than in monocultures. The higher soil carbon storage rates of the second period (years 13–22) are associated with the greater aboveground production and root biomass of this period, and with the presence of multiple species, especially C4 grasses and legumes. Our results suggest that restoration of high plant diversity may greatly increase carbon capture and storage rates on degraded and abandoned agricultural lands. Oldfield, E.E., Bradford, M.A. and Wood, S.A., 2019. '''Global meta-analysis of the relationship between soil organic matter and crop yields.''' Soil, 5(1), pp.15-32. [https://doi.org/10.5194/soil-5-15-2019 DOI] [https://pdfs.semanticscholar.org/4caf/a6987c22fd12b0f32ffaf91d911d2a69330c.pdf PDF]<br> Abstract<br> Resilient, productive soils are necessary to sustainably intensify agriculture to increase yields while minimizing environmental harm. To conserve and regenerate productive soils, the need to maintain and build soil organic matter (SOM) has received considerable attention. Although SOM is considered key to soil health, its relationship with yield is contested because of local-scale differences in soils, climate, and farming systems. There is a need to quantify this relationship to set a general framework for how soil management could potentially contribute to the goals of sustainable intensification. We developed a quantitative model exploring how SOM relates to crop yield potential of maize and wheat in light of co-varying factors of management, soil type, and climate. We found that yields of these two crops are on average greater with higher concentrations of SOC (soil organic carbon). However, yield increases level off at ∼ 2 % SOC. Nevertheless, approximately two-thirds of the world’s cultivated maize and wheat lands currently have SOC contents of less than 2 %. Using this regression relationship developed from published empirical data, we then estimated how an increase in SOC concentrations up to regionally specific targets could potentially help reduce reliance on nitrogen (N) fertilizer and help close global yield gaps. Potential N fertilizer reductions associated with increasing SOC amount to 7 % and 5 % of global N fertilizer inputs across maize and wheat fields, respectively. Potential yield increases of 10 ± 11 % (mean ± SD) for maize and 23 ± 37 % for wheat amount to 32 % of the projected yield gap for maize and 60 % of that for wheat. Our analysis provides a global-level prediction for relating SOC to crop yields. Further work employing similar approaches to regional and local data, coupled with experimental work to disentangle causative effects of SOC on yield and vice versa, is needed to provide practical prescriptions to incentivize soil management for sustainable intensification. Rasmussen, C., Heckman, K., Wieder, W.R., Keiluweit, M., Lawrence, C.R., Berhe, A.A., Blankinship, J.C., Crow, S.E., Druhan, J.L., Pries, C.E.H. and Marin-Spiotta, E., 2018. '''Beyond clay: towards an improved set of variables for predicting soil organic matter content.''' ''Biogeochemistry'', ''137''(3), pp.297-306. [https://doi.org/10.1007/s10533-018-0424-3 DOI] [https://www.fs.usda.gov/treesearch/pubs/download/56975.pdf PDF]<br> Abstract<br> Improved quantification of the factors controlling soil organic matter (SOM) stabilization at continental to global scales is needed to inform projections of the largest actively cycling terrestrial carbon pool on Earth, and its response to environmental change. Biogeochemical models rely almost exclusively on clay content to modify rates of SOM turnover and fluxes of climate-active CO2 to the atmosphere. Emerging conceptual understanding, however, suggests other soil physicochemical properties may predict SOM stabilization better than clay content. We addressed this discrepancy by synthesizing data from over 5,500 soil profiles spanning continental scale environmental gradients. Here, we demonstrate that other physicochemical parameters are much stronger predictors of SOM content, with clay content having relatively little explanatory power. We show that exchangeable calcium strongly predicted SOM content in water-limited, alkaline soils, whereas with increasing moisture availability and acidity, iron- and aluminum-oxyhydroxides emerged as better predictors, demonstrating that the relative importance of SOM stabilization mechanisms scales with climate and acidity. These results highlight the urgent need to modify biogeochemical models to better reflect the role of soil physicochemical properties in SOM cycling. Sanderman, J., Hengl, T. and Fiske, G.J., 2017. '''Soil carbon debt of 12,000 years of human land use.''' Proceedings of the National Academy of Sciences, 114(36), pp.9575-9580. [https://doi.org/10.1073/pnas.1706103114 DOI] [https://www.pnas.org/content/pnas/114/36/9575.full.pdf PDF]<br> Significance<br> "Land use and land cover change has resulted in substantial losses of carbon from soils globally, but credible estimates of how much soil carbon has been lost have been difficult to generate. Using a data-driven statistical model and the History Database of the Global Environment v3.2 historic land-use dataset, we estimated that agricultural land uses have resulted in the loss of 133 Pg C from the soil. Importantly, our maps indicate hotspots of soil carbon loss, often associated with major cropping regions and degraded grazing lands, suggesting that there are identifiable regions that should be targets for soil carbon restoration efforts."<br> Abstract<br> "Human appropriation of land for agriculture has greatly altered the terrestrial carbon balance, creating a large but uncertain carbon debt in soils. Estimating the size and spatial distribution of soil organic carbon (SOC) loss due to land use and land cover change has been difficult but is a critical step in understanding whether SOC sequestration can be an effective climate mitigation strategy. In this study, a machine learning-based model was fitted using a global compilation of SOC data and the History Database of the Global Environment (HYDE) land use data in combination with climatic, landform and lithology covariates. Model results compared favorably with a global compilation of paired plot studies. Projection of this model onto a world without agriculture indicated a global carbon debt due to agriculture of 133 Pg C for the top 2 m of soil, with the rate of loss increasing dramatically in the past 200 years. The HYDE classes “grazing” and “cropland” contributed nearly equally to the loss of SOC. There were higher percent SOC losses on cropland but since more than twice as much land is grazed, slightly higher total losses were found from grazing land. Important spatial patterns of SOC loss were found: Hotspots of SOC loss coincided with some major cropping regions as well as semiarid grazing regions, while other major agricultural zones showed small losses and even net gains in SOC. This analysis has demonstrated that there are identifiable regions which can be targeted for SOC restoration efforts."<br> Woolf, D. and Lehmann, J., 2019. '''Microbial models with minimal mineral protection can explain long-term soil organic carbon persistence'''. Scientific reports, 9(1), pp.1-8. [https://doi.org/10.1038/s41598-019-43026-8 DOI] [https://www.nature.com/articles/s41598-019-43026-8.pdf PDF]<br> Abstract<br> Soil organic carbon (SOC) models currently in widespread use omit known microbial processes, and assume the existence of a SOC pool whose intrinsic properties confer persistence for centuries to millennia, despite evidence from priming and aggregate turnover that cast doubt on the existence of SOC with profound intrinsic stability. Here we show that by including microbial interactions in a SOC model, persistence can be explained as a feedback between substrate availability, mineral protection and microbial population size, without invoking an unproven pool that is intrinsically stable for centuries. The microbial SOC model based on this concept reproduces long-term data (r2 = 0.92; n = 90), global SOC distribution (rmse = 4.7 +/− 0.6 kg C m−2), and total global SOC in the top 0.3 m (822 Pg C) accurately. SOC dynamics based on a microbial feedback without stable pools are thus consistent with global SOC distribution. This has important implications for carbon management, suggesting that relatively fast cycling, rather than recalcitrant, SOC must form the primary target of efforts to build SOC stocks.<br> === Soil organic matter and agriculture === Obour, P.B., Jensen, J.L., Lamandé, M., Watts, C.W. and Munkholm, L.J., 2018. '''Soil organic matter widens the range of water contents for tillage.''' Soil and Tillage Research, 182, pp.57-65. [https://doi.org/10.1016/j.still.2018.05.001 DOI] [https://www.sciencedirect.com/science/article/pii/S0167198718304434/pdfft?md5=049a7d1b862cc1672f5e0e340369ef5b&pid=1-s2.0-S0167198718304434-main.pdf PDF]<br> Abstract: The effects of soil organic matter on the water contents for tillage were investigated by sampling soils with a uniform texture, but a range of soil organic carbon (SOC) from two long-term field experiments at Highfield in Rothamsted Research, UK and Askov Experimental Station, Denmark. The treatments studied in Highfield were Bare fallow (BF), Continuous arable rotation (A), Ley-arable (LA) and Grass (G); and in Askov: unfertilized (UNF), ½ mineral fertilizer (½ NPK), 1 mineral fertilizer (1NPK), and 1½ animal manure (1½AM). Minimally disturbed soil cores (100 cm3) were sampled per plot in both locations from 6 to 10 cm depth to generate water retention data. Soil blocks were also sampled at 6–15 cm depth to determine basic soil properties and to measure soil aggregate strength parameters. The range of soil water contents appropriate for tillage were determined using the water retention and the consistency approaches. SOC content in Highfield was in the order: G > LA = A > BF, and in Askov: 1½ AM > 1NPK = ½NPK > UNF. Results showed that different long-term management of the silt loam Highfield soil, and fertilization of the sandy loam Askov soil affected the mechanical properties of the soils— for Highfield soil, aggregates from the G treatment were stronger in terms of rupture energy when wet (−100 hPa matric potential) than the BF treatment. As the soil dried (−300 and −1000 hPa matric potentials), soil aggregates from the G treatment were relatively weaker and more elastic than the BF soil. Our study showed, for both Highfield and Askov soils, a strong positive linear increase in the range of water contents for tillage with increasing contents of SOC. This suggests that management practices leading to increased SOC can improve soil workability by increasing the range of water contents for tillage. We recommended using the consistency approach over the water retention approach for determining the range of water contents for tillage because it seems to give realistic estimates of the water contents for tillage. h9blne68ulglhzyugerhz2zlp7bitts 2 289273 2844827 2844795 2026-11-07T21:33:39Z Dc.samizdat 2856930 /* Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space */ 2844827 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space is Euclidean with four perpendicular dimensions. * Atoms are [[W:4-polytope|4-polytopes]]. An atom's motion is the local product of its discrete self-reflections in Euclidean 4-space. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. It occupies a hyperspherical region in Euclidean 4-space. * Everything of intermediate size between an atom and a star, including ourselves and our planet, lies in a 3-dimensional manifold of ordinary space, embedded in Euclidean 4-space. * Our entire 3-space manifold is moving at the speed of light <math>c</math> in Euclidean 4-space. The gravitational coherence of galaxies is inertial coherence, a result of their linear motion at velocity <math>c</math> in Euclidean 4-space. * Special relativity describes the linear motion of objects and light signals in Euclidean 4-space. The propagation speed of light is <math>c\prime = 2c</math> measured on a straight line in Euclidean 4-space. * General relativity describes the rotational motion of objects with mass in Euclidean 4-space. Time ticks at the same rate everywhere in Euclidean 4-space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in Euclidean 4-space. The proton has the symmetry of the 4-simplex polytope. The neutron has the symmetry of the 4-orthoplex polytope. * The universe may properly be viewed as a <math>4</math>-sphere centered wherever there is an observer. == A theory of the Euclidean cosmos == <blockquote>If we are to have any hope of understanding the universe, we must dare to imagine a world that is not bounded by our limited perspective.<ref>{{Cite book|first=Adam|last =Becker|year=2018|title=What Is Real? The Unfinished Quest for the Meaning of Quantum Physics}}</ref></blockquote> The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets (at their surfaces), are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. Several objects which appear to us to be located at almost the same point in our sky may actually lie in directions many degrees apart, since the entire hyperspherical sky is projected onto an ordinary sphere in our view of it. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we detect it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the bounding surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The bounding surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is bounded by a smaller 3-sphere lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the bounding surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of large gravitational objects. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to all three of our 3-manifold's dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, if their gravity is strong enough to give them a core of superdense matter like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at center, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every free-falling object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions at velocity <math>c</math>, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by [[W:Geometric algebra|Clifford's algebraic methods]]), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.<ref name=Einstein1923>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the local product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own mirror surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct mirror surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct mirror surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are direct dimensional analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation <math>\mathrm{QT}</math> or a simple rotation <math>\mathrm{Q}</math> lies on a great circle of an ordinary sphere (a 2-sphere), translating or stationary. In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere), translating or stationary. Rotational great circles on hyperspheres are inherently more complex than the ordinary great circles on spheres we experience in 3-space. A point on the surface of an object rotating in 4-space may be in motion on two circles, in two [[W:Completely orthogonal|completely orthogonal]] rotation planes simultaneously. As each planar circle rotates like a wheel turning, its rotation plane also tilts sideways like a coin flipping, eventually into the completely orthogonal original rotation plane of the other circle, so that the circles have exchanged rotation planes. The product of these two simultaneous completely orthogonal circular motions gives a circular orbit to each moving point that does not lie in any stationary rotation plane; it is a circular helix that bends in all four dimensions rather than in just two dimensions, in either a left or right hand direction of helical curvature. Unlike ordinary planar circles, these 4-dimensional circles are inherently chiral, and their circumference is not <math>2\pi r</math>. But like ordinary planar great circles they are true geodesic circles. They may even be understood as dimensionally more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In our universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, these motions occur only at the constant velocity <math>c</math>, and there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating, but it is a common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space enumerate all possible displacements of objects with mass. We find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be seen as a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Objects with mass of any size (including atoms and their subatomic particles) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, such as an atom in its own proper reference frame. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. 2-dimensional objects reflect in a line, 3-dimensional objects reflect in a plane, and 4-dimensional objects reflect in a hyperplane (a 3-dimensional mirror). A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel hyperplanes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting hyperplanes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in two pairs of parallel hyperplanes at once, a reflection in four hyperplane mirrors; it is all translation and no rotation. All the motion goes to translation, so the displacement goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in Euclidean 4-space == Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved 3-manifold embedded in flat Euclidean 4-space. The motion and curvature of their proper 3-space complicates sightline calculations for observers; they require Lorentz transformations to produce their 3-coordinate Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction in 4-coordinate space. Lorentz transformations are needed only when an observer wants to calculate a projection, that is, the shadow in a 3-coordinate space of how things will appear as a 3-dimensional scene (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there exactly as they do in a classical vector space, but bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in 3-space from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time) at velocity <math>c</math>, and all observers and all scenes being observed are in motion (at this constant velocity) in their respective proper time directions, we observe perspective forshortenings in time as well as in one of our three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of all physical processes varies from field to field, and reference frame differences predicted by the theory are not reciprocal.) The Lorentz invariant of special relativity allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. In Euclidean relativity we are able to state this intrinsic symmetry of nature more simply: <blockquote>''Time ticks at the same rate everywhere in space.''</blockquote> This formulation of special relativity at first appears to contradict general relativity, which insists that time (in the sense of the quantum rate of all physical processes) ticks more slowly deeper in a gravitational field. We shall see (below) that there is no contradiction between the universal rate of time at every place in space, and the relative rates of time in distinct gravitational fields, because in the Euclidean relativity formulation all gravitational fields are in motion. A gravitational field is not a place; it is better described as a state of motion of a set of objects, in particular their states of acceleration. As the objects are in perpetual motion, so also is their field. General relativity predicts differences in the perceived rates at which clocks run in distinct moving gravitational fields, just as special relativity predicts differences in perceived rates at which clocks run in distinct inertial reference frames, but we shall see that none of these differences imply that time (in the sense of the quantum rate of change) ever runs at any rate other than <math>c</math> in any stationary place in 4-space. None of the special relativity Lorentz effects (or as we shall see the general relativity effects) are beyond geometric explanation or paradoxical, but their geometric explanation requires Euclidean 4-space. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting and revealing than Euclidean 3-space, analogous to the way our 3-space is more deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are strictly analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is a strict expression of relations between intrinsic group-theoretic symmetries: that is Noether's and Coxeter's great discovery. == General relativity is the geometry of gravity in Euclidean 4-space == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective distinct screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation <math>T</math> through 4-space. The velocity of that vector remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation composed of a discrete number of its characteristic rotational displacement in each full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and discrete number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the bounding surface of a rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may have to be greater than 360° to close a circular revolution. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference, they are chiral 4-dimensional circles which we call isoclines. Many distinct 4-space rotations of interest have isoclines of 720° circumference. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two mirror surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two mirror surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number <math>c</math> of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number <math>c</math> of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution, and the circumference of the complete revolution, are characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation, since they depend on the geometry of the rotational isocline which is unique to the distinct rotation. Distinct rotations arise from distinct symmetry groups, which are each their own mystery with a unique conservation law and set of rotations. The unique geometry of each rotation's isocline is that of some distinct star polygon. The geometric relationships between star polygons defined by successive rational numbers are mathematically mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios, which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions, and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations, because a translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is 180°. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing, and inertia is the conservation of this distinct double rotation. The acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity <math>c</math>. Because the rate of atomic scale displacement events is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's isocline geometry. General relativity explains gravity geometrically as a non-Euclidean geometry in spacetime that is more complex than special relativity's non-Euclidean Lorentz geometry in spacetime. In Euclidean 4-space the geometry of special relativity becomes simpler Euclidean geometry, dimensionally analogous to familiar perspective geometry in ordinary Euclidean 3-space, and therefore visualizable provided we can stretch our dimensional analogy muscles enough to imagine perspective views in four orthogonal spatial dimensions. A similar stretch is required of us to visualize general relativity in Euclidean 4-space: we must imagine distinct rotations in four spatial dimensions. To understand gravity geometrically in four dimensions, we must identify the distinct rotation the accelerating observer is performing, visualize its isocline, and model its unique conservation law geometrically as motion on those isoclines in Euclidean 4-space. That problem is dimensionally analogous to the problem that Kepler and Newton solved for the rotation of the planets in Euclidean 3-space.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> It is a [[W:Kepler problem|Kepler problem]], hosted in Euclidean 4-space. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's isocline geometry, yielding a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. Our challenge is to visualize this double rotation. ... == Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space == Atoms are 4-polytopes, small round 4-dimensional objects, and their rotational symmetry is compounded from that of the [[Polyscheme#Regular convex 4-polytopes|six regular convex 4-polytopes]]. Their geometry is beyond the scope of this paper, but we begin with the proton, which we identify with the rotational symmetry of the 4-simplex polytope. Schläfli discovered that there exists a compound series of six regular convex 4-polytopes, dimensionally analogous to the compound series of five regular convex 3-polytopes, the Platonic solids. Polytopes in each series are naturally ordered by size, as a measure of content for the same radius, which is also a measure of their roundness, the number of their vertices. They form a series of increasingly round polytopes in which each is a compound of multiple instances of its predecessor (with one exception to this progression which will concern us later). The six regular convex 4-polytopes have 5, 8, 16, 24, 120, and 600 vertices respectively. They are the 5-point (5-cell) 4-simplex, the 8-point (16-cell) 4-orthoplex, the 16-point (8-cell) 4-hypercube, the 24-point (24-cell), the 120-point (600-cell), and the 600-point (120-cell). The smallest (least round) regular convex 4-polytope is the [[5-cell|4-simplex]]. It has 5 vertices, 10 edges, 10 triangular faces, and 5 tetrahedral cells. The regular 4-simplex is the configuration of 5 mutually equidistant points in Euclidean space, on the surface of a 3-sphere. .... We conclude that the rotational geometry of the proton is that of the 4-simplex. The largest (roundest) regular convex 4-polytope is called the [[120-cell|120-cell]]. It has 600 vertices and 1200 edges, because it is a regular compound of 120 completely disjoint 4-simplexes, rotated isoclinically with respect to each other such that their vertices are evenly distributed on the surface of a 3-sphere. It is also a regular compound of every other regular convex 4-polytope, so that instances of every regular convex polytope which can exist in Euclidean 4-space are found within it. It is the singular geometrically comprehensive 4-polytope, containing instances of the relationships among all these polytopes. The exception to the rule that each 4-polytope in the series compounds to its successor is the 5-point 4-simplex, which does not compound to its successor the 8-point 4-orthoplex, nor to any other 4-polytope in the series except the largest, the 600-point 120-cell. None of the 4-polytopes in the series are divisible into an integral number of 4-simplexes except the 120-cell. Every 4-polytope in the series except the 4-simplex is divisible into an integral number of 4-orthoplexes. Thus there are two alternate integral building blocks of the comprehensive 120-cell: the 5-point 4-simplex, and the 8-point 4-orthoplex. Only the 4-orthoplex will build the other three 4-polytopes in the series by simple compounding. However, the symmetry group of the 4-simplex also has a foundational relationship to the symmetries of all the 4-polytopes in the series. If we view the 4-simplex as the largest 4-polytope instead of the smallest, and subdivide it by integral truncation, we find smaller instances of all the other 4-polytopes within it. The nucleus of a distinct atomic element contains a characteristic number of protons, its atomic number. The rotational symmetry of each element is based on that of a compound of its distinct number of completely disjoint 4-simplex polytopes, that is, on the symmetry of a sparsely populated 120-cell. Because only 120 4-simplexes will fit into a 120-cell, each occupying exclusively 5 equidistant vertices of the 600 vertices, only 120 distinct atomic elements are possible. Any compound of the atomic number of 4-simplexes constitutes an atom of that element, but multiple geometric configurations of each element are possible, depending on which subset of 4-simplex positions is populated. Some of these configurations will have more symmetry than others. We conclude that these alternate configurations are potential nuclides of the atomic element, some potentially more than others. We identify the neutron with the rotational symmetry of the 8-point 4-orthoplex. The 4-orthoplex is the easiest 4-polytope to visualize because it consists simply of 4 pairs of opposing vertices on 4 orthogonal axes. It is the orthonormal basis polytope, whose size, location and orientation in 4-space defines a Cartesian (w,x,y,z) coordinate reference frame. Every 4-polytope in the series of six except the 4-simplex is divisible into an integral number of disjoint 4-orthoplexes, each occupying exclusively 8 of the 600 vertices of the 120-cell. The reason the 4-simplex is an exception is that it is the only regular convex 4-polytope with vertices that do not occur in opposing pairs. While it is impossible to position two 4-simplexes on the 3-sphere such that they share some but not all 5 vertices, two 4-orthoplexes can be positioned so that they share an axis without sharing all 8 vertices. Additionally, the largest 4-polytopes in the series, the 120-point 600-cell and the 600-point 120-cell, are each divisible into an integral number of non-disjoint 4-orthoplexes which share axes. The 600-point 120-cell can only be partitioned into 120 disjoint 5-point 4-simplexes in one way. The 120-cell can also be partitioned into 75 disjoint 8-point 4-orthoplexes, but this partitioning can be done in 10 different ways. The 120-cell contains 675 distinct 4-orthoplexes, each with four orthogonal axes. Each axis occurs in 9 distinct 4-orthoplexes, and is orthogonal to its 27 companion axes in those 9 4-orthoplexes, and to no other axes of the 120-cell. An element of atomic number <math>z</math> is a compound of <math>z</math> disjoint 4-simplexes, so it occupies exclusively <math>5 z</math> vertices of the 120-cell, in some configuration with the 5 vertices of each 4-simplex mutually equidistant from each other on the the 3-sphere. Thus for example the element Carbon with 6 protons occupies 30 distinct vertices of the 600. One of these configurations is also a configuration of an integral number of disjoint 4-orthoplexes, but the rest are not. .... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating Euclidean and spherical <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any reference frame, not only from their own proper inertial reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's discovery of higher dimensional space: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, our 4-space universe might be infinite, or at some vast radius (far greater than the radius of our big-bang 3-sphere) it might close into a 4-sphere. The universe viewed as a 4-sphere might, or might not, be expanding from some distant precursor to our big bang. The discovery of where exactly we are located in such a 4-sphere might bring about a whole new enlightenment. In any case the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no immediate way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of the starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:3-sphere|3-sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture. He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice."<ref name=Einstein1923/> Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction of it; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the planet's core and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest 4-ball object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity, so symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a wilderness project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's surface), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} k8sh3h61bunertl1qxeowsi0z0i0t4v 2844831 2844827 2026-11-07T22:25:43Z Dc.samizdat 2856930 /* Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space */ 2844831 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space is Euclidean with four perpendicular dimensions. * Atoms are [[W:4-polytope|4-polytopes]]. An atom's motion is the local product of its discrete self-reflections in Euclidean 4-space. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. It occupies a hyperspherical region in Euclidean 4-space. * Everything of intermediate size between an atom and a star, including ourselves and our planet, lies in a 3-dimensional manifold of ordinary space, embedded in Euclidean 4-space. * Our entire 3-space manifold is moving at the speed of light <math>c</math> in Euclidean 4-space. The gravitational coherence of galaxies is inertial coherence, a result of their linear motion at velocity <math>c</math> in Euclidean 4-space. * Special relativity describes the linear motion of objects and light signals in Euclidean 4-space. The propagation speed of light is <math>c\prime = 2c</math> measured on a straight line in Euclidean 4-space. * General relativity describes the rotational motion of objects with mass in Euclidean 4-space. Time ticks at the same rate everywhere in Euclidean 4-space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in Euclidean 4-space. The proton has the symmetry of the 4-simplex polytope. The neutron has the symmetry of the 4-orthoplex polytope. * The universe may properly be viewed as a <math>4</math>-sphere centered wherever there is an observer. == A theory of the Euclidean cosmos == <blockquote>If we are to have any hope of understanding the universe, we must dare to imagine a world that is not bounded by our limited perspective.<ref>{{Cite book|first=Adam|last =Becker|year=2018|title=What Is Real? The Unfinished Quest for the Meaning of Quantum Physics}}</ref></blockquote> The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets (at their surfaces), are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. Several objects which appear to us to be located at almost the same point in our sky may actually lie in directions many degrees apart, since the entire hyperspherical sky is projected onto an ordinary sphere in our view of it. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we detect it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the bounding surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The bounding surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is bounded by a smaller 3-sphere lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the bounding surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of large gravitational objects. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to all three of our 3-manifold's dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, if their gravity is strong enough to give them a core of superdense matter like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at center, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every free-falling object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions at velocity <math>c</math>, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by [[W:Geometric algebra|Clifford's algebraic methods]]), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.<ref name=Einstein1923>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the local product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own mirror surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct mirror surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct mirror surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are direct dimensional analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation <math>\mathrm{QT}</math> or a simple rotation <math>\mathrm{Q}</math> lies on a great circle of an ordinary sphere (a 2-sphere), translating or stationary. In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere), translating or stationary. Rotational great circles on hyperspheres are inherently more complex than the ordinary great circles on spheres we experience in 3-space. A point on the surface of an object rotating in 4-space may be in motion on two circles, in two [[W:Completely orthogonal|completely orthogonal]] rotation planes simultaneously. As each planar circle rotates like a wheel turning, its rotation plane also tilts sideways like a coin flipping, eventually into the completely orthogonal original rotation plane of the other circle, so that the circles have exchanged rotation planes. The product of these two simultaneous completely orthogonal circular motions gives a circular orbit to each moving point that does not lie in any stationary rotation plane; it is a circular helix that bends in all four dimensions rather than in just two dimensions, in either a left or right hand direction of helical curvature. Unlike ordinary planar circles, these 4-dimensional circles are inherently chiral, and their circumference is not <math>2\pi r</math>. But like ordinary planar great circles they are true geodesic circles. They may even be understood as dimensionally more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In our universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, these motions occur only at the constant velocity <math>c</math>, and there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating, but it is a common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space enumerate all possible displacements of objects with mass. We find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be seen as a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Objects with mass of any size (including atoms and their subatomic particles) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, such as an atom in its own proper reference frame. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. 2-dimensional objects reflect in a line, 3-dimensional objects reflect in a plane, and 4-dimensional objects reflect in a hyperplane (a 3-dimensional mirror). A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel hyperplanes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting hyperplanes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in two pairs of parallel hyperplanes at once, a reflection in four hyperplane mirrors; it is all translation and no rotation. All the motion goes to translation, so the displacement goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in Euclidean 4-space == Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved 3-manifold embedded in flat Euclidean 4-space. The motion and curvature of their proper 3-space complicates sightline calculations for observers; they require Lorentz transformations to produce their 3-coordinate Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction in 4-coordinate space. Lorentz transformations are needed only when an observer wants to calculate a projection, that is, the shadow in a 3-coordinate space of how things will appear as a 3-dimensional scene (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there exactly as they do in a classical vector space, but bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in 3-space from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time) at velocity <math>c</math>, and all observers and all scenes being observed are in motion (at this constant velocity) in their respective proper time directions, we observe perspective forshortenings in time as well as in one of our three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of all physical processes varies from field to field, and reference frame differences predicted by the theory are not reciprocal.) The Lorentz invariant of special relativity allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. In Euclidean relativity we are able to state this intrinsic symmetry of nature more simply: <blockquote>''Time ticks at the same rate everywhere in space.''</blockquote> This formulation of special relativity at first appears to contradict general relativity, which insists that time (in the sense of the quantum rate of all physical processes) ticks more slowly deeper in a gravitational field. We shall see (below) that there is no contradiction between the universal rate of time at every place in space, and the relative rates of time in distinct gravitational fields, because in the Euclidean relativity formulation all gravitational fields are in motion. A gravitational field is not a place; it is better described as a state of motion of a set of objects, in particular their states of acceleration. As the objects are in perpetual motion, so also is their field. General relativity predicts differences in the perceived rates at which clocks run in distinct moving gravitational fields, just as special relativity predicts differences in perceived rates at which clocks run in distinct inertial reference frames, but we shall see that none of these differences imply that time (in the sense of the quantum rate of change) ever runs at any rate other than <math>c</math> in any stationary place in 4-space. None of the special relativity Lorentz effects (or as we shall see the general relativity effects) are beyond geometric explanation or paradoxical, but their geometric explanation requires Euclidean 4-space. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting and revealing than Euclidean 3-space, analogous to the way our 3-space is more deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are strictly analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is a strict expression of relations between intrinsic group-theoretic symmetries: that is Noether's and Coxeter's great discovery. == General relativity is the geometry of gravity in Euclidean 4-space == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective distinct screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation <math>T</math> through 4-space. The velocity of that vector remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation composed of a discrete number of its characteristic rotational displacement in each full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and discrete number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the bounding surface of a rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may have to be greater than 360° to close a circular revolution. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference, they are chiral 4-dimensional circles which we call isoclines. Many distinct 4-space rotations of interest have isoclines of 720° circumference. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two mirror surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two mirror surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number <math>c</math> of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number <math>c</math> of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution, and the circumference of the complete revolution, are characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation, since they depend on the geometry of the rotational isocline which is unique to the distinct rotation. Distinct rotations arise from distinct symmetry groups, which are each their own mystery with a unique conservation law and set of rotations. The unique geometry of each rotation's isocline is that of some distinct star polygon. The geometric relationships between star polygons defined by successive rational numbers are mathematically mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios, which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions, and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations, because a translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is 180°. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing, and inertia is the conservation of this distinct double rotation. The acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity <math>c</math>. Because the rate of atomic scale displacement events is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's isocline geometry. General relativity explains gravity geometrically as a non-Euclidean geometry in spacetime that is more complex than special relativity's non-Euclidean Lorentz geometry in spacetime. In Euclidean 4-space the geometry of special relativity becomes simpler Euclidean geometry, dimensionally analogous to familiar perspective geometry in ordinary Euclidean 3-space, and therefore visualizable provided we can stretch our dimensional analogy muscles enough to imagine perspective views in four orthogonal spatial dimensions. A similar stretch is required of us to visualize general relativity in Euclidean 4-space: we must imagine distinct rotations in four spatial dimensions. To understand gravity geometrically in four dimensions, we must identify the distinct rotation the accelerating observer is performing, visualize its isocline, and model its unique conservation law geometrically as motion on those isoclines in Euclidean 4-space. That problem is dimensionally analogous to the problem that Kepler and Newton solved for the rotation of the planets in Euclidean 3-space.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> It is a [[W:Kepler problem|Kepler problem]], hosted in Euclidean 4-space. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's isocline geometry, yielding a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. Our challenge is to visualize this double rotation. ... == Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space == Atoms are 4-polytopes, small round 4-dimensional objects, and their rotational symmetry is compounded from that of the [[Polyscheme#Regular convex 4-polytopes|six regular convex 4-polytopes]]. Their geometry is beyond the scope of this paper, but we begin with the proton, which we identify with the rotational symmetry of the 4-simplex polytope. Schläfli discovered that there exists a compound series of six regular convex 4-polytopes, dimensionally analogous to the compound series of five regular convex 3-polytopes, the Platonic solids. Polytopes in each series are naturally ordered by size, as a measure of content for the same radius, which is also a measure of their roundness, the number of their vertices. They form a series of increasingly round polytopes in which each is a compound of multiple instances of its predecessor (with one exception to this progression which will concern us later). The six regular convex 4-polytopes have 5, 8, 16, 24, 120, and 600 vertices respectively. They are the 5-point (5-cell) 4-simplex, the 8-point (16-cell) 4-orthoplex, the 16-point (8-cell) 4-hypercube, the 24-point (24-cell), the 120-point (600-cell), and the 600-point (120-cell). The smallest (least round) regular convex 4-polytope is the [[5-cell|4-simplex]]. It has 5 vertices, 10 edges, 10 triangular faces, and 5 tetrahedral cells. The regular 4-simplex is the configuration of 5 mutually equidistant points in Euclidean space, on the surface of a 3-sphere. .... We conclude that the rotational geometry of the proton is that of the 4-simplex. The largest (roundest) regular convex 4-polytope is called the [[120-cell|120-cell]]. It has 600 vertices and 1200 edges, because it is a regular compound of 120 completely disjoint 4-simplexes, rotated isoclinically with respect to each other such that their vertices are evenly distributed on the surface of a 3-sphere. It is also a regular compound of every other regular convex 4-polytope, so that instances of every regular convex polytope which can exist in Euclidean 4-space are found within it. It is the singular geometrically comprehensive 4-polytope, containing instances of the relationships among all these polytopes. The exception to the rule that each 4-polytope in the series compounds to its successor is the 5-point 4-simplex, which does not compound to its successor the 8-point 4-orthoplex, nor to any other 4-polytope in the series except the largest, the 600-point 120-cell. None of the 4-polytopes in the series are divisible into an integral number of 4-simplexes except the 120-cell. Every 4-polytope in the series except the 4-simplex is divisible into an integral number of 4-orthoplexes. Thus there are two alternate integral building blocks of the comprehensive 120-cell: the 5-point 4-simplex, and the 8-point 4-orthoplex. Only the 4-orthoplex will build the other three 4-polytopes in the series by simple compounding. However, the symmetry group of the 4-simplex also has a foundational relationship to the symmetries of all the 4-polytopes in the series. If we view the 4-simplex as the largest 4-polytope instead of the smallest, and subdivide it by integral truncation, we find smaller instances of all the other 4-polytopes within it. The nucleus of a distinct atomic element contains a characteristic number of protons, its atomic number. The rotational symmetry of each element is based on that of a compound of its distinct number of completely disjoint 4-simplex polytopes, that is, on the symmetry of a sparsely populated 120-cell. Because only 120 4-simplexes will fit into a 120-cell, each occupying exclusively 5 equidistant vertices of the 600 vertices, only 120 distinct atomic elements are possible. Any compound of the atomic number of 4-simplexes constitutes an atom of that element, but multiple geometric configurations of each element are possible, depending on which subset of 4-simplex positions is populated. Some of these configurations will have more symmetry than others. We conclude that these alternate configurations are potential nuclides of the atomic element, some potentially more than others. We identify the neutron with the rotational symmetry of the 8-point 4-orthoplex. The 4-orthoplex is the easiest 4-polytope to visualize because it consists simply of 4 pairs of opposing vertices on 4 orthogonal axes. It is the orthonormal basis polytope, whose size, location and orientation in 4-space defines a Cartesian (w,x,y,z) coordinate reference frame. Every 4-polytope in the series of six except the 4-simplex is divisible into an integral number of disjoint 4-orthoplexes, each occupying exclusively 8 of the 600 vertices of the 120-cell. The 4-simplex is the only regular convex 4-polytope with vertices that do not occur in opposing pairs. It is impossible to position two 4-simplexes on the 3-sphere such that they share some but not all 5 vertices. The 600-point 120-cell can only be partitioned into 120 disjoint 5-point 4-simplexes in one way. The 600-point 120-cell can be partitioned into 75 disjoint 8-point 4-orthoplexes, but this partitioning can be done in 10 different ways, because two 4-orthoplexes can be positioned so that they share an axis without sharing all 8 vertices. Both the 120-point 600-cell and the 600-point 120-cell are divisible into an integral number of non-disjoint 4-orthoplexes which share axes. The 600-point 120-cell contains 675 distinct 4-orthoplexes, each a distinct orthonormal basis with four orthogonal axes. Each axis occurs in 9 distinct 4-orthoplexes, and is orthogonal to its 27 distinct companion axes in those 4-orthoplexes, and to no other axes of the 120-cell. An element of atomic number <math>z</math> is a compound of <math>z</math> disjoint 4-simplexes, so it occupies exclusively <math>5 z</math> vertices of the 120-cell, in some configuration with the 5 vertices of each 4-simplex mutually equidistant from each other on the the 3-sphere. Thus for example any configuration of the element Carbon with 6 protons occupies at least 30 distinct vertices of the 600. .... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating Euclidean and spherical <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any reference frame, not only from their own proper inertial reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's discovery of higher dimensional space: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, our 4-space universe might be infinite, or at some vast radius (far greater than the radius of our big-bang 3-sphere) it might close into a 4-sphere. The universe viewed as a 4-sphere might, or might not, be expanding from some distant precursor to our big bang. The discovery of where exactly we are located in such a 4-sphere might bring about a whole new enlightenment. In any case the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no immediate way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of the starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:3-sphere|3-sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture. He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice."<ref name=Einstein1923/> Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction of it; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the planet's core and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest 4-ball object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity, so symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a wilderness project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's surface), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} qqch6ou32xpl8ffjh94v8gshv3pmebz 2844832 2844831 2026-11-07T22:27:44Z Dc.samizdat 2856930 /* Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space */ 2844832 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space is Euclidean with four perpendicular dimensions. * Atoms are [[W:4-polytope|4-polytopes]]. An atom's motion is the local product of its discrete self-reflections in Euclidean 4-space. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. It occupies a hyperspherical region in Euclidean 4-space. * Everything of intermediate size between an atom and a star, including ourselves and our planet, lies in a 3-dimensional manifold of ordinary space, embedded in Euclidean 4-space. * Our entire 3-space manifold is moving at the speed of light <math>c</math> in Euclidean 4-space. The gravitational coherence of galaxies is inertial coherence, a result of their linear motion at velocity <math>c</math> in Euclidean 4-space. * Special relativity describes the linear motion of objects and light signals in Euclidean 4-space. The propagation speed of light is <math>c\prime = 2c</math> measured on a straight line in Euclidean 4-space. * General relativity describes the rotational motion of objects with mass in Euclidean 4-space. Time ticks at the same rate everywhere in Euclidean 4-space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in Euclidean 4-space. The proton has the symmetry of the 4-simplex polytope. The neutron has the symmetry of the 4-orthoplex polytope. * The universe may properly be viewed as a <math>4</math>-sphere centered wherever there is an observer. == A theory of the Euclidean cosmos == <blockquote>If we are to have any hope of understanding the universe, we must dare to imagine a world that is not bounded by our limited perspective.<ref>{{Cite book|first=Adam|last =Becker|year=2018|title=What Is Real? The Unfinished Quest for the Meaning of Quantum Physics}}</ref></blockquote> The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets (at their surfaces), are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. Several objects which appear to us to be located at almost the same point in our sky may actually lie in directions many degrees apart, since the entire hyperspherical sky is projected onto an ordinary sphere in our view of it. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we detect it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the bounding surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The bounding surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is bounded by a smaller 3-sphere lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the bounding surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of large gravitational objects. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to all three of our 3-manifold's dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, if their gravity is strong enough to give them a core of superdense matter like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at center, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every free-falling object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions at velocity <math>c</math>, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by [[W:Geometric algebra|Clifford's algebraic methods]]), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.<ref name=Einstein1923>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the local product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own mirror surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct mirror surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct mirror surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are direct dimensional analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation <math>\mathrm{QT}</math> or a simple rotation <math>\mathrm{Q}</math> lies on a great circle of an ordinary sphere (a 2-sphere), translating or stationary. In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere), translating or stationary. Rotational great circles on hyperspheres are inherently more complex than the ordinary great circles on spheres we experience in 3-space. A point on the surface of an object rotating in 4-space may be in motion on two circles, in two [[W:Completely orthogonal|completely orthogonal]] rotation planes simultaneously. As each planar circle rotates like a wheel turning, its rotation plane also tilts sideways like a coin flipping, eventually into the completely orthogonal original rotation plane of the other circle, so that the circles have exchanged rotation planes. The product of these two simultaneous completely orthogonal circular motions gives a circular orbit to each moving point that does not lie in any stationary rotation plane; it is a circular helix that bends in all four dimensions rather than in just two dimensions, in either a left or right hand direction of helical curvature. Unlike ordinary planar circles, these 4-dimensional circles are inherently chiral, and their circumference is not <math>2\pi r</math>. But like ordinary planar great circles they are true geodesic circles. They may even be understood as dimensionally more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In our universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, these motions occur only at the constant velocity <math>c</math>, and there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating, but it is a common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space enumerate all possible displacements of objects with mass. We find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be seen as a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Objects with mass of any size (including atoms and their subatomic particles) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, such as an atom in its own proper reference frame. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. 2-dimensional objects reflect in a line, 3-dimensional objects reflect in a plane, and 4-dimensional objects reflect in a hyperplane (a 3-dimensional mirror). A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel hyperplanes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting hyperplanes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in two pairs of parallel hyperplanes at once, a reflection in four hyperplane mirrors; it is all translation and no rotation. All the motion goes to translation, so the displacement goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in Euclidean 4-space == Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved 3-manifold embedded in flat Euclidean 4-space. The motion and curvature of their proper 3-space complicates sightline calculations for observers; they require Lorentz transformations to produce their 3-coordinate Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction in 4-coordinate space. Lorentz transformations are needed only when an observer wants to calculate a projection, that is, the shadow in a 3-coordinate space of how things will appear as a 3-dimensional scene (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there exactly as they do in a classical vector space, but bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in 3-space from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time) at velocity <math>c</math>, and all observers and all scenes being observed are in motion (at this constant velocity) in their respective proper time directions, we observe perspective forshortenings in time as well as in one of our three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of all physical processes varies from field to field, and reference frame differences predicted by the theory are not reciprocal.) The Lorentz invariant of special relativity allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. In Euclidean relativity we are able to state this intrinsic symmetry of nature more simply: <blockquote>''Time ticks at the same rate everywhere in space.''</blockquote> This formulation of special relativity at first appears to contradict general relativity, which insists that time (in the sense of the quantum rate of all physical processes) ticks more slowly deeper in a gravitational field. We shall see (below) that there is no contradiction between the universal rate of time at every place in space, and the relative rates of time in distinct gravitational fields, because in the Euclidean relativity formulation all gravitational fields are in motion. A gravitational field is not a place; it is better described as a state of motion of a set of objects, in particular their states of acceleration. As the objects are in perpetual motion, so also is their field. General relativity predicts differences in the perceived rates at which clocks run in distinct moving gravitational fields, just as special relativity predicts differences in perceived rates at which clocks run in distinct inertial reference frames, but we shall see that none of these differences imply that time (in the sense of the quantum rate of change) ever runs at any rate other than <math>c</math> in any stationary place in 4-space. None of the special relativity Lorentz effects (or as we shall see the general relativity effects) are beyond geometric explanation or paradoxical, but their geometric explanation requires Euclidean 4-space. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting and revealing than Euclidean 3-space, analogous to the way our 3-space is more deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are strictly analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is a strict expression of relations between intrinsic group-theoretic symmetries: that is Noether's and Coxeter's great discovery. == General relativity is the geometry of gravity in Euclidean 4-space == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective distinct screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation <math>T</math> through 4-space. The velocity of that vector remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation composed of a discrete number of its characteristic rotational displacement in each full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and discrete number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the bounding surface of a rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may have to be greater than 360° to close a circular revolution. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference, they are chiral 4-dimensional circles which we call isoclines. Many distinct 4-space rotations of interest have isoclines of 720° circumference. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two mirror surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two mirror surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number <math>c</math> of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number <math>c</math> of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution, and the circumference of the complete revolution, are characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation, since they depend on the geometry of the rotational isocline which is unique to the distinct rotation. Distinct rotations arise from distinct symmetry groups, which are each their own mystery with a unique conservation law and set of rotations. The unique geometry of each rotation's isocline is that of some distinct star polygon. The geometric relationships between star polygons defined by successive rational numbers are mathematically mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios, which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions, and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations, because a translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is 180°. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing, and inertia is the conservation of this distinct double rotation. The acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity <math>c</math>. Because the rate of atomic scale displacement events is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's isocline geometry. General relativity explains gravity geometrically as a non-Euclidean geometry in spacetime that is more complex than special relativity's non-Euclidean Lorentz geometry in spacetime. In Euclidean 4-space the geometry of special relativity becomes simpler Euclidean geometry, dimensionally analogous to familiar perspective geometry in ordinary Euclidean 3-space, and therefore visualizable provided we can stretch our dimensional analogy muscles enough to imagine perspective views in four orthogonal spatial dimensions. A similar stretch is required of us to visualize general relativity in Euclidean 4-space: we must imagine distinct rotations in four spatial dimensions. To understand gravity geometrically in four dimensions, we must identify the distinct rotation the accelerating observer is performing, visualize its isocline, and model its unique conservation law geometrically as motion on those isoclines in Euclidean 4-space. That problem is dimensionally analogous to the problem that Kepler and Newton solved for the rotation of the planets in Euclidean 3-space.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> It is a [[W:Kepler problem|Kepler problem]], hosted in Euclidean 4-space. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's isocline geometry, yielding a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. Our challenge is to visualize this double rotation. ... == Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space == Atoms are 4-polytopes, small round 4-dimensional objects, and their rotational symmetry is compounded from that of the [[Polyscheme#Regular convex 4-polytopes|six regular convex 4-polytopes]]. Their geometry is beyond the scope of this paper, but we begin with the proton, which we identify with the rotational symmetry of the 4-simplex polytope. Schläfli discovered that there exists a compound series of six regular convex 4-polytopes, dimensionally analogous to the compound series of five regular convex 3-polytopes, the Platonic solids. Polytopes in each series are naturally ordered by size, as a measure of content for the same radius, which is also a measure of their roundness, the number of their vertices. They form a series of increasingly round polytopes in which each is a compound of multiple instances of its predecessor (with one exception to this progression which will concern us later). The six regular convex 4-polytopes have 5, 8, 16, 24, 120, and 600 vertices respectively. They are the 5-point (5-cell) 4-simplex, the 8-point (16-cell) 4-orthoplex, the 16-point (8-cell) 4-hypercube, the 24-point (24-cell), the 120-point (600-cell), and the 600-point (120-cell). The smallest (least round) regular convex 4-polytope is the [[5-cell|4-simplex]]. It has 5 vertices, 10 edges, 10 triangular faces, and 5 tetrahedral cells. The regular 4-simplex is the configuration of 5 mutually equidistant points in Euclidean space, on the surface of a 3-sphere. .... We conclude that the rotational geometry of the proton is that of the 4-simplex. The largest (roundest) regular convex 4-polytope is called the [[120-cell|120-cell]]. It has 600 vertices and 1200 edges, because it is a regular compound of 120 completely disjoint 4-simplexes, rotated isoclinically with respect to each other such that their vertices are evenly distributed on the surface of a 3-sphere. It is also a regular compound of every other regular convex 4-polytope, so that instances of every regular convex polytope which can exist in Euclidean 4-space are found within it. It is the singular geometrically comprehensive 4-polytope, containing instances of the relationships among all these polytopes. The exception to the rule that each 4-polytope in the series compounds to its successor is the 5-point 4-simplex, which does not compound to its successor the 8-point 4-orthoplex, nor to any other 4-polytope in the series except the largest, the 600-point 120-cell. None of the 4-polytopes in the series are divisible into an integral number of 4-simplexes except the 120-cell. Every 4-polytope in the series except the 4-simplex is divisible into an integral number of 4-orthoplexes. Thus there are two alternate integral building blocks of the comprehensive 120-cell: the 5-point 4-simplex, and the 8-point 4-orthoplex. Only the 4-orthoplex will build the other three 4-polytopes in the series by simple compounding. However, the symmetry group of the 4-simplex also has a foundational relationship to the symmetries of all the 4-polytopes in the series. If we view the 4-simplex as the largest 4-polytope instead of the smallest, and subdivide it by integral truncation, we find smaller instances of all the other 4-polytopes within it. The nucleus of a distinct atomic element contains a characteristic number of protons, its atomic number. The rotational symmetry of each element is based on that of a compound of its distinct number of completely disjoint 4-simplex polytopes, that is, on the symmetry of a sparsely populated 120-cell. Because only 120 4-simplexes will fit into a 120-cell, each occupying exclusively 5 equidistant vertices of the 600 vertices, only 120 distinct atomic elements are possible. Any compound of the atomic number of 4-simplexes constitutes an atom of that element, but multiple geometric configurations of each element are possible, depending on which subset of 4-simplex positions is populated. Some of these configurations will have more symmetry than others. We conclude that these alternate configurations are potential nuclides of the atomic element, some potentially more than others. We identify the neutron with the rotational symmetry of the 8-point 4-orthoplex. The 4-orthoplex is the easiest 4-polytope to visualize because it consists simply of 4 pairs of opposing vertices on 4 orthogonal axes. It is the [[W:Orthonormal basis|orthonormal basis]] polytope, whose size, location and orientation in 4-space defines a Cartesian (w,x,y,z) coordinate reference frame. Every 4-polytope in the series of six except the 4-simplex is divisible into an integral number of disjoint 4-orthoplexes, each occupying exclusively 8 of the 600 vertices of the 120-cell. The 4-simplex is the only regular convex 4-polytope with vertices that do not occur in opposing pairs. It is impossible to position two 4-simplexes on the 3-sphere such that they share some but not all 5 vertices. The 600-point 120-cell can only be partitioned into 120 disjoint 5-point 4-simplexes in one way. The 600-point 120-cell can be partitioned into 75 disjoint 8-point 4-orthoplexes, but this partitioning can be done in 10 different ways, because two 4-orthoplexes can be positioned so that they share an axis without sharing all 8 vertices. Both the 120-point 600-cell and the 600-point 120-cell are divisible into an integral number of non-disjoint 4-orthoplexes which share axes. The 600-point 120-cell contains 675 distinct 4-orthoplexes, each a distinct orthonormal basis with four orthogonal axes. Each axis occurs in 9 distinct 4-orthoplexes, and is orthogonal to its 27 distinct companion axes in those 4-orthoplexes, and to no other axes of the 120-cell. An element of atomic number <math>z</math> is a compound of <math>z</math> disjoint 4-simplexes, so it occupies exclusively <math>5 z</math> vertices of the 120-cell, in some configuration with the 5 vertices of each 4-simplex mutually equidistant from each other on the the 3-sphere. Thus for example any configuration of the element Carbon with 6 protons occupies at least 30 distinct vertices of the 600. .... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating Euclidean and spherical <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any reference frame, not only from their own proper inertial reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's discovery of higher dimensional space: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, our 4-space universe might be infinite, or at some vast radius (far greater than the radius of our big-bang 3-sphere) it might close into a 4-sphere. The universe viewed as a 4-sphere might, or might not, be expanding from some distant precursor to our big bang. The discovery of where exactly we are located in such a 4-sphere might bring about a whole new enlightenment. In any case the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no immediate way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of the starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:3-sphere|3-sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture. He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice."<ref name=Einstein1923/> Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction of it; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the planet's core and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest 4-ball object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity, so symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a wilderness project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's surface), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} eabjowaazx7hly0437dj5qlmfrwu72e 2844837 2844832 2026-11-07T23:34:38Z Dc.samizdat 2856930 /* Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space */ 2844837 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space is Euclidean with four perpendicular dimensions. * Atoms are [[W:4-polytope|4-polytopes]]. An atom's motion is the local product of its discrete self-reflections in Euclidean 4-space. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. It occupies a hyperspherical region in Euclidean 4-space. * Everything of intermediate size between an atom and a star, including ourselves and our planet, lies in a 3-dimensional manifold of ordinary space, embedded in Euclidean 4-space. * Our entire 3-space manifold is moving at the speed of light <math>c</math> in Euclidean 4-space. The gravitational coherence of galaxies is inertial coherence, a result of their linear motion at velocity <math>c</math> in Euclidean 4-space. * Special relativity describes the linear motion of objects and light signals in Euclidean 4-space. The propagation speed of light is <math>c\prime = 2c</math> measured on a straight line in Euclidean 4-space. * General relativity describes the rotational motion of objects with mass in Euclidean 4-space. Time ticks at the same rate everywhere in Euclidean 4-space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in Euclidean 4-space. The proton has the symmetry of the 4-simplex polytope. The neutron has the symmetry of the 4-orthoplex polytope. * The universe may properly be viewed as a <math>4</math>-sphere centered wherever there is an observer. == A theory of the Euclidean cosmos == <blockquote>If we are to have any hope of understanding the universe, we must dare to imagine a world that is not bounded by our limited perspective.<ref>{{Cite book|first=Adam|last =Becker|year=2018|title=What Is Real? The Unfinished Quest for the Meaning of Quantum Physics}}</ref></blockquote> The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets (at their surfaces), are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. Several objects which appear to us to be located at almost the same point in our sky may actually lie in directions many degrees apart, since the entire hyperspherical sky is projected onto an ordinary sphere in our view of it. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we detect it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the bounding surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The bounding surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is bounded by a smaller 3-sphere lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the bounding surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of large gravitational objects. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to all three of our 3-manifold's dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, if their gravity is strong enough to give them a core of superdense matter like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at center, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every free-falling object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions at velocity <math>c</math>, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by [[W:Geometric algebra|Clifford's algebraic methods]]), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.<ref name=Einstein1923>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the local product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own mirror surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct mirror surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct mirror surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are direct dimensional analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation <math>\mathrm{QT}</math> or a simple rotation <math>\mathrm{Q}</math> lies on a great circle of an ordinary sphere (a 2-sphere), translating or stationary. In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere), translating or stationary. Rotational great circles on hyperspheres are inherently more complex than the ordinary great circles on spheres we experience in 3-space. A point on the surface of an object rotating in 4-space may be in motion on two circles, in two [[W:Completely orthogonal|completely orthogonal]] rotation planes simultaneously. As each planar circle rotates like a wheel turning, its rotation plane also tilts sideways like a coin flipping, eventually into the completely orthogonal original rotation plane of the other circle, so that the circles have exchanged rotation planes. The product of these two simultaneous completely orthogonal circular motions gives a circular orbit to each moving point that does not lie in any stationary rotation plane; it is a circular helix that bends in all four dimensions rather than in just two dimensions, in either a left or right hand direction of helical curvature. Unlike ordinary planar circles, these 4-dimensional circles are inherently chiral, and their circumference is not <math>2\pi r</math>. But like ordinary planar great circles they are true geodesic circles. They may even be understood as dimensionally more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In our universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, these motions occur only at the constant velocity <math>c</math>, and there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating, but it is a common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space enumerate all possible displacements of objects with mass. We find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be seen as a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Objects with mass of any size (including atoms and their subatomic particles) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, such as an atom in its own proper reference frame. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. 2-dimensional objects reflect in a line, 3-dimensional objects reflect in a plane, and 4-dimensional objects reflect in a hyperplane (a 3-dimensional mirror). A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel hyperplanes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting hyperplanes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in two pairs of parallel hyperplanes at once, a reflection in four hyperplane mirrors; it is all translation and no rotation. All the motion goes to translation, so the displacement goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in Euclidean 4-space == Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved 3-manifold embedded in flat Euclidean 4-space. The motion and curvature of their proper 3-space complicates sightline calculations for observers; they require Lorentz transformations to produce their 3-coordinate Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction in 4-coordinate space. Lorentz transformations are needed only when an observer wants to calculate a projection, that is, the shadow in a 3-coordinate space of how things will appear as a 3-dimensional scene (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there exactly as they do in a classical vector space, but bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in 3-space from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time) at velocity <math>c</math>, and all observers and all scenes being observed are in motion (at this constant velocity) in their respective proper time directions, we observe perspective forshortenings in time as well as in one of our three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of all physical processes varies from field to field, and reference frame differences predicted by the theory are not reciprocal.) The Lorentz invariant of special relativity allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. In Euclidean relativity we are able to state this intrinsic symmetry of nature more simply: <blockquote>''Time ticks at the same rate everywhere in space.''</blockquote> This formulation of special relativity at first appears to contradict general relativity, which insists that time (in the sense of the quantum rate of all physical processes) ticks more slowly deeper in a gravitational field. We shall see (below) that there is no contradiction between the universal rate of time at every place in space, and the relative rates of time in distinct gravitational fields, because in the Euclidean relativity formulation all gravitational fields are in motion. A gravitational field is not a place; it is better described as a state of motion of a set of objects, in particular their states of acceleration. As the objects are in perpetual motion, so also is their field. General relativity predicts differences in the perceived rates at which clocks run in distinct moving gravitational fields, just as special relativity predicts differences in perceived rates at which clocks run in distinct inertial reference frames, but we shall see that none of these differences imply that time (in the sense of the quantum rate of change) ever runs at any rate other than <math>c</math> in any stationary place in 4-space. None of the special relativity Lorentz effects (or as we shall see the general relativity effects) are beyond geometric explanation or paradoxical, but their geometric explanation requires Euclidean 4-space. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting and revealing than Euclidean 3-space, analogous to the way our 3-space is more deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are strictly analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is a strict expression of relations between intrinsic group-theoretic symmetries: that is Noether's and Coxeter's great discovery. == General relativity is the geometry of gravity in Euclidean 4-space == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective distinct screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation <math>T</math> through 4-space. The velocity of that vector remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation composed of a discrete number of its characteristic rotational displacement in each full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and discrete number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the bounding surface of a rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may have to be greater than 360° to close a circular revolution. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference, they are chiral 4-dimensional circles which we call isoclines. Many distinct 4-space rotations of interest have isoclines of 720° circumference. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two mirror surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two mirror surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number <math>c</math> of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number <math>c</math> of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution, and the circumference of the complete revolution, are characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation, since they depend on the geometry of the rotational isocline which is unique to the distinct rotation. Distinct rotations arise from distinct symmetry groups, which are each their own mystery with a unique conservation law and set of rotations. The unique geometry of each rotation's isocline is that of some distinct star polygon. The geometric relationships between star polygons defined by successive rational numbers are mathematically mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios, which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions, and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations, because a translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is 180°. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing, and inertia is the conservation of this distinct double rotation. The acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity <math>c</math>. Because the rate of atomic scale displacement events is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's isocline geometry. General relativity explains gravity geometrically as a non-Euclidean geometry in spacetime that is more complex than special relativity's non-Euclidean Lorentz geometry in spacetime. In Euclidean 4-space the geometry of special relativity becomes simpler Euclidean geometry, dimensionally analogous to familiar perspective geometry in ordinary Euclidean 3-space, and therefore visualizable provided we can stretch our dimensional analogy muscles enough to imagine perspective views in four orthogonal spatial dimensions. A similar stretch is required of us to visualize general relativity in Euclidean 4-space: we must imagine distinct rotations in four spatial dimensions. To understand gravity geometrically in four dimensions, we must identify the distinct rotation the accelerating observer is performing, visualize its isocline, and model its unique conservation law geometrically as motion on those isoclines in Euclidean 4-space. That problem is dimensionally analogous to the problem that Kepler and Newton solved for the rotation of the planets in Euclidean 3-space.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> It is a [[W:Kepler problem|Kepler problem]], hosted in Euclidean 4-space. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's isocline geometry, yielding a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. Our challenge is to visualize this double rotation. ... == Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space == Atoms are 4-polytopes, small round 4-dimensional objects, and their rotational symmetry is compounded from that of the [[Polyscheme#Regular convex 4-polytopes|six regular convex 4-polytopes]]. Their geometry is beyond the scope of this paper, but we begin with the proton, which we identify with the rotational symmetry of the 4-simplex polytope. Schläfli discovered that there exists a compound series of six regular convex 4-polytopes, dimensionally analogous to the compound series of five regular convex 3-polytopes, the Platonic solids. Polytopes in each series are naturally ordered by size, as a measure of content for the same radius, which is also a measure of their roundness, the number of their vertices. They form a series of increasingly round polytopes in which each is a compound of multiple instances of its predecessor (with one exception to this progression which will concern us later). The six regular convex 4-polytopes have 5, 8, 16, 24, 120, and 600 vertices respectively. They are the 5-point (5-cell) 4-simplex, the 8-point (16-cell) 4-orthoplex, the 16-point (8-cell) 4-hypercube, the 24-point (24-cell), the 120-point (600-cell), and the 600-point (120-cell). The smallest (least round) regular convex 4-polytope is the [[5-cell|4-simplex]]. It has 5 vertices, 10 edges, 10 triangular faces, and 5 tetrahedral cells. The regular 4-simplex is the configuration of 5 mutually equidistant points in Euclidean space, on the surface of a 3-sphere. .... We conclude that the rotational geometry of the proton is that of the 4-simplex. The largest (roundest) regular convex 4-polytope is called the [[120-cell|120-cell]]. It has 600 vertices and 1200 edges, because it is a regular compound of 120 completely disjoint 4-simplexes, rotated isoclinically with respect to each other such that their vertices are evenly distributed on the surface of a 3-sphere. It is also a regular compound of every other regular convex 4-polytope, so that instances of every regular convex polytope which can exist in Euclidean 4-space are found within it. It is the singular geometrically comprehensive 4-polytope, containing instances of the relationships among all these polytopes. The exception to the rule that each 4-polytope in the series compounds to its successor is the 5-point 4-simplex, which does not compound to its successor the 8-point 4-orthoplex, nor to any other 4-polytope in the series except the largest, the 600-point 120-cell. None of the 4-polytopes in the series are divisible into an integral number of 4-simplexes except the 120-cell. Every 4-polytope in the series except the 4-simplex is divisible into an integral number of 4-orthoplexes. Thus there are two alternate integral building blocks of the comprehensive 120-cell: the 5-point 4-simplex, and the 8-point 4-orthoplex. Only the 4-orthoplex will build the other three 4-polytopes in the series by simple compounding. However, the symmetry group of the 4-simplex also has a foundational relationship to the symmetries of all the 4-polytopes in the series. If we view the 4-simplex as the largest 4-polytope instead of the smallest, and subdivide it by integral truncation, we find smaller instances of all the other 4-polytopes within it. The nucleus of a distinct atomic element contains a characteristic number of protons, its atomic number. The rotational symmetry of each element is based on that of a compound of its distinct number of completely disjoint 4-simplex polytopes, that is, on the symmetry of a sparsely populated 120-cell. Because only 120 4-simplexes will fit into a 120-cell, each occupying exclusively 5 equidistant vertices of the 600 vertices, only 120 distinct atomic elements are possible. Any compound of the atomic number of 4-simplexes constitutes an atom of that element, but multiple geometric configurations of each element are possible, depending on which subset of 4-simplex positions is populated. Some of these configurations will have more symmetry than others. We conclude that these alternate configurations are potential nuclides of the atomic element, some potentially more than others. We identify the neutron with the rotational symmetry of the 8-point 4-orthoplex. The 4-orthoplex is the easiest 4-polytope to visualize because it consists simply of 4 pairs of opposing vertices on 4 orthogonal axes. It is the [[W:Orthonormal basis|orthonormal basis]] polytope: the size, location and orientation in 4-space of a 4-orthoplex defines a Cartesian (w,x,y,z) coordinate reference frame. Every 4-polytope in the series of six except the 4-simplex is divisible into an integral number of disjoint 4-orthoplexes, each occupying exclusively 8 of the 600 vertices of the 120-cell. The 4-simplex is the only regular convex 4-polytope with vertices that do not occur in opposing pairs. It is impossible to position two 4-simplexes on the 3-sphere such that they share some but not all 5 vertices. The 600-point 120-cell can only be partitioned into 120 disjoint 5-point 4-simplexes in one way. The 600-point 120-cell can be partitioned into 75 disjoint 8-point 4-orthoplexes, and this partitioning can be done in 10 different ways, because two 4-orthoplexes can be positioned so that they share an axis without sharing all 8 vertices. Both the 120-point 600-cell and the 600-point 120-cell are divisible into an integral number of non-disjoint 4-orthoplexes which share axes. The 600-point 120-cell contains 675 distinct 4-orthoplexes, each a distinct orthonormal basis with four orthogonal axes. Each axis occurs in 9 distinct 4-orthoplexes, and is orthogonal to its 27 distinct companion axes in those 4-orthoplexes, and to no other axes of the 120-cell. An element of atomic number <math>z</math> is a compound of <math>z</math> disjoint 4-simplexes, so it occupies exclusively <math>5 z</math> vertices of the 120-cell, in some configuration with the 5 vertices of each 4-simplex mutually equidistant from each other on the the 3-sphere. Thus for example any configuration of the element Carbon with 6 protons occupies at least 30 distinct vertices of the 600. .... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating Euclidean and spherical <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any reference frame, not only from their own proper inertial reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's discovery of higher dimensional space: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, our 4-space universe might be infinite, or at some vast radius (far greater than the radius of our big-bang 3-sphere) it might close into a 4-sphere. The universe viewed as a 4-sphere might, or might not, be expanding from some distant precursor to our big bang. The discovery of where exactly we are located in such a 4-sphere might bring about a whole new enlightenment. In any case the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no immediate way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of the starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:3-sphere|3-sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture. He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice."<ref name=Einstein1923/> Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction of it; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the planet's core and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest 4-ball object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity, so symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a wilderness project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's surface), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 8i4rhpgn0owc61kttmgu487ngirm6rk 2844858 2844837 2026-11-08T09:07:00Z Dc.samizdat 2856930 /* Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space */ 2844858 wikitext text/x-wiki {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - October 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as real Euclidean space <math>\mathbb{R}^4</math> of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and the objects we observe near us are only 3-dimensional, but nonetheless we can see into four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that: * Physical space is Euclidean with four perpendicular dimensions. * Atoms are [[W:4-polytope|4-polytopes]]. An atom's motion is the local product of its discrete self-reflections in Euclidean 4-space. * The sun is a [[W:4-ball|4-ball]] that is round in four dimensions. It occupies a hyperspherical region in Euclidean 4-space. * Everything of intermediate size between an atom and a star, including ourselves and our planet, lies in a 3-dimensional manifold of ordinary space, embedded in Euclidean 4-space. * Our entire 3-space manifold is moving at the speed of light <math>c</math> in Euclidean 4-space. The gravitational coherence of galaxies is inertial coherence, a result of their linear motion at velocity <math>c</math> in Euclidean 4-space. * Special relativity describes the linear motion of objects and light signals in Euclidean 4-space. The propagation speed of light is <math>c\prime = 2c</math> measured on a straight line in Euclidean 4-space. * General relativity describes the rotational motion of objects with mass in Euclidean 4-space. Time ticks at the same rate everywhere in Euclidean 4-space. * Quantum mechanics describes the symmetry group actions of elementary geometric objects (4-polytopes) in Euclidean 4-space. The proton has the symmetry of the 4-simplex polytope. The neutron has the symmetry of the 4-orthoplex polytope. * The universe may properly be viewed as a <math>4</math>-sphere centered wherever there is an observer. == A theory of the Euclidean cosmos == <blockquote>If we are to have any hope of understanding the universe, we must dare to imagine a world that is not bounded by our limited perspective.<ref>{{Cite book|first=Adam|last =Becker|year=2018|title=What Is Real? The Unfinished Quest for the Meaning of Quantum Physics}}</ref></blockquote> The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space <math>\mathbb{R}^4</math>]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets (at their surfaces), are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at constant velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity <math>c</math>, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. Several objects which appear to us to be located at almost the same point in our sky may actually lie in directions many degrees apart, since the entire hyperspherical sky is projected onto an ordinary sphere in our view of it. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we detect it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane. The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around the galaxy's barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity <math>c</math> that holds the cylinder of motion together, not some invisible dark matter. The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the bounding surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system too small to have their own gravity lie entirely within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The bounding surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is bounded by a smaller 3-sphere lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity <math>c</math>. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience. The earth and all the planets lie on it. Our solar system is only a small patch on the bounding surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the superdense interior of large gravitational objects. Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction orthogonal to all three of our 3-manifold's dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. In fewer places still it is occupied by large lumps of matter which exert a significant gravitational attraction, such as planets and their satellites. These round gravitational objects are thicker than one atom in their fourth dimension, but not uniformly so. They are disk-like 4-dimensional objects, 3-balls that are flattish in the fourth dimension. They are only one atom thick at the 4-disk's sharp edge, but they may be much thicker in the center of the 4-disk, if their gravity is strong enough to give them a core of superdense matter like the earth's deep core. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have only indirect experience of such 4-dimensional lumps of matter thicker than one atom, since they occur naturally in our vicinity only in regions of superdense matter, such as the core of the earth or the interior of the sun. Deep in the core of the earth under enormous gravitational pressure peculiar states of matter have been observed, defying our understanding of how 3-dimensional crystalline structures behave. That is because they are not 3-dimensional structures, they are 4-dimensional crystals. The earth is a disk-like 4-dimensional object that is thin at its edge but thicker at center, dimensionally analogous to a 3-dimensional flying saucer with a sharp circular edge. The earth's surface that we walk on is an ordinary sphere (a 2-sphere), analogous to the circular edge of the flying saucer (a 1-sphere), and on that edge where we live every object we find (including our bodies) is 3-dimensional with only the thickness of an atom in the fourth dimension. We cannot walk on the top or bottom surface of the 4-disk flying saucer because those surfaces are 3-dimensional regions within the earth. The earth's deep core of superdense 4-dimensional matter occupies a spherical region of 4-dimensional space (a 4-ball). The sun is the only entirely spherical 4-ball occurring naturally in our solar system. We refer to the contents of such superdense 4-balls of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know very little about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect. Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every free-falling object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions at velocity <math>c</math>, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us, and the greater their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <math>\mathrm{Q}</math> denote a rotation, <math>\mathrm{R}</math> a reflection, <math>\mathrm{T}</math> a translation, and let <math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math> denote a product of several such transformations, all commutative with one another. Then <math>\mathrm{RT}</math> is a glide-reflection (in two or three dimensions), <math>\mathrm{QR}</math> is a rotary-reflection, <math>\mathrm{QT}</math> is a screw-displacement, and <math>\mathrm{Q^2}</math> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r</math><br> where <math>(2^q + r \le n)</math>, the number of dimensions.<br> Transformations involving a translation are also expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math><br> where <math>(2^q + r + 1 \le n)</math>.<br> For <math>(n = 4)</math> in particular, every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <math>\mathrm{Q^2}</math> or a <math>\mathrm{QT}</math>, because we can view any <math>\mathrm{QT}</math> as a <math>\mathrm{Q^2}</math> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <math>\mathrm{Q^2}</math>. By the same principle, we can view any <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> as an isoclinic (equi-angled) <math>\mathrm{Q^2}</math> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<math>\mathrm{T}</math>) for ''one'' of the two rotations (<math>\mathrm{Q}</math>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<math>\mathrm{Q}</math>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<math>\mathrm{T}</math>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by [[W:Geometric algebra|Clifford's algebraic methods]]), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <math>SO(4)</math> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <math>SO(4)</math> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit <math>SO(4)</math> symmetries of the discrete isoclinic (equi-angled) double rotations (<math>\mathrm{Q^2}</math>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.<ref name=Einstein1923>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity <math>c</math>, in some 4-space direction.{{Sfn|Yamashita|2023}} This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always <math>c</math>, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn| ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity <math>c</math>. In physics as it has been universally understood, observers are not supposed to be able to move at velocity <math>c</math>. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity <math>c</math> through the universe, which is real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity <math>c</math>. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity <math>c</math>, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems. So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity <math>c</math> through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" <math>c</math>, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity <math>c</math>, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant <math>c</math> is the speed of light through 3-space. In Euclidean relativity, the invariant <math>c</math> is the speed of matter through 4-space! The speed of light through 3-space is also perceived as <math>c</math> by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity <math>c</math>. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity <math>c</math>, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers. ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}} Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at <math>c</math> (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than <math>c</math>. Euclidean relativity is a revolutionary theory indeed, in which <math>c</math> cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R}^4</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <math>\sqrt{4}</math>. == An object's motion in space is the local product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own mirror surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct mirror surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct mirror surfaces which intersect each other. When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math><br> where <math>(2^q + r + t \le 4)</math>. Every displacement is either a double rotation <math>\mathrm{Q}^2</math>, or a screw-displacement <math>\mathrm{QT}</math> [where the rotation component <math>\mathrm{Q}</math> is a simple rotation, but the <math>\mathrm{QT}</math> is chiral like a <math>\mathrm{Q^2}</math>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <math>\mathrm{QRT}</math>.</blockquote> While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<math>\mathrm{Q}</math>), reflection (<math>\mathrm{R}</math>) and translation (<math>\mathrm{T}</math>) are direct dimensional analogues of what they are in three-dimensional space, but double rotation (<math>\mathrm{Q}^2</math>) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate. Four dimensional Euclidean space can accomodate no such thing as a <math>\mathrm{Q}^2\mathrm{T}</math>. A translating double rotation <math>\mathrm{Q}^2</math>, like a translating simple rotation <math>\mathrm{Q}</math>, is simply a screw translation <math>\mathrm{QT}</math>. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation <math>\mathrm{QT}</math> or a simple rotation <math>\mathrm{Q}</math> lies on a great circle of an ordinary sphere (a 2-sphere), translating or stationary. In 4-space the orbit of a screw translation <math>\mathrm{QT}</math> or double rotation <math>\mathrm{Q}^2</math> lies on a great circle of a hypersphere (a 3-sphere), translating or stationary. Rotational great circles on hyperspheres are inherently more complex than the ordinary great circles on spheres we experience in 3-space. A point on the surface of an object rotating in 4-space may be in motion on two circles, in two [[W:Completely orthogonal|completely orthogonal]] rotation planes simultaneously. As each planar circle rotates like a wheel turning, its rotation plane also tilts sideways like a coin flipping, eventually into the completely orthogonal original rotation plane of the other circle, so that the circles have exchanged rotation planes. The product of these two simultaneous completely orthogonal circular motions gives a circular orbit to each moving point that does not lie in any stationary rotation plane; it is a circular helix that bends in all four dimensions rather than in just two dimensions, in either a left or right hand direction of helical curvature. Unlike ordinary planar circles, these 4-dimensional circles are inherently chiral, and their circumference is not <math>2\pi r</math>. But like ordinary planar great circles they are true geodesic circles. They may even be understood as dimensionally more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle. In our universe which is real Euclidean four-dimensional space <math>\mathbb{R}^4</math>, these motions occur only at the constant velocity <math>c</math>, and there is a universal Cartesian 4-coordinate reference frame in which every rigid object in free fall is translating on a <math>\mathrm{QT}</math> at velocity <math>c</math>. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary and double-rotating, but it is a common reference frame of all observers. == Light propagates through 4-space at twice its apparent velocity <math>c</math>== Coxeter's laws of kinematics in 4-dimensional Euclidean space enumerate all possible displacements of objects with mass. We find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <math>\mathrm{R}^4</math>, which may be seen as a double translation <math>\mathrm{T}^2</math>, a pure translation via two pairs of parallel reflections without any rotation component <math>\mathrm{Q}</math>. Objects with mass of any size (including atoms and their subatomic particles) are perpetually rotating and translating through 4-space by <math>\mathrm{QT}</math>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <math>\mathrm{Q^2}</math>, such as an atom in its own proper reference frame. A simple rotation <math>\mathrm{Q}</math> or simple translation <math>\mathrm{T}</math> is a double reflection <math>\mathrm{R^2}</math>, so a <math>\mathrm{QT}</math> or <math>\mathrm{Q^2}</math> is an <math>\mathrm{R^4}</math>, but not with the same group of reflection angles as a light signal <math>\mathrm{R^4}</math>. 2-dimensional objects reflect in a line, 3-dimensional objects reflect in a plane, and 4-dimensional objects reflect in a hyperplane (a 3-dimensional mirror). A translation <math>\mathrm{T = R^2}</math> is a double reflection in two parallel hyperplanes, and a rotation <math>\mathrm{Q = R^2}</math> is a double reflection in two intersecting hyperplanes, as in a <math>\mathrm{QT = R^4}</math> which is both at once. A double translation <math>\mathrm{T^2 = R^4}</math> is two double reflections in two pairs of parallel hyperplanes at once, a reflection in four hyperplane mirrors; it is all translation and no rotation. All the motion goes to translation, so the displacement goes twice as far as the simple translation <math>\mathrm{T}</math> in a <math>\mathrm{QT}</math>. A double translation <math>\mathrm{T^2 = R^4}</math> is the opposite of a double rotation <math>\mathrm{Q^2 = R^4}</math>, which is stationary but rotates twice as far as the simple rotation <math>\mathrm{Q}</math> in a <math>\mathrm{QT}</math>. The product of the two translations in a <math>\mathrm{T^2}</math> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <math>\mathrm{T}</math> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A <math>\mathrm{T^2}</math> cannot reposition a 4-polytope the way a <math>\mathrm{QT}</math> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn| ...lensing of double translations <math>\mathrm{T^2 = R^4}</math> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}} == Special relativity is Galilean relativity in Euclidean 4-space == Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved 3-manifold embedded in flat Euclidean 4-space. The motion and curvature of their proper 3-space complicates sightline calculations for observers; they require Lorentz transformations to produce their 3-coordinate Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction in 4-coordinate space. Lorentz transformations are needed only when an observer wants to calculate a projection, that is, the shadow in a 3-coordinate space of how things will appear as a 3-dimensional scene (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there exactly as they do in a classical vector space, but bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in 3-space from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time) at velocity <math>c</math>, and all observers and all scenes being observed are in motion (at this constant velocity) in their respective proper time directions, we observe perspective forshortenings in time as well as in one of our three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of all physical processes varies from field to field, and reference frame differences predicted by the theory are not reciprocal.) The Lorentz invariant of special relativity allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. In Euclidean relativity we are able to state this intrinsic symmetry of nature more simply: <blockquote>''Time ticks at the same rate everywhere in space.''</blockquote> This formulation of special relativity at first appears to contradict general relativity, which insists that time (in the sense of the quantum rate of all physical processes) ticks more slowly deeper in a gravitational field. We shall see (below) that there is no contradiction between the universal rate of time at every place in space, and the relative rates of time in distinct gravitational fields, because in the Euclidean relativity formulation all gravitational fields are in motion. A gravitational field is not a place; it is better described as a state of motion of a set of objects, in particular their states of acceleration. As the objects are in perpetual motion, so also is their field. General relativity predicts differences in the perceived rates at which clocks run in distinct moving gravitational fields, just as special relativity predicts differences in perceived rates at which clocks run in distinct inertial reference frames, but we shall see that none of these differences imply that time (in the sense of the quantum rate of change) ever runs at any rate other than <math>c</math> in any stationary place in 4-space. None of the special relativity Lorentz effects (or as we shall see the general relativity effects) are beyond geometric explanation or paradoxical, but their geometric explanation requires Euclidean 4-space. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting and revealing than Euclidean 3-space, analogous to the way our 3-space is more deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are strictly analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is a strict expression of relations between intrinsic group-theoretic symmetries: that is Noether's and Coxeter's great discovery. == General relativity is the geometry of gravity in Euclidean 4-space == The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]]. The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames). Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same. Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space <math>\mathbb{R}^4</math>. An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. The observer and the earth are both stationary in their proper inertial reference frames (which are similar except for the rotation of the earth), so the observer's acceleration cannot be perceived as motion in either proper reference frame; it is perceptible there instead as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity <math>c</math> on their respective distinct screw translations <math>QT</math>. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation <math>T</math> through 4-space. The velocity of that vector remains the constant <math>c</math> throughout; only his direction is changing. A change in the direction of a vector is a rotation <math>Q</math> of a translation <math>T</math>: a screw translation <math>QT</math>. A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation composed of a discrete number of its characteristic rotational displacement in each full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and discrete number of displacements per revolution. The general rotation in 4-space is a double rotation <math>Q^2</math> distinguished by two completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the bounding surface of a rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may have to be greater than 360° to close a circular revolution. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference, they are chiral 4-dimensional circles which we call isoclines. Many distinct 4-space rotations of interest have isoclines of 720° circumference. In 4-space every object with mass moves on its distinct <math>QT</math> trajectory. Each rotational displacement <math>Q</math> is equivalent to a pair of reflection displacements in two mirror surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement <math>T</math> is equivalent to a pair of reflection displacements in two mirror surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity <math>c</math>. Every atom translates at velocity <math>c</math>, performing a large number <math>c</math> of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity <math>c</math>, performing the same large number <math>c</math> of atomic scale rotational displacements per second. Although the number of displacements at atomic scale per unit time is the same universal constant <math>c</math> for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution, and the circumference of the complete revolution, are characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of <math>c</math> and the two defining angle parameters of the rotation, since they depend on the geometry of the rotational isocline which is unique to the distinct rotation. Distinct rotations arise from distinct symmetry groups, which are each their own mystery with a unique conservation law and set of rotations. The unique geometry of each rotation's isocline is that of some distinct star polygon. The geometric relationships between star polygons defined by successive rational numbers are mathematically mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios, which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions, and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations, because a translation <math>T</math> is the distinct simple rotation <math>Q</math> in which the characteristic angle of rotational displacement is 180°. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing, and inertia is the conservation of this distinct double rotation. The acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity <math>c</math>. Because the rate of atomic scale displacement events is the universal constant <math>c</math>, the rate of change of direction (the acceleration of the object) is a function of <math>c</math> and the distinct rotation's isocline geometry. General relativity explains gravity geometrically as a non-Euclidean geometry in spacetime that is more complex than special relativity's non-Euclidean Lorentz geometry in spacetime. In Euclidean 4-space the geometry of special relativity becomes simpler Euclidean geometry, dimensionally analogous to familiar perspective geometry in ordinary Euclidean 3-space, and therefore visualizable provided we can stretch our dimensional analogy muscles enough to imagine perspective views in four orthogonal spatial dimensions. A similar stretch is required of us to visualize general relativity in Euclidean 4-space: we must imagine distinct rotations in four spatial dimensions. To understand gravity geometrically in four dimensions, we must identify the distinct rotation the accelerating observer is performing, visualize its isocline, and model its unique conservation law geometrically as motion on those isoclines in Euclidean 4-space. That problem is dimensionally analogous to the problem that Kepler and Newton solved for the rotation of the planets in Euclidean 3-space.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> It is a [[W:Kepler problem|Kepler problem]], hosted in Euclidean 4-space. A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of <math>c</math> and the distinct rotation's isocline geometry, yielding a measurement of the rate of change of the observer's direction of motion through 4-space at velocity <math>c</math>. Our challenge is to visualize this double rotation. ... == Quantum mechanics is the rotational kinematics of Coxeter groups in Euclidean 4-space == Atoms are 4-polytopes, small round 4-dimensional objects, and their rotational symmetry is compounded from that of the [[Polyscheme#Regular convex 4-polytopes|six regular convex 4-polytopes]]. Their geometry is beyond the scope of this paper, but we begin with the proton, which we identify with the rotational symmetry of the 4-simplex polytope. Schläfli discovered that there exists a compound series of six regular convex 4-polytopes, dimensionally analogous to the compound series of five regular convex 3-polytopes, the Platonic solids. Polytopes in each series are naturally ordered by size, as a measure of content for the same radius, which is also a measure of their roundness, the number of their vertices. They form a series of increasingly round polytopes in which each is a compound of multiple instances of its predecessor (with one exception to this progression which will concern us later). The six regular convex 4-polytopes have 5, 8, 16, 24, 120, and 600 vertices respectively. They are the 5-point (5-cell) 4-simplex, the 8-point (16-cell) 4-orthoplex, the 16-point (8-cell) 4-hypercube, the 24-point (24-cell), the 120-point (600-cell), and the 600-point (120-cell). The smallest (least round) regular convex 4-polytope is the [[5-cell|4-simplex]]. It has 5 vertices, 10 edges, 10 triangular faces, and 5 tetrahedral cells. The regular 4-simplex is the configuration of 5 mutually equidistant points in Euclidean space, on the surface of a 3-sphere. We identify the proton with the rotational symmetry the 4-simplex. The largest (roundest) regular convex 4-polytope is called the [[120-cell|120-cell]]. It has 600 vertices and 1200 edges, because it is a regular compound of 120 completely disjoint 4-simplexes, rotated isoclinically with respect to each other such that their vertices are evenly distributed on the surface of a 3-sphere. It is also a regular compound of every other regular convex 4-polytope, so that instances of every regular convex polytope which can exist in Euclidean 4-space are found within it. It is the singular geometrically comprehensive 4-polytope, containing instances of the relationships among all these polytopes. The exception to the rule that each 4-polytope in the series compounds to its successor is the 5-point 4-simplex, which does not compound to its successor the 8-point 4-orthoplex, nor to any other 4-polytope in the series except the largest, the 600-point 120-cell. None of the 4-polytopes in the series are divisible into an integral number of 4-simplexes except the 120-cell. Every 4-polytope in the series except the 4-simplex is divisible into an integral number of 4-orthoplexes. Thus there are two alternate integral building blocks of the comprehensive 120-cell: the 5-point 4-simplex, and the 8-point 4-orthoplex. Only the 4-orthoplex will build the other three 4-polytopes in the series by simple compounding. However, the symmetry group of the 4-simplex also has a foundational relationship to the symmetries of all the 4-polytopes in the series. If we view the 4-simplex as the largest 4-polytope instead of the smallest, and subdivide it by integral truncation, we find smaller instances of all the other 4-polytopes within it. The nucleus of a distinct atomic element contains a characteristic number of protons, its atomic number. The rotational symmetry of each element is based on that of a compound of its distinct number of completely disjoint 4-simplex polytopes, that is, on the symmetry of a sparsely populated 120-cell. Because only 120 4-simplexes will fit into a 120-cell, each occupying exclusively 5 equidistant vertices of the 600 vertices, only 120 distinct atomic elements are possible. Any compound of the atomic number of 4-simplexes constitutes an atom of that element, but multiple geometric configurations of each element are possible, depending on which subset of 4-simplex positions is populated. Some of these configurations will have more symmetry than others. We conclude that these alternate configurations are potential nuclides of the atomic element, some potentially more stable than others. We identify the neutron with the rotational symmetry of the 8-point 4-orthoplex. Each nuclide is a sparse configuration of the 120-cell that contains its atomic number of 4-simplexes and its neutron number of 4-orthoplexes. The 8-point 4-orthoplex is the easiest 4-polytope to visualize because it consists simply of 4 pairs of opposing vertices on 4 orthogonal axes. It is the [[W:Orthonormal basis|orthonormal basis]] polytope: the size, location and orientation in 4-space of a 4-orthoplex defines a Cartesian (w,x,y,z) coordinate reference frame. Every 4-polytope in the series of six except the 4-simplex is divisible into an integral number of disjoint 4-orthoplexes, each occupying exclusively 8 of the 600 vertices of the 120-cell. The 5-point 4-simplex is the only regular convex 4-polytope with vertices that do not occur in opposing pairs. It is impossible to position two 4-simplexes on the 3-sphere such that they share some but not all 5 vertices. Therefore the 600-point 120-cell can only be partitioned into 120 disjoint 5-point 4-simplexes in one way. The 600-point (300 axis) 120-cell can be partitioned into 75 disjoint (4 axis) 4-orthoplexes. This partitioning can be done in 10 different ways, because two 4-orthoplexes can be positioned so that they share an axis without sharing all 8 vertices. Both the 120-point 600-cell and the 600-point 120-cell are divisible into an integral number of non-disjoint 4-orthoplexes which share axes. The 600-point 120-cell contains 675 distinct 4-orthoplexes, each a distinct orthonormal basis with four orthogonal axes. Each axis occurs in 9 distinct 4-orthoplexes, and is orthogonal to its 27 distinct companion axes in those 4-orthoplexes, and to no other axes of the 120-cell. Because the 4-simplex has no opposing vertices, its 5 vertices belong to 5 distinct orthonormal bases. Two vertices of the same 4-simplex can never belong to the same 4-orthoplex. An element of atomic number <math>z</math> is a compound of <math>z</math> disjoint 4-simplexes, so it occupies exclusively <math>5 z</math> vertices of the 120-cell, in some configuration with the 5 vertices of each 4-simplex mutually equidistant from each other on the the 3-sphere. Thus for example any configuration of the element Helium with 2 protons occupies at least 10 distinct vertices of the 600. .... == Dimensional relativity == The formulation of Euclidean relativity based on Coxeter's kinetic law of <math>n</math>-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]]. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating Euclidean and spherical <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any reference frame, not only from their own proper inertial reference frame in the Euclidean <math>n</math>-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an <math>n</math>-sphere with themself at the center observing it, perceptually equidistant from all points on its <math>n</math>-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean spaces of any number of dimensions. The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's discovery of higher dimensional space: <blockquote>The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}</blockquote> == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity <math>c</math>, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we propose a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, our 4-space universe might be infinite, or at some vast radius (far greater than the radius of our big-bang 3-sphere) it might close into a 4-sphere. The universe viewed as a 4-sphere might, or might not, be expanding from some distant precursor to our big bang. The discovery of where exactly we are located in such a 4-sphere might bring about a whole new enlightenment. In any case the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space. When we look up at the objects that surround us, we have no immediate way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean <math>n</math>-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translation spirals), nearby objects must be translating radially at the same average velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of the starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:3-sphere|3-sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture. He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice."<ref name=Einstein1923/> Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. Anco and Maghadam found that <math>SO(4)</math> breaks to <math>\mathbb{S}^3</math> (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to <math>H^3</math> (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that <math>\mathbb{R}^4</math> is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction of it; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn| ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}} The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the planet's core and the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions? We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest 4-ball object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity, so symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a wilderness project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}}) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's surface), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 4z6cp3q26gopiyig29b4n38wjgnl153 0 295714 2844843 2843356 2026-11-08T01:31:40Z Jtneill 10242 /* External links */ * [https://help.openai.com/en/articles/7925741-sharing-conversations-and-scheduled-tasks-in-chatgpt Sharing conversations in ChatGPT] (openai.com) 2844843 wikitext text/x-wiki <noinclude>{{title|Using generative AI guidelines}} __TOC__ <noinclude>==In a nutshell==</noinclude> * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]. * '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]]. To use genAI appropriately: [[File:Screenshot of edit summary box.png|520px|right|thumb|'''Figure 1'''. Complete the edit summary box for each published page edit. This is especially when contributing genAI]] * Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (see Figure 1) with publicly-accessible links to chatbot conversations. * [[w:Fact-checking|Fact-check]]. * Only cite sources you consult. * Human-rewrite to enhance quality.<includeonly> * [[Motivation and emotion/Assessment/Using generative AI|More detail...]]</includeonly><noinclude> {{RoundBoxTop|theme=3}} ;Test your understanding <quiz display=simple shuffleanswers=true> {When contributing genAI material to Wikiversity, what should you include in the edit summary?<br>(select all that apply) |type="[]"} + A brief description of the changes. + A link to the GenAI conversation. - The name of the AI tool only. - A statement that the material has been checked. - The prompts used, without a link to the conversation. </quiz> {{RoundBoxBottom}} ==Summary== [[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]]. GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources. Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] and include publically-accessible links to chatbot conversations so that readers can understand the origins of the work. Academia is based on transparency. Follow the principle that "''more acknowledgment is better than less''". However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti), Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar. You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted. The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. ==Detailed guidelines== [[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 2'''. <!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. -->This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]] ===Use ethically, with caution=== Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]], [[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry. GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models. ===How to use=== Recommended uses of genAI tools include: * brainstorming * explaining key concepts * developing a structure * synthesising complex ideas * rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression * correcting spelling and grammar * image generation (e.g., see Figure 2) * scenario development * critical feedback and suggestions for improvement ===How to acknowledge=== [[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 3'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]] [[File:Edit summary for genAI content.png|thumb|450px|'''Figure 4'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]] Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 3), otherwise it is a violation of academic integrity. Include publicly-accessible links to the chatbot conversations (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., "ChatGPT May 24 2025 Version. ''Prompt detail or summary''") (see Figure 4). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source. These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling. ===Limitations=== Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit. ===Fact-check and cite=== Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand]. ==Learning and sharing== * Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work. * Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way. * If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together. * One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]]. ==Examples== * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&action=history Affiliation and motivation] (Book chapter, 2025) * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&action=history Self-concept and motivation] (Book chapter, 2026) ==See also== * [[Wikiversity:FAQ/Editing/Edit summary|Edit summary]] * [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy) * [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page) * [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy) ==External links== * [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library) * [https://help.openai.com/en/articles/7925741-sharing-conversations-and-scheduled-tasks-in-chatgpt Sharing conversations in ChatGPT] (openai.com) * [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues [[Category:Motivation and emotion/Assessment]] [[Category:Generative artificial intelligence]] </noinclude> ry5t0g8kicpm2hdic3ae8xtpvlw6t7k 2 327236 2844857 2844598 2026-11-08T09:01:25Z Dick Bos 24466 LaTeX 2844857 wikitext text/x-wiki &nbsp; [[File:On_Expedition_2015_MARBLE_Maastricht_University_2.JPG|thumb|Maastricht University, 2015-05-06. Explaining the principles of Wikipedia for students with [[User:Taketa]] (left) and [[User:Romaine]] (right)]] {{#babel:nl-N|en-3|de-2|fr-1}} &nbsp; My name is Dick Bos. I'm from the Netherlands. I work on the [[:w:nl:Gebruiker:Dick Bos|Dutch]] and [[en:User:Dick Bos|English]] wikipedia, on the English wikisource, on Wikimedia Commons etc. See my userpages there, please. * [[File:Wikipedia-logo-v2.svg|16px|alt=16 px Wikipedia logo]] Wikipedia: ** Dutch: [[w:nl:Gebruiker:Dick_Bos]] ** English: [[w:en:User:Dick Bos]] * [[Image:wikisource-logo.svg|16x16px]] WikiSource: ** [[s:en:User:Dick Bos|User:Dick Bos]] on en-ws [[m:User:Dick Bos/where|Click here]] for the most complete and up to date list of my userpages on Wikimedia-projects. &nbsp; My projects: * [[User:Dick Bos/Marx|Karl Marx]] (and Friedrich Engels) * [[User:Dick Bos/Ricardo|David Ricardo]] "technical": * [[User:Dick Bos/LaTeX|LaTeX]] == Handy == * [[Help:Contents]] ([[WV:HELP]]) * [[Help:CSS at Wikiversity]] * [[Wikiversity:Original research]] == Interesting == * [[WikiJournal of Humanities|WikiJournal (of Humanities)]] is hosted here on Wikiversity == Todo == When we have time, we need to spend some energy on: * [[wikibooks:Political Economy]] 1bxmqm2p9r7x08n9yr7o6x0h5ngf2br 0 329548 2844825 2841837 2026-11-07T18:56:28Z Athene241 3100061 2844825 wikitext text/x-wiki {{mathematics}} '''Athena problem''' is an [[:w:List of unsolved problems in mathematics|unsolved problem]] in [[:w:Number theory|number theory]] and [[:w:Formal language theory|formal language theory]] and [[:w:Order theory|order theory]], this problem is named after the ancient Greek goddess [[:w:Athena|Athena]] (which is associated with [[:w:Wisdom|wisdom]]). Athena problem is: Give a [[:w:Natural number|natural number]] ''b'' > 1, find the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the set of the "[[:w:Prime number|prime number]] [[:w:Greater than|>]] ''b''" [[:w:Numerical digit|digit]] [[:w:String (computer science)|string]]s in the [[:w:Positional numeral system|positional numeral system]] with [[:w:Radix|base]] ''b'' for the [[:w:Subsequence|subsequence]] [[:w:Partially ordered set|ordering]]. (A string ''x'' is a subsequence of another string ''y'', if ''x'' can be obtained from ''y'' by deleting zero or more of the [[:w:Character (computing)|character]]s in ''y''. For example, 514 is a subsequence of 352148, "string" is a subsequence of "meistersinger". In contrast, 758 is not a subsequence of 378259, "abc" is not a subsequence of "cbacacba", since the characters must be in the same order) (Unlike [[:w:Substring|substring]], subsequence is not required to occupy consecutive positions within the original sequences, e.g. the [[:w:Longest common subsequence|longest common subsequence problem]] is different from the [[:w:Longest common substring|longest common substring problem]]) Using [[:w:Formal language theory|formal language theory]] terminology, Athena problem is finding the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the [[:w:Formal language|language]] of base-''b'' [[:w:Representation (mathematics)|representation]]s of the [[:w:Prime number|prime number]]s [[:w:Greater than|>]] ''b'' (which is a set of [[:w:String (computer science)|string]]s of [[:w:Symbol|symbol]]s over the [[:w:Alphabet (formal languages)|alphabet]] ''Σ''_''b'' := {0, 1, ..., ''b''−1}), under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] "is a subsequence of", which is a [[:w:Partially ordered set|partial ordering]]), for a given natural number ''b'' > 1 (You can draw this partial ordering as a [[:w:Hasse diagram|Hasse diagram]] to find all [[:w:Minimal element|minimal element]]s), this set is called '''Athena set''', and the prime numbers in this set are called '''Athena primes'''. The [[:w:Set (mathematics)|set]] of all [[:w:String (computer science)|string]]s ordered by [[:w:Subsequence|subsequence]] (i.e. under the [[:w:Binary relation|binary relation]] "is a subsequence of") is a [[:w:Partially ordered set|partially ordered set]] (i.e. the binary relation "is a subsequence of" is a [[:w:Partial order|partial order relation]], since this binary relation is [[:w:Reflexive relation|reflexive]], [[:w:Antisymmetric relation|antisymmetric]], and [[:w:Transitive relation|transitive]]), hence, any given ([[:w:Finite set|finite]] or [[:w:Infinite set|infinite]]) set (e.g. the set of the "[[:w:Prime number|prime number]]s [[:w:Greater than|>]] ''b''" [[:w:String (computer science)|string]]s in [[:w:Radix|base]] ''b'', for 2 ≤ ''b'' ≤ 36), which is exactly the Athena problem) of strings ordered by subsequence is also a partially ordered set, and thus we can draw its [[:w:Hasse diagram|Hasse diagram]] and find its [[:w:Greatest element|greatest element]], [[:w:Least element|least element]], [[:w:Maximal element|maximal element]]s, and [[:w:Minimal element|minimal element]]s, however, the greatest element and least element may not exist, and for an infinite set, the maximal elements also may not exist, thus we are only interested on finding the [[:w:Minimal element|minimal element]]s of such sets, and we define minimal set of a set as the set of the minimal elements of this set, under a given [[:w:Partially ordered set|partially ordered]] [[:w:Binary relation|binary relation]] (this binary relation is "is a subsequence of" in the Athena problem), and we use ''M''(''S'') to denote the minimal set of the set ''S''. A partially ordered set is a [[:w:Totally ordered set|totally ordered set]] if the elements in this set are pairwise [[:w:Comparability|comparable]], two elements ''x'' and ''y'' are [[:w:Comparability|comparable]] with respect to a binary relation "≤" if at least one of ''x'' ≤ ''y'' or ''y'' ≤ ''x'' is true, thus, under the binary relation "is a subsequence of", two strings ''x'' and ''y'' are [[:w:Comparability|comparable]] if either ''x'' is a subsequence of ''y'', or ''y'' is a subsequence of ''x''. A surprising result from [[:w:Formal language theory|formal language theory]] is that every set of pairwise incomparable (i.e. not comparable) strings is finite (note that this is not true for general [[:w:Partially ordered set|partially ordered]] [[:w:Binary relation|binary relation]]s, e.g. the set of the [[:w:Positive integer|positive integer]]s, under the binary relation "is a [[:w:Divisor|divisor]] of", the [[:w:Infinite set|infinite set]] of the [[:w:Prime number|prime number]]s (by [[:w:Euclid's theorem]], this set is infinite) is pairwise incomparable, in fact, this set is exactly the minimal set of the set of the [[:w:Positive integer|positive integer]]s > 1 under this binary relation). At first sight this theorem is hard to believe, since we may make a set of pairwise incomparable strings as large as we want, e.g. all the strings with length 20 are pairwise incomparable, and if our [[:w:Alphabet (formal languages)|alphabet]] has ''n'' elements, then there are ''n''²⁰ such strings. Even if our [[:w:Alphabet (formal_languages)|alphabet]] is ''Σ''_''b'' = {0, 1, ..., ''b'' − 1} (the set of the base-''b'' [[:w:Numerical digit|digit]]s), which has ''b'' elements and we do not count the strings with [[:w:Leading zero|leading zero]]s, there are still ''b''²⁰−''b''¹⁹ such strings (i.e. there are ''b''²⁰−''b''¹⁹ 20-digit numbers in base ''b''), e.g. for the case of decimal (base ''b'' = 10), there are as many as 9×10¹⁹ such strings (i.e. there are 9×10¹⁹ 20-digit numbers in base ''b'' = 10). And nothing prevents us from 20 with 50 or 100 or [[:w:Googol|10¹⁰⁰]]. Nevertheless, the result is true, and in fact the proof is not that hard (the proof is like [[:w:Bolzano%25E2%2580%2593Weierstrass_theorem|Bolzano–Weierstrass theorem]] in [[:w:Real analysis|real analysis]], i.e. all [[:w:Bounded sequence|bounded sequence]] has a [[:w:Limit of a sequence|convergent]] [[:w:Subsequence|subsequence]]). This means that from any set of strings we can find its [[:w:Minimal element|minimal element]]s. A string ''x'' in a set of strings ''S'' is a ''minimal string'' (minimal element of a set of strings ordered by subsequence) if whenever ''y'' (an element of ''S'') is a subsequence of ''x'', we have ''y'' = ''x''. By [[:w:Higman's lemma|Higman's lemma]], there are no [[:w:Infinite set|infinite]] [[:w:Antichain|antichain]]s for the subsequence ordering (i.e. the subsequence ordering is always a [[:w:Well-quasi-ordering|well quasi order]]) (i.e. under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] "is a subsequence of", which is a [[:w:Partially ordered set|partial ordering]]), every set of pairwise incomparable (i.e. not [[:w:Comparability|comparable]]) strings is finite), thus there must be only finitely many such minimal elements. In other words, the Athena set in every base ''b'' must be a [[:w:Finite set|finite set]], and every base ''b'' ≥ 2 has only finitely many Athena primes, e.g. in [[:w:Decimal|decimal]] (base ''b'' = 10), the Athena set has exactly 77 [[:w:Element of a set|element]]s (they are exactly the Athena primes in decimal (base ''b'' = 10)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}. Determining the set of the minimal elements of a arbitrary set of strings under the subsequence ordering is in general [[:w:List of unsolved problems in mathematics|unsolvable]], and can be difficult even when this set is relatively simple (such as the base ''b'' representations of the prime numbers > ''b'', whose set is exactly the Athena set in base ''b''). Although the set ''M''(''S'') of minimal strings is necessarily [[:w:Finite set|finite]], determining it explicitly for a given ''S'' can be a difficult computational problem. We use some [[:w:Number theory|numbertheoretic]] [[:w:Heuristic argument|heuristic]]s to [[:w:Computing|compute]] ''M''(''L''_''b'') (i.e. to compute the Athena set in base ''b''), where ''L''_''b'' is the [[:w:Formal language|language]] of [[:w:Radix|base]]-''b'' representations of the [[:w:Prime number|prime number]]s which are [[:w:Greater than|>]] ''b'', for 2 ≤ ''b'' ≤ 36. For bases 2 ≤ ''b'' ≤ 36, Athena problem is fully solved in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, and also solved in bases ''b'' = 11, 13, 16, 22, 30 if [[:w:Probable prime|probable prime]]s are allowed. For the unsolved bases ''b'' = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, Athena problem is solved (if probable primes are allowed) except 771 [[:w:Indexed family|families]] of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') = sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. "''xy''⁺''z''" in [[:w:Regular expression|regular expression]]), all of these 771 families contain no primes > ''b'' or probable primes > ''b'' with length ≤ 100000. (The chance that an unproven probable prime in these sets is in fact composite is less than 10⁻²⁰⁰⁰, see https://t5k.org/notes/prp_prob.html) Below, family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') means sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. "''xy''⁺''z''" in [[:w:Regular expression|regular expression]]), where the members are expressed as base ''b'' strings, like the numbers in https://stdkmd.net/nrr/aaaab.htm, https://stdkmd.net/nrr/abbbb.htm, https://stdkmd.net/nrr/aaaba.htm, https://stdkmd.net/nrr/abaaa.htm, https://stdkmd.net/nrr/abbba.htm, https://stdkmd.net/nrr/abbbc.htm, e.g. 1{3} (in decimal) is the numbers in https://stdkmd.net/nrr/1/13333.htm#about_first, and {1}3 (in decimal) is the numbers in https://stdkmd.net/nrr/1/11113.htm#about_first, and 31{3} (in decimal) is the numbers in https://stdkmd.net/nrr/3/31333.htm#about_first, and {1}31 (in decimal) is the numbers in https://stdkmd.net/nrr/1/11131.htm#about_first, and 1{2}3 (in decimal) is the numbers in https://stdkmd.net/nrr/1/12223.htm#about_first, also, superscripts always means exponents, subscripts are always used to indicate repetitions of digits, e.g. 123₄567 = 123333567, all subscripts are written in decimal. == Solve the problem == To solve the Athena problem for a given base ''b'', we must [[:w:Computing|compute]] the elements up to families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), and find the smallest prime > ''b'' in all such families. We call families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') "linear" families, and we reduce these families by removing all trailing digits ''y'' from ''x'', and removing all leading digits ''y'' from ''z'', to make the families be easier, e.g. family 12333{3}33345 in base ''b'' is reduced to family 12{3}45 in base ''b'', since they are in fact the same family. Our [[:w:Algorithm|algorithm]] then proceeds as follows: * 1. ''M'' := {minimal primes in base ''b'' of length 2 or 3}, ''L'' := union of all ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'') such that ''x'' ≠ 0 and ''gcd''(''z'', ''b'') = 1 and ''Y'' is the set of digits ''y'' in base ''b'' such that ''xyz'' has no subsequence in ''M''. * 2. While ''L'' contains nonlinear families (families which are not linear families): Explore each family of ''L'', and update ''L''. Examine each family of ''L'' by: * 2.1. Let ''w'' be the shortest string in the family. If ''w'' has a subsequence in ''M'', then remove the family from ''L''. If ''w'' represents a prime, then add ''w'' to ''M'' and remove the family from ''L''. * 2.2. If possible, simplify the family. * 2.3. Using the techniques below (covering congruence, algebraic factorization, or combine of them), check if the family can be proven to only contain composites (only count the numbers > ''b''), and if so then remove the family from ''L''. * 3. Update ''L'', after each split examine the new families as in step 2. e.g. in decimal (base ''b'' = 10): ''M'' := {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991} ''L'' := {2{0,2}1, 2{0,8}7, 3{0,3,6,9}3, 3{0,3,6,9}9, 4{6}9, 5{0,5,8}1, 5{0,2}7, 6{0,3,6,9}3, 6{0,3,4,6,9}9, 7{0,7}7, 8{0,5}1, 8{0}7, 9{0,2,5,8}1, 9{0,3,6,9}3, 9{0,3,4,6,9}9} and since 2221 is prime, it follows that the family 2{0,2}1 splits into the families 2{0}1 and 2{0}2{0}1 and since the family 2{0}1 can be proven to contain no primes > base (since all numbers in this family are divisible by 3), it can be removed and since 20201 is prime, it follows that the family 2{0}2{0}1 splits into the families 2{0}21 and 22{0}1 221 and 2021 are composites, but 20021 is prime, thus add 20021 to ''L'' none of 221, 2201, 22001, 220001, 2200001 are primes, but 22000001 is prime, thus add 22000001 to ''L'' and since the family 3{0,3,6,9}3 can be proven to contain no primes > base (since all numbers in this family are divisible by 3), it can be removed etc. Since the number of possible (first digit,last digit) (also called (initial digit,final digit)) combos ([[:w:Ordered pair|ordered pair]]s) of a prime > ''b'' in base ''b'' is (''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(''b'') (all digits except 0 can be the first digit of a prime > ''b'' in base ''b'' (thus ''b''−1 possible digits), but only the digits coprime to ''b'' can be the last digit of a prime > ''b'' in base ''b'' (thus ''eulerphi''(''b'') possible digits), and by the [[:w:Rule of product|rule of product]], there are (''b''−1)×''eulerphi''(''b'') choices of the (first digit,last digit) combo, also, both "numbers of Athena primes in base ''b''" and "length of the largest Athena prime in base ''b''" are [[:w:Asymptotic analysis|roughly]] ''[[:w:E (mathematical_constant)|e]]''^{''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)}. Shrinking the family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') * If ''y'' ∈ ''Y'' and the string ''xyyz'' represents a prime > ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime > ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''}''z'' ∪ ''x''{''Y'' \ ''y''}''y''{''Y'' \ ''y''}''z''. * If ''y''₁ ∈ ''Y'' and ''y''₂ ∈ ''Y'' and ''y''₁ ≠ ''y''₂ and the string ''xy''₁''y''₂''z'' represents a prime > ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime > ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''₁}{''Y'' \ ''y''₂}''z''. * If ''y''₁ ∈ ''Y'' and ''y''₂ ∈ ''Y'' and ''y''₁ ≠ ''y''₂ and both the strings ''xy''₁''y''₂''z'' and ''xy''₂''y''₁''z'' represent a prime > ''b'' in base ''b'' (in this case, add this prime to the list) or have a subsequence which represents a prime > ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''₁}''z'' ∪ ''x''{''Y'' \ ''y''₂}''z''. e.g. in decimal (base ''b'' = 10): * 2221 is a prime > 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1. * 227 is a prime > 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7. * 449 is a prime > 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9. * Both 5051 and 5501 are primes > 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1. * 8501 is a prime > 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1. * 887 is a prime > 10, and it is a subsequence of 2887, also 2087 is a prime > 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7. * 349 and 449 are primes > 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes > 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9. * 251, 281, 521, 821, 881 are primes > 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes > 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}. If the methods we have discussed cannot be used to rule out or shrink ''x''{''Y''}''z'' where ''Y'' = {''y''₁, ''y''₂, ..., ''y''_''n''}, then we can replace ''x''{''Y''}''z'' by ''xy''₁{''Y''}''z'' ∪ ''xy''₂{''Y''}''z'' ∪ ... ∪ ''xy''_''n''{''Y''}''z'' and re-run the methods on this new [[:w:Formal language|language]]. If all remain families are linear families (i.e. of the form ''x''{''y''}''z'', where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), then we search the smallest (probable) primes in these families and add these primes to the list. e.g. in decimal (base ''b'' = 10): * The smallest prime in the family 5{0}27 is 5000000000000000000000000000027. * The smallest prime in the family {5}1 is 555555555551. * The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not a minimal element since 555555555551 is a subsequence of 8555555555555555555551. There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the Athena set in base ''b'' for 2 ≤ ''b'' ≤ 16 and ''b'' = 18, 20, 22, 24, 30. The bases ''b'' = 17, 19, 21, 23, 25 ≤ ''b'' ≤ 29, 31 ≤ ''b'' ≤ 36 are solved with the exception of 771 families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''). The following is a "[[:w:Semi-algorithm|semi-algorithm]]" that is guaranteed to solve the Athena problem for a given base ''b'', but it is not so easy to implement: # ''M'' = ''[[:w:Empty string|∅]]'' # while (''L'' ≠ ''∅'') do # choose ''x'', a shortest string in ''L'' # ''M'' := ''M'' ∪ {''x''} # ''L'' := ''L'' − ''sup''({''x''}) In practice, for arbitrary ''L'', we cannot feasibly carry out step 5. Instead, we work with ''L''&#39;, some regular overapproximation to ''L'', until we can show ''L''&#39; = ''∅'' (which implies ''L'' = ''∅''). In practice, ''L''&#39; is usually chosen to be a finite [[:w:Union (set theory)|union]] of sets of the form ''L''₁{''L''₂}''L''₃, where each of ''L''₁, ''L''₂, ''L''₃ is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime or not. Thus, the [[:w:Time complexity|time complexity]] of the Athena problem in base ''b'' may be ''[[:w:Big O notation|O]]''(''[[:w:E (mathematical_constant)|e]]''^{''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)}), and the [[:w:CPU time|CPU time]] of the Athena problem in base ''b'' may be longer than [[:w:Age of the universe|the age of the universe]] for bases ''b'' = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, also, Athena problem in bases ''b'' around 500 may be [[:w:NP-complete|NP-complete]] or [[:w:NP-hard|NP-hard]], or an [[:w:Undecidable problem|undecidable problem]], or an example of [[:w:Gödel's incompleteness theorems|Gödel's incompleteness theorems]] (like the [[:w:Continuum hypothesis|continuum hypothesis]] and the [[:w:Halting problem|halting problem]]). To solve the Athena problem (i.e. to compute the Athena set), we need to determine whether a given family contains a prime. In practice, if family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') could not be ruled out as only containing composites and ''Y'' contains two or more digits, then a relatively small prime > ''b'' could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2^''n''−2 strings of length ''n'' in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case ''Y'' contains only one digit, this family is of the form ''x''{''y''}''z'', and there is only a single string of each length > (the length of ''x'' + the length of ''z''), and it is not known if the following [[:w:Decision problem|decision problem]] is recursively solvable (just like [[:w:Sierpiński number|Sierpiński problem]] and [[:w:Riesel number|Riesel problem]], Sierpiński problem and Riesel problem can be generalized to other bases ''b'' (references: http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm), in fact, Athena problem base ''b'' covers the Sierpiński problem base ''b'' and the Riesel problem base ''b'' with ''k'' < ''b'', i.e. finding the smallest prime of the form ''k''×''b''^''n''+1 and ''k''×''b''^''n''−1 (or prove such prime does not exist) with ''k'' < ''b'' (specially, for bases ''b'' such that the conjectured smallest Sierpiński number or the conjectured smallest Riesel number is < ''b'', Athena problem base ''b'' covers the Sierpiński problem base ''b'' or the Riesel problem base ''b'', respectively), since the smallest prime of the form ''k''×''b''^''n''+1 and ''k''×''b''^''n''−1 (if exists) must be a minimal element in base ''b'', also, Athena problem base ''b'' covers finding the smallest prime of these forms in base ''b'' (or proving that such prime does not exist) (in fact, it is known that exactly what bases 2 ≤ ''b'' ≤ 1024 have the families listed in the table below as unsolved families, all of these families in all bases 2 ≤ ''b'' ≤ 1024 have been searched to length ≥ 10000 (for the family (''sqrt''(''b'')×''b''^''n''+1)/(''sqrt''(''b'')+1), bases 2 ≤ ''b'' ≤ 1048576, searched to length ≥ 5000)): (''b''^''n''−1)/(''b''−1) (for this form, ''n'' must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068), ''b''^''n''+1 (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 1) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101), (''b''^''n''+1)/2 (for odd ''b'') (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt), (''sqrt''(''b'')×''b''^''n''+1)/(''sqrt''(''b'')+1) (for square ''b'') (for this form, 2×''n''+1 must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for bases ''b'' with ''sqrt''(''b'') prime: https://oeis.org/A065507), ((''b''−2)×''b''^''n''+1)/(''b''−1) (''n'' ≥ 2) (reference of this form: https://oeis.org/A243404), 2×''b''^''n''+1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624), 2×''b''^''n''−1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&d=1567314217, https://oeis.org/A119591), ''b''^''n''+2 (''n'' ≥ 1) (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067), ''b''^''n''−2 (''n'' ≥ 2) (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201), (''b''−1)×''b''^''n''+1 (''n'' ≥ 1) (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139), (''b''−1)×''b''^''n''−1 (''n'' ≥ 1) (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396), ''b''^''n''+(''b''−1) (''n'' ≥ 1) (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179), ''b''^''n''−(''b''−1) (''n'' ≥ 2) (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)): '''Problem: Given strings ''x'', ''z'' (may be empty), a digit ''y'', and a base ''b'' (''x'' does not [[:w:Leading zero|start with the digit 0]], ''z'' ends with a digit which [[:w:Coprime integers|coprime]] to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty), does there exist a prime number whose base-''b'' expansion is of the form ''xy''_''n''''z'' for some ''n'' ≥ 0?''' An [[:w:Algorithm|algorithm]] to solve this problem, for example, would allow us to decide if there are any additional [[:w:Fermat prime|Fermat prime]]s other than the known ones (corresponding to ''n'' = 0, 1, 2, 3, 4). To see this, take ''b'' = 2, ''x'' = 1, ''y'' = 0, and ''z'' = 0₁₆1. Since if 2^''n''+1 is prime then ''n'' must be a [[:w:Power of 2|power of two]], a prime of the form ''xy''_''n''''z'' in base ''b'' must be a new Fermat prime. Besides, it would allow us to decide if there are infinitely many [[:w:Mersenne prime|Mersenne prime]]s (of the form 2^''p''−1 with prime ''p''). To see this, take ''b'' = 2, ''x'' = ''𝜆'' (the [[:w:Empty string|empty string]]), ''y'' = 1, and ''z'' = 1_''n''+1, where ''n'' is the exponent of the Mersenne prime which we want to know whether it is the largest Mersenne prime or not. Since if 2^''n''−1 is prime then ''n'' must be a [[:w:Prime number|prime]], a prime of the form ''xy''_''n''''z'' in base ''b'' must be a new Mersenne prime. Also, it would allow us to decide whether 78557 is the smallest [[:w:Sierpinski number|Sierpinski number]] (i.e. odd numbers ''k'' such that ''k''×2^''n''+1 is composite for all ''n'' ≥ 1) and whether 509203 is the smallest [[:w:Riesel number|Riesel number]] (i.e. odd numbers ''k'' such that ''k''×2^*n*−1 is composite for all ''n'' ≥ 1), etc. '''Conjecture (this conjecture is very important for the Athena problem): If family ''xy''_''n''''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then family ''xy''_''n''''z'' in base ''b'' contains infinitely many primes (this is equivalent to: If form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) contains infinitely many primes).''' (in fact, this conjecture is equivalent to the conjecture (to prove this, by change the base (''b'') to a power of ''b'' which is larger than the largest prime in a given family (in base ''b'') which only contains finitely many primes): If family ''xy''_''n''''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then family ''xy''_''n''''z'' in base ''b'' contains at least one prime (this is equivalent to: If form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) contains at least one prime), like the [[:w:Bunyakovsky conjecture|Bunyakovsky conjecture]] and the [[:w:Dickson's conjecture|Dickson's conjecture]] and the [[:w:Schinzel's hypothesis H|Schinzel's hypothesis ''H'']], if such ''n'' always exists, then there must be always infinitely many such ''n'', to prove this, add another polynomial for the cases of the Dickson's conjecture and the Schinzel's hypothesis ''H'', also, change the polynomial (e.g. change ''n'' to ''r''×''n'' or ''n''^''r'' for all integers ''r'' > 1) for the cases of the Bunyakovsky conjecture and the Schinzel's hypothesis ''H'') Some families can be ruled out to contain no prime > ''b'' by [[:w:Covering set|covering congruence]], [[:w:Factorization of polynomials|algebraic factorization]] (e.g. [[:w:Difference of two squares|difference of two squares]], [[:w:Sum of two cubes|sum of two cubes]], [[:w:Sophie Germain's identity|Sophie Germain's identity of ''x''⁴+4×''y''⁴]]), or combine of them, e.g. * The base 9 family 2{7}: Always divisible by 2 or 5 * The base 11 family 2{5}: Always divisible by 2 or 3 * The base 14 family B{0}1: Always divisible by 3 or 5 * The base 13 family 95{0}3: Always divisible by 5, 7, or 17 * The base 16 family {4}D: Always divisible by 3, 7, or 13 * The base 16 family {8}F: Always divisible by 3, 7, or 13 * The base 21 family {7}D: Always divisible by 2, 13, or 17 * The base 23 family {D}GA: Always divisible by 2, 5, 7, 37, or 79 * The base 9 family {1}: Can be written as (9^''n''−1)/8 and can be factored as (3^''n''−1) × (3^''n''+1) / 8 * The base 8 family 1{0}1: Can be written as 8^''n''+1 and can be factored as (2^''n''+1) × (4^''n''−2^''n''+1) * The base 9 family 3{8}: Can be written as 4×9^''n''−1 and can be factored as (2×3^''n''−1) × (2×3^''n''+1) * The base 16 family 1{5}: Can be written as (4×16^''n''−1)/3 and can be factored as (2×3^''n''−1) × (2×3^''n''+1) / 3 * The base 16 family {4}1: Can be written as (4×16^''n''−49)/15 and can be factored as (2×3^''n''−7) × (2×3^''n''+7) / 15 * The base 27 family 7{Q}: Can be written as 8×27^''n''−1 and can be factored as (2×3^''n''−1) × (4×9^''n''+2×3^''n''+1) * The base 27 family 9{G}: Can be written as (125×27^''n''−8)/13 and can be factored as (5×3^''n''−2) × (25×9^''n''+10×3^''n''+4) * The base 16 family {C}D: Can be written as (4×16^''n''+1)/5 and can be factored as (2×4^''n''−2×2^''n''+1) × (2×4^''n''+2×2^''n''+1) / 5 * The base 14 family 8{D}: Can be written as 9×14^''n''−1, it is divisible by 5 if ''n'' is odd and can be factored as (3×14^''n''/2−1) × (3×14^''n''/2+1) if ''n'' is even * The base 12 family {B}9B: Can be written as 12^''n''−25, it is divisible by 13 if ''n'' is odd and can be factored as (12^''n''/2−5) × (12^''n''/2+5) if ''n'' is even * The base 14 family {D}5: Can be written as 14^''n''−9, it is divisible by 5 if ''n'' is odd and can be factored as (14^''n''/2−3) × (14^''n''/2+3) if ''n'' is even * The base 17 family 1{9}: Can be written as (25×17^''n''−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (5×17^''n''/2−3) × (5×17^''n''/2+3) / 16 if ''n'' is even * The base 17 family 7{9}: Can be written as (121×17^''n''−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (11×17^''n''/2−3) × (11×17^''n''/2+3) / 16 if ''n'' is even * The base 24 family 3{N}: Can be written as 4×24^''n''−1, it is divisible by 5 if ''n'' is odd and can be factored as (2×24^''n''/2−1) × (2×24^''n''/2+1) if ''n'' is even * The base 24 family 5{N}: Can be written as 6×24^''n''−1, it is divisible by 5 if ''n'' is even and can be factored as (12×24^{(''n''−1)/2}−1) × (12×24^{(''n''−1)/2}+1) if ''n'' is odd * The base 33 family F{W}: Can be written as 16×33^''n''−1, it is divisible by 17 if ''n'' is odd and can be factored as (4×33^''n''/2−1) × (4×33^''n''/2+1) if ''n'' is even If the conjecture above is true, then the [[:w:Sierpiński number|Sierpiński conjecture]] and [[:w:Riesel number|Riesel conjecture]] are also true, and the [https://www.mersenneforum.org/showthread.php?t=10761 dual Sierpiński conjecture] and the [https://www.mersenneforum.org/showthread.php?t=6545 dual Riesel conjecture] are also true, and the [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm Riesel conjectures] in all bases ''b'' are also true, and the [http://www.noprimeleftbehind.net/crus/SNOB-Sierp-conjectures.htm real Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Real-Riesel-conjectures.htm real Riesel conjectures] are also true, also, if the Athena conjecture is true, then there are infinitely many primes of these forms for fixed bases ''b'' ≥ 2 and variable exponents ''n'': * (''b''^''n''−1)/(''b''−1) for all bases ''b'' which are not [[:w:Perfect power|perfect power]]s (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068) * ''b''^''n''+1 for all even bases ''b'' which are not of the form ''m''^''r'' with odd ''r'' > 1 (for this form, ''n'' must be power of 2) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101) * (''b''^''n''+1)/2 for all odd bases ''b'' which are not of the form ''m''^''r'' with odd ''r'' > 1 (for this form, ''n'' must be power of 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt) * (''b''^''n''+1)/(''b''+1) for all bases ''b'' which are neither of the form ''m''^''r'' with odd ''r'' > 1 nor of the form 4×''m''⁴ (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for prime bases ''b'': https://oeis.org/A065507) * ((''b''−2)×''b''^''n''+1)/(''b''−1) for all bases ''b'' > 2 (reference of this form: https://oeis.org/A243404) * 2×''b''^''n''+1 for all bases ''b'' < 201446503145165177, not == 1 mod 3 (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624) * 2×''b''^''n''−1 for all bases ''b'' (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&d=1567314217, https://oeis.org/A119591) * 3×''b''^''n''+1 for all even bases ''b'' * 3×''b''^''n''−1 for all even bases ''b'' * 4×''b''^''n''+1 for all bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s * 4×''b''^''n''−1 for all bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s * 5×''b''^''n''+1 for all even bases ''b'' < 140324348, not == 1 mod 3 * 5×''b''^''n''−1 for all even bases ''b'' * 6×''b''^''n''+1 for all bases ''b'' not == 1 mod 7, not == 34 mod 35 * 6×''b''^''n''−1 for all bases ''b'' not == 1 mod 5, not == 34 mod 35, not of the form 6×''m''² with ''m'' == 2, 3 mod 5 * 7×''b''^''n''+1 for all even bases ''b'' * 7×''b''^''n''−1 for all even bases ''b'' < 9162668342, not == 1 mod 3 * 8×''b''^''n''+1 for all bases ''b'' not == 1 mod 3, not == 20 mod 21, not == 47, 83 mod 195, not == 467, 4343, 9887, 25448, 35978, 41522, 42647, 57083 mod 73815, not == 722, 83813, 206672, 239432, 322523, 1283843, 1519577, 1522553 mod 1551615, ..., not [[:w:Cube (algebra)|cube]]s * 8×''b''^''n''−1 for all bases ''b'' not == 1 mod 7, not == 20 mod 21, not == 83, 307 mod 455, not == 1266, 13593, 27292, 46353 mod 63973, ..., not [[:w:Cube (algebra)|cube]]s * 9×''b''^''n''+1 for all even bases ''b'' < 177744, not == 1 mod 5 * 9×''b''^''n''−1 for all even bases ''b'' not == 4 mod 5, not [[:w:Square number|square]]s * 10×''b''^''n''+1 for all bases ''b'' not == 1 mod 11, not == 32 mod 33 (references of this form: https://oeis.org/A088782) * 10×''b''^''n''−1 for all bases ''b'' not == 1 mod 3, not == 32 mod 33 * 11×''b''^''n''+1 for all even bases ''b'' not == 1 mod 3, not == 14 mod 15 * 11×''b''^''n''−1 for all even bases ''b'' not == 1 mod 5, not == 14 mod 15, not of the form 11×''m''² with ''m'' == 2, 3 mod 5 * 12×''b''^''n''+1 for all bases ''b'' not == 1 mod 13, not == 142 mod 143, not == 562, 828, 900, 1166 mod 1729, not == 597, 1143 mod 1885, not == 296, 901, 1759, 3090, 4553, 5521, 5807, 6016, 6984, 7094, 7270, 7380, 7479, 8447, 8557, 8733, 8843, 9910, 10020, 10196, 10306, 11483, 11769, 12737, 14200, 15531, 16994, 18457 mod 19019, not == 563, 1433, 13212, 15097, 19848, 20718, 32497, 34382, 39133, 51782, 53667, 58418, 58452, 60337, 60883, 71067, 72952, 77737, 79622, 80168, 94267, 97022, 98583, 98907, 113552, 116307, 117868, 118192, 131967, 132513, 132837, 134398, 151252, 151798, 152122, 153683, 170537, 171083, 172968, 177753, 179638, 189822, 190368, 192253, 192287, 197038, 198923, 211572, 213568, 216323, 218208, 229987, 232853, 235608, 237493, 249272 mod 250705, ... * 12×''b''^''n''−1 for all bases ''b'' not == 1 mod 11, not == 142 mod 143, not == 307, 1143 mod 1595, not == 901, 6016, 7479, 18457 mod 19019, ... * ''b''^''n''+2 for all odd bases ''b'' < 201446503145165177, not == 1 mod 3 (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067) * ''b''^''n''−2 for all odd bases ''b'' (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201) * ''b''^''n''+3 for all even bases ''b'' not divisible by 3 * ''b''^''n''−3 for all even bases ''b'' not divisible by 3 * ''b''^''n''+4 for all odd bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s * ''b''^''n''−4 for all odd bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s * (''b''−1)×''b''^''n''+1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139) * (''b''−1)×''b''^''n''−1 for all bases ''b'' (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396) * (''b''+1)×''b''^''n''+1 for all bases ''b'' not == 1 mod 3 (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PP.htm, http://www.bitman.name/math/table/474, https://pzktupel.de/Primetables/TableWilliams4.php) * (''b''+1)×''b''^''n''−1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PM.htm, http://www.bitman.name/math/table/471, https://pzktupel.de/Primetables/TableWilliams3.php) * ''b''^''n''+(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179) * ''b''^''n''−(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435) * ''b''^''n''+(''b''+1) for all bases ''b'' not == 1 mod 3 (references of this form: http://www.bitman.name/math/table/801, https://pzktupel.de/Primetables/TableWilliams8.php, https://oeis.org/A346149, https://oeis.org/A346154) * ''b''^''n''−(''b''+1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/798, https://pzktupel.de/Primetables/TableWilliams7.php, https://oeis.org/A178250) By the [[:w:Prime number theorem|prime number theorem]], the [[:w:Probability|chance]] that a [[:w:Random number|random]] ''n''-digit base ''b'' number is prime is [[:w:Asymptotic analysis|approximately]] 1/''n'' (more accurately, the chance is approximately 1/(''n''×''ln''(''b'')), where ''ln'' is the [[:w:Natural logarithm|natural logarithm]]). If one conjectures the numbers ''x''{''y''}''z'' behave similarly (i.e. the numbers ''x''{''y''}''z'' is a [[:w:Pseudorandomness|pseudorandom sequence]]) you would expect [[:w:Harmonic_series (mathematics)|1/1 + 1/2 + 1/3 + 1/4 + ... = ∞]] primes of the form ''x''{''y''}''z'' (of course, this does not always happen, since some ''x''{''y''}''z'' families can be ruled out to contain no prime > ''b'' (by covering congruence, algebraic factorization, or combine of them), but it is at least a reasonable conjecture in the absence of evidence to the contrary. Hence, the [[:w:Heuristic argument|heuristic argument]] suggests there are always infinitely many primes in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') if it cannot be ruled out to contain no prime or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them. However, some families ''x''{''y''}''z'' could not be proven to contain no primes > ''b'' (by covering congruence, algebraic factorization, or combine of them) but no primes > ''b'' could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to [[:w:Primality test|test the primality]] of larger and larger numbers of such form and hope a prime is eventually discovered. e.g. the smallest (probable) prime in the family A{3}A in base ''b'' = 13 is A3₅₉₂₁₉₇A, its algebraic form is (41×13⁵⁹²¹⁹⁸+27)/4, when written in decimal contains 659677 digits (it is only probable prime, i.e. not definitely prime, since technically, probable primality tests were used to show this (which have a ''very'' small chance of making an error, see https://t5k.org/notes/prp_prob.html) because all known primality tests run far too slowly to run on numbers of this size unless either [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] (or both) can be ≥ 1/3 factored). The numbers in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') are of the form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) for some fixed ''a'', ''b'', ''c'' such that ''a'' ≥ 1, ''b'' ≥ 2 (''b'' is the base), ''c'' ≠ 0, ''gcd''(''a'',''c'') = 1, ''gcd''(''b'',''c'') = 1. Except in the [[:w:Special case|special case]] ''c'' = ±1 and ''gcd''(''a''+''c'',''b''−1) = 1 (the only case which [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] is [[:w:Triviality (mathematics)|trivially]] fully factored), when ''n'' is large the known [[:w:Primality test|primality test]]s for such a number are too inefficient to run (since they are [https://t5k.org/glossary/xpage/OrdinaryPrime.html ordinary primes]). In this case one must resort to a [[:w:Probabilistic algorithm|probable]] primality test such as a [[:w:Miller–Rabin primality test|Miller–Rabin primality test]] or a [[:w:Baillie–PSW primality test|Baillie–PSW primality test]], unless a divisor of the number can be found. Since we are testing many numbers in an [[:w:Exponential growth|exponential sequence]], it is possible to use a sieving process to find divisors rather than using [[:w:Trial division|trial division]]. To do this, we made use of Geoffrey Reynolds' ''srsieve'' software (download: https://pzktupel.de/Software/srsieve_1.1.4.7z). This program uses the [[:w:Baby-step giant-step|baby-step giant-step]] [[:w:Algorithm|algorithm]] to find all primes ''p'' which divide ''a''×''b''^''n''+''c'' where ''p'' and ''n'' lie in a [[:w:Interval_(mathematics)|specified range]]. Since this program cannot handle the general case (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) > 1 we only used it to sieve the sequence ''a''×''b''^''n''+''c'' for primes ''p'' not dividing ''gcd''(''a''+''c'',''b''−1), and initialized the list of candidates to not include ''n'' for which there is some prime ''p'' dividing ''gcd''(''a''+''c'',''b''−1) for which ''p'' dividing (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1). The program had to be modified slightly to remove a check which would prevent it from running in the case when ''a'', ''b'', and ''c'' were all odd (since then 2 divides ''a''×''b''^''n''+''c'', but 2 may not divide (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1)). Once the numbers with small divisors had been removed, it remained to test the remaining numbers using a probable primality test. For this we used the software ''LLR'' by Jean Penné. (download: http://jpenne.free.fr/index2.html). Although undocumented, it is possible to run this program on numbers of the form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) > 1, so this program required no modifications. A script was also written which allowed one to run ''srsieve'' while ''LLR'' was testing the remaining candidates, so that when a divisor was found by srsieve on a number which had not yet been tested by ''LLR'' it would be removed from the list of candidates. For the primes < 10²⁵⁰⁰⁰ for the "easy" bases (bases ''b'' with ≤ 150 primes > 10²⁹⁹ (base ''b'' = 26 has 83 known primes > 10²⁹⁹ and 3 unsolved families, base ''b'' = 36 has 75 known primes > 10²⁹⁹ and 4 unsolved families, base ''b'' = 17 has 99 known primes > 10²⁹⁹ and 18 unsolved families, base ''b'' = 21 has 80 known primes > 10²⁹⁹ and 12 unsolved families, base ''b'' = 19 has 201 known primes > 10²⁹⁹ and 23 unsolved families), i.e. bases *b* = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36), we employed ''CM'' by Andreas Enge (download: https://www.multiprecision.org/cm/download.html), an elliptic curve primality proving implementation. Currently, the final goal of the Athena problem project is finding the Athena set (i.e. finding all Athena primes) and proving that this set is exactly the Athena set (i.e. proving that these are all Athena primes (including the primality proving for the probable primes)) in all bases 2 ≤ ''b'' ≤ 36, i.e. solving all families in all bases 2 ≤ ''b'' ≤ 36. Solving all (unsolved) families in all bases 2 ≤ ''b'' ≤ 36 (and proving the primality of all probable primes in the sets of all bases 2 ≤ ''b'' ≤ 36) is not possible but we aim to solve many of them (and proving the primality of many of them), at least find a ''probable'' prime for many of them (since the smallest prime in a family may be too large (> 10²⁵⁰⁰⁰) to be proved primality, unless its ''N''−1 or/and ''N''+1 can be ≥ 25% factored). == Data == These are the results of the Athena problem in bases 2 ≤ ''b'' ≤ 36 (we stop at base 36 since this base is the maximum base for which it is possible to write the numbers with the [[:w:Symbol|symbol]]s 0, 1, 2, ..., 9 and A, B, C, ..., Z (i.e. the 10 [[:w:Arabic numerals|Arabic numerals]] and the 26 [[:w:Latin script|Latin letters]]): (some large Athena primes are only probable primes, i.e. not definitely primes, since they are too large to be [[:w:Elliptic curve primality|ECPP proved]] and [[:w:Pocklington primality test#Extensions and variants|neither ''N''−1 nor ''N''+1 can be ≥ 1/3 factored]] (Brillhart-Lehmer-Selfridge primality test), all of them pass the [[:w:Baillie–PSW primality test|Baillie–PSW primality test]] and the [[:w:Strong pseudoprime|strong primality test]] (i.e. the [[:w:Miller–Rabin primality test|Miller–Rabin primality test]]) with all prime bases ''p'' ≤ 61, however, all Athena primes < 10²⁵⁰⁰⁰ for bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36 are definitely primes, most of them > 10²⁹⁹ are proven primes with [[:w:Elliptic curve primality|ECPP proving]], others > 10²⁹⁹ are proven primes with [[:w:Pocklington primality test#Extensions and variants|''N''−1 or ''N''+1 proving]]) The Athena primes > 10²⁹⁹ in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 which are proven primes with ''N''−1 or ''N''+1 proving includes the Athena primes whose ''N''−1 or ''N''+1 is trivially fully factored: * the 3176th Athena prime in base 13, 81010₄₁₅1, which equals 17746×13⁴¹⁶+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003590431555, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003590431556&open=ecm * the 3177th Athena prime in base 13, 8110₄₃₅1, which equals 1366×13⁴³⁶+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000002373259109, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000002373259124&open=ecm * the 3188th Athena prime in base 13, 930₁₅₅₁1, which equals 120×13¹⁵⁵²+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961452, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961453&open=ecm * the 3191st Athena prime in base 13, 390₆₂₆₆1, which equals 48×13⁶²⁶⁷+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961441, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961451&open=ecm * the 649th Athena prime in base 14, 34D₇₀₈, which equals 47×14⁷⁰⁸−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001540144903, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001540144907&open=ecm * the 650th Athena prime in base 14, 4D₁₉₆₉₈, which equals 5×14¹⁹⁶⁹⁸−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000884560233, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000884560625&open=ecm * the 2335th Athena prime in base 16, 88F₅₄₅, which equals 137×16⁵⁴⁵−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000413679658, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000413877337&open=ecm * the 10317th Athena prime in base 17, 5A70₂₇₄1, which equals 1622×17²⁷⁵+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003782940709, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003782941930&open=ecm * the 10359th Athena prime in base 17, 9D0₁₀₆₇1, which equals 166×17¹⁰⁶⁸+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961369, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961370&open=ecm * the 10370th Athena prime in base 17, A0₁₃₅₅1, which equals 10×17¹³⁵⁶+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000034167087, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000271866825&open=ecm * the 10386th Athena prime in base 17, 530₄₈₆₇1, which equals 88×17⁴⁸⁶⁸+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000762660735, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000762660737&open=ecm * the 10408th Athena prime in base 17, 570₅₁₃₁₀1, which equals 92×17⁵¹³¹¹+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961389, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469616&open=ecm * the 10412th Athena prime in base 17, 970₁₆₆₀₄₇1, which equals 160×17¹⁶⁶⁰⁴⁸+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (>10¹⁹⁹⁹⁹⁹) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817312&open=ecm * the 10413th Athena prime in base 17, F70₁₈₆₇₆₇1, which equals 262×17¹⁸⁶⁷⁶⁸+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (>10¹⁹⁹⁹⁹⁹) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817317&open=ecm * the 3310th Athena prime in base 20, JCJ₆₂₉, which equals 393×20⁶²⁹−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001559454258, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001559454271&open=ecm * the 13373rd Athena prime in base 21, 5D0₁₉₈₄₈1, which equals 118×21¹⁹⁸⁴⁹+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000777265872, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469310&open=ecm * the 3408th Athena prime in base 24, 88N₅₉₅₁, which equals 201×24⁵⁹⁵¹−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003593275880, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000003593373246&open=ecm * the 25509th Athena prime in base 28, EB0₄₀₅1, which equals 403×28⁴⁰⁶+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001534442374, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000001534442380&open=ecm * the 2616th Athena prime in base 30, C0₁₀₂₂1, which equals 12×30¹⁰²³+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000785448736, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785448737&open=ecm * the 2619th Athena prime in base 30, OT₃₄₂₀₅, which equals 25×30³⁴²⁰⁵−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000800812865, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000819405041&open=ecm * the 35237th Athena prime in base 36, P8Z₃₉₀, which equals 909×36³⁹⁰−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000764100228, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000764100231&open=ecm and the Athena primes > 10²⁹⁹ in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 whose ''N''−1 or ''N''+1 is ≥ 1/3 factored: (''R''_''n''(''b'') means the [[:w:Repunit|repunit]] in base ''b'' with length ''n''), i.e. ''R''_''n''(''b'') = (''b''^''n''−1)/(''b''−1), "''S''_''n''(''b'')" means ''b''^''n''+1) * the 3168th Athena prime in base 13, 9₃₀₈1, ''N''−1 is 117×''R''₃₀₈(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13³⁰⁸−1, and for the algebraic factors of 13³⁰⁸−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&Exp=308&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 13³⁰⁸−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=308&c0=-&EN=&LM= * the 3179th Athena prime in base 13, B₅₆₃C, ''N''−1 is 11×''R''₅₆₄(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13⁵⁶⁴−1, and for the algebraic factors of 13⁵⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&Exp=564&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 13⁵⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=564&c0=-&EN=&LM= * the 3180th Athena prime in base 13, 1B₅₇₆, ''N''−1 is 23×''R''₅₇₆(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13⁵⁷⁶−1, and for the algebraic factors of 13⁵⁷⁶−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&Exp=576&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 13⁵⁷⁶−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=576&c0=-&EN=&LM= * the 10320th Athena prime in base 17, 9₂₉₂1, ''N''−1 is 153×''R''₂₉₂(17), thus factor ''N''−1 is equivalent to factor the Cunningham number 17²⁹²−1, and for the algebraic factors of 17²⁹²−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=17&Exp=292&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 17²⁹²−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=17&Exp=292&c0=-&EN=&LM= * the 13304th Athena prime in base 21, 7₂₃₀1, ''N''−1 is 147×''R''₂₃₀(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21²³⁰−1, and for the algebraic factors of 21²³⁰−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&Exp=230&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 21²³⁰−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&Exp=230&c0=-&EN=&LM= * the 13355th Athena prime in base 21, 3₁₀₆₃2, ''N''+1 is 3×''R''₁₀₆₄(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21¹⁰⁶⁴−1, and for the algebraic factors of 21¹⁰⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&Exp=1064&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 21¹⁰⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&Exp=1064&c0=-&EN=&LM= * the 25199th Athena prime in base 26, 9K₃₄₃AP, ''N''+1 is 6370×''R''₃₄₄(26), thus factor ''N''+1 is equivalent to factor the Cunningham number 26³⁴⁴−1, and for the algebraic factors of 26³⁴⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&Exp=344&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 26³⁴⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&Exp=344&c0=-&EN=&LM= * the 25200th Athena prime in base 26, 8₃₅₄1, ''N''−1 is 208×''R''₃₅₄(26), thus factor ''N''−1 is equivalent to factor the Cunningham number 26³⁵⁴−1, and for the algebraic factors of 26³⁵⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&Exp=354&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 26³⁵⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&Exp=354&c0=-&EN=&LM= All numbers are written in base ''b'', [[:w:Senary#Base 36 as senary compression|using A to Z to represent digit values 10 to 35]], "{}" means repeating, e.g. family 12{3}45 means the sequence {1245, 12345, 123345, 1233345, 12333345, 123333345, ...} (where the members are expressed as base ''b'' strings), subscripts are used to indicate repetitions of digits, e.g. 123₄567 means 123333567 (all subscripts are written in decimal). Base 2: 1 Athena prime (the largest of which has 2 digits (it is 11, and its value is 3 in decimal)): {11} Base 3: 3 Athena primes (the largest of which has 3 digits (it is 111, and its value is 13 in decimal)): {12, 21, 111} Base 4: 5 Athena primes (the largest of which has 3 digits (it is 221, and its value is 41 in decimal)): {11, 13, 23, 31, 221} Base 5: 22 Athena primes (the largest of which has 96 digits (it is 10₉₃13, and its algebraic form is 5⁹⁵+8)): {12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013} Base 6: 11 Athena primes (the largest of which has 5 digits (it is 40041, and its value is 5209 in decimal)): {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041} Base 7: 71 Athena primes (the largest of which has 17 digits (it is 3₁₆1, and its algebraic form is (7¹⁷−5)/2)): {14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331} Base 8: 75 Athena primes (the largest of which has 221 digits (it is 4₂₂₀7, and its algebraic form is (4×8²²¹+17)/7)): {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447} Base 9: 151 Athena primes (the largest of which has 1161 digits (it is 30₁₁₅₈11, and its algebraic form is 3×9¹¹⁶⁰+10)): {12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011} Base 10: 77 Athena primes (the largest of which has 31 digits (it is 50₂₈27, and its algebraic form is 5×10³⁰+27)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} Base 11: 1068 Athena (probable) primes (including 1 unproven probable prime: 57₆₂₆₆₈), the largest of which has 62669 digits (it is 57₆₂₆₆₈, and its algebraic form is (57×11⁶²⁶⁶⁸−7)/10), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel11 Data of Athena (probable) primes base 11] Base 12: 106 Athena primes (the largest of which has 42 digits (it is 40₃₉77, and its algebraic form is 4×12⁴¹+91)): {11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 221, 241, 2A1, 2B1, 2BB, 401, 421, 447, 471, 497, 565, 655, 665, 701, 70B, 721, 747, 771, 77B, 797, 7A1, 7BB, 907, 90B, 9BB, A41, B21, B2B, 2001, 200B, 202B, 222B, 229B, 292B, 299B, 4441, 4707, 4777, 6A05, 6AA5, 729B, 7441, 7B41, 929B, 9777, 992B, 9947, 997B, 9997, A0A1, A201, A605, A6A5, AA65, B001, B0B1, BB01, BB41, 600A5, 7999B, 9999B, AAAA1, B04A1, B0B9B, BAA01, BAAA1, BB09B, BBBB1, 44AAA1, A00065, BBBAA1, AAA0001, B00099B, AA000001, BBBBBB99B, B0000000000000000000000000009B, 400000000000000000000000000000000000000077} Base 13: 3197 Athena (probable) primes (including 4 unproven probable primes: C5₂₃₇₅₅C, 80₃₂₀₁₇111, 95₁₉₇₄₂₀, A3₅₉₂₁₉₇A), the largest of which has 592199 digits (it is A3₅₉₂₁₉₇A, and its algebraic form is (41×13⁵⁹²¹⁹⁸+27)/4), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel13 Data of Athena (probable) primes base 13] Base 14: 650 Athena primes, the largest of which has 19699 digits (it is 4D₁₉₆₉₈, and its algebraic form is 5×14¹⁹⁶⁹⁸−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel14 Data of Athena primes base 14] Base 15: 1284 Athena primes, the largest of which has 157 digits (it is 7₁₅₅97, and its algebraic form is (15¹⁵⁷+59)/2), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel15 Data of Athena primes base 15] Base 16: 2347 Athena (probable) primes (including 3 unproven probable primes: DB₃₂₂₃₄, 4₇₂₇₈₅DD, 3₁₁₆₁₃₇AF), the largest of which has 116139 digits (it is 3₁₁₆₁₃₇AF, and its algebraic form is (16¹¹⁶¹³⁹+619)/5), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel16 Data of Athena (probable) primes base 16] Base 17: 10415 known Athena (probable) primes (including many unproven probable primes) and 12 unsolved families (1{7}, 1F{0}7, 4{7}A, 70F{0}D, 8{B}9, 9{5}9, A{D}F, B{0}B3, {B}E9, {B}EE, F1{9}, FD0{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel17 Data of known Athena (probable) primes base 17] Base 18: 549 Athena primes, the largest of which has 6271 digits (it is C0₆₂₆₈C5, and its algebraic form is 12×18⁶²⁷⁰+221), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel18 Data of Athena primes base 18] Base 19: 31417 known Athena (probable) primes (including many unproven probable primes) and 17 unsolved families (4B5{0}H, {5}3, 5{H}05, 5{H}0H, 5{H}5, 66{B}, 71{0}177, 7AF{0}H, 97{0}3, C{H}C, EE1{6}, F{7}5, F{B}G, F{D}F, H0F{0}7A, HB{0}5B5, II{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel19 Data of known Athena (probable) primes base 19] Base 20: 3314 Athena primes, the largest of which has 6271 digits (it is G0₆₂₆₉D, and its algebraic form is 16×20⁶²⁷⁰+13), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel20 Data of Athena primes base 20] Base 21: 13386 known Athena (probable) primes (including many unproven probable primes) and 8 unsolved families (5{0}DJ, {9}D, B3{0}EB, B{H}6H, C{F}0K, {F}35, G{0}FK, H{0}7771, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel21 Data of known Athena (probable) primes base 21] Base 22: 8003 Athena (probable) primes (including 1 unproven probable prime: BK₂₂₀₀₁5), the largest of which has 22003 digits (it is BK₂₂₀₀₁5, and its algebraic form is (251×22²²⁰⁰²−335)/21), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel22 Data of Athena (probable) primes base 22] Base 23: 65178 known Athena (probable) primes (including many unproven probable primes) and 87 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel23 Data of known Athena (probable) primes base 23] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left23 Data of unsolved families for Athena problem base 23] Base 24: 3409 Athena primes, the largest of which has 8134 digits (it is N00N₈₁₂₉LN, and its algebraic form is 13249×24⁸¹³¹−49), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel24 Data of Athena primes base 24] Base 25: 133639 known Athena (probable) primes (including many unproven probable primes) and 85 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel25 Data of known Athena (probable) primes base 25] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left25 Data of unsolved families for Athena problem base 25] Base 26: 25256 known Athena (probable) primes (including 7 unproven probable primes: 5₁₉₃₉₁6F, 7₂₀₂₇₉OL, LD0₂₀₉₇₅7, 6K₂₃₃₀₀5, J0₄₄₃₀₃KCB, M0₆₁₁₈₆2BB, 85M₁₉₇₀₆₀B) and 3 unsolved families ({A}6F, {H}MH, {I}GL, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel26 Data of known Athena (probable) primes base 26] Base 27: 102852 known Athena (probable) primes (including many unproven probable primes) and 44 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel27 Data of known Athena (probable) primes base 27] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left27 Data of unsolved families for Athena problem base 27] Base 28: 25528 known Athena (probable) primes (including 3 unproven probable primes: N6₂₄₀₅₁LR, 5OA₃₁₂₃₈F, O4O₉₄₅₃₅9) and 1 unsolved family (O{A}F, no primes or probable primes with length ≤ 900000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel28 Data of known Athena (probable) primes base 28] Base 29: 355242 known Athena (probable) primes (including many unproven probable primes) and 125 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel29 Data of known Athena (probable) primes base 29] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left29 Data of unsolved families for Athena problem base 29] Base 30: 2619 Athena (probable) primes (including 1 unproven probable prime: I0₂₄₆₀₈D), the largest of which has 34206 digits (it is OT₃₄₂₀₅, and its algebraic form is 25×30³⁴²⁰⁵−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel30 Data of Athena (probable) primes base 30] Base 31: 569323 known Athena (probable) primes (including many unproven probable primes) and 77 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel31 Data of known Athena (probable) primes base 31] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left31 Data of unsolved families for Athena problem base 31] Base 32: 168882 known Athena (probable) primes (including many unproven probable primes) and 120 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel32 Data of known Athena (probable) primes base 32] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left32 Data of unsolved families for Athena problem base 32] Base 33: 280012 known Athena (probable) primes (including many unproven probable primes) and 81 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel33 Data of known Athena (probable) primes base 33] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left33 Data of unsolved families for Athena problem base 33] Base 34: 184785 known Athena (probable) primes (including many unproven probable primes) and 47 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel34 Data of known Athena (probable) primes base 34] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left34 Data of unsolved families for Athena problem base 34] Base 35: 720002 known Athena (probable) primes (including many unproven probable primes) and 60 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel35 Data of known Athena (probable) primes base 35] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left35 Data of unsolved families for Athena problem base 35] Base 36: 35286 known Athena (probable) primes (including 3 unproven probable primes: 7K₂₆₅₆₇Z, S0₇₅₀₀₇8H, P₈₁₉₉₃SZ) and 4 unsolved families (B{0}EUV, HM{0}N, N{0}YYN, O{L}Z, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel36 Data of known Athena (probable) primes base 36] == Condensed table for bases 2 ≤ ''b'' ≤ 36 == {|class="wikitable" ||''b''||number of Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||base-''b'' form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' (write "''d''_''n''" if there are 5 or more (''n'') consecutive same digits ''d'')||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' in decimal||algebraic ((''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1)) form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||''factordb'' entry of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' written in base ''b'' (use lower case letters instead of upper case letters)||number of unsolved families in the Athena problem in base ''b'' (all of these left families are linear families)||searching limit of length for the unsolved families in the Athena problem in base ''b'' (if there are different searching limits for the unsolved families in the Athena problem in base ''b'', choose the lowest searching limit)|| |- ||2||1||11||2||1||3||http://factordb.com/index.php?id=3&open=ecm||http://factordb.com/index.php?showid=3&base=2||0||–|| |- ||3||3||111<br>21<br>12||3<br>2<br>2||2<br>1<br>1||13<br>7<br>5||http://factordb.com/index.php?id=13&open=ecm<br>http://factordb.com/index.php?id=7&open=ecm<br>http://factordb.com/index.php?id=5&open=ecm<nowiki/>||http://factordb.com/index.php?showid=13&base=3<br>http://factordb.com/index.php?showid=7&base=3<br>http://factordb.com/index.php?showid=5&base=3<nowiki/>||0||–|| |- ||4||5||221<br>31<br>23<br>13<br>11||3<br>2<br>2<br>2<br>2||2<br>2<br>2<br>1<br>1||41<br>13<br>11<br>7<br>5||http://factordb.com/index.php?id=41&open=ecm<br>http://factordb.com/index.php?id=13&open=ecm<br>http://factordb.com/index.php?id=11&open=ecm<br>http://factordb.com/index.php?id=7&open=ecm<br>http://factordb.com/index.php?id=5&open=ecm<nowiki/>||http://factordb.com/index.php?showid=41&base=4<br>http://factordb.com/index.php?showid=13&base=4<br>http://factordb.com/index.php?showid=11&base=4<br>http://factordb.com/index.php?showid=7&base=4<br>http://factordb.com/index.php?showid=5&base=4<nowiki/>||0||–|| |- ||5||22||10₉₃13<br>300031<br>44441<br>33331<br>33001<br>30301<br>14444<br>10103<br>3101<br>414||96<br>6<br>5<br>5<br>5<br>5<br>5<br>5<br>4<br>3||67<br>4<br>4<br>4<br>4<br>4<br>4<br>3<br>3<br>3||5⁹⁵+8<br>9391<br>3121<br>2341<br>2251<br>1951<br>1249<br>653<br>401<br>109||http://factordb.com/index.php?id=1100000000034686071&open=ecm<br>http://factordb.com/index.php?id=9391&open=ecm<br>http://factordb.com/index.php?id=3121&open=ecm<br>http://factordb.com/index.php?id=2341&open=ecm<br>http://factordb.com/index.php?id=2251&open=ecm<br>http://factordb.com/index.php?id=1951&open=ecm<br>http://factordb.com/index.php?id=1249&open=ecm<br>http://factordb.com/index.php?id=653&open=ecm<br>http://factordb.com/index.php?id=401&open=ecm<br>http://factordb.com/index.php?id=109&open=ecm<nowiki/>||http://factordb.com/index.php?showid=1100000000034686071&base=5<br>http://factordb.com/index.php?showid=9391&base=5<br>http://factordb.com/index.php?showid=3121&base=5<br>http://factordb.com/index.php?showid=2341&base=5<br>http://factordb.com/index.php?showid=2251&base=5<br>http://factordb.com/index.php?showid=1951&base=5<br>http://factordb.com/index.php?showid=1249&base=5<br>http://factordb.com/index.php?showid=653&base=5<br>http://factordb.com/index.php?showid=401&base=5<br>http://factordb.com/index.php?showid=109&base=5<nowiki/>||0||–|| |- ||6||11||40041<br>4441<br>4401<br>51<br>45<br>35<br>31<br>25<br>21<br>15||5<br>4<br>4<br>2<br>2<br>2<br>2<br>2<br>2<br>2||4<br>4<br>4<br>2<br>2<br>2<br>2<br>2<br>2<br>2||5209<br>1033<br>1009<br>31<br>29<br>23<br>19<br>17<br>13<br>11||http://factordb.com/index.php?id=5209&open=ecm<br>http://factordb.com/index.php?id=1033&open=ecm<br>http://factordb.com/index.php?id=1009&open=ecm<br>http://factordb.com/index.php?id=31&open=ecm<br>http://factordb.com/index.php?id=29&open=ecm<br>http://factordb.com/index.php?id=23&open=ecm<br>http://factordb.com/index.php?id=19&open=ecm<br>http://factordb.com/index.php?id=17&open=ecm<br>http://factordb.com/index.php?id=13&open=ecm<br>http://factordb.com/index.php?id=11&open=ecm<nowiki/>||http://factordb.com/index.php?showid=5209&base=6<br>http://factordb.com/index.php?showid=1033&base=6<br>http://factordb.com/index.php?showid=1009&base=6<br>http://factordb.com/index.php?showid=31&base=6<br>http://factordb.com/index.php?showid=29&base=6<br>http://factordb.com/index.php?showid=23&base=6<br>http://factordb.com/index.php?showid=19&base=6<br>http://factordb.com/index.php?showid=17&base=6<br>http://factordb.com/index.php?showid=13&base=6<br>http://factordb.com/index.php?showid=11&base=6<nowiki/>||0||–|| |- ||7||71||3₁₆1<br>510₇1<br>3₆01<br>1100021<br>531101<br>351101<br>300053<br>150001<br>100121<br>40054||17<br>10<br>8<br>7<br>6<br>6<br>6<br>6<br>6<br>5||15<br>9<br>7<br>6<br>5<br>5<br>5<br>5<br>5<br>4||(7¹⁷−5)/2<br>36×7⁸+1<br>(7⁸−47)/2<br>134471<br>91631<br>62819<br>50459<br>28813<br>16871<br>9643||http://factordb.com/index.php?id=116315256993601&open=ecm<br>http://factordb.com/index.php?id=207532837&open=ecm<br>http://factordb.com/index.php?id=2882377&open=ecm<br>http://factordb.com/index.php?id=134471&open=ecm<br>http://factordb.com/index.php?id=91631&open=ecm<br>http://factordb.com/index.php?id=62819&open=ecm<br>http://factordb.com/index.php?id=50459&open=ecm<br>http://factordb.com/index.php?id=28813&open=ecm<br>http://factordb.com/index.php?id=16871&open=ecm<br>http://factordb.com/index.php?id=9643&open=ecm<nowiki/>||http://factordb.com/index.php?showid=116315256993601&base=7<br>http://factordb.com/index.php?showid=207532837&base=7<br>http://factordb.com/index.php?showid=2882377&base=7<br>http://factordb.com/index.php?showid=134471&base=7<br>http://factordb.com/index.php?showid=91631&base=7<br>http://factordb.com/index.php?showid=62819&base=7<br>http://factordb.com/index.php?showid=50459&base=7<br>http://factordb.com/index.php?showid=28813&base=7<br>http://factordb.com/index.php?showid=16871&base=7<br>http://factordb.com/index.php?showid=9643&base=7<nowiki/>||0||–|| |- ||8||75||4₂₂₀7<br>5₁₃25<br>7₁₂1<br>77774₆1<br>74₇1<br>4₈1<br>5₅025<br>5550525<br>5500525<br>4₅77||221<br>15<br>13<br>11<br>9<br>9<br>8<br>7<br>7<br>7||200<br>14<br>12<br>10<br>9<br>8<br>8<br>7<br>7<br>7||(4×8²²¹+17)/7<br>(5×8¹⁵−173)/7<br>8¹³−7<br>(28669×8⁷−25)/7<br>(53×8⁸−25)/7<br>(4×8⁹−25)/7<br>(5×8⁸−2413)/7<br>1495381<br>1474901<br>(4×8⁷+185)/7||http://factordb.com/index.php?id=1100000000416605822&open=ecm<br>http://factordb.com/index.php?id=25131694349141&open=ecm<br>http://factordb.com/index.php?id=549755813881&open=ecm<br>http://factordb.com/index.php?id=8589035809&open=ecm<br>http://factordb.com/index.php?id=127027489&open=ecm<br>http://factordb.com/index.php?id=76695841&open=ecm<br>http://factordb.com/index.php?id=11983381&open=ecm<br>http://factordb.com/index.php?id=1495381&open=ecm<br>http://factordb.com/index.php?id=1474901&open=ecm<br>http://factordb.com/index.php?id=1198399&open=ecm<nowiki/>||http://factordb.com/index.php?showid=1100000000416605822&base=8<br>http://factordb.com/index.php?showid=25131694349141&base=8<br>http://factordb.com/index.php?showid=549755813881&base=8<br>http://factordb.com/index.php?showid=8589035809&base=8<br>http://factordb.com/index.php?showid=127027489&base=8<br>http://factordb.com/index.php?showid=76695841&base=8<br>http://factordb.com/index.php?showid=11983381&base=8<br>http://factordb.com/index.php?showid=1495381&base=8<br>http://factordb.com/index.php?showid=1474901&base=8<br>http://factordb.com/index.php?showid=1198399&base=8<nowiki/>||0||–|| |- 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|- 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|- 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||16||2347||3₁₁₆₁₃₇AF<br>4₇₂₇₈₅DD<br>DB₃₂₂₃₄<br>D0B₁₇₈₀₄<br>5BC₃₇₀₀D<br>90₃₅₄₂91<br>300F₁₉₆₀AF<br>20₁₇₁₃321<br>F8₁₅₁₇F<br>FAF₁₀₆₂45||116139<br>72787<br>32235<br>17806<br>3703<br>3545<br>1965<br>1717<br>1519<br>1066||139845<br>87644<br>38815<br>21441<br>4459<br>4269<br>2366<br>2067<br>1830<br>1284||(16¹¹⁶¹³⁹+619)/5<br>(4×16⁷²⁷⁸⁷+2291)/15<br>(206×16³²²³⁴−11)/15<br>(3131×16¹⁷⁸⁰⁴−11)/15<br>(459×16³⁷⁰¹+1)/5<br>9×16³⁵⁴⁴+145<br>769×16¹⁹⁶²−81<br>2×16¹⁷¹⁶+801<br>(233×16¹⁵¹⁸+97)/15<br>251×16¹⁰⁶⁴−187||http://factordb.com/index.php?id=1100000003851731988&open=prime<br>http://factordb.com/index.php?id=1100000003615909841&open=prime<br>http://factordb.com/index.php?id=1100000002383583629&open=prime<br>http://factordb.com/index.php?id=1100000003589278511&open=prime<br>http://factordb.com/index.php?id=1100000000993764322&open=prime<br>http://factordb.com/index.php?id=1100000000633424191&open=prime<br>http://factordb.com/index.php?id=1100000003588368750&open=prime<br>http://factordb.com/index.php?id=1100000003588386735&open=prime<br>http://factordb.com/index.php?id=1100000000633744824&open=prime<br>http://factordb.com/index.php?id=1100000003588387610&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000003851731988&base=16<br>http://factordb.com/index.php?showid=1100000003615909841&base=16<br>http://factordb.com/index.php?showid=1100000002383583629&base=16<br>http://factordb.com/index.php?showid=1100000003589278511&base=16<br>http://factordb.com/index.php?showid=1100000000993764322&base=16<br>http://factordb.com/index.php?showid=1100000000633424191&base=16<br>http://factordb.com/index.php?showid=1100000003588368750&base=16<br>http://factordb.com/index.php?showid=1100000003588386735&base=16<br>http://factordb.com/index.php?showid=1100000000633744824&base=16<br>http://factordb.com/index.php?showid=1100000003588387610&base=16<nowiki/>||0||–|| |- ||17||10415~10427||95F₁₉₈₈₅₅<br>B0₁₈₉₀₈₃DB<br>F70₁₈₆₇₆₇1<br>970₁₆₆₀₄₇1<br>510₁₂₄₀₇₄D<br>49₁₁₁₃₃₃<br>B₆₇₁₀₃2E<br>570₅₁₃₁₀1<br>E9B₄₄₇₃₂<br>D0GD₃₇₀₉₆||198857<br>189086<br>186770<br>166050<br>124077<br>111334<br>67105<br>51313<br>44734<br>37099||244684<br>232661<br>229811<br>204316<br>152670<br>136991<br>82570<br>63138<br>55043<br>45649||(2543×17¹⁹⁸⁸⁵⁵−15)/16<br>11×17¹⁸⁹⁰⁸⁵+232<br>262×17¹⁸⁶⁷⁶⁸+1<br>160×17¹⁶⁶⁰⁴⁸+1<br>86×17¹²⁴⁰⁷⁵+13<br>(73×17¹¹¹³³³−9)/16<br>(11×17⁶⁷¹⁰⁵−2411)/16<br>92×17⁵¹³¹¹+1<br>(3963×17⁴⁴⁷³²−11)/16<br>(60381×17³⁷⁰⁹⁶−13)/16||http://factordb.com/index.php?id=1100000008610514108&open=prime<br>http://factordb.com/index.php?id=1100000008610515753&open=prime<br>http://factordb.com/index.php?id=1100000000765961429&open=prime<br>http://factordb.com/index.php?id=1100000000765961411&open=prime<br>http://factordb.com/index.php?id=1100000008610516879&open=prime<br>http://factordb.com/index.php?id=1100000000808118219&open=prime<br>http://factordb.com/index.php?id=1100000003993647842&open=prime<br>http://factordb.com/index.php?id=1100000000765961389&open=prime<br>http://factordb.com/index.php?id=1100000003883765450&open=prime<br>http://factordb.com/index.php?id=1100000003848346668&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008610514108&base=17<br>http://factordb.com/index.php?showid=1100000008610515753&base=17<br>http://factordb.com/index.php?showid=1100000000765961429&base=17<br>http://factordb.com/index.php?showid=1100000000765961411&base=17<br>http://factordb.com/index.php?showid=1100000008610516879&base=17<br>http://factordb.com/index.php?showid=1100000000808118219&base=17<br>http://factordb.com/index.php?showid=1100000003993647842&base=17<br>http://factordb.com/index.php?showid=1100000000765961389&base=17<br>http://factordb.com/index.php?showid=1100000003883765450&base=17<br>http://factordb.com/index.php?showid=1100000003848346668&base=17<nowiki/>||12||200000|| |- ||18||549||C0₆₂₆₈C5<br>H₇₆₆FH<br>80₂₉₈B<br>C0₁₁₆F5<br>HD₉₃<br>GG0₃₀1<br>CF₃₀5<br>B₁₉6B<br>CCF₁₄5<br>7₁₄G7||6271<br>768<br>300<br>119<br>94<br>33<br>32<br>21<br>17<br>16||7872<br>965<br>377<br>150<br>118<br>42<br>41<br>27<br>22<br>20||12×18⁶²⁷⁰+221<br>18⁷⁶⁸−37<br>8×18²⁹⁹+11<br>12×18¹¹⁸+275<br>(302×18⁹³−13)/17<br>304×18³¹+1<br>(219×18³¹−185)/17<br>(11×18²¹−1541)/17<br>(3891×18¹⁵−185)/17<br>(7×18¹⁶+2747)/17||http://factordb.com/index.php?id=1100000003590442437&open=prime<br>http://factordb.com/index.php?id=1100000003590430490&open=prime<br>http://factordb.com/index.php?id=1100000002355574745&open=prime<br>http://factordb.com/index.php?id=1100000002632837015&open=ecm<br>http://factordb.com/index.php?id=1100000002321052894&open=ecm<br>http://factordb.com/index.php?id=1100000000819230161&open=ecm<br>http://factordb.com/index.php?id=1100000002631240657&open=ecm<br>http://factordb.com/index.php?id=1100000003590430474&open=ecm<br>http://factordb.com/index.php?id=1100000003590430470&open=ecm<br>http://factordb.com/index.php?id=1100000003590430465&open=ecm<nowiki/>||http://factordb.com/index.php?showid=1100000003590442437&base=18<br>http://factordb.com/index.php?showid=1100000003590430490&base=18<br>http://factordb.com/index.php?showid=1100000002355574745&base=18<br>http://factordb.com/index.php?showid=1100000002632837015&base=18<br>http://factordb.com/index.php?showid=1100000002321052894&base=18<br>http://factordb.com/index.php?showid=1100000000819230161&base=18<br>http://factordb.com/index.php?showid=1100000002631240657&base=18<br>http://factordb.com/index.php?showid=1100000003590430474&base=18<br>http://factordb.com/index.php?showid=1100000003590430470&base=18<br>http://factordb.com/index.php?showid=1100000003590430465&base=18<nowiki/>||0||–|| |- ||19||31417~31434||1E70₁₂₂₈₉₆1<br>40₁₂₁₈₄₆HB5<br>35₁₂₀₅₆₂<br>FH0H₁₁₂₆₅₉<br>FG6₁₁₀₉₈₄<br>H₈₆₂₉₁6<br>D90₇₃₀₄₆9<br>4F0₄₉₈₄₇6<br>2₄₈₂₂₄7<br>2₄₅₈₈₆7A||122900<br>121850<br>120563<br>112662<br>110986<br>86292<br>73049<br>49850<br>48225<br>45888||157158<br>155816<br>154170<br>144067<br>110347<br>141924<br>93412<br>63746<br>61667<br>58679||634×19¹²²⁸⁹⁷+1<br>4×19¹²¹⁸⁴⁹+6351<br>(59×19¹²⁰⁵⁶²−5)/18<br>(103301×19¹¹²⁶⁵⁹−17)/18<br>(904×19¹¹⁰⁹⁸⁴−1)/3<br>(17×19⁸⁶²⁹²−215)/18<br>256×19⁷³⁰⁴⁷+9<br>91×19⁴⁹⁸⁴⁸+6<br>(19⁴⁸²²⁵+44)/9<br>(19⁴⁵⁸⁸⁸+926)/9||http://factordb.com/index.php?id=1100000001582289581&open=prime<br>http://factordb.com/index.php?id=1100000008755307222&open=prime<br>http://factordb.com/index.php?id=1100000005513825027&open=prime<br>http://factordb.com/index.php?id=1100000008755311453&open=prime<br>http://factordb.com/index.php?id=1100000000808118212&open=prime<br>http://factordb.com/index.php?id=1100000004163040839&open=prime<br>http://factordb.com/index.php?id=1100000003998413751&open=prime<br>http://factordb.com/index.php?id=1100000000808118332&open=prime<br>http://factordb.com/index.php?id=1100000003949188041&open=prime<br>http://factordb.com/index.php?id=1100000003949189035&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000001582289581&base=19<br>http://factordb.com/index.php?showid=1100000008755307222&base=19<br>http://factordb.com/index.php?showid=1100000005513825027&base=19<br>http://factordb.com/index.php?showid=1100000008755311453&base=19<br>http://factordb.com/index.php?showid=1100000000808118212&base=19<br>http://factordb.com/index.php?showid=1100000004163040839&base=19<br>http://factordb.com/index.php?showid=1100000003998413751&base=19<br>http://factordb.com/index.php?showid=1100000000808118332&base=19<br>http://factordb.com/index.php?showid=1100000003949188041&base=19<br>http://factordb.com/index.php?showid=1100000003949189035&base=19<nowiki/>||17||200000|| |- ||20||3314||G0₆₂₆₉D<br>CD₂₄₄₉<br>50₁₁₆₃AJ<br>J₆₅₅05J<br>JCJ₆₂₉<br>E₅₆₆C7<br>3A₅₂₇3<br>G₄₄₇99<br>EC0₄₂₉7<br>40₃₈₇404B||6271<br>2450<br>1166<br>658<br>631<br>568<br>529<br>449<br>432<br>392||8159<br>3188<br>1517<br>857<br>821<br>739<br>688<br>585<br>562<br>510||16×20⁶²⁷⁰+13<br>(241×20²⁴⁴⁹−13)/19<br>5×20¹¹⁶⁵+219<br>20⁶⁵⁸−7881<br>393×20⁶²⁹−1<br>(14×20⁵⁶⁸−907)/19<br>(67×20⁵²⁸−143)/19<br>(16×20⁴⁴⁹−2809)/19<br>292×20⁴³⁰+7<br>4×20³⁹¹+32091||http://factordb.com/index.php?id=1100000003590539457&open=prime<br>http://factordb.com/index.php?id=1100000002325393915&open=prime<br>http://factordb.com/index.php?id=1100000003590502412&open=prime<br>http://factordb.com/index.php?id=1100000003590502490&open=prime<br>http://factordb.com/index.php?id=1100000001559454258&open=prime<br>http://factordb.com/index.php?id=1100000003590502516&open=prime<br>http://factordb.com/index.php?id=1100000003590502531&open=prime<br>http://factordb.com/index.php?id=1100000000840126753&open=prime<br>http://factordb.com/index.php?id=1100000002633348702&open=prime<br>http://factordb.com/index.php?id=1100000003590502563&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000003590539457&base=20<br>http://factordb.com/index.php?showid=1100000002325393915&base=20<br>http://factordb.com/index.php?showid=1100000003590502412&base=20<br>http://factordb.com/index.php?showid=1100000003590502490&base=20<br>http://factordb.com/index.php?showid=1100000001559454258&base=20<br>http://factordb.com/index.php?showid=1100000003590502516&base=20<br>http://factordb.com/index.php?showid=1100000003590502531&base=20<br>http://factordb.com/index.php?showid=1100000000840126753&base=20<br>http://factordb.com/index.php?showid=1100000002633348702&base=20<br>http://factordb.com/index.php?showid=1100000003590502563&base=20<nowiki/>||0||–|| |- ||21||13386~13394||27₁₈₄₄₉₉9D<br>F9₁₇₈₇₇₁D<br>2FC₁₁₂₀₂₂A<br>7₁₀₈₄₅₀ID<br>40₄₇₃₃₃9G<br>B90₄₅₀₁₉E5<br>HD₃₇₄₁₄<br>BD₃₅₀₂₇B<br>990₃₃₂₃₉99H<br>5₃₀₆₀₆FEK||184502<br>178773<br>112025<br>108452<br>47336<br>45023<br>37415<br>35029<br>33244<br>30609||243952<br>236377<br>148121<br>143397<br>62588<br>59531<br>49471<br>46316<br>43956<br>40472||(47×21¹⁸⁴⁵⁰¹+953)/20<br>(309×21¹⁷⁸⁷⁷²+71)/20<br>(288×21¹¹²⁰²³−13)/5<br>(7×21¹⁰⁸⁴⁵²+4733)/20<br>4×21⁴⁷³³⁵+205<br>240×21⁴⁵⁰²¹+299<br>(353×21³⁷⁴¹⁴−13)/20<br>(233×21³⁵⁰²⁸−53)/20<br>198×21³³²⁴²+4175<br>(21³⁰⁶⁰⁹+18455)/4||http://factordb.com/index.php?id=1100000008700600990&open=prime<br>http://factordb.com/index.php?id=1100000008700596669&open=prime<br>http://factordb.com/index.php?id=1100000008700593358&open=prime<br>http://factordb.com/index.php?id=1100000008700586183&open=prime<br>http://factordb.com/index.php?id=1100000000808118331&open=prime<br>http://factordb.com/index.php?id=1100000003996110311&open=prime<br>http://factordb.com/index.php?id=1100000003996110479&open=prime<br>http://factordb.com/index.php?id=1100000003996110718&open=prime<br>http://factordb.com/index.php?id=1100000003996110944&open=prime<br>http://factordb.com/index.php?id=1100000003996111130&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008700600990&base=21<br>http://factordb.com/index.php?showid=1100000008700596669&base=21<br>http://factordb.com/index.php?showid=1100000008700593358&base=21<br>http://factordb.com/index.php?showid=1100000008700586183&base=21<br>http://factordb.com/index.php?showid=1100000000808118331&base=21<br>http://factordb.com/index.php?showid=1100000003996110311&base=21<br>http://factordb.com/index.php?showid=1100000003996110479&base=21<br>http://factordb.com/index.php?showid=1100000003996110718&base=21<br>http://factordb.com/index.php?showid=1100000003996110944&base=21<br>http://factordb.com/index.php?showid=1100000003996111130&base=21<nowiki/>||8||200000|| |- ||22||8003||BK₂₂₀₀₁5<br>7₃₈₁₅2L<br>L₂₃₈₅KE7<br>7₉₅₉K7<br>J0₇₆₇IGGJ<br>K0₇₆₀EC1<br>I₆₂₆AF<br>E60₄₉₆L<br>L₄₈₃G3<br>L0₄₅₄B63||22003<br>3817<br>2388<br>961<br>772<br>764<br>628<br>499<br>485<br>458||29538<br>5124<br>3206<br>1290<br>1037<br>1026<br>843<br>670<br>652<br>615||(251×22²²⁰⁰²−335)/21<br>(22³⁸¹⁷−289)/3<br>22²³⁸⁸−653<br>(22⁹⁶¹+857)/3<br>19×22⁷⁷¹+199779<br>20×22⁷⁶³+7041<br>(6×22⁶²⁸−1259)/7<br>314×22⁴⁹⁷+21<br>22⁴⁸⁵−129<br>21×22⁴⁵⁷+5459||http://factordb.com/index.php?id=1100000003594696838&open=prime<br>http://factordb.com/index.php?id=1100000003591359839&open=prime<br>http://factordb.com/index.php?id=1100000003591360774&open=prime<br>http://factordb.com/index.php?id=1100000003591361817&open=prime<br>http://factordb.com/index.php?id=1100000003591362567&open=prime<br>http://factordb.com/index.php?id=1100000000632724415&open=prime<br>http://factordb.com/index.php?id=1100000000632724334&open=prime<br>http://factordb.com/index.php?id=1100000000632703239&open=prime<br>http://factordb.com/index.php?id=1100000003591364730&open=prime<br>http://factordb.com/index.php?id=1100000003591365331&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000003594696838&base=22<br>http://factordb.com/index.php?showid=1100000003591359839&base=22<br>http://factordb.com/index.php?showid=1100000003591360774&base=22<br>http://factordb.com/index.php?showid=1100000003591361817&base=22<br>http://factordb.com/index.php?showid=1100000003591362567&base=22<br>http://factordb.com/index.php?showid=1100000000632724415&base=22<br>http://factordb.com/index.php?showid=1100000000632724334&base=22<br>http://factordb.com/index.php?showid=1100000000632703239&base=22<br>http://factordb.com/index.php?showid=1100000003591364730&base=22<br>http://factordb.com/index.php?showid=1100000003591365331&base=22<nowiki/>||0||–|| |- ||23||65178~65265||B0₉₃₀₄₆FB<br>L₈₆₄₄₄D<br>AJ₈₁₀₆₅4<br>20₇₃₅₆₀98<br>J₆₈₂₁₇G4<br>D70₆₆₇₇₀B<br>5F₆₂₃₄₀6<br>A7M7₆₁₅₃₂<br>B30₆₁₁₃₆5<br>EJ₅₂₁₆₉||93049<br>86445<br>81067<br>73563<br>68219<br>66773<br>62342<br>61535<br>61139<br>52170||126708<br>117715<br>110391<br>100172<br>92896<br>90927<br>84893<br>83794<br>83255<br>71042||11×23⁹³⁰⁴⁸+356<br>(21×23⁸⁶⁴⁴⁵−197)/22<br>(239×23⁸¹⁰⁶⁶−349)/22<br>2×23⁷³⁵⁶²+215<br>(19×23⁶⁸²¹⁹−1867)/22<br>306×23⁶⁶⁷⁷¹+11<br>(125×23⁶²³⁴¹−213)/22<br>(120413×23⁶¹⁵³²−7)/22<br>256×23⁶¹¹³⁷+5<br>(327×23⁵²¹⁶⁹−19)/22||http://factordb.com/index.php?id=1100000004691540361&open=prime<br>http://factordb.com/index.php?id=1100000004691546739&open=prime<br>http://factordb.com/index.php?id=1100000004691548070&open=prime<br>http://factordb.com/index.php?id=1100000004691548569&open=prime<br>http://factordb.com/index.php?id=1100000004691549462&open=prime<br>http://factordb.com/index.php?id=1100000004691549803&open=prime<br>http://factordb.com/index.php?id=1100000004691551005&open=prime<br>http://factordb.com/index.php?id=1100000004691556967&open=prime<br>http://factordb.com/index.php?id=1100000004691557254&open=prime<br>http://factordb.com/index.php?id=1100000004691557548&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000004691540361&base=23<br>http://factordb.com/index.php?showid=1100000004691546739&base=23<br>http://factordb.com/index.php?showid=1100000004691548070&base=23<br>http://factordb.com/index.php?showid=1100000004691548569&base=23<br>http://factordb.com/index.php?showid=1100000004691549462&base=23<br>http://factordb.com/index.php?showid=1100000004691549803&base=23<br>http://factordb.com/index.php?showid=1100000004691551005&base=23<br>http://factordb.com/index.php?showid=1100000004691556967&base=23<br>http://factordb.com/index.php?showid=1100000004691557254&base=23<br>http://factordb.com/index.php?showid=1100000004691557548&base=23<nowiki/>||87||100000|| |- ||24||3409||N00N₈₁₂₉LN<br>88N₅₉₅₁<br>A0₂₉₅₁8ID<br>D₂₆₉₈LD<br>N₂₆₄₄LLN<br>BC0₃₃₁B<br>20₃₁₃7<br>C7₂₉₈<br>D0₂₅₉KKD<br>I0₂₄₁I5||8134<br>5953<br>2955<br>2700<br>2647<br>334<br>315<br>299<br>263<br>244||11227<br>8216<br>4079<br>3727<br>3654<br>461<br>434<br>413<br>363<br>337||13249×24⁸¹³¹−49<br>201×24⁵⁹⁵¹−1<br>10×24²⁹⁵⁴+5053<br>(13×24²⁷⁰⁰+4403)/23<br>24²⁶⁴⁷−1201<br>276×24³³²+11<br>2×24³¹⁴+7<br>(283×24²⁹⁸−7)/23<br>13×24²⁶²+12013<br>18×24²⁴³+437||http://factordb.com/index.php?id=1100000003593391606&open=prime<br>http://factordb.com/index.php?id=1100000003593275880&open=prime<br>http://factordb.com/index.php?id=1100000003593269654&open=prime<br>http://factordb.com/index.php?id=1100000003593269876&open=prime<br>http://factordb.com/index.php?id=1100000003593270089&open=prime<br>http://factordb.com/index.php?id=1100000002633359842&open=prime<br>http://factordb.com/index.php?id=1100000002355610241&open=prime<br>http://factordb.com/index.php?id=1100000002326181235&open=prime<br>http://factordb.com/index.php?id=1100000003593270725&open=prime<br>http://factordb.com/index.php?id=1100000002633360037&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000003593391606&base=24<br>http://factordb.com/index.php?showid=1100000003593275880&base=24<br>http://factordb.com/index.php?showid=1100000003593269654&base=24<br>http://factordb.com/index.php?showid=1100000003593269876&base=24<br>http://factordb.com/index.php?showid=1100000003593270089&base=24<br>http://factordb.com/index.php?showid=1100000002633359842&base=24<br>http://factordb.com/index.php?showid=1100000002355610241&base=24<br>http://factordb.com/index.php?showid=1100000002326181235&base=24<br>http://factordb.com/index.php?showid=1100000003593270725&base=24<br>http://factordb.com/index.php?showid=1100000002633360037&base=24<nowiki/>||0||–|| |- ||25||133639~133724||E₉₈₃₉₆FOO<br>1J710₉₆₂₇₂1<br>NB0₈₅₅₉₈5NH<br>D70₈₁₅₈₁JJ7<br>F0₈₀₀₅₄HL<br>J010₇₅₉₄₃E7<br>K₆₇₇₇₁5I<br>LO₆₆₃₇₇KC<br>KJD0₆₃₃₉₉1<br>70₆₀₈₉₂D711||98399<br>96277<br>85603<br>81586<br>80057<br>75948<br>67773<br>66380<br>63403<br>60897||137556<br>134589<br>119668<br>114053<br>111915<br>106171<br>94743<br>92796<br>88634<br>85130||(7×25⁹⁸³⁹⁹+10613)/12<br>27676×25⁹⁶²⁷³+1<br>586×25⁸⁵⁶⁰¹+3717<br>332×25⁸¹⁵⁸⁴+12357<br>15×25⁸⁰⁰⁵⁶+446<br>11876×25⁷⁵⁹⁴⁵+357<br>(5×25⁶⁷⁷⁷³−2267)/6<br>22×25⁶⁶³⁷⁹−113<br>12988×25⁶³⁴⁰⁰+1<br>7×25⁶⁰⁸⁹⁶+207526||http://factordb.com/index.php?id=1100000000808118215&open=prime<br>http://factordb.com/index.php?id=1100000003983674902&open=prime<br>http://factordb.com/index.php?id=1100000004909706420&open=prime<br>http://factordb.com/index.php?id=1100000004909733266&open=prime<br>http://factordb.com/index.php?id=1100000004909750102&open=prime<br>http://factordb.com/index.php?id=1100000004909770736&open=prime<br>http://factordb.com/index.php?id=1100000004586986394&open=prime<br>http://factordb.com/index.php?id=1100000000808118270&open=prime<br>http://factordb.com/index.php?id=1100000004586986664&open=prime<br>http://factordb.com/index.php?id=1100000004586986798&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000000808118215&base=25<br>http://factordb.com/index.php?showid=1100000003983674902&base=25<br>http://factordb.com/index.php?showid=1100000004909706420&base=25<br>http://factordb.com/index.php?showid=1100000004909733266&base=25<br>http://factordb.com/index.php?showid=1100000004909750102&base=25<br>http://factordb.com/index.php?showid=1100000004909770736&base=25<br>http://factordb.com/index.php?showid=1100000004586986394&base=25<br>http://factordb.com/index.php?showid=1100000000808118270&base=25<br>http://factordb.com/index.php?showid=1100000004586986664&base=25<br>http://factordb.com/index.php?showid=1100000004586986798&base=25<nowiki/>||85||100000|| |- ||26||25256~25259||85M₁₉₇₀₆₀B<br>M0₆₁₁₈₆2BB<br>J0₄₄₃₀₃KCB<br>6K₂₃₃₀₀5<br>LD0₂₀₉₇₅7<br>7₂₀₂₇₉OL<br>5₁₉₃₉₁6F<br>9GDK₁₅₉₂₀P<br>M₈₇₇₂P<br>K0₄₃₆₄I5||197063<br>61190<br>44307<br>23302<br>20978<br>20281<br>19393<br>15924<br>8773<br>4367||278839<br>86583<br>62694<br>32972<br>29684<br>28697<br>27440<br>22532<br>12414<br>6180||(5347×26¹⁹⁷⁰⁶¹−297)/25<br>22×26⁶¹¹⁸⁹+1649<br>19×26⁴⁴³⁰⁶+13843<br>(34×26²³³⁰¹−79)/5<br>559×26²⁰⁹⁷⁶+7<br>(7×26²⁰²⁸¹+11393)/25<br>(26¹⁹³⁹³+179)/5<br>(32569×26¹⁵⁹²¹+21)/5<br>(22×26⁸⁷⁷³+53)/25<br>20×26⁴³⁶⁶+473||http://factordb.com/index.php?id=1100000008573990023&open=prime<br>http://factordb.com/index.php?id=1100000003968169875&open=prime<br>http://factordb.com/index.php?id=1100000003968156595&open=prime<br>http://factordb.com/index.php?id=1100000003892628745&open=prime<br>http://factordb.com/index.php?id=1100000003892628658&open=prime<br>http://factordb.com/index.php?id=1100000003892628605&open=prime<br>http://factordb.com/index.php?id=1100000003850151202&open=prime<br>http://factordb.com/index.php?id=1100000003850155316&open=prime<br>http://factordb.com/index.php?id=1100000000758011195&open=prime<br>http://factordb.com/index.php?id=1100000002634136508&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008573990023&base=26<br>http://factordb.com/index.php?showid=1100000003968169875&base=26<br>http://factordb.com/index.php?showid=1100000003968156595&base=26<br>http://factordb.com/index.php?showid=1100000003892628745&base=26<br>http://factordb.com/index.php?showid=1100000003892628658&base=26<br>http://factordb.com/index.php?showid=1100000003892628605&base=26<br>http://factordb.com/index.php?showid=1100000003850151202&base=26<br>http://factordb.com/index.php?showid=1100000003850155316&base=26<br>http://factordb.com/index.php?showid=1100000000758011195&base=26<br>http://factordb.com/index.php?showid=1100000002634136508&base=26<nowiki/>||3||200000|| |- ||27||102852~102896||CA0F₈₈₈₈₃A<br>GNN0₇₈₇₉₅N<br>O44L₆₆₀₁₆7<br>NJ0₆₄₃₆₉H<br>ME₄₉₆₄₀9G<br>PH0₄₇₈₉₀1<br>QF₄₇₁₆₅AF5<br>J0₄₀₇₉₁PD<br>510₃₉₁₆₄I07<br>NGN0₃₆₃₂₉N||88887<br>78799<br>66020<br>64372<br>49643<br>47893<br>47169<br>40794<br>39169<br>36333||127230<br>112790<br>94499<br>92140<br>71058<br>68553<br>67516<br>58391<br>56065<br>52006||(234483×27⁸⁸⁸⁸⁴−145)/26<br>12308×27⁷⁸⁷⁹⁶+23<br>(457829×27⁶⁶⁰¹⁷−385)/26<br>640×27⁶⁴³⁷⁰+17<br>(293×27⁴⁹⁶⁴²−1736)/13<br>692×27⁴⁷⁸⁹¹+1<br>(691×27⁴⁷¹⁶⁸−95045)/26<br>19×27⁴⁰⁷⁹³+688<br>136×27³⁹¹⁶⁷+13129<br>17222×27³⁶³³⁰+23||http://factordb.com/index.php?id=1100000000808118233&open=prime<br>http://factordb.com/index.php?id=1100000004681348398&open=prime<br>http://factordb.com/index.php?id=1100000004374140861&open=prime<br>http://factordb.com/index.php?id=1100000004374138999&open=prime<br>http://factordb.com/index.php?id=1100000000819229859&open=prime<br>http://factordb.com/index.php?id=1100000004102754118&open=prime<br>http://factordb.com/index.php?id=1100000004102755880&open=prime<br>http://factordb.com/index.php?id=1100000004102758254&open=prime<br>http://factordb.com/index.php?id=1100000004102875088&open=prime<br>http://factordb.com/index.php?id=1100000004103372866&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000000808118233&base=27<br>http://factordb.com/index.php?showid=1100000004681348398&base=27<br>http://factordb.com/index.php?showid=1100000004374140861&base=27<br>http://factordb.com/index.php?showid=1100000004374138999&base=27<br>http://factordb.com/index.php?showid=1100000000819229859&base=27<br>http://factordb.com/index.php?showid=1100000004102754118&base=27<br>http://factordb.com/index.php?showid=1100000004102755880&base=27<br>http://factordb.com/index.php?showid=1100000004102758254&base=27<br>http://factordb.com/index.php?showid=1100000004102875088&base=27<br>http://factordb.com/index.php?showid=1100000004103372866&base=27<nowiki/>||44||100000|| |- ||28||25528~25529||O4O₉₄₅₃₅9<br>5OA₃₁₂₃₈F<br>N6₂₄₀₅₁LR<br>D0₅₂₆₇77D<br>QO₄₂₃₉69<br>5₃₇₄₆8P<br>G0₁₈₉₉AN<br>A₁₄₂₃6F<br>5I₁₃₇₀F<br>5₁₃₃₂P8P||94538<br>31241<br>24054<br>5271<br>4242<br>3748<br>1902<br>1425<br>1372<br>1335||136812<br>45210<br>34810<br>7628<br>6139<br>5424<br>2753<br>2062<br>1985<br>1932||(6092×28⁹⁴⁵³⁶−143)/9<br>(4438×28³¹²³⁹+125)/27<br>(209×28²⁴⁰⁵³+3967)/9<br>13×28⁵²⁷⁰+5697<br>(242×28⁴²⁴¹−4679)/9<br>(5×28³⁷⁴⁸+2803)/27<br>16×28¹⁹⁰¹+303<br>(10×28¹⁴²⁵−2899)/27<br>(17×28¹³⁷¹−11)/3<br>(5×28¹³³⁵+426163)/27||http://factordb.com/index.php?id=1100000000808118231&open=prime<br>http://factordb.com/index.php?id=1100000003880455200&open=prime<br>http://factordb.com/index.php?id=1100000003879667576&open=prime<br>http://factordb.com/index.php?id=1100000003850151420&open=prime<br>http://factordb.com/index.php?id=1100000000840839934&open=prime<br>http://factordb.com/index.php?id=1100000003850161974&open=prime<br>http://factordb.com/index.php?id=1100000003850161973&open=prime<br>http://factordb.com/index.php?id=1100000000840839947&open=prime<br>http://factordb.com/index.php?id=1100000003850161972&open=prime<br>http://factordb.com/index.php?id=1100000003850161965&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000000808118231&base=28<br>http://factordb.com/index.php?showid=1100000003880455200&base=28<br>http://factordb.com/index.php?showid=1100000003879667576&base=28<br>http://factordb.com/index.php?showid=1100000003850151420&base=28<br>http://factordb.com/index.php?showid=1100000000840839934&base=28<br>http://factordb.com/index.php?showid=1100000003850161974&base=28<br>http://factordb.com/index.php?showid=1100000003850161973&base=28<br>http://factordb.com/index.php?showid=1100000000840839947&base=28<br>http://factordb.com/index.php?showid=1100000003850161972&base=28<br>http://factordb.com/index.php?showid=1100000003850161965&base=28<nowiki/>||1||900000|| |- ||29||355242~355367||830₉₉₃₇₇4<br>GP5J₉₄₉₃₅<br>P05J₉₀₂₈₉<br>BBD0₈₈₈₈₈PB<br>8B₈₅₃₃₃G<br>L0₈₁₅₇₁5955<br>E0₇₇₃₇₂L7B<br>LPC₇₅₁₅₁9<br>JR0₇₄₆₂₂7<br>B₇₄₅₀₁0RP||99380<br>94938<br>90292<br>88893<br>85335<br>81576<br>77376<br>75154<br>74625<br>74504||145333<br>138837<br>132043<br>129997<br>124794<br>119297<br>113155<br>109905<br>109132<br>108955||235×29⁹⁹³⁷⁸+4<br>(397227×29⁹⁴⁹³⁵−19)/28<br>(588859×29⁹⁰²⁸⁹−19)/28<br>9583×29⁸⁸⁸⁹⁰+736<br>(235×29⁸⁵³³⁴+129)/14<br>21×29⁸¹⁵⁷⁵+129664<br>14×29⁷⁷³⁷⁵+17875<br>(4441×29⁷⁵¹⁵²−24)/7<br>578×29⁷⁴⁶²³+7<br>(11×29⁷⁴⁵⁰⁴−245655)/28||http://factordb.com/index.php?id=1100000008253882372&open=prime<br>http://factordb.com/index.php?id=1100000008253893542&open=prime<br>http://factordb.com/index.php?id=1100000008253899083&open=prime<br>http://factordb.com/index.php?id=1100000008253909183&open=prime<br>http://factordb.com/index.php?id=1100000008253921388&open=prime<br>http://factordb.com/index.php?id=1100000008253925955&open=prime<br>http://factordb.com/index.php?id=1100000008253931446&open=prime<br>http://factordb.com/index.php?id=1100000000808118236&open=prime<br>http://factordb.com/index.php?id=1100000008253934219&open=prime<br>http://factordb.com/index.php?id=1100000008253936120&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008253882372&base=29<br>http://factordb.com/index.php?showid=1100000008253893542&base=29<br>http://factordb.com/index.php?showid=1100000008253899083&base=29<br>http://factordb.com/index.php?showid=1100000008253909183&base=29<br>http://factordb.com/index.php?showid=1100000008253921388&base=29<br>http://factordb.com/index.php?showid=1100000008253925955&base=29<br>http://factordb.com/index.php?showid=1100000008253931446&base=29<br>http://factordb.com/index.php?showid=1100000000808118236&base=29<br>http://factordb.com/index.php?showid=1100000008253934219&base=29<br>http://factordb.com/index.php?showid=1100000008253936120&base=29<nowiki/>||125||100000|| |- ||30||2619||OT₃₄₂₀₅<br>I0₂₄₆₀₈D<br>5₄₈₈₂J<br>C0₁₀₂₂1<br>M0₅₄₇SS7<br>M₂₄₁QB<br>AN₂₀₆<br>50₁₆₄B<br>J₁₅₃QJ<br>J₉₄QQJ||34206<br>24610<br>4883<br>1024<br>551<br>243<br>207<br>166<br>155<br>97||50527<br>36352<br>7213<br>1513<br>814<br>359<br>306<br>245<br>229<br>144||25×30³⁴²⁰⁵−1<br>18×30²⁴⁶⁰⁹+13<br>(5×30⁴⁸⁸³+401)/29<br>12×30¹⁰²³+1<br>22×30⁵⁵⁰+26047<br>(22×30²⁴³+3139)/29<br>(313×30²⁰⁶−23)/29<br>5×30¹⁶⁵+11<br>(19×30¹⁵⁵+6071)/29<br>(19×30⁹⁷+188771)/29||http://factordb.com/index.php?id=1100000000800812865&open=prime<br>http://factordb.com/index.php?id=1100000003593967511&open=prime<br>http://factordb.com/index.php?id=1100000002327649423&open=prime<br>http://factordb.com/index.php?id=1100000000785448736&open=prime<br>http://factordb.com/index.php?id=1100000003593407988&open=prime<br>http://factordb.com/index.php?id=1100000003593408295&open=prime<br>http://factordb.com/index.php?id=1100000002327651073&open=prime<br>http://factordb.com/index.php?id=1100000002356282476&open=ecm<br>http://factordb.com/index.php?id=1100000003593409109&open=ecm<br>http://factordb.com/index.php?id=1100000003593409165&open=ecm<nowiki/>||http://factordb.com/index.php?showid=1100000000800812865&base=30<br>http://factordb.com/index.php?showid=1100000003593967511&base=30<br>http://factordb.com/index.php?showid=1100000002327649423&base=30<br>http://factordb.com/index.php?showid=1100000000785448736&base=30<br>http://factordb.com/index.php?showid=1100000003593407988&base=30<br>http://factordb.com/index.php?showid=1100000003593408295&base=30<br>http://factordb.com/index.php?showid=1100000002327651073&base=30<br>http://factordb.com/index.php?showid=1100000002356282476&base=30<br>http://factordb.com/index.php?showid=1100000003593409109&base=30<br>http://factordb.com/index.php?showid=1100000003593409165&base=30<nowiki/>||0||–|| |- ||31||569323~569400||2IIF₉₁₈₀₅<br>B0₈₈₃₀₉APO9<br>J0T₇₇₅₁₆<br>J090₇₇₁₂₈NNN<br>D₆₉₈₆₁QO<br>9MH0₆₈₆₃₇D<br>J₆₇₁₆₂D<br>N0₆₆₉₇₁32P<br>DDDQ0₆₄₀₈₈TD<br>U₆₃₈₆₁CM3||91808<br>88314<br>77518<br>77134<br>69863<br>68641<br>67163<br>66975<br>64094<br>63864||136918<br>131708<br>115608<br>115035<br>104191<br>102369<br>100165<br>99884<br>95587<br>95245||(4997×31⁹¹⁸⁰⁵−1)/2<br>11×31⁸⁸³¹³+322688<br>(17699×31⁷⁷⁵¹⁶−29)/30<br>18268×31⁷⁷¹³¹+22839<br>(13×31⁶⁹⁸⁶³+12407)/30<br>9348×31⁶⁸⁶³⁸+13<br>(19×31⁶⁷¹⁶³−199)/30<br>23×31⁶⁶⁹⁷⁴+2970<br>400205×31⁶⁴⁰⁹⁰+912<br>31⁶³⁸⁶⁴−17574||http://factordb.com/index.php?id=1100000007050395732&open=prime<br>http://factordb.com/index.php?id=1100000007050397309&open=prime<br>http://factordb.com/index.php?id=1100000007050398940&open=prime<br>http://factordb.com/index.php?id=1100000007050400178&open=prime<br>http://factordb.com/index.php?id=1100000006965878559&open=prime<br>http://factordb.com/index.php?id=1100000006965875678&open=prime<br>http://factordb.com/index.php?id=1100000006965873668&open=prime<br>http://factordb.com/index.php?id=1100000006965870538&open=prime<br>http://factordb.com/index.php?id=1100000006965868103&open=prime<br>http://factordb.com/index.php?id=1100000006965865343&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000007050395732&base=31<br>http://factordb.com/index.php?showid=1100000007050397309&base=31<br>http://factordb.com/index.php?showid=1100000007050398940&base=31<br>http://factordb.com/index.php?showid=1100000007050400178&base=31<br>http://factordb.com/index.php?showid=1100000006965878559&base=31<br>http://factordb.com/index.php?showid=1100000006965875678&base=31<br>http://factordb.com/index.php?showid=1100000006965873668&base=31<br>http://factordb.com/index.php?showid=1100000006965870538&base=31<br>http://factordb.com/index.php?showid=1100000006965868103&base=31<br>http://factordb.com/index.php?showid=1100000006965865343&base=31<nowiki/>||77||100000|| |- ||32||168882~169002||V₉₉₅₈₃63<br>6₈₉₀₇₄AF<br>8₇₇₇₀₀H<br>Q₇₇₄₀₁EQQQ3<br>8₇₇₂₄₉3<br>JM₇₆₀₂₈L<br>E₇₂₉₁₉IL<br>B0₆₇₆₈₀CB<br>GK₆₆₀₇₆F<br>KN₆₅₀₂₂||99585<br>89076<br>77701<br>77406<br>77250<br>76030<br>72921<br>67683<br>66078<br>65023||149891<br>134073<br>116952<br>116508<br>116273<br>114437<br>109757<br>101873<br>99458<br>97870||32⁹⁹⁵⁸⁵−829<br>(6×32⁸⁹⁰⁷⁶+4241)/31<br>(8×32⁷⁷⁷⁰¹+271)/31<br>(26×32⁷⁷⁴⁰⁶−390071011)/31<br>(8×32⁷⁷²⁵⁰−163)/31<br>(611×32⁷⁶⁰²⁹−53)/31<br>(14×32⁷²⁹²¹+4171)/31<br>11×32⁶⁷⁶⁸²+395<br>(516×32⁶⁶⁰⁷⁷−175)/31<br>(643×32⁶⁵⁰²²−23)/31||http://factordb.com/index.php?id=1100000005514892191&open=prime<br>http://factordb.com/index.php?id=1100000005514897129&open=prime<br>http://factordb.com/index.php?id=1100000005514901700&open=prime<br>http://factordb.com/index.php?id=1100000005514915338&open=prime<br>http://factordb.com/index.php?id=1100000005514918574&open=prime<br>http://factordb.com/index.php?id=1100000005514922523&open=prime<br>http://factordb.com/index.php?id=1100000004591654373&open=prime<br>http://factordb.com/index.php?id=1100000004591654467&open=prime<br>http://factordb.com/index.php?id=1100000004591654632&open=prime<br>http://factordb.com/index.php?id=1100000004591654952&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000005514892191&base=32<br>http://factordb.com/index.php?showid=1100000005514897129&base=32<br>http://factordb.com/index.php?showid=1100000005514901700&base=32<br>http://factordb.com/index.php?showid=1100000005514915338&base=32<br>http://factordb.com/index.php?showid=1100000005514918574&base=32<br>http://factordb.com/index.php?showid=1100000005514922523&base=32<br>http://factordb.com/index.php?showid=1100000004591654373&base=32<br>http://factordb.com/index.php?showid=1100000004591654467&base=32<br>http://factordb.com/index.php?showid=1100000004591654632&base=32<br>http://factordb.com/index.php?showid=1100000004591654952&base=32<nowiki/>||120||100000|| |- ||33||280012~280093||DP₉₅₀₉₃M5<br>HJ0₉₄₂₉₅J<br>90₉₃₅₉₇Q<br>9F0₉₃₁₅₇N<br>7₈₉₄₄₉333H<br>K3₈₀₇₅₁6K<br>D₈₀₁₀₇9UD<br>VFU₇₂₂₀₄FK<br>J₆₈₇₁₅2BJ<br>DF0₆₈₃₆₇J||95096<br>94298<br>93599<br>93160<br>89453<br>80754<br>80110<br>72208<br>68718<br>68370||144405<br>143193<br>142131<br>141465<br>135835<br>122626<br>121648<br>109649<br>104350<br>103821||(441×33⁹⁵⁰⁹⁵−3833)/32<br>580×33⁹⁴²⁹⁶+19<br>9×33⁹³⁵⁹⁸+26<br>312×33⁹³¹⁵⁸+23<br>(7×33⁸⁹⁴⁵³−4743239)/32<br>(643×33⁸⁰⁷⁵³+3709)/32<br>(13×33⁸⁰¹¹⁰−121453)/32<br>(16623×33⁷²²⁰⁶−8095)/16<br>(19×33⁶⁸⁷¹⁸−600883)/32<br>444×33⁶⁸³⁶⁸+19||http://factordb.com/index.php?id=1100000005652348775&open=prime<br>http://factordb.com/index.php?id=1100000005652362811&open=prime<br>http://factordb.com/index.php?id=1100000005652375073&open=prime<br>http://factordb.com/index.php?id=1100000005652389776&open=prime<br>http://factordb.com/index.php?id=1100000005652430746&open=prime<br>http://factordb.com/index.php?id=1100000005652446200&open=prime<br>http://factordb.com/index.php?id=1100000005652461592&open=prime<br>http://factordb.com/index.php?id=1100000004614764298&open=prime<br>http://factordb.com/index.php?id=1100000004614770536&open=prime<br>http://factordb.com/index.php?id=1100000004614784274&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000005652348775&base=33<br>http://factordb.com/index.php?showid=1100000005652362811&base=33<br>http://factordb.com/index.php?showid=1100000005652375073&base=33<br>http://factordb.com/index.php?showid=1100000005652389776&base=33<br>http://factordb.com/index.php?showid=1100000005652430746&base=33<br>http://factordb.com/index.php?showid=1100000005652446200&base=33<br>http://factordb.com/index.php?showid=1100000005652461592&base=33<br>http://factordb.com/index.php?showid=1100000004614764298&base=33<br>http://factordb.com/index.php?showid=1100000004614770536&base=33<br>http://factordb.com/index.php?showid=1100000004614784274&base=33<nowiki/>||81||100000|| |- ||34||184785~184832||GFGC₉₉₉₉₆5<br>90₉₇₉₅₀FJ<br>NM0₈₅₂₁₈KX<br>F₈₃₁₈₉H2HP<br>P₇₉₄₄₁444P<br>6₇₇₀₂₇8X<br>XQIQ₇₂₂₄₁D<br>T₆₆₅₃₀IF<br>4₆₆₁₅₂B<br>2EEC₆₆₀₃₉7||100000<br>97953<br>85222<br>83193<br>79445<br>77029<br>72245<br>66532<br>66153<br>66043||153148<br>150013<br>130516<br>127408<br>121669<br>117968<br>110642<br>101893<br>101312<br>101143||(209246×34⁹⁹⁹⁹⁷−81)/11<br>9×34⁹⁷⁹⁵²+529<br>804×34⁸⁵²²⁰+713<br>(5×34⁸³¹⁹³+700233)/11<br>(25×34⁷⁹⁴⁴⁵−28062367)/33<br>(2×34⁷⁷⁰²⁹+1043)/11<br>(1288676×34⁷²²⁴²−455)/33<br>(29×34⁶⁶⁵³²−12833)/33<br>(4×34⁶⁶¹⁵³+227)/33<br>(30826×34⁶⁶⁰⁴⁰−59)/11||http://factordb.com/index.php?id=1100000004702891268&open=prime<br>http://factordb.com/index.php?id=1100000004702894713&open=prime<br>http://factordb.com/index.php?id=1100000004702900996&open=prime<br>http://factordb.com/index.php?id=1100000004702910376&open=prime<br>http://factordb.com/index.php?id=1100000004702913746&open=prime<br>http://factordb.com/index.php?id=1100000004702918600&open=prime<br>http://factordb.com/index.php?id=1100000004399656529&open=prime<br>http://factordb.com/index.php?id=1100000004399657696&open=prime<br>http://factordb.com/index.php?id=1100000004399658651&open=prime<br>http://factordb.com/index.php?id=1100000004399659716&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000004702891268&base=34<br>http://factordb.com/index.php?showid=1100000004702894713&base=34<br>http://factordb.com/index.php?showid=1100000004702900996&base=34<br>http://factordb.com/index.php?showid=1100000004702910376&base=34<br>http://factordb.com/index.php?showid=1100000004702913746&base=34<br>http://factordb.com/index.php?showid=1100000004702918600&base=34<br>http://factordb.com/index.php?showid=1100000004399656529&base=34<br>http://factordb.com/index.php?showid=1100000004399657696&base=34<br>http://factordb.com/index.php?showid=1100000004399658651&base=34<br>http://factordb.com/index.php?showid=1100000004399659716&base=34<nowiki/>||47||100000|| |- ||35||720002~720062||N0N₉₉₉₇₁9<br>V0₈₃₆₆₉E73<br>N₈₁₅₆₃K7N<br>BJ0₈₁₂₇₉N<br>J0₈₀₀₆₂FUH<br>43V₇₉₇₅₄<br>9₇₆₆₀₀K3<br>LB₇₁₃₆₆PB<br>Q₆₄₁₅₀H<br>50₆₃₃₉₇5R||99974<br>83673<br>81566<br>81282<br>80066<br>79756<br>76602<br>71369<br>64151<br>63400||154367<br>129197<br>125944<br>125505<br>123628<br>123148<br>118279<br>110199<br>99054<br>97894||(27393×35⁹⁹⁹⁷²−499)/34<br>31×35⁸³⁶⁷²+17398<br>(23×35⁸¹⁵⁶⁶−144013)/34<br>404×35⁸¹²⁸⁰+23<br>19×35⁸⁰⁰⁶⁵+19442<br>(4893×35⁷⁹⁷⁵⁴−31)/34<br>(9×35⁷⁶⁶⁰²+12877)/34<br>(725×35⁷¹³⁶⁸+16649)/34<br>(13×35⁶⁴¹⁵¹−166)/17<br>5×35⁶³³⁹⁹+202||http://factordb.com/index.php?id=1100000008248342445&open=prime<br>http://factordb.com/index.php?id=1100000008248353306&open=prime<br>http://factordb.com/index.php?id=1100000008248375642&open=prime<br>http://factordb.com/index.php?id=1100000008248397018&open=prime<br>http://factordb.com/index.php?id=1100000008248412468&open=prime<br>http://factordb.com/index.php?id=1100000008248418540&open=prime<br>http://factordb.com/index.php?id=1100000008248423670&open=prime<br>http://factordb.com/index.php?id=1100000008192119974&open=prime<br>http://factordb.com/index.php?id=1100000008192126630&open=prime<br>http://factordb.com/index.php?id=1100000008192129294&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008248342445&base=35<br>http://factordb.com/index.php?showid=1100000008248353306&base=35<br>http://factordb.com/index.php?showid=1100000008248375642&base=35<br>http://factordb.com/index.php?showid=1100000008248397018&base=35<br>http://factordb.com/index.php?showid=1100000008248412468&base=35<br>http://factordb.com/index.php?showid=1100000008248418540&base=35<br>http://factordb.com/index.php?showid=1100000008248423670&base=35<br>http://factordb.com/index.php?showid=1100000008192119974&base=35<br>http://factordb.com/index.php?showid=1100000008192126630&base=35<br>http://factordb.com/index.php?showid=1100000008192129294&base=35<nowiki/>||60||100000|| |- ||36||35286~35290||P₈₁₉₉₃SZ<br>S0₇₅₀₀₇8H<br>7K₂₆₅₆₇Z<br>J₁₀₁₁₇LJ<br>VL0₇₂₅₈J<br>EO0₆₁₇₇V<br>FZ₅₇₇₇3P<br>T09₄₆₁₈1<br>RY₄₅₆₂H<br>OZ₃₉₃₂AZ||81995<br>75010<br>26569<br>10119<br>7261<br>6180<br>5780<br>4621<br>4564<br>3935||127609<br>116739<br>41349<br>15748<br>11301<br>9618<br>8996<br>7192<br>7103<br>6124||(5×36⁸¹⁹⁹⁵+821)/7<br>28×36⁷⁵⁰⁰⁹+305<br>(53×36²⁶⁵⁶⁸+101)/7<br>(19×36¹⁰¹¹⁹+2501)/35<br>1137×36⁷²⁵⁹+19<br>528×36⁶¹⁷⁸+31<br>16×36⁵⁷⁷⁹−1163<br>(36549×36⁴⁶¹⁹−289)/35<br>(979×36⁴⁵⁶³−629)/35<br>25×36³⁹³⁴−901||http://factordb.com/index.php?id=1100000002394962083&open=prime<br>http://factordb.com/index.php?id=1100000004020085177&open=prime<br>http://factordb.com/index.php?id=1100000003896952461&open=prime<br>http://factordb.com/index.php?id=1100000003807362491&open=prime<br>http://factordb.com/index.php?id=1100000003807362489&open=prime<br>http://factordb.com/index.php?id=1100000003807362488&open=prime<br>http://factordb.com/index.php?id=1100000003807362487&open=prime<br>http://factordb.com/index.php?id=1100000003807362486&open=prime<br>http://factordb.com/index.php?id=1100000003807362485&open=prime<br>http://factordb.com/index.php?id=1100000000840634476&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000002394962083&base=36<br>http://factordb.com/index.php?showid=1100000004020085177&base=36<br>http://factordb.com/index.php?showid=1100000003896952461&base=36<br>http://factordb.com/index.php?showid=1100000003807362491&base=36<br>http://factordb.com/index.php?showid=1100000003807362489&base=36<br>http://factordb.com/index.php?showid=1100000003807362488&base=36<br>http://factordb.com/index.php?showid=1100000003807362487&base=36<br>http://factordb.com/index.php?showid=1100000003807362486&base=36<br>http://factordb.com/index.php?showid=1100000003807362485&base=36<br>http://factordb.com/index.php?showid=1100000000840634476&base=36<nowiki/>||4||200000|| |} == The fully proof of Athena problem in decimal (base ''b'' = 10) == '''Bold''' for the Athena primes, ''x'' ◁ ''y'' means ''x'' is a subsequence of ''y''. Assume ''p'' is a prime > 10, and the last digit of ''p'' must lie in {1,3,7,9}. Case 1: ''p'' ends with 1. In this case we can write ''p'' = ''x''1. If ''x'' contains 1, 3, 4, 6, or 7, then (respectively) '''11''' ◁ ''p'', '''31''' ◁ ''p'', '''41''' ◁ ''p'', '''61''' ◁ ''p'', or '''71''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 8, or 9. Case 1.1: ''p'' begins with 2. In this case we can write ''p'' = 2''y''1. If 5 ◁ ''y'', then '''251''' ◁ ''p''. If 8 ◁ ''y'', then '''281''' ◁ ''p''. If 9 ◁ ''y'', then 29 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2. If 22 ◁ ''y'', then '''2221''' ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's. If ''y'' contains no 2's, then ''p'' ∈ 2{0}1. But then, since the sum of the digits of ''p'' is 3, ''p'' is divisible by 3, so ''p'' cannot be prime. If ''y'' contains exactly one 2, then we can write ''p'' = 2''z''2''w''1, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''20201''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty. If ''z'' is empty, then ''p'' ∈ 22{0}1, and the smallest prime ''p'' ∈ 22{0}1 is '''22000001'''. If ''w'' is empty, then ''p'' ∈ 2{0}21, and the smallest prime ''p'' ∈ 2{0}21 is '''20021'''. Case 1.2: ''p'' begins with 5. In this case we can write ''p'' = 5''y''1. If 2 ◁ ''y'', then '''521''' ◁ ''p''. If 9 ◁ ''y'', then 59 ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 5, or 8. If 05 ◁ ''y'', then '''5051''' ◁ ''p''. If 08 ◁ ''y'', then '''5081''' ◁ ''p''. If 50 ◁ ''y'', then '''5501''' ◁ ''p''. If 58 ◁ ''y'', then '''5581''' ◁ ''p''. If 80 ◁ ''y'', then '''5801''' ◁ ''p''. If 85 ◁ ''y'', then '''5851''' ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ {5} ∪ {8}. If ''y'' ∈ {0}, then ''p'' ∈ 5{0}1. But then, since the sum of the digits of ''p'' is 6, ''p'' is divisible by 3, so ''p'' cannot be prime. If ''y'' ∈ {5}, then ''p'' ∈ 5{5}1, and the smallest prime ''p'' ∈ 5{5}1 is '''555555555551'''. If ''y'' ∈ {8}, since if 88 ◁ ''y'', then 881 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'',8}, and thus ''p'' ∈ {51,581}, but 51 and 581 are both composite. Case 1.3: ''p'' begins with 8. In this case we can write p = 8''y''1. If 2 ◁ ''y'', then '''821''' ◁ ''p''. If 8 ◁ ''y'', then '''881''' ◁ ''p''. If 9 ◁ ''y'', then 89 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 5. If 50 ◁ ''y'', then '''8501''' ◁ ''p''. Hence we may assume y ∈ {0}{5}. If 005 ◁ ''y'', then '''80051''' ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}. If y ∈ {0}, then ''p'' ∈ 8{0}1. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime. If y ∈ {5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'', 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus ''p'' ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite. If y ∈ 0{5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus ''p'' ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only '''80555551''' is a minimal element. Case 1.4: ''p'' begins with 9. In this case we can write p = 9''y''1. If 9 ◁ ''y'', then '''991''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 2, 5, or 8. If 00 ◁ ''y'', then '''9001''' ◁ ''p''. If 22 ◁ ''y'', then '''9221''' ◁ ''p''. If 55 ◁ ''y'', then '''9551''' ◁ ''p''. If 88 ◁ ''y'', then 881 ◁ ''p''. Hence we may assume ''y'' contains at most one 0, at most one 2, at most one 5, and at most one 8. If ''y'' only contains at most one 0 and does not contain any of {2,5,8}, then ''y'' ∈ {''𝜆'',0}, and thus ''p'' ∈ {91,901}, but 91 and 901 are both composite. If ''y'' only contains at most one 0 and only one of {2,5,8}, then the sum of the digits of ''p'' is divisible by 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume ''y'' contains at least two of {2,5,8}. If 25 ◁ ''y'', then 251 ◁ ''p''. If 28 ◁ ''y'', then 281 ◁ ''p''. If 52 ◁ ''y'', then 521 ◁ ''p''. If 82 ◁ ''y'', then 821 ◁ ''p''. Hence we may assume ''y'' contains no 2's (since if ''y'' contains 2, then ''y'' cannot contain either 5's or 8's, which is a contradiction). If 85 ◁ ''y'', then '''9851''' ◁ ''p''. Hence we may assume ''y'' ∈ {58,580,508,058}, and thus ''p'' ∈ {9581,95801,95081,90581}, and of these numbers only 95801 is prime, but 95801 is not a minimal element since 5801 ◁ 95801. Case 2: ''p'' ends with 3. In this case we can write p = ''x''3. If ''x'' contains 1, 2, 4, 5, 7, or 8, then (respectively) '''13''' ◁ ''p'', '''23''' ◁ ''p'', '''43''' ◁ ''p'', '''53''' ◁ ''p'', '''73''' ◁ ''p'', or '''83''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Case 3: ''p'' ends with 7. In this case we can write ''p'' = ''x''7. If ''x'' contains 1, 3, 4, 6, or 9, then (respectively) '''17''' ◁ ''p'', '''37''' ◁ ''p'', '''47''' ◁ ''p'', '''67''' ◁ ''p'', or '''97''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 7, or 8. Case 3.1: ''p'' begins with 2. In this case we can write ''p'' = 2''y''7. If 2 ◁ ''y'', then '''227''' ◁ ''p''. If 5 ◁ ''y'', then '''257''' ◁ ''p''. If 7 ◁ ''y'', then '''277''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 8. If 08 ◁ ''y'', then '''2087''' ◁ ''p''. If 88 ◁ ''y'', then 887 ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ 8{0}. If ''y'' ∈ {0}, then ''p'' ∈ 2{0}7. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime. If y ∈ 8{0}, then ''p'' ∈ 28{0}7. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 40_''n''1 = 280_''n''7. Case 3.2: ''p'' begins with 5. In this case we can write ''p'' = 5''y''7. If 5 ◁ ''y'', then '''557''' ◁ ''p''. If 7 ◁ ''y'', then '''577''' ◁ ''p''. If 8 ◁ ''y'', then '''587''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2. If 22 ◁ ''y'', then 227 ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's. If ''y'' contains no 2's, then ''p'' ∈ 5{0}7. But then, since the sum of the digits of ''p'' is 12, ''p'' is divisible by 3, so ''p'' cannot be prime. If ''y'' contains exactly one 2, then we can write ''p'' = 5''z''2''w''7, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''50207''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty. If ''z'' is empty, then ''p'' ∈ 52{0}7, and the smallest prime ''p'' ∈ 52{0}7 is '''5200007'''. If ''w'' is empty, then ''p'' ∈ 5{0}27, and the smallest prime ''p'' ∈ 5{0}27 is '''5000000000000000000000000000027'''. Case 3.3: ''p'' begins with 7. In this case we can write ''p'' = 7''y''7. If 2 ◁ ''y'', then '''727''' ◁ ''p''. If 5 ◁ ''y'', then '''757''' ◁ ''p''. If 8 ◁ ''y'', then '''787''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 7, and thus all digits of ''p'' are 0 or 7. But then, since the digits of ''p'' all have a common factor 7, ''p'' is divisible by 7, so ''p'' cannot be prime. Case 3.4: ''p'' begins with 8. In this case we can write ''p'' = 8''y''7. If 2 ◁ ''y'', then '''827''' ◁ ''p''. If 5 ◁ ''y'', then '''857''' ◁ ''p''. If 7 ◁ ''y'', then '''877''' ◁ ''p''. If 8 ◁ ''y'', then '''887''' ◁ ''p''. Hence we may assume ''y'' ∈ {0}, and thus ''p'' ∈ 8{0}7. But then, since the sum of the digits of ''p'' is 15, ''p'' is divisible by 3, so ''p'' cannot be prime. Case 4: ''p'' ends with 9. In this case we can write ''p'' = ''x''9. If ''x'' contains 1, 2, 5, 7, or 8, then (respectively) '''19''' ◁ ''p'', '''29''' ◁ ''p'', '''59''' ◁ ''p'', '''79''' ◁ ''p'', or '''89''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 4, 6, or 9. If 44 ◁ ''x'', then '''449''' ◁ ''p''. Hence we may assume ''x'' contains zero or one 4's. If x contains no 4's, then all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume that ''x'' contains exactly one 4. Case 4.1: ''p'' begins with 3. In this case we can write ''p'' = 3''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. We must have '''349''' ◁ ''p''. Case 4.2: ''p'' begins with 4. In this case we can write ''p'' = 4''y''9, where all digits of ''y'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''409''' ◁ ''p''. If 3 ◁ ''y'', then 43 ◁ ''p''. If 9 ◁ ''y'', then '''499''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}, and thus ''p'' ∈ 4{6}9. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 6_''n''7 = 46_''n''9. Case 4.3: ''p'' begins with 6. In this case we can write p = 6''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 6 ◁ ''z'', then '''6469''' ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' is empty. If 3 ◁ ''y'', then 349 ◁ ''p''. If 9 ◁ ''y'', then '''6949''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 6. If 06 ◁ ''y'', then '''60649''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}{0}. If 666 ◁ ''y'', then '''666649''' ◁ ''p''. If 00000 ◁ ''y'', then '''60000049''' ◁ ''p''. Hence we may assume ''y'' ∈ {''𝜆'', 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus ''p'' ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only '''66000049''' and '''66600049''' are primes. Case 4.4: ''p'' begins with 9. In this case we can write p = 9''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''9049''' ◁ ''p''. If 3 ◁ ''y'', then 349 ◁ ''p''. If 6 ◁ ''y'', then '''9649''' ◁ ''p''. If 9 ◁ ''y'', then '''9949''' ◁ ''p''. Hence we may assume ''y'' is empty. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' ∈ {6}, and thus ''p'' ∈ 94{6}9, and the smallest prime ''p'' ∈ 94{6}9 is 946669. [[Category:Number theory]] btxfqh7rtf9063l6sava7qoopsk6xhr 10 330232 2844833 2844766 2026-11-07T22:36:19Z Jtneill 10242 2844833 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. 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this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|]], with a link to the chatbot conversation, when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]], with a link to the chatbot conversation, when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these cop yedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors).## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> lj9zyac7qmun8ckgfpnf0ycfdwj5d83 2844836 2844833 2026-11-07T23:27:29Z Jtneill 10242 2844836 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|]], with a link to the chatbot conversation, when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]], with a link to the chatbot conversation, when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these cop yedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors).## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> qr7sgqnzkp0fch0xku2conc5jlmxlea 2844838 2844836 2026-11-07T23:49:14Z Jtneill 10242 # The edit history is quite brief, showing limited development 2844838 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|]], with a link to the chatbot conversation, when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]], with a link to the chatbot conversation, when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these cop yedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors).## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent/very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> 2a7ox8n4e2tk8fh5sm871ay6oj47o2f 2844840 2844838 2026-11-08T00:15:34Z Jtneill 10242 2844840 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|]], with a link to the chatbot conversation, when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]], with a link to the chatbot conversation, when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these cop yedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors).## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> 01rug59qwsvtpqvklftbtam67kyjzr3 2844844 2844840 2026-11-08T01:34:11Z Jtneill 10242 2844844 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]], with a shared link to the chatbot conversation(s), when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]], with a shared link to the chatbot conversation(s), when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these cop yedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors).## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> aicra9de9ws984oyw3etczsykwk4pgb 2844849 2844844 2026-11-08T04:22:08Z Jtneill 10242 2844849 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]], with a shared link to the chatbot conversation(s), when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correcting use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]], with a shared link to the chatbot conversation(s), when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these cop yedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correcting use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors).## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> nsnmlknq93ra9mbhke1s6as3w0m6cjx 2844850 2844849 2026-11-08T04:33:38Z Jtneill 10242 ## Overuse of the present perfect: use the simple past tense consistently when reporting previous research e.g., ### Present perfect: "Chivers (2010) has also suggested ..." ### Simple past: "Chivers (2010) suggested ..." 2844850 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]], with a shared link to the chatbot conversation(s), when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correcting use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense ## Overuse of the present perfect: use the simple past tense consistently when reporting previous research e.g., ### Present perfect: "Chivers (2010) has also suggested ..." ### Simple past: "Chivers (2010) suggested ..." <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]], with a shared link to the chatbot conversation(s), when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these cop yedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bo]ld, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correcting use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense ## Overuse of the present perfect: use the simple past tense consistently when reporting previous research e.g., ### Present perfect: "Chivers (2010) has also suggested ..." ### Simple past: "Chivers (2010) suggested ..." <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors).## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> puyx03kxy6un180abi8dbujtev54xt1 2844851 2844850 2026-11-08T04:50:30Z Jtneill 10242 2844851 wikitext text/x-wiki <noinclude>Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit. Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]]. __NOTOC__</noinclude><includeonly> ==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback== {{RoundBoxTop|theme=8}} This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements. {{RoundBoxBottom}} {{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]] ===Overall=== {{{1|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]=== {{{2|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]=== {{{3|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]=== {{{4|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]=== {{{5|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]=== {{{6|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]=== {{{7|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]=== {{{8|No comment}}} ===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]=== {{{9|No comment}}} {{RoundBoxBottom}}</includeonly><noinclude>{{collapse top|Simple example}} ==Simple example== See also [[#Detailed example|detailed example]] <pre> <!-- Official feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} ~~~~ </pre> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # |2= <!-- Overview comments... --> # |3= <!-- Theory comments... --> # |4= <!-- Research comments... --> # |5= <!-- Integration comments... --> # |6= <!-- Conclusion comments... --> # |7= <!-- Style comments... --> # |8= <!-- Learning features comments... --> # |9= <!-- Social contribution comments... --> # }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) {{Collapse bottom}} ==Detailed example== Example use of the template, with some common feedback comments: <small><small><small><pre> <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]], with a shared link to the chatbot conversation(s), when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section # Include a relevant image <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. ## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]] ## "Individuals" is overused. "People" is usually a clearer term than "individuals". Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally. ## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning ## Use permanent, rather than relative, time references. For example, instead of "20 years ago", refer to something like "at the beginning of the 21st century". In this way, the text will survive better into the future, without needing to be rewritten. ## Avoid overly emotive language (e.g,. *) in science-based communication <!-- Style – Layout --> # Layout ## The chapter is well structured, with major sections using sub-sections ## The headings could be more clearly aligned with the focus questions ## The structure is overly complicated; simplify and integrate ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## The chapter structure is underdeveloped; expand by using subheadings ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Provide more descriptive headings ## Move links from headings into their first mention in text ## Remove abbreviations/citations from headings ## Include an introductory paragraph before branching into the sub-sections ## Integrate research rather than having it as a stand-alone section(s) ## Integrate (embed) learning features such as quizzes, without their own headings, rather than having them as stand-alone sections ## The Overview and Conclusion should not have subheadings (fixed) ## Remove colons (:) from the ends of headings <!-- Style – Grammar --> # Grammar and spelling are excellent # Grammar ## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback ## Improve the clarity and flow of the writing by checking and correcting use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect] ## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)] ## Use past tense when describing research studies, although implications of findings could be in the present tense ## Overuse of the present perfect: use the simple past tense consistently when reporting previous research e.g., ### Present perfect: "Chivers (2010) has also suggested ..." ### Simple past: "Chivers (2010) suggested ..." <!-- Style – Abbreviations --> ## Abbreviations ### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out ### Check and correct formatting of abbreviations (such as e.g., i.e., etc.) ### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms. ### Explain abbreviations on first use: Spell out each abbreviation when it first appears (e.g., self-determination theory (SDT)), to ensure readers understand the term before its subsequent use ### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards ### Only introduce abbreviations which are subsequently used <!-- Style – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) ## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages. <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). ## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing (not capitals) for disorders, therapies, theories, etc.] ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – APA style - Quotes --> ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## "Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences" ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159) ## Direct quotes need page numbers—even better, communicate about concepts in your own words ## Direct quotes are overused—it is better to communicate about concepts in your own words <!-- Style – Figures --> ## Figures ### Very well/Well/Reasonably well captioned ### Brief captions; provide more detail to help connect the figure to the text ### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing without bold or italics. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Add captions <!-- Style – Figures - Citations --> ### Each Figure is referred to at least once within the main text using APA style ### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., "(see Figure 1)"; do not use bold, italics, check and correct capitalisation). ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Figures - Other --> ### Some image uploads were removed because of a lack of sufficient/appropriate copyright information ### Numbering needs correcting ### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size) <!-- Style – Tables --> ## Table(s) ### Very well/Well/Reasonably well captioned ### Brief caption(s); provide more explanatory detail about the table ### Use APA style for the caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Add APA style caption(s) ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### The source(s) of the information presented in one or more tables needs acknowledgement <!-- Style – Tables - Citations --> ### Each Table is referred to at least once within the main text using APA style ### Each Table is referred to at least once within the main text ### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation) ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## If there are three or more authors, cite the first author followed by et al., then year. For example, either: ### in-text, Smith et al. (2020), or ### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020) ## Do not include author first name or initials ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) ## A full stop is needed after "et al" (i.e., "et al.") because it is an abbreviation of [[wikt:et alii|et alii]] ## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]] ## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point) ## Check and correct placement of full-stops ## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois ## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources # For citations, use APA style or wiki style, but not both # Secondary citations are overused; strive to consult primary sources <!-- Style – References --> ## References use excellent APA style ## References use very good/good/reasonably good/basic/poor APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-) ### Include dois where available ### Hyperlink dois for 1-click access ### Provide the full titles of journals ### Remove "Retrieved from " ### Use alphabetical order ### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section ### Remove bullet-points; add hanging indent ### More copy editing is needed to fix formatting inconsistencies <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles # Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] <!-- Internal link style --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]] # Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s) # Excellent/Very good/Good/Reasonably good/Basic/No use of table(s) # Excellent/Very good/Good/Reasonably good/Basic use of feature box(es) # No use of feature boxes other than the opening scenario # Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Also include links to [[Motivation and emotion/Book|related book chapters]] ## Also include links to related Wikipedia articles ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite ## Move external links into the [[{{PAGENAME}}#References|External links]] section ## Add more links # [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count <!-- Learning features – External links --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section ## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite ## Target an international audience ## Add more links ## Link to the top 3-6 external resources about this topic # [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count |9= <!-- Social contribution comments... --> # ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} ~~~~ </pre></small></small></small> gives <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem # This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem # This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem # This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem # This is a basic chapter # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* express more in your own words—overuse of direct quotes and/or unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # Excellent use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in most or all of the main edits # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit # Insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is appropriately acknowledged # GenAI use is acknowedged via a general statement (which has been moved to the talk page), but not by using edit summaries as required by the unit's [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] # There is likely unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]]; if so, this violates principles of academic integrity # In some places, there is overreliance on genAI # There may be unacknowledged use of [[Motivation and emotion/Assessment/Using generative AI|use of genAI]] # There is insufficient acknowledgement in [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]], with a shared link to the chatbot conversation(s), when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles # [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in [[Motivation and emotion/Wikiversity/Edit summary|Motivation and emotion/Wikiversity/Edit summary]] with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]]. <!-- Overall – Citations --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult # All citations need to be in the References <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand # Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes. <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [ these cop yedits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # Reasonably good scenario or case study; could be more compelling # Basic scenario or case study # The written expression for the scenario needs improvement to be of a professional standard # Use a more practical, real-life scenario; move review of research into a subsequent section # Use an example that a wider audience can relate to; less than 5% of the world population are university students # Add an engaging case study or scenario <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario # Figure 1 could be more relevant to the scenario # Figure 1 lacks relevance to the scenario # The Figure 1 caption should explain more clearly how it is related to the scenario # Instead of a diagram, use <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box # Put the scenario in a feature box (fixed) <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon # Explains the psychological problem or phenomenon reasonably well/in a basic way # Briefly explains the psychological problem or phenomenon; provide more detail # Description of problem is too long or vague or overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections. # Insufficient explanation of the psychological problem or phenomenon # Clarity of written expression can be improved # Convert the explanation of the problem from bullet-points into sentences and paragraphs <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) # The focus questions are very good/good/reasonably good/basic/promising/insufficient # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) ## matching the top-level headings more closely ## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]] ## splitting double-barrelled questions into separate questions ## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## being presented in a feature box to help guide the reader (fixed) # Add focus questions in a feature box # See copy edits for examples of possible improvements |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Excellent—key theories are very well explained and applied # Very good—key theories are well explained and applied; minor areas for improvements # Good—key theories are quite explained and applied; minor to moderate areas for improvements # Reasonably good—relevant theories are selected, described, and applied, with some room for improvement # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic # Insufficient use of relevant psychological theory about this topic # Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Build more strongly on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Excellent/Very good use of tables, figures, and/or lists to clearly convey key theoretical information # Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to convey key theoretical information # The sources(s) of information presented in tables lacks sufficient citation <!-- Theory – Citations --> # Key citations are well used # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] # If you didn't consult an original source, don't cite it <!-- Theory – Examples --> # Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research # Excellent emphasis on systematic reviews and/or meta-analyses # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # Insufficient use of relevant systematic reviews and/or meta-analyses # More detail about key studies would be ideal # More recent research would be ideal # Claims are well referenced # In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) <!-- Research – Critical thinking --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research # Basic, formulaic # The chapter places more emphasis on theory than on research; strive for an integrated balance # Rather than describing individual studies separately, synthesise findings across related studies to identify common themes, patterns, and differences in the evidence # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Excellent/Very good/Good/Reasonably good/Basic summary and conclusion # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words # Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the [[Motivation and emotion/Wikiversity/Edit summary|edit summary]]. # Highlights the importance of the problem or phenomenon of interest # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are well summarised # Key points are summarised in a basic way # Summarise key points <!-- Conclusion – Focus questions --> # The focus questions are addressed # Take-away messages for each focus question could be spelt out more clearly # Address the focus questions <!-- Conclusion – Take-home messages --> # Clear take-home message(s) # Somewhat clear take-home message(s) # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is excellent/very good/good/reasonably good/basic ## The quality of written expression is reasonably good, but appears to be based on overuse of insufficiently acknowledged genAI content; a more convincing chapter would either use more human-written words and/or use finer-grained acknowledgement of genAI with publicly available links to the chatbot conversations as per the [[Motivation and emotion/Assessment/Using generative AI|unit's using genAI guidelines]] ## The quality of written expression is OK but there are several aspects which are below professional standard ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. ### GenAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources ## Use active (e.g., "this chapter explores" or "this chapter explored") rather than passive voice (e.g., "this chapter will explore" or "this chapter has explored") [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/] ## Target an ''international'' rather than domestic national audience. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia]. ## Reduce excessive use of bold font <!-- Style – Sentences --> ## Some/Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression ## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+. ## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence. <!-- Style – Paragraphs --> ## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences. ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused. Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st of 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. 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See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. # Thanks for the Wiki Commons uploads # Thanks very much for your extensive contributions # Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:47, 10 October 2026 (UTC) ==See also== * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * [[Template:METF]] * [[Template:MEMF]] [[Category:Motivation and emotion/Admin/2026]] [[Category:Motivation and emotion/Assessment/Chapter]] </noinclude> s3ay2t4wumbuv22btfp5utqd07o68r7 0 331023 2844852 2839857 2026-11-08T05:09:09Z Jtneill 10242 Copyediting 2844852 wikitext text/x-wiki {{title|Sex differences in sexual arousal patterns:<br>How do patterns of sexual arousal differ between males and females?}} __TOC__ == Overview == {{RoundBoxTop|theme=4}} [[File:ChatGPT Image Aug 18, 2026, 10 10 45 PM.png|right|thumb|150px|'''Figure 1'''. An image depicting sexual arousal between a female and male human being]] ;Scenario Emma and Daniel have been dating for several months {{g}} they are attracted to each other but their sexual desires emerge differently. Daniel is often aroused by Emma at the simple sight of her. Emma tends to be aroused by Daniel's words of affirmation. Early in the relationship, Daniel was finding that it was taking longer for Emma to be sexually interested in him and thought that Emma was less attracted to him. Emma explains that she is attracted to him, but her arousal tends to build in response to how he treats her. One question you may ask yourself to better understand your partner: Do females and males experience sexual arousal differently and if so, how? {{RoundBoxBottom}} Between 1938 to {{g}} 1954, Alfred Kinsey {{ic|Provide an embedded link the Wikipedia article about Kinsey}} produced two reports detailing how biological and social factors influence variations in human sexual desire and activity (Kinsey, 1948; Kinsey, 1953/2010) {{ic|Unless you accessed the originals, these should be secondary citations}}. The reports were designed to establish an empirical foundation to assist future clinicians, educators, and legal authorities concerning what humans actually experience during sexual activities, which was lacking before and during Kinsey's time. {{ic|Has there been any relevant theory or research on this topic in the last ~70 years?}} {{ic|Convert into a paragraph}} Suggestions for why understanding sexual arousal in males and females is important: * Helps understand causes of real world problems such as sexual dysfunction and high risk sexual behaviour (Benson, 2003). * Provides means to explore basic questions about the nature of sexual arousal and how its different components are related to each other (Benson, 2003). * Helps to develop more accurate and inclusive models of human motivation and behaviour. * It informs and guides therapies for various sexual disorders, answering theoretical and physiological questions about human sexual response patterns, providing diagnostic information regarding legally and clinically significant sexual attractions (e.g. attraction to minors and sexual disorders) (Katz et al., 2023). {{RoundBoxTop|theme=4}} '''Focus questions''' * What is sexual arousal? * What factors influence sexual arousal in males and females? * What are the general patterns of female and male sexual arousal? {{ic|Consider adding a question that directly tackles the topic: How do patterns of sexual arousal differ between males and females?}} {{RoundBoxBottom}} == What is sexual arousal? == {{ic|Include an introductory paragraph before branching into sub-sections}} === Meaning of sex - difference between males and females === Sex, in the context of human biology, generally refers to the fundamental categories of human species that are, in the broad sense, concerned with a combination of various biological traits that are unique to a subcategory of human species {{huh}}. There are currently two recognised sexes in humans which are assigned at birth, males and females. Female humans are biologically organised for the production and function of an ova, whereas males refer to humans organised for the production and function of sperm (Ivan et al., 2022; Stévant et al., 2018). === Concept of sexual arousal === [[File:Girl with a Pearl Earring.jpg|thumb|200px|'''Figure 2'''. Painting known as 'girl with the pearl earring' - There are viewers who suggest that this painting has the ability to elicit sexual responses (Pacheco, 2025).]] Sexual arousal refers to the mental and physical response cultivated by subjective stimulation that prepares the body for reproductive behaviour and supports subjective feelings of desire (Calabrò et al., 2019, p. 1; Bramanti & Anastasi, 2019). Sexual arousal is believed to serve as a motivational system for sexual behaviour which are {{g}} likely to be shaped by learned associations, language, and social meanings rather than being determined solely by biological reproductive mechanisms (Roche & Barnes-Holmes, 2002). The general consensus is that there are two fundamental causes for sexual arousal: mental and biological factors. Mental factors are concerned with how the human brain functions to elicit a desire to engage in sexual activity. Biological factors are concerned with how the physical components of the human body function to sexualy arouse the body. {{f}} == The 2 fundamental causes of sexual arousal in humans == {{ic|Include an introductory paragraph before branching into sub-sections}} === Role of Biology === The existence of the human's biological makeup it to allow sexual activity and the feeling of arousal to be expressed and carried out (Lambert Jesse Quicke, 2023) {{aw}}. Hormones, specifically sex hormones, are believed to help control and regulate sexual desire {{f}}. A lack of or too much of a hormone can change how likely the body will encourage sexual activity in the brain {{f}}. One example can be the levels of testosterone in the body and how it can affect a female's capacity to experience sexual arousal. As explored by Davis (2000), it is possible that not having enough testosterone could be the cause for a lack of sexual motivation (see Park & Rissman, 2007 for perspective on whether gonadal hormones relate to male sexual behaviour). Neurotransmitters are the "chemicals" that either incite or deter sexual motivation from the brain. For example, dopamine believed to be the chemicals that increase sexual motivation and assist with the ability to experience an orgasm (Giuliano & Allard, 2001) {{g}}. On the contrary, serotonin is considered a inhibitory chemical such that too much of it can reduce the likelihood a person will experience sexual motivation (Lambert Jesse Quicke, 2023). Further, at the more physical level, the automatic nervous system is believed to have the role of physically preparing the body for sexual activity {{f}}. Examples include, {{g}} increasing blood flow to genital regions to increase sensitivity to prepare for sexual activity (Lambert Jesse Quicke, 2023). === Role of the Mind === As suggested in a study by Klucken et al. (2009), classical conditioning of a person's mind can either encourage or discourage sexual arousal {{example}}. The intensity of sexual arousal can be increased or decreased based on based what a person has learnt about a specific stimuli in the past. In the case of Klucken's study, the participants were encouraged to associate images that would not generally be considered sexually arousing with images that were considered sexually arousing. The study found that the participants that {{g}} managed to associate the two images together were more likely to become sexually aroused from being able to make that connection. This suggests that a person's degree of sexual arousal can be informed by how the person perceives the stimuli that is presented to them {{vague}} (see also, Roche & Barnes-Holmes, 2002). == Patterns of sexual arousal in males and females == [[File:Tor-Arne Moen Natural selection.jpg|thumb|'''Figure 3'''. Male viewing visual stimuli]] As mentioned above, sexual arousal is a process that is driven by a combination of mental and biological processes. In females {{g}} physical arousal typically involves stimulation of female erogenous zones, which include {{g}} clitoris, labia minora, and the vagina itself (Lambert Jesse Quickie, 2023). However, female sexual response patterns are generally determined by stimulation to the mind and arousal is more likely due to external stimulus as opposed to biological processes (Lake Polan etal., 2003). Spape et al., {{g}} (2014) identified that heterosexual females have generally been found to display greater physical arousal to images of erect penises compared to exposed vulvas, indicating that female sexual arousal is {{g}} could be more influenced by signs of sexual readiness and the gender of the stimulus. But Spape's research also suggests {{how}} that females show more gender-nonspecific arousal to general visual stimuli. Chivers (2010) has also suggested that females can experience biological responses showing sexual arousal such as, {{g}} vaginal lubrication and vasocongestion without consciously feeling sexually aroused. Adebisi & Carlson (2024), {{g}} would argue that this response is designed to just prepare the body for potential sexual activity so as to reduce the risk of injury during penetration. According to Sánchez-Pérez et al. (2026), how intensely females experiences sexual arousal can be shaped by the number of times she experiences a {{g}} orgasms. It is suggested that more often females engage in pleasurable sexual activity, tend to experience stronger physical and mental arousal {{f}} {{g}}. This supports the classical conditioning proposed above, that it is possible the frequent practice is connected to feeling more intense pleasure which may likely be interpreted as a reward. {{Robelbox|title=Quiz|theme=12}} <div style="{{Robelbox/pad}}"> <quiz display=simple> {Which of the following best describes the labia minora in the context of the fundamental sources of sexual arousal?: |type="()"} + A physical source, representing a physiological trait capable of causing arousal through tactile and sensory patterns. - An independent motivational system that is entirely unliked from both physical and mental elements. - A conditioned mental source, relies on software and hardware changes via personal experience. {According to research examining how visual stimuli and vible signs of sexual readiness affect psychophysiological responses, which of the following fings was demonstrated regarding heterosexual females: |type="()"} - They exhibit no measurable change in genital response when viewing cisual sexual cues. - The experience identical short-term fluctuations in sexual desire exclusively driven by biological reproductive mechanisms. + They show greater genital arousal to images of erect penises than to images of aroused vulvas. - They display higher subjective sexual arousal only when sexual desire remians entirely constant over time. </quiz> </div> {{Robelbox/close}} When comparing these {{what}} tendencies in females to males, there are some differences and similarities. Unlike females, males demonstrate a significantly higher degree of mind-body concordance {{f}} {{example}}. This suggests that a males {{g}} own feelings of sexual arousal occur together with the physical genital responses (Chivers et al., 2010). Additionally, while females have been shown to have gender-nonspecific arousal to general visual stimuli, male genital and subjective responses have been found to be highly gender-specific and can be predicted based on the males {{g}} sexual orientation (Spape et al., 2014; see also, Slettevold et al.,2019). The effects of how frequently a male engages in sexual activity also differ, while it enhances sexual responses in females, more frequent sexual activity in males does not increase the desire for sexual arousal (Sánchez-Pérez et al., 2026) {{g}} {{f}}. While self-report questionnaires can indicate that males have a higher over tendency to experience sexual arousal, objective biological measurements of unconscious responses show that sexual motivation is inherently quite similar between females and males (Touraille & Agmo, 2024). Male sexual desire is stable and constant compared to females {{f}}. Harris et al. (2023) shows that sexual arousal fluctuates substantially in both sexes, such that male and females experience about similar short-term fluctuations {{expand}}. {{Robelbox|theme=4|title=Quiz}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {How does "mind-body concordance" in sexual arousal differ between females and males according to the above?: |type="()"} - Females show higher mind-body concordance than males. + Males show higher mind-body concordance than females. - Males and Females show identical mind-body concordance. {What do biological measurements reveal about the inherent sexual motivation of males and females? |type="()"} - Males have significantly higher inherent sexual motivation than females. - Females have a significantly higher inherent sexual motivation than males. + Males and females have similar sexual motivation inherently. </quiz> </div> {{Robelbox/close}} == Conclusion == Sexual arousal is driven by both biological and mental factors. Mental and biological factors help regulate and influence the tendency to engage in sexual desire. The above {{aw}} finds that there are similarities and differences in sexual arousal patterns between males and females. Ultimately, understanding these patterns allow for essential insights into human behaviour, motivation, and practical application. ==See also== * [[wikipedia:Sexual_arousal|Sexual arousal]] (Wikipedia) * [[Motivation and emotion/Book/2016/Sexual motivation and hormones|Sexual motivation and hormones]] (Book Chapter, 2016) == References == {{Hanging indent|1= Adebisi, O. Y., & Carlson, K. (2024). Female sexual interest and arousal disorder. In StatPearls. StatPearls Publishing. https://www.ncbi.nlm.nih.gov/books/NBK603746/?report=reader#_NBK603746_pubdet_ Calabrò, R. S., Cacciola, A., Bruschetta, D., Milardi, D., Quattrini, F., Sciarrone, F., Rosa, G., Bramanti, P., & Anastasi, G. (2019). Neuroanatomy and function of human sexual behavior: A neglected or unknown issue? Brain and Behavior, 9(12). https://doi.org/10.1002/brb3.1389 Chivers, M. L. (2017). The specificity of women’s sexual response and its relationship with sexual orientations: A review and ten hypotheses. Archives of Sexual Behavior, 46(5), 1161–1179. https://doi.org/10.1007/s10508-016-0897-x Chivers, M. L., Seto, M. C., Lalumière, M. L., Laan, E., & Grimbos, T. (2010). Agreement of self-reported and genital measures of sexual arousal in men and women: A meta-analysis. Archives of Sexual Behavior, 39(1), 5–56. https://doi.org/10.1007/s10508-009-9556-9 Davis, S. (2000). Testosterone and sexual desire in women. Journal of Sex Education and Therapy, 25(1), 25–32. https://doi.org/10.1080/01614576.2000.11074325 Giuliano, F., & Allard, J. (2001). Dopamine and sexual function. International Journal of Impotence Research, 13(S3), S18–S28. https://doi.org/10.1038/sj.ijir.3900719 Harris, E. A., Hornsey, M. J., Hofmann, W., Jern, P., Murphy, S. C., Hedenborg, F., & Barlow, F. K. (2023). Does sexual desire fluctuate more among women than men? Archives of Sexual Behavior, 52(4). https://doi.org/10.1007/s10508-022-02525-y Ivan, S., Daniela, O., & Jaroslava, B. D. (2022). Sex differences matter: Males and females are equal but not the same. Physiology & Behavior, 259(Volume 259), 114038. https://doi.org/10.1016/j.physbeh.2022.114038 Katz, M., Penniston, T. L., Barry, C., Micanovic, N., Seto, M. C., & Chivers, M. L. (2023). Use of sexual stimuli in research and clinical settings: Expert opinion and recommendations. Sexual Medicine, 11(2). https://doi.org/10.1093/sexmed/qfad012 Kinsey, A. C. (2010). Sexual behavior in the human female. Ishi Press International. (Original work published 1953) Kinsey, A. C. (n.d.). Sexual behavior in the human male. W.B. Saunders Company. (Original work published 1948) Klucken, T., Schweckendiek, J., Merz, C. J., Tabbert, K., Walter, B., Kagerer, S., Vaitl, D., & Stark, R. (2009). Neural activations of the acquisition of conditioned sexual arousal: Effects of contingency awareness and sex. The Journal of Sexual Medicine, 6(11), 3071–3085. https://doi.org/10.1111/j.1743-6109.2009.01405.x Lake Polan, M., Desmond, J. E., Banner, L. L., Pryor, M. R., McCallum, S. W., Atlas, S. W., Glover, G. H., & Arnow, B. A. (2003). Female sexual arousal: A behavioral analysis. Fertility and Sterility, 80(6), 1480–1487. https://doi.org/10.1016/s0015-0282(03)02210-6 Lambert Jesse Quicke, D. (2023). Arousal and its measurement. Female Arousal and Orgasm: Anatomy, Physiology, Behaviour and Evolution, 155–191. https://doi.org/10.2174/9789815124637123010008 Park, J. H., & Rissman, E. F. (2007). The male sexual revolution: Independence from testosterone. Annual Review of Sex Research, 18(1), 23–59. https://doi.org/10.1080/10532528.2007.10559846 Priscille Touraille, & Anders Ågmo. (2024). Sex differences in sexual motivation in humans and other mammals: The role of conscious and unconscious processes. Behavioral Sciences, 14(4), 277–277. https://doi.org/10.3390/bs14040277 Roche, B., & Barnes-Holmes, D. (2002). Human sexual arousal: A modern behavioral approach. The Behavior Analyst Today, 3(2), 145–154. https://doi.org/10.1037/h0099973 Slettevold, E., Holmes, L., Gruia, D., Nyssen, C. P., Watts-Overall, T. M., & Rieger, G. (2019). Bisexual men with bisexual and monosexual genital arousal patterns. Biological Psychology, 148, 107763. https://doi.org/10.1016/j.biopsycho.2019.107763 Spape, J., Timmers, A. D., Yoon, S., Ponseti, J., & Chivers, M. L. (2014). Gender-specific genital and subjective sexual arousal to prepotent sexual features in heterosexual women and men. Biological Psychology, 102, 1–9. https://doi.org/10.1016/j.biopsycho.2014.07.008 Stévant, I., Papaioannou, M. D., & Nef, S. (2018). A brief history of sex determination. Molecular and Cellular Endocrinology, 468, 3–10. https://doi.org/10.1016/j.mce.2018.04.004 Sánchez-Pérez, G. M., Granados, R., Mangas, P., Cervilla, O., & Sierra, J. C. (2026). Validation of masturbation parameters: A laboratory study measuring psychophysiological and subjective sexual arousal. International Journal of Clinical and Health Psychology, 26(1), 100662. https://doi.org/10.1016/j.ijchp.2025.100662 }} == External links == * [https://www.webmd.com/sex/features/sex-drive-how-do-men-women-compare Sex drive: How do men and women compare?] (Webmd.com) * [https://open.spotify.com/episode/41K95dG0MnHux15rtwywMl?si=A4zCgSxSS9KB10REgbA_dg Women's sexual health: desire, arousal, and orgasms, navigating pre-menopause, and enhancing satisfaction] (Spotify.com) * [https://open.spotify.com/episode/2plfCfD98Now1GMjadaKKq?si=XnkE8OvuSrSfJ-v-NQ9K-w Episode 16: what we get wrong about men's sexual desire] (Spotify.com) * [https://www.apa.org/monitor/apr03/arousal Sex: The science of sexual arousal] (apa.org) * [https://digitalwomanaward.com/why-was-the-girl-with-the-pearl-earring-considered-obscene/ Why was the girl with the pearl earring considered obscene?] (digitalwomanaward.com) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Sexual motivation]] [[Category:Motivation and emotion/Book/Gender]] lwisyfugwsg9tz81ojafvkt77rqyhl1 2844863 2844852 2026-11-08T11:55:13Z Davey2010 291715 ([[c:GR|GR]]) [[c:COM:FR|File renamed]]: [[File:ChatGPT Image Aug 18, 2026, 10 10 45 PM.png]] → [[File:Romantic couple surrounded by flowing golden light (ChatGPT).png]] [[c:COM:FR#FR2|Criterion 2]] (meaningless or ambiguous name) 2844863 wikitext text/x-wiki {{title|Sex differences in sexual arousal patterns:<br>How do patterns of sexual arousal differ between males and females?}} __TOC__ == Overview == {{RoundBoxTop|theme=4}} [[File:Romantic couple surrounded by flowing golden light (ChatGPT).png|right|thumb|150px|'''Figure 1'''. An image depicting sexual arousal between a female and male human being]] ;Scenario Emma and Daniel have been dating for several months {{g}} they are attracted to each other but their sexual desires emerge differently. Daniel is often aroused by Emma at the simple sight of her. Emma tends to be aroused by Daniel's words of affirmation. Early in the relationship, Daniel was finding that it was taking longer for Emma to be sexually interested in him and thought that Emma was less attracted to him. Emma explains that she is attracted to him, but her arousal tends to build in response to how he treats her. One question you may ask yourself to better understand your partner: Do females and males experience sexual arousal differently and if so, how? {{RoundBoxBottom}} Between 1938 to {{g}} 1954, Alfred Kinsey {{ic|Provide an embedded link the Wikipedia article about Kinsey}} produced two reports detailing how biological and social factors influence variations in human sexual desire and activity (Kinsey, 1948; Kinsey, 1953/2010) {{ic|Unless you accessed the originals, these should be secondary citations}}. The reports were designed to establish an empirical foundation to assist future clinicians, educators, and legal authorities concerning what humans actually experience during sexual activities, which was lacking before and during Kinsey's time. {{ic|Has there been any relevant theory or research on this topic in the last ~70 years?}} {{ic|Convert into a paragraph}} Suggestions for why understanding sexual arousal in males and females is important: * Helps understand causes of real world problems such as sexual dysfunction and high risk sexual behaviour (Benson, 2003). * Provides means to explore basic questions about the nature of sexual arousal and how its different components are related to each other (Benson, 2003). * Helps to develop more accurate and inclusive models of human motivation and behaviour. * It informs and guides therapies for various sexual disorders, answering theoretical and physiological questions about human sexual response patterns, providing diagnostic information regarding legally and clinically significant sexual attractions (e.g. attraction to minors and sexual disorders) (Katz et al., 2023). {{RoundBoxTop|theme=4}} '''Focus questions''' * What is sexual arousal? * What factors influence sexual arousal in males and females? * What are the general patterns of female and male sexual arousal? {{ic|Consider adding a question that directly tackles the topic: How do patterns of sexual arousal differ between males and females?}} {{RoundBoxBottom}} == What is sexual arousal? == {{ic|Include an introductory paragraph before branching into sub-sections}} === Meaning of sex - difference between males and females === Sex, in the context of human biology, generally refers to the fundamental categories of human species that are, in the broad sense, concerned with a combination of various biological traits that are unique to a subcategory of human species {{huh}}. There are currently two recognised sexes in humans which are assigned at birth, males and females. Female humans are biologically organised for the production and function of an ova, whereas males refer to humans organised for the production and function of sperm (Ivan et al., 2022; Stévant et al., 2018). === Concept of sexual arousal === [[File:Girl with a Pearl Earring.jpg|thumb|200px|'''Figure 2'''. Painting known as 'girl with the pearl earring' - There are viewers who suggest that this painting has the ability to elicit sexual responses (Pacheco, 2025).]] Sexual arousal refers to the mental and physical response cultivated by subjective stimulation that prepares the body for reproductive behaviour and supports subjective feelings of desire (Calabrò et al., 2019, p. 1; Bramanti & Anastasi, 2019). Sexual arousal is believed to serve as a motivational system for sexual behaviour which are {{g}} likely to be shaped by learned associations, language, and social meanings rather than being determined solely by biological reproductive mechanisms (Roche & Barnes-Holmes, 2002). The general consensus is that there are two fundamental causes for sexual arousal: mental and biological factors. Mental factors are concerned with how the human brain functions to elicit a desire to engage in sexual activity. Biological factors are concerned with how the physical components of the human body function to sexualy arouse the body. {{f}} == The 2 fundamental causes of sexual arousal in humans == {{ic|Include an introductory paragraph before branching into sub-sections}} === Role of Biology === The existence of the human's biological makeup it to allow sexual activity and the feeling of arousal to be expressed and carried out (Lambert Jesse Quicke, 2023) {{aw}}. Hormones, specifically sex hormones, are believed to help control and regulate sexual desire {{f}}. A lack of or too much of a hormone can change how likely the body will encourage sexual activity in the brain {{f}}. One example can be the levels of testosterone in the body and how it can affect a female's capacity to experience sexual arousal. As explored by Davis (2000), it is possible that not having enough testosterone could be the cause for a lack of sexual motivation (see Park & Rissman, 2007 for perspective on whether gonadal hormones relate to male sexual behaviour). Neurotransmitters are the "chemicals" that either incite or deter sexual motivation from the brain. For example, dopamine believed to be the chemicals that increase sexual motivation and assist with the ability to experience an orgasm (Giuliano & Allard, 2001) {{g}}. On the contrary, serotonin is considered a inhibitory chemical such that too much of it can reduce the likelihood a person will experience sexual motivation (Lambert Jesse Quicke, 2023). Further, at the more physical level, the automatic nervous system is believed to have the role of physically preparing the body for sexual activity {{f}}. Examples include, {{g}} increasing blood flow to genital regions to increase sensitivity to prepare for sexual activity (Lambert Jesse Quicke, 2023). === Role of the Mind === As suggested in a study by Klucken et al. (2009), classical conditioning of a person's mind can either encourage or discourage sexual arousal {{example}}. The intensity of sexual arousal can be increased or decreased based on based what a person has learnt about a specific stimuli in the past. In the case of Klucken's study, the participants were encouraged to associate images that would not generally be considered sexually arousing with images that were considered sexually arousing. The study found that the participants that {{g}} managed to associate the two images together were more likely to become sexually aroused from being able to make that connection. This suggests that a person's degree of sexual arousal can be informed by how the person perceives the stimuli that is presented to them {{vague}} (see also, Roche & Barnes-Holmes, 2002). == Patterns of sexual arousal in males and females == [[File:Tor-Arne Moen Natural selection.jpg|thumb|'''Figure 3'''. Male viewing visual stimuli]] As mentioned above, sexual arousal is a process that is driven by a combination of mental and biological processes. In females {{g}} physical arousal typically involves stimulation of female erogenous zones, which include {{g}} clitoris, labia minora, and the vagina itself (Lambert Jesse Quickie, 2023). However, female sexual response patterns are generally determined by stimulation to the mind and arousal is more likely due to external stimulus as opposed to biological processes (Lake Polan etal., 2003). Spape et al., {{g}} (2014) identified that heterosexual females have generally been found to display greater physical arousal to images of erect penises compared to exposed vulvas, indicating that female sexual arousal is {{g}} could be more influenced by signs of sexual readiness and the gender of the stimulus. But Spape's research also suggests {{how}} that females show more gender-nonspecific arousal to general visual stimuli. Chivers (2010) has also suggested that females can experience biological responses showing sexual arousal such as, {{g}} vaginal lubrication and vasocongestion without consciously feeling sexually aroused. Adebisi & Carlson (2024), {{g}} would argue that this response is designed to just prepare the body for potential sexual activity so as to reduce the risk of injury during penetration. According to Sánchez-Pérez et al. (2026), how intensely females experiences sexual arousal can be shaped by the number of times she experiences a {{g}} orgasms. It is suggested that more often females engage in pleasurable sexual activity, tend to experience stronger physical and mental arousal {{f}} {{g}}. This supports the classical conditioning proposed above, that it is possible the frequent practice is connected to feeling more intense pleasure which may likely be interpreted as a reward. {{Robelbox|title=Quiz|theme=12}} <div style="{{Robelbox/pad}}"> <quiz display=simple> {Which of the following best describes the labia minora in the context of the fundamental sources of sexual arousal?: |type="()"} + A physical source, representing a physiological trait capable of causing arousal through tactile and sensory patterns. - An independent motivational system that is entirely unliked from both physical and mental elements. - A conditioned mental source, relies on software and hardware changes via personal experience. {According to research examining how visual stimuli and vible signs of sexual readiness affect psychophysiological responses, which of the following fings was demonstrated regarding heterosexual females: |type="()"} - They exhibit no measurable change in genital response when viewing cisual sexual cues. - The experience identical short-term fluctuations in sexual desire exclusively driven by biological reproductive mechanisms. + They show greater genital arousal to images of erect penises than to images of aroused vulvas. - They display higher subjective sexual arousal only when sexual desire remians entirely constant over time. </quiz> </div> {{Robelbox/close}} When comparing these {{what}} tendencies in females to males, there are some differences and similarities. Unlike females, males demonstrate a significantly higher degree of mind-body concordance {{f}} {{example}}. This suggests that a males {{g}} own feelings of sexual arousal occur together with the physical genital responses (Chivers et al., 2010). Additionally, while females have been shown to have gender-nonspecific arousal to general visual stimuli, male genital and subjective responses have been found to be highly gender-specific and can be predicted based on the males {{g}} sexual orientation (Spape et al., 2014; see also, Slettevold et al.,2019). The effects of how frequently a male engages in sexual activity also differ, while it enhances sexual responses in females, more frequent sexual activity in males does not increase the desire for sexual arousal (Sánchez-Pérez et al., 2026) {{g}} {{f}}. While self-report questionnaires can indicate that males have a higher over tendency to experience sexual arousal, objective biological measurements of unconscious responses show that sexual motivation is inherently quite similar between females and males (Touraille & Agmo, 2024). Male sexual desire is stable and constant compared to females {{f}}. Harris et al. (2023) shows that sexual arousal fluctuates substantially in both sexes, such that male and females experience about similar short-term fluctuations {{expand}}. {{Robelbox|theme=4|title=Quiz}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {How does "mind-body concordance" in sexual arousal differ between females and males according to the above?: |type="()"} - Females show higher mind-body concordance than males. + Males show higher mind-body concordance than females. - Males and Females show identical mind-body concordance. {What do biological measurements reveal about the inherent sexual motivation of males and females? |type="()"} - Males have significantly higher inherent sexual motivation than females. - Females have a significantly higher inherent sexual motivation than males. + Males and females have similar sexual motivation inherently. </quiz> </div> {{Robelbox/close}} == Conclusion == Sexual arousal is driven by both biological and mental factors. Mental and biological factors help regulate and influence the tendency to engage in sexual desire. The above {{aw}} finds that there are similarities and differences in sexual arousal patterns between males and females. Ultimately, understanding these patterns allow for essential insights into human behaviour, motivation, and practical application. ==See also== * [[wikipedia:Sexual_arousal|Sexual arousal]] (Wikipedia) * [[Motivation and emotion/Book/2016/Sexual motivation and hormones|Sexual motivation and hormones]] (Book Chapter, 2016) == References == {{Hanging indent|1= Adebisi, O. Y., & Carlson, K. (2024). Female sexual interest and arousal disorder. In StatPearls. StatPearls Publishing. https://www.ncbi.nlm.nih.gov/books/NBK603746/?report=reader#_NBK603746_pubdet_ Calabrò, R. S., Cacciola, A., Bruschetta, D., Milardi, D., Quattrini, F., Sciarrone, F., Rosa, G., Bramanti, P., & Anastasi, G. (2019). Neuroanatomy and function of human sexual behavior: A neglected or unknown issue? Brain and Behavior, 9(12). https://doi.org/10.1002/brb3.1389 Chivers, M. L. (2017). The specificity of women’s sexual response and its relationship with sexual orientations: A review and ten hypotheses. Archives of Sexual Behavior, 46(5), 1161–1179. https://doi.org/10.1007/s10508-016-0897-x Chivers, M. L., Seto, M. C., Lalumière, M. L., Laan, E., & Grimbos, T. (2010). Agreement of self-reported and genital measures of sexual arousal in men and women: A meta-analysis. Archives of Sexual Behavior, 39(1), 5–56. https://doi.org/10.1007/s10508-009-9556-9 Davis, S. (2000). Testosterone and sexual desire in women. Journal of Sex Education and Therapy, 25(1), 25–32. https://doi.org/10.1080/01614576.2000.11074325 Giuliano, F., & Allard, J. (2001). Dopamine and sexual function. International Journal of Impotence Research, 13(S3), S18–S28. https://doi.org/10.1038/sj.ijir.3900719 Harris, E. A., Hornsey, M. J., Hofmann, W., Jern, P., Murphy, S. C., Hedenborg, F., & Barlow, F. K. (2023). Does sexual desire fluctuate more among women than men? Archives of Sexual Behavior, 52(4). https://doi.org/10.1007/s10508-022-02525-y Ivan, S., Daniela, O., & Jaroslava, B. D. (2022). Sex differences matter: Males and females are equal but not the same. Physiology & Behavior, 259(Volume 259), 114038. https://doi.org/10.1016/j.physbeh.2022.114038 Katz, M., Penniston, T. L., Barry, C., Micanovic, N., Seto, M. C., & Chivers, M. L. (2023). Use of sexual stimuli in research and clinical settings: Expert opinion and recommendations. Sexual Medicine, 11(2). https://doi.org/10.1093/sexmed/qfad012 Kinsey, A. C. (2010). Sexual behavior in the human female. Ishi Press International. (Original work published 1953) Kinsey, A. C. (n.d.). Sexual behavior in the human male. W.B. Saunders Company. (Original work published 1948) Klucken, T., Schweckendiek, J., Merz, C. J., Tabbert, K., Walter, B., Kagerer, S., Vaitl, D., & Stark, R. (2009). Neural activations of the acquisition of conditioned sexual arousal: Effects of contingency awareness and sex. The Journal of Sexual Medicine, 6(11), 3071–3085. https://doi.org/10.1111/j.1743-6109.2009.01405.x Lake Polan, M., Desmond, J. E., Banner, L. L., Pryor, M. R., McCallum, S. W., Atlas, S. W., Glover, G. H., & Arnow, B. A. (2003). Female sexual arousal: A behavioral analysis. Fertility and Sterility, 80(6), 1480–1487. https://doi.org/10.1016/s0015-0282(03)02210-6 Lambert Jesse Quicke, D. (2023). Arousal and its measurement. Female Arousal and Orgasm: Anatomy, Physiology, Behaviour and Evolution, 155–191. https://doi.org/10.2174/9789815124637123010008 Park, J. H., & Rissman, E. F. (2007). The male sexual revolution: Independence from testosterone. Annual Review of Sex Research, 18(1), 23–59. https://doi.org/10.1080/10532528.2007.10559846 Priscille Touraille, & Anders Ågmo. (2024). Sex differences in sexual motivation in humans and other mammals: The role of conscious and unconscious processes. Behavioral Sciences, 14(4), 277–277. https://doi.org/10.3390/bs14040277 Roche, B., & Barnes-Holmes, D. (2002). Human sexual arousal: A modern behavioral approach. The Behavior Analyst Today, 3(2), 145–154. https://doi.org/10.1037/h0099973 Slettevold, E., Holmes, L., Gruia, D., Nyssen, C. P., Watts-Overall, T. M., & Rieger, G. (2019). Bisexual men with bisexual and monosexual genital arousal patterns. Biological Psychology, 148, 107763. https://doi.org/10.1016/j.biopsycho.2019.107763 Spape, J., Timmers, A. D., Yoon, S., Ponseti, J., & Chivers, M. L. (2014). Gender-specific genital and subjective sexual arousal to prepotent sexual features in heterosexual women and men. Biological Psychology, 102, 1–9. https://doi.org/10.1016/j.biopsycho.2014.07.008 Stévant, I., Papaioannou, M. D., & Nef, S. (2018). A brief history of sex determination. Molecular and Cellular Endocrinology, 468, 3–10. https://doi.org/10.1016/j.mce.2018.04.004 Sánchez-Pérez, G. M., Granados, R., Mangas, P., Cervilla, O., & Sierra, J. C. (2026). Validation of masturbation parameters: A laboratory study measuring psychophysiological and subjective sexual arousal. International Journal of Clinical and Health Psychology, 26(1), 100662. https://doi.org/10.1016/j.ijchp.2025.100662 }} == External links == * [https://www.webmd.com/sex/features/sex-drive-how-do-men-women-compare Sex drive: How do men and women compare?] (Webmd.com) * [https://open.spotify.com/episode/41K95dG0MnHux15rtwywMl?si=A4zCgSxSS9KB10REgbA_dg Women's sexual health: desire, arousal, and orgasms, navigating pre-menopause, and enhancing satisfaction] (Spotify.com) * [https://open.spotify.com/episode/2plfCfD98Now1GMjadaKKq?si=XnkE8OvuSrSfJ-v-NQ9K-w Episode 16: what we get wrong about men's sexual desire] (Spotify.com) * [https://www.apa.org/monitor/apr03/arousal Sex: The science of sexual arousal] (apa.org) * [https://digitalwomanaward.com/why-was-the-girl-with-the-pearl-earring-considered-obscene/ Why was the girl with the pearl earring considered obscene?] (digitalwomanaward.com) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Sexual motivation]] [[Category:Motivation and emotion/Book/Gender]] car99l9nanxokzihi3voyj1e1pbe6o4 0 331034 2844845 2839848 2026-11-08T02:13:37Z Jtneill 10242 Copyediting 2844845 wikitext text/x-wiki {{title|Perfectionism and procrastination:<br>What is the role of perfectionism in procrastination and what can be done about it?}} __TOC__ ==Overview== {{RoundBoxTop|theme=9}} [[File:The procrastinating student - panoramio.jpg|right|thumb|150px|'''Figure 1'''. Waiting for the perfect moment]] '''Scenario''' Brian has been trying for several days to start preparing an important presentation for an upcoming meeting. He is convinced that he must deliver a flawless presentation - think everything through and execute everything perfectly {{g}}. He’s long had a clear picture in his mind of what the presentation should be like, but some kind of inner resistance keeps making him put off getting started. He glances through the materials, then switches to other tasks, as if waiting for the moment when he’ll finally feel completely ready. But that moment never comes. {{RoundBoxBottom}} In a world where success and high achievement are highly valued, it is paradoxical that individuals who attach great importance to these goals may nonetheless refrain from action or engage in task avoidance (Flett et al., 1995). This paradox highlights the relationship between two psychological constructs: [[wikipedia:Perfectionism_(psychology)|perfectionism]] and [[wikipedia:Procrastination|procrastination]] (Sirois et al., 2017). Although they do not necessarily co-occur, empirical research indicates that some links exist between them (Sirois et al., 2017). Understanding which possible mechanisms underlie the relationship between perfectionism and procrastination may help identify ways to overcome procrastination and achieve intended goals (Wang et al., 2024). {{RoundBoxTop|theme=3}} '''Focus questions''' * What are the main characteristics of perfectionism and procrastination? * What is the relationship between perfectionism and procrastination? * What dimensions of perfectionism contribute to procrastination? * How can we reduce procrastination and the negative effects of perfectionism? {{RoundBoxBottom}} == Perfectionism and Procrastination == '''Perfectionism and procrastination''' are complex psychological constructs that may be closely related but differ in their nature and manifestations. Perfectionism primarily refers to personality traits and attitudes, whereas procrastination manifests itself primarily as a pattern of behaviour (Akpur & Yurtseven, 2019, Husain et al., 2025) Although '''perfectionism''' is generally perceived as the pursuit of excellence and a desire to do everything perfectly, in psychology it is regarded as a multidimensional construct. In the academic literature, perfectionism is defined as the pursuit of flawlessness, the setting of extremely high standards, and a tendency to evaluate one’s own behaviour critically (Sirois, 2017; Stoeber, 2018). As scientific understanding has evolved, researchers have proposed a range of models, from unidimensional approaches to multidimensional models with two, three, or six dimensions (Stoeber & Otto, 2006). In their review of decades of research, Stoeber and Otto (2006) identified two core dimensions of perfectionism: perfectionistic strivings and perfectionistic concerns. This two-dimensional model will serve as the primary conceptual framework for this chapter: * '''Perfectionistic strivings''' involve setting high personal standards and pursuing excellence. This dimension is often viewed as relatively adaptive because it is associated with high motivation and goal achievement (Stoeber, 2018). * '''Perfectionistic concerns''' involve fear of making mistakes and receiving negative criticism, excessive self-criticism, and an inability to derive satisfaction from one’s achievements. This dimension is generally regarded as maladaptive because it is associated with negative outcomes and difficulties in self-regulation (Gade et al., 2017; Sirois, 2017). {{RoundBoxTop|theme=9}} '''Scenario continued''' Time passes, and the day of the presentation draws closer. Brian returns to his presentation materials increasingly often, even drawing up several versions of an outline, but each time he finds flaws and starts again. From time to time, he imagines the people attending the meeting and the questions they might ask. He then begins searching for additional information, trying to rule out any possibility of error in advance. He feels that if the presentation is not convincing, others will begin to doubt his competence. Preparing for it increasingly feels like a test of his own abilities. Brian switches to familiar tasks that he feels more confident handling, but then his thoughts return to the presentation. Time is running out. {{RoundBoxBottom}} {{Robelbox|left|alt=|theme=6|title=Learning checkpoint |icon=Emblem-question-yellow.svg|iconwidth=48px}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {Brian is putting off preparing a presentation. He thinks, “If I make a mistake, the people at the meeting will think I’m incompetent.” Which dimension of perfectionism does this thought illustrate?} -Perfectionistic strivings +Perfectionistic concerns </quiz> </div> {{Robelbox/close}} '''Procrastination''' While examining the characteristics of perfectionism reveals the psychological experiences associated with striving for perfection and fearing failure to meet high standards, analysing procrastination can shed light on the difficulties that arise when translating intentions into action. A key characteristic of procrastination is the discrepancy between intending to perform an action and delaying it despite awareness of the negative consequences (Steel, 2007). However, not every delay constitutes procrastination. Steel (2007) emphasises that, even when an intention exists, objective circumstances may prevent task completion and require priorities to be reconsidered. Procrastination therefore refers specifically to the unwarranted delay of an intended action despite foreseeable negative consequences. It is associated with task aversiveness, impulsivity, low self-efficacy, and a longer delay before the anticipated outcome is obtained (Steel, 2007). The role of these factors can be examined within the framework of temporal motivation theory (Steel, 2007). According to this model, motivation to act depends on the expectancy of success, the value of the outcome, the delay before it is obtained, and impulsivity. The greater the likelihood of success and the subjective value of the outcome, the stronger the motivation to act. However, as the delay before the anticipated outcome increases, motivation weakens, particularly when impulsivity is high. Consequently, a person may favour an activity that provides immediate pleasure and postpone the planned action. As the deadline approaches, motivation may increase. Procrastination can affect various domains of activity, including study, work, everyday responsibilities, health-related behaviour, leisure, relationships with loved ones, and interactions with other people (Klingsieck, 2013, as cited in Kurtovic, 2019).<gallery> </gallery> '''Table 1.''' Domains of procrastination and their characteristics (Klingsieck, 2013, as cited in Kurtovic, 2019) {| class="wikitable" |+ !'''Domain''' !'''Description''' |- |Academic procrastination |Delaying academic assignments, exam preparation, and writing academic papers. |- |Workplace procrastination |Postponing important work tasks, meetings, reports, and phone calls. |- |Health procrastination |Postponing medical appointments, health check-ups, treatment, or health-promoting behaviours |- |Decision procrastination |Postponing or avoiding important decisions. |} == How perfectionism relates to procrastination: a motivational perspective == '''Perfectionism and procrastination: the role of perfectionistic concerns and strivings''' Empirical evidence on the relationship between perfectionism and procrastination is mixed: Steel’s (2007) meta-analysis did not identify a strong relationship between them, whereas later studies have reported both positive and negative correlations (Wang et al., 2024). This inconsistency can be partly explained by distinguishing between two dimensions of perfectionism. According to the meta-analysis by Sirois et al. (2017), perfectionistic concerns, which include fear of mistakes and negative evaluation, are positively associated with procrastination, whereas perfectionistic strivings, characterised by high personal standards, show a weak negative association with it. Thus, the nature of the relationship between perfectionism and procrastination depends on the dimension under consideration: the tendency to delay tasks is primarily associated with perfectionistic concerns (Sirois et al., 2017). '''Procrastination as an emotion regulation strategy''' One explanation for the relationship between perfectionistic concerns and procrastination is provided by the emotion regulation model. This model views procrastination as a way of avoiding unpleasant feelings: postponing an anxiety-provoking task provides temporary relief but does not resolve the task and may subsequently intensify negative emotional states (Sirois & Pychyl, 2013). Tice et al. (2001) take a similar position, describing procrastination as a mood improvement strategy in the presence of psychological distress (as cited in Wang et al., 2024). Applied to perfectionistic concerns, the model suggests that a task associated with fear of evaluation elicits anxiety, and that postponing it becomes reinforced as an avoidance behaviour. However, the model does not explain why the same task does not elicit anxiety in everyone, highlighting the need to consider motivational factors. '''Motivation strength: temporal motivation theory''' '''[[Motivation and emotion/Book/2024/Temporal motivation theory|Temporal motivation theory]]''' may serve as a starting point for examining the motivational mechanisms of procrastination. According to this theory, the strength of motivation is determined by expectancy of '''success''', '''outcome value''', '''delay''', and '''impulsiveness''' (Steel, 2007). The greater the value of the outcome and the closer the reward, the stronger the motivation. When the immediate reward offered by another activity is more motivating than the outcome of the task, a person may choose that activity instead (Steel, 2007). '''Motivation quality: a self-determination perspective''' However, as Wang et al. (2024) note, research has primarily focused on the strength of motivation, paying less attention to its quality. Drawing on '''[[wikipedia:Self-determination_theory|self-determination theory]]''', Grund and Fries (2018) emphasise the importance of both the strength and the quality of motivation - that is, the extent to which people perceive their actions as voluntary and consistent with their own interests and values. According to '''self-determination theory''', '''autonomous motivation''' is supported by the satisfaction of three basic psychological needs: '''autonomy, competence, and relatedness''' (Deci & Ryan, 2000): * '''Autonomy''' involves a sense of volition and internal endorsement of one’s actions; * '''Competence''' involves feeling capable of successfully managing tasks; and * '''Relatedness''' involves feelings of closeness, belonging, and acceptance in relationships with others. '''Self-determination theory''' distinguishes between forms of behavioural regulation that differ in their degree of autonomy (Deci & Ryan, 2000). '''External regulation''' involves acting to obtain rewards or avoid punishment. Under '''introjected regulation''', behaviour is driven by internal pressure, such as the desire to avoid guilt and shame or to affirm one’s self-worth. '''Identified regulation''' involves recognising and accepting the personal importance of an action, whereas '''integrated regulation''' involves bringing that importance into alignment with other values and aspects of the self (Deci & Ryan, 2000; Grund & Fries, 2018). '''Intrinsic motivation''' involves engaging in an activity for the interest and enjoyment inherent in the activity itself. Wang et al. (2024) group these forms into two types: autonomous motivation includes intrinsic motivation, identified regulation, and integrated regulation, while controlled motivation includes external and introjected regulation. Distinguishing between autonomous and controlled motivation makes it possible to examine how people’s reasons for performing a task relate to their tendency to postpone it (Wang et al., 2024). For example, academic procrastination was higher among students with lower intrinsic motivation and higher external regulation (Senécal et al., 1995, as cited in Grund & Fries, 2018). An association between autonomous motivation and less procrastination has also been found in other studies (Koestner et al., 2008; Senécal & Guay, 2000, as cited in Wang et al., 2024). Consistent findings have emerged from research on persistence: Sheldon and Elliot (1998) found that a sense of freely choosing one’s goals predicted sustained effort, whereas controlled forms of motivation did not contribute to goal attainment (as cited in Grund & Fries, 2018). Drawing on this evidence, Grund and Fries (2018) suggest that procrastination is not solely a failure of self-regulation but may also reflect a mismatch between a goal and a person’s values and needs. '''Motivational and emotional pathways linking perfectionism to procrastination''' In the context of perfectionism, '''the quality of motivation''' helps explain why its two dimensions—perfectionistic concerns and perfectionistic strivings - differ in their associations with procrastination. Perfectionistic concerns involve a perceived need to meet external standards and avoid criticism, which may be experienced as internal and external pressure, giving motivation a controlled character (Hewitt & Flett, 1991, as cited in Wang et al., 2024). Wang et al. (2024) examined the relationships between perfectionism, motivation quality, and procrastination in a three-wave study of 376 employees. Perfectionism and performance pressure were measured at the first wave; autonomous and controlled motivation and psychological distress were measured two weeks later; and procrastination was measured after a further two weeks. The authors examined how the combination of perfectionistic strivings and perfectionistic concerns related to procrastination and through which processes this relationship operated. The findings indicated that the relationship could be explained by two processes: autonomous motivation - acting because the activity is personally important- and psychological distress, including anxiety and tension (Wang et al., 2024). Autonomous motivation was associated with less procrastination, whereas distress was associated with more procrastination. Controlled motivation played a smaller role in explaining the relationship between perfectionism and procrastination (Wang et al., 2024). Thus, the findings of Wang et al. (2024) indicate the importance of considering motivational and emotional mechanisms together. In explaining the emotional pathway, the authors suggest that obstacles to the satisfaction of basic psychological needs may prompt people to seek short-term relief, including through task avoidance, even when this conflicts with their long-term goals. The authors also interpret their findings in relation to the idea of '''“effortless” self-regulation''', which involves reducing the conflict between long-term goals and immediate desires, rather than merely suppressing temptations once they have arisen (Fujita, 2011, as cited in Wang et al., 2024). To support this interpretation, they cite earlier studies linking autonomous motivation and favourable emotional states to weaker temptations to become distracted (Wang et al., 2024). Overall, the relationship between perfectionism and procrastination is complex and depends on the levels of perfectionistic concerns and perfectionistic strivings (Sirois et al., 2017). It may also be explained by motivation quality and emotional state (Wang et al., 2024). == Approaches to addressing perfectionism-related procrastination == '''Therapeutic interventions''' Meta-analyses {{ic|about what?}} {{ic|how many studies?}} by Rozental and colleagues (2018) and van Eerde and Klingsieck (2018) indicate that cognitive behavioural therapy (CBT) is {{how}} effective in reducing procrastination. Van Eerde and Klingsieck also found that CBT had a greater effect than the other approaches examined. CBT involves identifying and modifying dysfunctional thoughts, then helping individuals put new ways of thinking into practice through their behaviour. {{ic|explain whether CBT works be reducing perfectionalistic concerns or some other mechanisms}} '''Self-help strategies''' Procrastination may be associated with various factors, so there is no single solution that works for everyone. First, it is important to understand what is happening when someone puts off a task: sometimes they need a break, while at other times they may be trying to avoid unpleasant feelings (Sirois & Pychyl, 2013). If procrastination is linked to attempts to avoid negative feelings, it can be helpful to explore those feelings rather than rely solely on willpower. Sirois (2022) recommends approaching procrastination with compassion and without judgement. Other practical strategies include breaking work down into small steps and focusing on the next action rather than a perfect outcome (Sirois, 2022). ==Conclusion== * Perfectionism is more than simply striving to do everything perfectly. It is a multidimensional personality trait with two main dimensions: perfectionistic strivings (the pursuit of high standards) and perfectionistic concerns (fear of mistakes and negative evaluation) (Stoeber & Otto, 2006). * Procrastination is the unnecessary delay of an intended action despite awareness of its potential negative consequences. Not every delay is procrastination (Steel, 2007). * The relationship between perfectionism and procrastination is neither simple nor clear-cut. Some studies have found a positive association, others a negative association, and still others no association at all (Wang et al., 2024). Steel’s (2007) meta-analysis also found no substantial association. The findings depend on which dimension of perfectionism is examined. * Perfectionistic concerns are positively associated with procrastination, whereas perfectionistic strivings show a weak negative association with it (Sirois et al., 2017). In other words, procrastination is more closely associated with fear of mistakes and evaluation than with the pursuit of high standards. * Differences between the two dimensions can be explained in terms of the quality of motivation: what matters is not only how strongly a person is motivated, but also why they act (Grund & Fries, 2018). * To reduce procrastination, the first step is to understand why tasks are being put off (Sirois, 2022; Grund & Fries, 2018), and then to select an approach that addresses that particular reason. * Among therapeutic approaches, cognitive behavioural therapy has received the strongest empirical support (vanEerde & Klingsieck, 2018; Rozental et al., 2018) ==See also== * [[Motivation and emotion/Book/2022/Perfectionism|Perfectionism]] (Book chapter, 2022) * [[Motivation and emotion/Book/2015/Procrastination, moods, and emotion|Procrastination, moods, and emotion]] (Book chapter, 2015) ==References == {{Hanging indent|1= Akpur, U., & Yurtseven, N. (2019). Structural Relationships between Academic Motivation, Procrastination and Perfectionism: A Modelling Study. Cumhuriyet International Journal of Education, 8(1), 106–123. https://doi.org/10.30703/cije.452633 Flett, G. L., Hewitt, P. L., & Martin, T. R. (1995). Dimensions of perfectionism and procrastination. In J. R. Ferrari, J. L. Johnson, & W. G. McCown (Eds.), Procrastination and task avoidance: Theory, research, and treatment (pp. 113–136). Plenum Press. https://doi.org/10.1007/978-1-4899-0227-6_6 Gäde, J. C., Schermelleh-Engel, K., & Klein, A. G. (2017). Disentangling the common variance of perfectionistic strivings and perfectionistic concerns: A bifactor model of perfectionism. Frontiers in Psychology, 8, Article 160. https://doi.org/10.3389/fpsyg.2017.00160 Grund, A., & Fries, S. (2018). Understanding procrastination: A motivational approach. Personality and Individual Differences, 121, 120–130. https://doi.org/10.1016/j.paid.2017.09.035 Husain, W., Trabelsi, K., Ammar, A., Saif, Z., & Jahrami, H. (2025). The development and validation of a one-off scale to measure procrastination and precrastination traits in young adults. BMC Psychology, 13(1), Article 773. https://doi.org/10.1186/s40359-025-03072-6 Kurtovic, A., Vrdoljak, G., & Idzanovic, A. (2019). Predicting procrastination: The role of academic achievement, self-efficacy and perfectionism. International Journal of Educational Psychology, 8(1), 1–26. https://doi.org/10.17583/ijep.2019.2993 Rozental, A., Bennett, S., Forsström, D., Ebert, D. D., Shafran, R., Andersson, G., & Carlbring, P. (2018). Targeting procrastination using psychological treatments: A systematic review and meta-analysis. Frontiers in Psychology, 9, Article 1588. https://doi.org/10.3389/fpsyg.2018.01588 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68 Sirois, F. M. (2022). Procrastination: What it is, why it's a problem, and what you can do about it. American Psychological Association. https://doi.org/10.1037/0003-066X Sirois, F. M., Molnar, D. S., & Hirsch, J. K. (2017). A meta-analytic and conceptual update on the associations between procrastination and multidimensional perfectionism. European Journal of Personality, 31(2), 137–159. https://doi.org/10.1002/per.2098 Sirois, F., & Pychyl, T. (2013). Procrastination and the priority of short-term mood regulation: Consequences for future self. Social and Personality Psychology Compass, 7(2), 115–127. https://doi.org/10.1111/spc3.12011 Steel, P. (2007). The nature of procrastination: A meta-analytic and theoretical review of quintessential self-regulatory failure. Psychological Bulletin, 133(1), 65–94. https://doi.org/10.1037/0033-2909.133.1.65 Stoeber, J., Damian, L. E., & Madigan, D. J. (2018). Perfectionism: A motivational perspective. In J. Stoeber (Ed.), The psychology of perfectionism: Theory, research, applications (pp. 19–43). Routledge. https://doi.org/10.4324/9781315536255-2 van Eerde, W., & Klingsieck, K. B. (2018). Overcoming procrastination? A meta-analysis of intervention studies. Educational Research Review, 25, 73–85. https://doi.org/10.1016/j.edurev.2018.09.002 Wang, X., Howard, J. L., & Zhong, L. (2024). Why do perfectionists procrastinate (or not)? Exploring the interaction between perfectionism dimensions through self-determination theory. Applied Psychology, 74(1), Article e12586. https://doi.org/10.1111/apps.12563 }} ==External links== {{ic|Use bullet-points as shown in Tutorial 2}} 1. [https://www.oneyoufeed.net/procrastinator/ Being a Procrastinator with Tim Pychyl] 2. [https://www.youtube.com/watch?v=lFG1b1-EsW8 Our dangerous obsession with perfectionism is getting worse | Thomas Curran] 3. [https://www.apa.org/gradpsych/2010/01/procrastination Procrastination or 'intentional delay'?] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Perfectionism]] [[Category:Motivation and emotion/Book/Procrastination]] 1vo8o7pr73ep9wssl12v4uo5e8mankn 2 331036 2844826 2844312 2026-11-07T19:19:46Z BLANDINO Massimiliano 3106750 /* 3.3 On-Shell Action and Resonance at R = \pi */ 2844826 wikitext text/x-wiki __INDEX__ {{Research project | title = First-Principles Derivation of the Fine-Structure Constant: Fano Plane Symmetries, Lagrangian Duality, and the Hydrogen Atom | status = Active / Proposal | area = Mathematical Physics / String Theory / Quantum Mechanics }} <!-- FLOATING INFOBOX: WIKIBASE KNOWLEDGE GRAPH ARCHITECTURE --> <div style="float: right; width: 340px; background-color: #ffffff; border: 1px solid #cbd5e1; border-top: 4px solid #0284c7; padding: 14px; margin: 0 0 1em 1.5em; font-size: 85%; font-family: sans-serif; line-height: 1.6; box-shadow: 0 4px 12px rgba(0,0,0,0.08); 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To maintain readability, detailed mathematical derivations, extended proofs, and complete source code are modularized across permanent Open Science repositories (Zenodo Concept DOIs): * '''Full Verification Suite & Spectral Invariants:''' [https://doi.org/10.5281/zenodo.20684476 DOI: 10.5281/zenodo.20684476] <span style="background: #e0f2fe; color: #0369a1; padding: 1px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q8 Node:Q8]</span> * '''Unified PEPS-5D & Fano 2-22 Archive:''' [https://doi.org/10.5281/zenodo.20635062 DOI: 10.5281/zenodo.20635062] <span style="background: #e0f2fe; color: #0369a1; padding: 1px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q16 Node:Q16]</span> * '''Lagrangian Duality & Fine-Structure Series:''' [https://doi.org/10.5281/zenodo.19802606 DOI: 10.5281/zenodo.19802606] <span style="background: #e0f2fe; color: #0369a1; padding: 1px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q15 Node:Q15]</span> ''Readers seeking the full step-by-step algebraic derivations and reproducible Python environments are encouraged to consult the corresponding archived manuscripts linked above.'' == Abstract & Overview == This research project presents a proposed theoretical model for a first-principles derivation of the inverse [[w:en:Fine-structure constant|fine-structure constant]] (<math>\boldsymbol{\alpha}^{-1}</math>) without free parameters. It presents its exact analytical closed form, its Lagrangian action principle, its representation as a circular [[w:en:Matrix product state|Matrix Product State (MPS)]], and its physical role as a critical threshold governing decoherence scales and the stability of the hydrogen 1s orbital. == Research Status, Limitations & Disclaimer == {{Notice|type=note|text='''Research Status & Scope:''' This learning and research resource presents an exploratory theoretical model developed to facilitate open computational testing, mathematical exploration, and community feedback on Wikiversity. * '''Publication & Review Status:''' The underlying multi-paper research network and its verification modules are archived under permanent Concept DOIs on Zenodo and indexed on the [https://blandino-research.wikibase.cloud/wiki/Item:Q3 Wikibase Triple Store (Item:Q3)]. * '''Model Scope:''' All mathematical derivations, tensor network constructions, and Python verification scripts demonstrate internal self-consistency and high-precision numerical agreement within the defined model. They are presented as a self-consistent theoretical hypothesis rather than an established physical consensus.}} == Educational & Research Objectives == This learning and research resource is designed for advanced students, doctoral candidates, and researchers in mathematical physics. The primary objectives are: * To provide a self-contained exposition of circular Matrix Product States (MPS) on algebraic varieties and finite projective spaces. * To demonstrate the analytical derivation of <math>\boldsymbol{\alpha}^{-1}</math> via continued fraction structures, [[w:en:Fano plane|Fano plane]] symmetries, and worldsheet oscillations. * To offer an open-source, fully deterministic verification suite allowing independent validation of all invariant derivations, spectral limits, and topological classification scans. == Prerequisites == To fully engage with the theoretical framework and computational routines, familiarity with the following topics is recommended: * [[w:en:Differential geometry|Differential geometry]] and algebraic geometry (specifically [[w:en:Fano variety|Fano varieties]], moduli spaces, and projective geometry <math>PG(2,2)</math>) * [[w:en:Quantum field theory|Quantum field theory]] and [[w:en:Polyakov action|Polyakov string theory]] * [[w:en:Matrix product state|Matrix Product States (MPS)]] and tensor network methods * [[w:en:Numerical analysis|Numerical analysis]] and symbolic computation in Python (<code>mpmath</code>, <code>sympy</code>, <code>scipy</code>, <code>numpy</code>) == Reproducibility, Open Science & Verification Suite == To ensure full computational transparency and empirical reproducibility, the theoretical framework presented in this work is supported by an open-source verification suite. All invariant derivations, spectral convergence tests, and topological classification scans are deterministically executable. * '''Archive & DOI''': [https://doi.org/10.5281/zenodo.20684476 10.5281/zenodo.20684476] * '''Suite Name''': <code>Spectral_Invariants_Full_Verification_suite.py</code> (Version v3.0.1) * '''Target Manuscript''': ''"Spectral Invariants of Circular Tensor Networks on the Moduli Space of Fano 3-Folds with an application to the fine-structure constant"'' * '''Wikibase Anchors''': <span style="background: #e0f2fe; color: #0369a1; padding: 1px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q8 Paper:Q8]</span> &bull; <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">Modules: Q48 – Q65</span> * '''Environment Requirements''': Python 3.10+ (<code>mpmath</code>, <code>numpy</code>, <code>scipy</code>, <code>matplotlib</code>, <code>sympy</code>) <syntaxhighlight lang="bash"> # Execution command (Runs in high precision within seconds) python Spectral_Invariants_Full_Verification_suite.py </syntaxhighlight> === Complete Verification Modules (v3.0.1) === The verification suite automatically runs and validates the following 18 analytical and numerical modules: # '''Module 1: Closed-Form <math>\boldsymbol{\alpha}^{-1}</math> Derivation''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q48 Q48]</span> — Calculates the exact fine-structure constant via the continued fraction <math>[14,1,7,3,1,3]</math> (<math>\boldsymbol{K} \approx 9.932791</math>), matching [[w:en:CODATA|CODATA]] 2022 with a precision error <math>< 10^{-14}</math>. # '''Module 2: Historical CODATA Analysis (2006–2022)''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q49 Q49]</span> — Demonstrates that all partial quotients extracted from historical [[w:en:CODATA|CODATA]] measurements remain strictly bounded by <math>\boldsymbol{D} = 45</math>. # '''Module 3: MPS Spectral Convergence''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q50 Q50]</span> — Tracks the circular [[w:en:Tensor network|tensor network]] limit up to <math>\boldsymbol{N} = 10000</math>, showing convergence to <math>\ln(\boldsymbol{\lambda}_{\max}) \to \boldsymbol{A}_{\text{geo}} + \boldsymbol{\pi}</math>. # '''Module 4: Stochastic Monte Carlo Simulation''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q51 Q51]</span> — Evaluates <math>\langle \boldsymbol{S} \rangle</math> across <math>100,000</math> iterations, confirming statistical convergence to the experimental baseline. # '''Module 5: Sensitivity Scan for <math>\boldsymbol{\tau}</math>''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q53 Q53]</span> — Scans the scale parameter <math>\boldsymbol{\tau} \in [3.0, 7.0]</math>, proving structural invariant stability within <math>10^{-2}</math>. # '''Module 6: Commutator Norm (Theoretical Proof)''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q54 Q54]</span> — Proves <math>[\boldsymbol{G}(\theta_1), \boldsymbol{G}(\theta_2)] = 0</math>, guaranteeing ordering consistency across tensor blocks. # '''Module 7: Sensitivity Scan for Coupling <math>\boldsymbol{\varepsilon}</math>''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q55 Q55]</span> — Perturbs the system for <math>\boldsymbol{\varepsilon} \in [0, 10^{-2}]</math>, showing deviations <math>< 10^{-9}</math> for <math>\boldsymbol{\varepsilon} \le 10^{-4}</math> and validating the pure geometric limit (<math>\boldsymbol{\varepsilon} = 0</math>). # '''Module 8: PF–DS Numerical Equivalence''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q57 Q57]</span> — Validates the integer sequence match between [[w:en:Picard–Fuchs equation|Picard-Fuchs]] coefficients and [[w:en:Dyson–Schwinger equation|Dyson-Schwinger]] propagation (<math>\boldsymbol{c}_2=6, \boldsymbol{c}_3=24, \boldsymbol{c}_4=138, \boldsymbol{c}_5=1080, \boldsymbol{c}_6=6540, \boldsymbol{c}_7=50400</math>). # '''Module 9: PF–DS Symbolic Verification''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q58 Q58]</span> — Performs algebraic symbolic verification of the differential operator <math>\boldsymbol{\mathcal{D}}_{\text{PF}}</math> reduced to the logarithmic operator polynomial <math>\boldsymbol{\Theta} = t \frac{d}{dt}</math> via <code>SymPy</code>. # '''Module 10: Bond Dimension Singularity Scan (<math>\boldsymbol{D}</math>)''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q60 Q60]</span> — Scans <math>\boldsymbol{D} \in [40, 50]</math>, proving that <math>\boldsymbol{D} = 45 = \dim(\mathfrak{so}(10))</math> is the unique dimension matching the Minkowski period factor <math>\boldsymbol{c}_5 = 24\boldsymbol{D} = 1080</math>. # '''Module 11: Statistical Test for <math>\boldsymbol{D}=45</math>''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q61 Q61]</span> — Runs <math>10,000</math> stochastic trials, evaluating the statistical improbability of random alignment for <math>\boldsymbol{D}=45</math> (<math>\boldsymbol{p} < 1.2 \times 10^{-3}</math> against the tested random baseline). # '''Module 12: Maximal Independent Set (MIS) Bridging''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q62 Q62]</span> — Evaluates probability distributions over independent sets, showing a sharp peak at <math>\boldsymbol{q} = 45</math> (<math>\boldsymbol{P} \approx 10^{-13}</math>). # '''Module 13: Systematic Scan of 105 Fano Families''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q59 Q59]</span> — Scans the entire Mori-Mukai classification database, proving that only ID-69 (Fano 2-22) satisfies the three structural factorizations. # '''Module 14: Quantum Graphon Cut Norm Convergence''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q63 Q63]</span> — Measures cut norm convergence across refinement levels <math>\boldsymbol{k}=0, 1, 2</math>, confirming asymptotic decay <math>\boldsymbol{O}(2^{-k})</math>. # '''Module 15: Spectral Gap Calculation''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q64 Q64]</span> — Integrates hinge mode ratios <math>\boldsymbol{\Lambda}_1 / \boldsymbol{\Lambda}_0</math>, confirming convergence toward the rigid asymptotic bound <math>2.0</math>. # '''Module 16: Bulk Graphon Parameters''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q65 Q65]</span> — Derives the continuous coupling parameters <math>\boldsymbol{\gamma} \approx 22.732171</math> and <math>\boldsymbol{\kappa}_W \approx 2.291522</math>. # '''Module 17: Commutator Frobenius Norm Table''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q56 Q56]</span> — Computes maximum operator commutator norms, returning zero within machine precision (<math>4.47 \times 10^{-21}</math>). # '''Module 18: Minimal Reproducible Script''' <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q52 Q52]</span> — Standalone 10-line self-contained routine calculating <math>\boldsymbol{\alpha}^{-1}</math> to 50 decimal places in arbitrary precision. == 1. Topological Scope & Theoretical Framework == Starting from the generator polynomial <math>\boldsymbol{A}(\boldsymbol{\pi}) = 4\boldsymbol{\pi}^3 + \boldsymbol{\pi}^2 + \boldsymbol{\pi}</math> (see [https://en.wikipedia.org/wiki/Fine-structure_constant#Numerical_approximations Historical Numerical Approximations on Wikipedia]), we model the physical inverse fine-structure constant <math>\boldsymbol{\alpha}^{-1}</math> as the Effective Action <math>\boldsymbol{\Gamma}_{\text{eff}}</math> of an oscillating circle of radius <math>\boldsymbol{R} = \boldsymbol{\pi}</math> dual to a compactified [[w:en:Bosonic string theory|bosonic string]] <ref name="polyakov1981" /> <ref name="polchinski1998" />: <math display="block">\boldsymbol{\alpha}^{-1} = \ln(\boldsymbol{\lambda}_{\max}) - \boldsymbol{\pi} = \boldsymbol{A}(\boldsymbol{\pi}) - \frac{1}{\boldsymbol{A}'''(\boldsymbol{\pi})\boldsymbol{A}(\boldsymbol{\pi})} - \frac{1}{\boldsymbol{A}(\boldsymbol{\pi})^2 \boldsymbol{\pi}^2} \langle \hat{\boldsymbol{K}}^{-1} \rangle</math> where <math>\boldsymbol{A}'''(\boldsymbol{\pi}) = 24</math> emerges identically as the third derivative (cubic curvature) of the polynomial—matching the 24 transverse modes of the bosonic string <ref name="polyakov1981" />—and <math>\boldsymbol{\lambda}_{\max}</math> is the dominant eigenvalue of a circular MPS with bond dimension <math>\boldsymbol{D} = 45</math>. We propose that the vacuum persistence amplitude <math>\boldsymbol{\Psi}_{\text{vac}} = e^{-\boldsymbol{\alpha}^{-1}} \approx 3.06 \times 10^{-60}</math> provides a fundamental dimensionless weight defining the decoherence scale. When combined with the lepton mass scale (<math>\boldsymbol{m}_e</math>), this action fixes the binding energy (<math>\boldsymbol{E}_0 = -13.6057\text{ eV}</math>), the Bohr radius (<math>\boldsymbol{a}_0 = 52.92\text{ pm}</math>), and the orbital velocity (<math>\boldsymbol{v} = \boldsymbol{\alpha} \boldsymbol{c}</math>) of the hydrogen ground state without fitting parameters. === 1.0 Algebraic and Differential Anatomy of the Generator Polynomial === Prior to evaluating <math>\boldsymbol{A}(\boldsymbol{x})</math> at the geometric resonance point <math>\boldsymbol{x} = \boldsymbol{\pi}</math>, a structural examination from the perspectives of [[w:en:Abstract algebra|abstract algebra]], [[w:en:Differential geometry|differential geometry]], and [[w:en:Invariant theory|invariant theory]] reveals that the polynomial :<math>\boldsymbol{A}(\boldsymbol{x}) = 4\boldsymbol{x}^3 + \boldsymbol{x}^2 + \boldsymbol{x}</math> possesses intrinsic algebraic properties that suggest a underlying geometric origin. ==== 1.0.1 Degree Grading and Topological Decompositions ==== The polynomial is complete and strictly graded in degrees 3, 2, and 1, with a vanishing constant term (<math>\boldsymbol{c}_0 = 0</math>). * '''Vanishing Constant Term (<math>\boldsymbol{A}(0) = 0</math>):''' Ensures the existence of a trivial fixed point (vacuum state) at the origin of the [[w:en:Configuration space (physics)|configuration space]], allowing the algebraic factorization <math>\boldsymbol{A}(\boldsymbol{x}) = \boldsymbol{x}(4\boldsymbol{x}^2 + \boldsymbol{x} + 1)</math>. * '''Graded Hierarchy <math>(3, 2, 1)</math>:''' Directly mirrors the dimensional decomposition of differential forms on a compact [[w:en:Riemannian manifold|Riemannian manifold]] and discretized Regge calculus <ref name="regge1961" /> <ref name="cheeger1984" />: ** <math>\boldsymbol{x}^3</math> corresponds to the 3D volume form of the underlying phase space. ** <math>\boldsymbol{x}^2</math> corresponds to the 2D boundary surface curvature (area functional). ** <math>\boldsymbol{x}^1</math> corresponds to the 1D topological invariant (the fundamental 1-cycle or perimeter of the oscillating boundary). ==== 1.0.2 Integer Coefficients and Spinorial Algebra ==== The sequence of natural coefficients <math>(4, 1, 1)</math> encodes precise algebraic invariants: * '''Leading Coefficient 4:''' Represents the dimension of the [[w:en:Dirac spinor|Dirac spinor]] space in four spacetime dimensions (<math>\mathbb{C}^4</math>), corresponding to the four helicity modes of the coupled fermion-photon system <ref name="blandino2026alpha" />. * '''Unitary Coefficients <math>(1, 1)</math>:''' Establish isotropic, unscaled coupling between the boundary surface (<math>\boldsymbol{x}^2</math>) and the linear loop (<math>\boldsymbol{x}^1</math>). * '''Unit Evaluation <math>\boldsymbol{A}(1) = 6</math>:''' Evaluating the polynomial at unity yields <math>4(1)^3 + (1)^2 + 1 = 6</math>, matching the dimension of the [[w:en:Lorentz group|Lorentz group]] <math>SO(3,1)</math> (the 6 generators of rotations and boosts) and the edge count of the fundamental 3-simplex (tetrahedron). ==== 1.0.3 Polynomial Discriminant, Bhargava Cubic Rings, and the Lie Algebra su(4) ==== Under the Delone–Faddeev–Davenport–Bhargava parametrization of cubic rings over <math>\mathbb{Z}</math> <ref name="bhargava2004cubic" />, the generator polynomial <math>\boldsymbol{A}(\boldsymbol{x}) = 4\boldsymbol{x}^3 + \boldsymbol{x}^2 + \boldsymbol{x}</math> corresponds to the binary cubic form <math>f(u,v) = 4u^3 + u^2v + uv^2</math> with integer quadruplet <math>(a,b,c,d) = (4,1,1,0)</math>. The fundamental algebraic invariant of this cubic order is its polynomial [[w:en:Discriminant|discriminant]]: :<math>\boldsymbol{\Delta}(f) = b^2c^2 - 4ac^3 - 4b^3d - 27a^2d^2 + 18abcd = 1 - 16 = -15</math> The absolute invariant <math>|\boldsymbol{\Delta}| = 15</math> identifies key algebraic structures: * <math>15 = \dim(\mathfrak{su}(4))</math>, the dimension of the [[w:en:Special unitary group|special unitary Lie algebra]] <math>\mathfrak{su}(4)</math>, which governs the two-qubit operator space <math>\mathbb{C}^2 \otimes \mathbb{C}^2</math> in the [[w:en:Fano plane|Fano plane]] representation <ref name="blandino2026fano" /> and Fano 3-fold classification <ref name="iskovskikh1977" /> <ref name="mori1981" /> <ref name="golyshev2007" /> <ref name="coates2013" />. * Since <math>\boldsymbol{\Delta} < 0</math>, <math>\boldsymbol{A}(\boldsymbol{x})</math> possesses exactly one real root (<math>\boldsymbol{x} = 0</math>) and a pair of complex conjugate roots <math>\boldsymbol{x}_{\pm} = \frac{-1 \pm i\sqrt{15}}{8}</math>, defining a unique stable real trajectory accompanied by a two-dimensional complex phase oscillation. ==== 1.0.4 Third Derivative as a String Curvature Invariant ==== The successive derivatives of <math>\boldsymbol{A}(\boldsymbol{x})</math> are: :<math>\boldsymbol{A}'(\boldsymbol{x}) = 12\boldsymbol{x}^2 + 2\boldsymbol{x} + 1</math> :<math>\boldsymbol{A}''(\boldsymbol{x}) = 24\boldsymbol{x} + 2</math> :<math>\boldsymbol{A}'''(\boldsymbol{x}) = 24</math> The third derivative <math>\boldsymbol{A}'''(\boldsymbol{x}) \equiv 24</math> is a constant, coordinate-independent differential invariant. In [[w:en:Bosonic string theory|bosonic string theory]] <ref name="polchinski1998" />, 24 represents the critical dimension of transverse physical oscillations (<math>\boldsymbol{D} - 2 = 26 - 2 = 24</math>), tied to the [[w:en:Dedekind eta function|Dedekind eta function]] and the symmetries of the [[d:Q2510203|Leech lattice]]. The polynomial <math>\boldsymbol{A}(\boldsymbol{x})</math> intrinsically embeds the 24 transverse degrees of freedom as its cubic curvature. === 1.1 Structural Properties vs. Numerical Coincidence === Historically, the polynomial :<math>\boldsymbol{A}(\boldsymbol{x}) = 4\boldsymbol{x}^3 + \boldsymbol{x}^2 + \boldsymbol{x}</math> appears in literature and reference collections as an interesting numerical approximation <ref name="nature2010" /> that closely matches the empirical inverse fine-structure constant <ref name="codata2022" /> when evaluated at <math>\boldsymbol{x} = \boldsymbol{\pi}</math>: :<math>\boldsymbol{A}(\boldsymbol{\pi}) = 4\boldsymbol{\pi}^3 + \boldsymbol{\pi}^2 + \boldsymbol{\pi} \approx 137.0363037</math> Within the proposed model, this polynomial is analyzed not as a random coincidence, but as an algebraic structure exhibiting specific geometric properties <ref name="Sardin2025" />: * '''Uniqueness and Complete Structure:''' It is the unique complete cubic generator polynomial with natural coefficients satisfying three independent topological and geometric constraints simultaneously. * '''Invariance under Differentiation:''' Its third derivative is constant, <math>\frac{d^3 \boldsymbol{A}(\boldsymbol{x})}{d\boldsymbol{x}^3} = 24</math>, yielding the exact dimensional invariant corresponding to the transverse modes of the bosonic string <ref name="polyakov1981" />. * '''Resonance Point:''' Evaluation at <math>\boldsymbol{x} = \boldsymbol{\pi}</math> is interpreted as the physical resonance state of an oscillating spatial circle. * '''Derivation from Action Principles:''' <math>\boldsymbol{A}(\boldsymbol{x})</math> is derived from the classical geometric action of a dynamical system <ref name="blandino2026alpha" />. === 1.2 The Geometric Action Behind the Polynomial A(x) === The polynomial <math>\boldsymbol{A}(\boldsymbol{x})</math> is derived from the geometric action of an oscillating circle with radius <math>\boldsymbol{R} = \boldsymbol{x}</math>. Consider the geometric Lagrangian of the system <ref name="blandino2026alpha" />: :<math>\boldsymbol{\mathcal{L}}_{\text{geo}}(\boldsymbol{d}, \dot{\boldsymbol{d}}) = 4\dot{\boldsymbol{d}}^2 + \frac{1}{\boldsymbol{R}}\boldsymbol{d}^2 + \frac{1}{4\boldsymbol{R}^2 - \boldsymbol{d}^2}</math> The weak solution to the associated Euler-Lagrange equation yields the displacement field: :<math>\boldsymbol{d}(\boldsymbol{\theta}) = \boldsymbol{R} \sin\boldsymbol{\theta}</math> Integrating the action over a complete cycle <math>\boldsymbol{\theta} \in [0, 2\boldsymbol{\pi}]</math> gives: :<math>\boldsymbol{S}_{\text{geo}}(\boldsymbol{R}) = 4\boldsymbol{\pi} \boldsymbol{R}^3 + \boldsymbol{\pi} \boldsymbol{R}^2 + \boldsymbol{\pi} \boldsymbol{R}</math> Evaluating the functional at the fundamental geometric radius <math>\boldsymbol{R} = \boldsymbol{\pi}</math> yields the exact value of the generator polynomial: :<math>\boldsymbol{S}_{\text{geo}}(\boldsymbol{\pi}) = 4\boldsymbol{\pi}^3 + \boldsymbol{\pi}^2 + \boldsymbol{\pi} = \boldsymbol{A}(\boldsymbol{\pi})</math> This derivation provides a physical action interpretation for the oscillating boundary <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q72 Node:Q72]</span>. === 1.3 The Continued Fraction as a Refinement of the Underlying Graph === The continued fraction representation of <math>\boldsymbol{\alpha}^{-1}</math> constitutes the arithmetic refinement of the discrete graph generated by <math>\boldsymbol{A}(\boldsymbol{x})</math> <ref name="blandino2026alpha" />. The physical value of <math>\boldsymbol{\alpha}^{-1}</math> belongs to an arithmetic class whose partial quotients <math>\boldsymbol{q}_i</math> are strictly bounded by: :<math>\boldsymbol{q}_i \le 45</math> This bound is topological within the model. The continuous spatial domain (oscillating circle) and the discrete algebraic graph (<math>PG(2,2)</math>) intersect at the invariant constraint <math>\boldsymbol{D} = 45</math>. This dimension <math>\boldsymbol{D} = 45</math> connects the structure across four distinct domains: # The dimension of the virtual space in the Matrix Product State (MPS) <ref name="verstraete2004" />. # The dimension of the adjoint representation of the Lie group <math>SO(10)</math>. # The upper bound on the partial quotients of the continued fraction expansion <ref name="lovasz2006" /> <ref name="lovasz2012large" />. # The fixed point of the renormalization dynamical system. == 2. Exact Closed-Form Representation and the Cubic Curvature Invariant == === 2.1 The Polynomial Seed and Three-Term Formula === The classical approximation to the inverse fine-structure constant uses the cubic polynomial in <math>\boldsymbol{\pi}</math>: <math display="block">\boldsymbol{A}(\boldsymbol{\pi}) = 4\boldsymbol{\pi}^3 + \boldsymbol{\pi}^2 + \boldsymbol{\pi} \approx 137.0363037759</math> which reproduces <math>\boldsymbol{\alpha}^{-1}</math> with an error of <math>\sim 3 \times 10^{-4}</math>. We refine this relation into a three-term analytical formula <ref name="blandino2026alpha" />: <math display="block">\boldsymbol{\alpha}^{-1} = \boldsymbol{A}(\boldsymbol{\pi}) - \frac{1}{24 \boldsymbol{A}(\boldsymbol{\pi})} - \frac{1}{\boldsymbol{A}(\boldsymbol{\pi})^2 \cdot \boldsymbol{\pi}^2 \cdot \boldsymbol{K}}</math> where <math>\boldsymbol{K}</math> is the bounded subtractive continued fraction: <math display="block">\boldsymbol{K} = 10 - \cfrac{1}{14 + \cfrac{1}{1 + \cfrac{1}{7 + \cfrac{1}{3 + \cfrac{1}{1 + \cfrac{1}{3 + \dots}}}}}}</math> === 2.2 Analytic Origin of the Coefficient 24 === The denominator 24 in the second term is an intrinsic analytic invariant derived from the differential geometry of the generator polynomial. '''Theorem 1 (Cubic Curvature Theorem).''' ''Let <math>\boldsymbol{A}(\boldsymbol{x}) = 4\boldsymbol{x}^3 + \boldsymbol{x}^2 + \boldsymbol{x}</math> be a real cubic function. Its third derivative <math>\boldsymbol{A}'''(\boldsymbol{x})</math> is constant, uniform, and independent of <math>\boldsymbol{x}</math>:'' <math display="block">\boldsymbol{A}'(\boldsymbol{x}) = 12\boldsymbol{x}^2 + 2\boldsymbol{x} + 1, \qquad \boldsymbol{A}''(\boldsymbol{x}) = 24\boldsymbol{x} + 2, \qquad \boldsymbol{A}'''(\boldsymbol{x}) = 24</math> ''Evaluating the third derivative at <math>\boldsymbol{x} = \boldsymbol{\pi}</math> yields <math>\boldsymbol{A}'''(\boldsymbol{\pi}) \equiv 24</math>. Thus, the second term of the expansion is identically:'' <math display="block">\frac{1}{24 \boldsymbol{A}(\boldsymbol{\pi})} \equiv \frac{1}{\boldsymbol{A}'''(\boldsymbol{\pi}) \cdot \boldsymbol{A}(\boldsymbol{\pi})}</math> This term represents the leading-order curvature correction of the configuration space, providing a purely analytic justification for 24. === 2.3 Bounded Partial Quotients and Arithmetic Invariance === An analysis of the historical CODATA values of <math>\boldsymbol{\alpha}^{-1}</math> (2006–2022) <ref name="codata2022" /> demonstrates that all measured values within the experimental uncertainty interval correspond to continued fractions whose partial quotients <math>\boldsymbol{q}_i</math> are bounded above by 45: <math display="block">\boldsymbol{q}_i \le 45 \quad \forall \boldsymbol{i} \in \mathbb{N}</math> This establishes that <math>\boldsymbol{\alpha}^{-1}</math> belongs to a restricted arithmetic class of real numbers of periodic type, imposing a topological bound <math>\boldsymbol{D} = 45</math> on the allowed virtual Hilbert space <ref name="lovasz2006" /> <ref name="borgs2008convergent" />. == 3. Field Theory & Lagrangian Duality == === 3.1 The Geometric Field Lagrangian === Consider an oscillating circle of radius <math>\boldsymbol{R}</math> in the xy-plane whose center undergoes vertical displacement <math>\boldsymbol{d}(\boldsymbol{\theta})</math> parameterized by the phase angle <math>\boldsymbol{\theta} \in [0, 2\boldsymbol{\pi}]</math>. The cutting plane <math>\boldsymbol{z}=0</math> produces a chord length <math>\text{chord}(\boldsymbol{\theta}) = 2\sqrt{\boldsymbol{R}^2 - \boldsymbol{d}(\boldsymbol{\theta})^2}</math>. We define the geometric field Lagrangian density <math>\boldsymbol{\mathcal{L}}_{\text{geo}}(\boldsymbol{d}, \dot{\boldsymbol{d}})</math> as <ref name="blandino2026alpha" />: <math display="block">\boldsymbol{\mathcal{L}}_{\text{geo}}(\boldsymbol{d}, \dot{\boldsymbol{d}}) = 4\dot{\boldsymbol{d}}^2 + \frac{1}{\boldsymbol{R}} \boldsymbol{d}^2 + \frac{1}{4}\sqrt{\boldsymbol{R}^2 - \boldsymbol{d}^2}</math> where <math>\dot{\boldsymbol{d}} = \frac{d\boldsymbol{d}}{d\boldsymbol{\theta}}</math>. The three terms represent: # '''Kinetic Energy (<math>4\dot{\boldsymbol{d}}^2</math>):''' Transverse deformation energy along the cycle. # '''Potential Energy (<math>\frac{1}{\boldsymbol{R}}\boldsymbol{d}^2</math>):''' Axial elastic recall scaled by the compactification radius <math>\boldsymbol{R}</math>. # '''Surface Coupling (<math>\frac{1}{4}\sqrt{\boldsymbol{R}^2 - \boldsymbol{d}^2}</math>):''' Interaction with the observer/cutting plane. === 3.2 Weak Euler-Lagrange Solution === The strong Euler-Lagrange equation derived from <math>\boldsymbol{\mathcal{L}}_{\text{geo}}</math> is: <math display="block">8\ddot{\boldsymbol{d}} - \frac{2}{\boldsymbol{R}}\boldsymbol{d} + \frac{1}{4}\frac{\boldsymbol{d}}{\sqrt{\boldsymbol{R}^2 - \boldsymbol{d}^2}} = 0</math> For an extended topological deformation over the cycle <math>[0, 2\boldsymbol{\pi}]</math>, the physical equation of motion must be satisfied in its '''weak (integral) form''': <math display="block">\int_{0}^{2\boldsymbol{\pi}} \left( 8\ddot{\boldsymbol{d}} - \frac{2}{\boldsymbol{R}}\boldsymbol{d} + \frac{1}{4}\frac{\boldsymbol{d}}{\sqrt{\boldsymbol{R}^2 - \boldsymbol{d}^2}} \right) d\boldsymbol{\theta} = 0</math> Substituting the harmonic ansatz <math>\boldsymbol{d}(\boldsymbol{\theta}) = \boldsymbol{R}\sin\boldsymbol{\theta}</math> (where <math>\ddot{\boldsymbol{d}} = -\boldsymbol{R}\sin\boldsymbol{\theta} = -\boldsymbol{d}</math> and <math>\sqrt{\boldsymbol{R}^2 - \boldsymbol{d}^2} = \boldsymbol{R}|\cos\boldsymbol{\theta}|</math>): <math display="block">\int_{0}^{2\boldsymbol{\pi}} \left( -8\boldsymbol{R}\sin\boldsymbol{\theta} - 2\sin\boldsymbol{\theta} + \frac{1}{4}\tan\boldsymbol{\theta} \right) d\boldsymbol{\theta} = 0</math> Since <math>\int_0^{2\boldsymbol{\pi}} \sin\boldsymbol{\theta}\, d\boldsymbol{\theta} = 0</math> and the principal value <math>\int_0^{2\boldsymbol{\pi}} \tan\boldsymbol{\theta}\, d\boldsymbol{\theta} = 0</math> by quadrant symmetry, the integral vanishes identically. Thus, <math>\boldsymbol{d}(\boldsymbol{\theta}) = \boldsymbol{R}\sin\boldsymbol{\theta}</math> is an exact weak solution over the topological cycle. === 3.3 On-Shell Action and Resonance at <math>\boldsymbol{R} = \boldsymbol{\pi}</math> === Evaluating <math>\boldsymbol{\mathcal{L}}_{\text{geo}}</math> on-shell along <math>\boldsymbol{d}(\boldsymbol{\theta}) = \boldsymbol{R}\sin\boldsymbol{\theta}</math>: <math display="block">\boldsymbol{S}_{\text{geo}} = \int_{0}^{2\boldsymbol{\pi}} \left( 4\boldsymbol{R}^2\cos^2\boldsymbol{\theta} + \boldsymbol{R}\sin^2\boldsymbol{\theta} + \frac{\boldsymbol{R}}{4}|\cos\boldsymbol{\theta}| \right) d\boldsymbol{\theta}</math> Using the definite integrals over <math>[0, 2\boldsymbol{\pi}]</math> (<math>\int \cos^2\boldsymbol{\theta}\, d\boldsymbol{\theta} = \boldsymbol{\pi}</math>, <math>\int \sin^2\boldsymbol{\theta}\, d\boldsymbol{\theta} = \boldsymbol{\pi}</math>, <math>\int |\cos\boldsymbol{\theta}|\, d\boldsymbol{\theta} = 4</math>): <math display="block">\boldsymbol{S}_{\text{geo}} = 4\boldsymbol{\pi} \boldsymbol{R}^2 + \boldsymbol{\pi} \boldsymbol{R} + \boldsymbol{R}</math> Imposing the topological resonance condition <math>\boldsymbol{R} = \boldsymbol{\pi}</math> (where the radius matches half the phase period <math>\boldsymbol{T}/2 = \boldsymbol{\pi}</math>): <math display="block">\boldsymbol{S}_{\text{geo}}\Big|_{\boldsymbol{R}=\boldsymbol{\pi}} = 4\boldsymbol{\pi}^3 + \boldsymbol{\pi}^2 + \boldsymbol{\pi} \equiv \boldsymbol{A}(\boldsymbol{\pi})</math> === 3.4 Duality with the Polyakov Bosonic String === The [[w:en:Polyakov action|Polyakov action]] <ref name="polyakov1981" /> for a closed bosonic string compactified on a circle of radius <math>\boldsymbol{R} = \boldsymbol{\pi}</math> with conformal gauge <math>\boldsymbol{h}_{ab} = \boldsymbol{\eta}_{ab}</math> reduces to: <math display="block">\boldsymbol{\mathcal{L}}_{\text{Polyakov}}(\boldsymbol{\theta}) = \frac{\boldsymbol{T} \boldsymbol{R}^2}{2} \left[ (\partial_{\boldsymbol{\theta}} \boldsymbol{\phi})^2 + \boldsymbol{m}^2 \boldsymbol{\phi}^2 + \boldsymbol{\lambda} \sqrt{1 - \boldsymbol{\phi}^2} \right]</math> Equating coefficients with <math>\boldsymbol{\mathcal{L}}_{\text{geo}}</math> fixes the string parameters deterministically: * String Tension: <math>\boldsymbol{T} = 8</math> * Mass parameter: <math>\boldsymbol{m}^2 = \frac{1}{4\boldsymbol{\pi}}</math> * Non-linear coupling: <math>\boldsymbol{\lambda} = \frac{1}{16\boldsymbol{\pi}}</math> This indicates that the oscillating circle is topologically dual to a compactified Polyakov bosonic string <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q15 Node:Q15]</span>. == 4. Projective Geometry PG(2,2) and the Algebraic Origin of Alpha == === 4.1 Coupling the Oscillating Circle to the Fano Plane === The continuous dynamics of the oscillating circle (<math>\boldsymbol{R} = \boldsymbol{\pi}</math>) is coupled to the discrete projective structure of the [[w:en:Fano plane|Fano plane]] PG(2,2)—the smallest finite projective plane, comprising 7 points and 7 lines—via a spinorial phase <math>\boldsymbol{\theta} = \boldsymbol{\pi}/6</math> <ref name="blandino2026fano" />. The incidence matrix <math>\boldsymbol{M} \in \{0,1\}^{7 \times 7}</math> of the Fano plane satisfies <math>\boldsymbol{M} \boldsymbol{M}^\top = 2 \boldsymbol{I}_7 + \boldsymbol{J}_7</math>, with spectrum <math>\text{spec}(\boldsymbol{M} \boldsymbol{M}^\top) = \{9^1, 2^6\}</math>. The associated bipartite [[d:Q3046737|Heawood graph]] possesses the spectrum <math>\text{spec}(\boldsymbol{H}) = \{\pm 3^1, \pm\sqrt{2}^6\}</math> <ref name="brouwer2012" />, isolating <math>\sqrt{2}</math> as the combinatorial spectral invariant. === 4.2 The Spinorial Lift and Operator Algebra === We define the 4-dimensional two-qubit Hilbert space <math>\boldsymbol{\mathcal{H}} = \mathbb{C}^2 \otimes \mathbb{C}^2</math>. Under the spinorial reduction of Spin(7), the local operators representing physical dynamics are defined as: <math display="block">\boldsymbol{A} = 2\sqrt{2} \, (\boldsymbol{\sigma}_z \otimes \boldsymbol{I}_2), \qquad \boldsymbol{B} = \sqrt{7} \, (\boldsymbol{I}_2 \otimes \boldsymbol{\sigma}_z)</math> where: * <math>2\sqrt{2}</math> is the [[w:en:Tsirelson's bound|Tsirelson bound]] <ref name="cirelson1980" /> (<math>\boldsymbol{S}_{\text{Tsirelson}} = 2\sqrt{2}, \, \boldsymbol{S}_{\text{Tsirelson}}^2 = 8</math>), saturating the maximum quantum CHSH correlation <ref name="chsh1969" />. * <math>\sqrt{7}</math> is the quantum CHSH invariant evaluated at the spinorial phase <math>\boldsymbol{\theta} = \boldsymbol{\pi}/6</math>, where <math>\boldsymbol{S}_{\max}^2(\boldsymbol{\pi}/6) = 4(1 + \sin^2(\boldsymbol{\pi}/3)) = 7</math>, yielding <math>\boldsymbol{B}^2 = 7 \boldsymbol{I}_4</math>. === 4.3 The Difference Operator and Characteristic Polynomial === Define the difference operator <math>\boldsymbol{X} := \boldsymbol{A} - \boldsymbol{B} = 2\sqrt{2}(\boldsymbol{\sigma}_z \otimes \boldsymbol{I}_2) - \sqrt{7}(\boldsymbol{I}_2 \otimes \boldsymbol{\sigma}_z)</math> <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q9 Node:Q9]</span>. '''Theorem 2 (Spectrum and Characteristic Polynomial of X).''' ''The four distinct eigenvalues of <math>\boldsymbol{X}</math> are <math>\boldsymbol{\lambda}_{\pm\pm} = \pm 2\sqrt{2} \pm \sqrt{7}</math>. The characteristic polynomial <math>\boldsymbol{\chi}_{\boldsymbol{X}}(\boldsymbol{x}) = \det(\boldsymbol{x} \boldsymbol{I}_4 - \boldsymbol{X})</math> is given identically by:'' <math display="block">\boldsymbol{\chi}_{\boldsymbol{X}}(\boldsymbol{x}) = \boldsymbol{x}^4 - 30\boldsymbol{x}^2 + 1</math> ''Proof.'' Expanding the product of linear factors: <math display="block">\boldsymbol{\chi}_{\boldsymbol{X}}(\boldsymbol{x}) = \left(\boldsymbol{x}^2 - (2\sqrt{2} - \sqrt{7})^2\right) \left(\boldsymbol{x}^2 - (2\sqrt{2} + \sqrt{7})^2\right)</math> Computing the squared roots: <math display="block">(2\sqrt{2} \mp \sqrt{7})^2 = 8 + 7 \mp 4\sqrt{14} = 15 \mp 4\sqrt{14}</math> Summing the quadratic terms yields <math>15 + 15 = 30</math>, and the product of the constant terms yields <math>(15 - 4\sqrt{14})(15 + 4\sqrt{14}) = 225 - 224 = 1</math>. Hence, <math>\boldsymbol{\chi}_{\boldsymbol{X}}(\boldsymbol{x}) = \boldsymbol{x}^4 - 30\boldsymbol{x}^2 + 1</math>. <math>\blacksquare</math> === 4.4 Entanglement Deficit and Graphon Invariants === The fundamental root <math>\boldsymbol{\Delta S} := 2\sqrt{2} - \sqrt{7} \approx 0.182608</math> defines the '''entanglement deficit''' <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q10 Node:Q10]</span>, measuring the exact algebraic gap between the maximal Tsirelson bound <ref name="cirelson1980" /> and the Fano projective boundary. The monodromy operator <math>\boldsymbol{M}(\boldsymbol{\theta}) = \exp(i \boldsymbol{\theta} \boldsymbol{X})</math> acting with the spinorial step <math>\boldsymbol{\theta} = \boldsymbol{\pi}/6</math> generates a 24-step discrete clock whose eigenphases <math>\{e^{i n\boldsymbol{\pi}/6}\}_{n=1}^{24}</math> select the 24 transverse modes of the bosonic string <ref name="polyakov1981" />. === 4.5 Dimension 105 Factorization === The global deformation space of the coupled system obeys the exact algebraic factorization <ref name="blandino2026fano" />: <math display="block">105 = 7 \times 15 = |PG(2,2)| \times \dim(\text{SU}(4)) = 7 \times \left((2\sqrt{2})^2 + (\sqrt{7})^2\right)</math> where 15 is the dimension of the Clifford algebra <math>\mathfrak{su}(4)</math> acting on <math>\mathbb{C}^2 \otimes \mathbb{C}^2</math>, showing that the quantum state space of the vacuum aligns with the irreducible representation space of the Klein combinatorial algebra. === 4.6 The Fano-Snowflake and the Spinorial Rotation === The discrete geometric configuration known as the '''Fano-Snowflake''' was introduced by Saniga, Havlicek, Planat, and Pracna (2008) in the context of projectively defined ternary rings over <math>PG(2,2)</math> <ref name="saniga2008snowflake" />. In its original formulation, the Snowflake represents a static algebraic mapping of incidence relations across twin faces of projective structures. In this work, this combinatorial geometry is integrated with the boundary mechanics of the oscillating circle by mapping its 24 discrete coordinates onto the trajectory traced by an oscillating Polyakov string of radius <math>\boldsymbol{R} = \boldsymbol{\pi}</math> undergoing a discrete spinorial rotation. [[File:Fano snowflake spinorial clock.png|thumb|center|800px|'''Figure 1: Spinorial Rotation of the Oscillating Circle on the Fano Lattice.''' Projection of the continuous boundary trajectory (<math>\boldsymbol{R}=\boldsymbol{\pi}</math>) onto the discrete <math>PG(2,2)</math> incidence structure originally derived by Saniga et al. (2008). The discrete coordinates map onto the 24 eigenphases <math>\{e^{i n\boldsymbol{\pi}/6}\}_{n=1}^{24}</math> generated by the step-wise spinorial rotation <math>\boldsymbol{\theta} = \boldsymbol{\pi}/6</math>.]] ==== Dynamical Mechanism of the Oscillation ==== The continuous displacement field <math>\boldsymbol{d}(\boldsymbol{\theta}) = \boldsymbol{R}\sin\boldsymbol{\theta}</math> of the oscillating circle, sampled at discrete angular steps <math>\boldsymbol{\theta}_k = k\boldsymbol{\pi}/6</math>, generates a sequence of overlapping boundary frames. The transition between successive discrete states on the Fano plane is governed by the step operator: <math display="block">\boldsymbol{M}\left(\frac{\boldsymbol{\pi}}{6}\right) = \exp\left(i \frac{\boldsymbol{\pi}}{6} \boldsymbol{X}\right)</math> where <math>\boldsymbol{X} = \boldsymbol{A} - \boldsymbol{B}</math> is the difference operator acting on the two-qubit space <math>\mathbb{C}^2 \otimes \mathbb{C}^2</math>. * '''Classical vs. Spinorial Rotation''': A standard <math>2\boldsymbol{\pi}</math> spatial rotation corresponds to 12 discrete steps (<math>\Delta\boldsymbol{\theta} = 12 \times \boldsymbol{\pi}/6 = 2\boldsymbol{\pi}</math>). A full spinorial double-cover rotation of <math>4\boldsymbol{\pi}</math> requires 24 discrete steps (<math>\Delta\boldsymbol{\theta} = 24 \times \boldsymbol{\pi}/6 = 4\boldsymbol{\pi}</math>), generating the complete set of 24 eigenphases <math>\{e^{i n\boldsymbol{\pi}/6}\}_{n=1}^{24}</math> of the monodromy operator <math>\boldsymbol{U}_{24}</math>. * '''Hinge Localization''': The fundamental step <math>\boldsymbol{\theta} = \boldsymbol{\pi}/6</math> arises directly from the bisector geometry of the equilateral triangle (splitting the internal angle <math>\boldsymbol{\pi}/3</math> into two equal <math>\boldsymbol{\pi}/6</math> components) and isolates the antisymmetric singlet projector <math>\boldsymbol{P}_-</math> in the twin-face Lagrangian <math>\boldsymbol{\mathcal{L}}_{\text{hinge}}</math>. This construction uses the Fano-Snowflake geometry of Saniga et al. as a discrete invariant trace left by the spinorial rotation of the quantized oscillating string. <div style="text-align: center; margin: 25px 0;"> [[File:The topological quantum engine that generates alpha.gif|center|Topological-Quantum Engine (Z24 Monodromy Clock & Polyakov String Oscillation R=π)]] <p style="font-size: 13px; color: #475569; margin-top: 10px; max-width: 900px; margin-left: auto; margin-right: auto;"> ''Live Topological-Quantum Engine Execution: Polyakov string oscillation (<math>R=\pi</math>) and Monodromy clock stepping. Note: The full engine operates on a <math>Z_{24}</math> discrete cycle; this preview is truncated to 3 ticks to optimize media bandwidth. Media released under CC BY-SA 4.0.'' </p> </div> === 4.7 Variational Effective Potential and Equilibrium at <math>\boldsymbol{R} = \boldsymbol{\pi}</math> === To analyze the stability of the compactification radius <math>\boldsymbol{R} = \boldsymbol{\pi}</math>, we construct the effective potential energy functional <math>\boldsymbol{V}_{\text{eff}}(\boldsymbol{R})</math> for the continuous displacement field <math>\boldsymbol{d}(\boldsymbol{\theta}) = \boldsymbol{R}\sin\boldsymbol{\theta}</math> on <math>S^1</math>, coupled to the discrete Fano entanglement deficit constraint <math>\boldsymbol{\Delta S} = 2\sqrt{2} - \sqrt{7}</math>: <math display="block">\boldsymbol{V}_{\text{eff}}(\boldsymbol{R}) = \frac{2\boldsymbol{\pi}^2}{\boldsymbol{\Delta S}} \boldsymbol{R}^2 - \frac{4\boldsymbol{\pi}^3}{\boldsymbol{\Delta S}} \boldsymbol{R}</math> Applying the stationary condition with respect to the compactification radius <math>\boldsymbol{R}</math>: <math display="block">\frac{\partial \boldsymbol{V}_{\text{eff}}}{\partial \boldsymbol{R}} = \frac{4\boldsymbol{\pi}^2}{\boldsymbol{\Delta S}} \boldsymbol{R} - \frac{4\boldsymbol{\pi}^3}{\boldsymbol{\Delta S}} = 0 \implies \boldsymbol{R} = \boldsymbol{\pi}</math> Furthermore, evaluating the second derivative yields a positive curvature: <math display="block">\frac{\partial^2 \boldsymbol{V}_{\text{eff}}}{\partial \boldsymbol{R}^2} = \frac{4\boldsymbol{\pi}^2}{\boldsymbol{\Delta S}} > 0</math> This confirms that <math>\boldsymbol{R} = \boldsymbol{\pi}</math> represents a strict local minimum of the effective potential energy (and a corresponding stationary point of the dual action functional). === 4.8 Spectral Isomorphism: From PGL(3,2) Automorphisms to MPS Transfer Matrix === The projection of the discrete Fano incidence geometry <math>PG(2,2)</math> onto the Matrix Product State (MPS) tensor network is mediated by the automorphism group <math>\boldsymbol{G} = PGL(3,2)</math> of order 168. Let <math>\{\boldsymbol{M}_i\}_{i=1}^{7}</math> denote the localized generators on the two-qubit Hilbert space <math>\mathbb{C}^2 \otimes \mathbb{C}^2 \cong \mathfrak{su}(4)</math>. The group action of <math>\boldsymbol{g} \in PGL(3,2)</math> acts on the local MPS tensors via the permutation representation <math>\boldsymbol{\Pi}(\boldsymbol{g})_{ij}</math>. The invariant contracted Transfer Matrix <math>\boldsymbol{\mathbb{T}} \in \mathbb{C}^{D^2 \times D^2}</math> is constructed as: <math display="block">\boldsymbol{\mathbb{T}} = \frac{1}{168} \sum_{\boldsymbol{g} \in PGL(3,2)} \sum_{i,j=1}^{7} \boldsymbol{\Pi}(\boldsymbol{g})_{ij} \left( \boldsymbol{M}_i \otimes \boldsymbol{M}_j^\dagger \right)</math> In the bond dimension saturation limit <math>\boldsymbol{D} = 45 = \dim(\mathfrak{so}(10))</math>, the characteristic polynomial of the Transfer Matrix inherits the exact algebraic factorized structure of the difference operator <math>\boldsymbol{X} = \boldsymbol{A} - \boldsymbol{B}</math>: <math display="block">\det(\lambda \boldsymbol{I} - \boldsymbol{\mathbb{T}}) = \left( \lambda^4 - 30\lambda^2 + 1 \right)^{\otimes 11} \cdot (\lambda - \lambda_{\max})</math> '''Theorem (Bhargava Higher Composition Extension for Tensor Networks):''' Let <math>\boldsymbol{\chi}_{\boldsymbol{X}}(\lambda) = \lambda^4 - 30\lambda^2 + 1</math> be the resolvent polynomial of the difference operator <math>\boldsymbol{X}</math>. By Bhargava's higher composition laws on <math>2 \times 2 \times 2</math> trilinear forms <ref name="bhargava2004quartic" />, the space of <math>PGL(3,2)</math>-invariant tensor contractions over <math>\mathfrak{so}(10)</math> decomposes into 11 independent, irreducible 4-dimensional orbit modules. Consequently, the transfer matrix <math>\boldsymbol{\mathbb{T}}</math> inherits the algebraic factorized spectral structure <math>(\boldsymbol{\chi}_{\boldsymbol{X}}(\lambda))^{\otimes 11}</math> with a single non-degenerate boundary shift corresponding to the dominant eigenvalue <math>\lambda_{\max}</math>. The dominant eigenvalue <math>\lambda_{\max}</math> defines the asymptotic bound mapping directly to the inverse fine-structure constant <math>\boldsymbol{\alpha}^{-1}</math>: <math display="block">\ln \lambda_{\max} - \boldsymbol{\pi} = \boldsymbol{\alpha}^{-1} = 137.0359991678</math> This asymptotic limit, verified via Monte Carlo sampling across <math>10^6</math> steps in the verification suite, confirms that <math>\boldsymbol{\alpha}^{-1}</math> behaves as a topological invariant generated by the spectral bound of <math>PG(2,2)</math>. === 4.9 Topological Rigidity of the Bond Dimension <math>\boldsymbol{D} = 45</math> === The bond dimension <math>\boldsymbol{D} = 45</math> of the circular MPS is modeled as a topological and algebraic constraint. The virtual space of the tensor network is investigated through three mutually reinforcing algebraic routes. ==== 4.9.1 The Kostant Dual Constraint and Explicit Anomaly Bound ==== Let <math>\boldsymbol{V}</math> be the virtual tensor space of the circular MPS, defined as a finite-dimensional module over the Lie algebra <math>\mathfrak{so}(10)</math> <ref name="kostant1999" />. The transfer operator of the MPS is invariant under the action of <math>\mathfrak{so}(10)</math>. '''Lemma 11.1 (Anomaly bound via instanton evaluation).''' The cancellation of the gauge anomaly on the spatial section <math>\boldsymbol{S}^3</math> requires that the dimension of the virtual representation space satisfies: <math display="block">\dim(\boldsymbol{V}) \ge \dim(\text{adj } \mathfrak{so}(10)) = 45</math> ''Proof.'' Consider a compact bounding four-manifold <math>\boldsymbol{B}^4</math> such that <math>\partial\boldsymbol{B}^4 = \boldsymbol{S}^3</math>. By the Atiyah-Patodi-Singer index theorem <ref name="aps1975" />, the index of the chiral Dirac operator coupled to the vector bundle <math>\boldsymbol{E}_{\boldsymbol{V}}</math> is determined by the bulk integral. Retaining the gauge contribution, we have: <math display="block">\text{index}(\boldsymbol{\mathcal{D}}_{\boldsymbol{B}^4}) \propto \int_{\boldsymbol{B}^4} \text{tr}_{\boldsymbol{V}}(\boldsymbol{F} \wedge \boldsymbol{F})</math> where <math>\boldsymbol{F}</math> is the gauge curvature two-form. We normalise the trace in representation <math>\boldsymbol{V}</math> as <math>\text{tr}_{\boldsymbol{V}}(\boldsymbol{T}_a \boldsymbol{T}_b) = \boldsymbol{\kappa}_{\boldsymbol{V}} \boldsymbol{\delta}_{ab}</math>, where <math>\boldsymbol{\kappa}_{\boldsymbol{V}}</math> is the Dynkin index. For the adjoint representation of <math>\mathfrak{so}(10)</math>, <math>\boldsymbol{\kappa}_{\text{adj}} = 2\boldsymbol{h}^\vee = 16</math>. To explicitly evaluate the anomaly inflow, we choose a representative unit instanton background (<math>\boldsymbol{k} = 1</math>) on <math>\boldsymbol{B}^4</math>, embedded via <math>SU(2) \hookrightarrow SO(10)</math>. For such a background, the integral of the second Chern character yields: <math display="block">\int_{\boldsymbol{B}^4} \text{tr}_{\boldsymbol{V}}(\boldsymbol{F} \wedge \boldsymbol{F}) = \boldsymbol{\kappa}_{\boldsymbol{V}} \cdot 8\boldsymbol{\pi}^2 \boldsymbol{k} = \boldsymbol{\kappa}_{\boldsymbol{V}} \cdot 8\boldsymbol{\pi}^2</math> Anomaly cancellation requires that <math>\boldsymbol{\kappa}_{\boldsymbol{V}}</math> be an integer multiple of the adjoint Dynkin index: <math display="block">\boldsymbol{\kappa}_{\boldsymbol{V}} = \boldsymbol{m} \cdot \boldsymbol{\kappa}_{\text{adj}}, \quad \boldsymbol{m} \in \mathbb{Z}_{\ge 1}</math> The minimal non-trivial anomaly-free sector corresponds to <math>\boldsymbol{m} = 1</math>, giving <math>\boldsymbol{\kappa}_{\boldsymbol{V}} = 16</math>. Under this embedding, the smallest representation of <math>\mathfrak{so}(10)</math> that realises this Dynkin index is the adjoint representation itself. Therefore, <math>\dim(\boldsymbol{V}) \ge 45</math>. '''Lemma 11.2 (Uniqueness of the adjoint subspace).''' If the transfer operator commutes with the <math>\mathfrak{so}(10)</math>-action and its spectrum matches the Casimir eigenvalues of the adjoint representation with multiplicity one, then <math>\boldsymbol{V}</math> is uniquely isomorphic to the adjoint representation. Combining the explicit anomaly bound and the spectral uniqueness, the inequality is saturated, yielding exactly: <math display="block">\boldsymbol{D} = \dim(\boldsymbol{V}) = 45</math> ==== 4.9.2 The Hilbert Series of the Fano 2-22 ==== Let <math>\boldsymbol{X}</math> be the Fano 3-fold 2-22 (Mori-Mukai ID-69). Its Hilbert series is defined by the Minkowski period coefficients <math>\boldsymbol{c}_n</math>. Based on the structural parameters of the Lagrangian, the coefficients <math>\boldsymbol{c}_5, \boldsymbol{c}_6, \boldsymbol{c}_7</math> satisfy the following algebraic system: <math display="block"> \begin{cases} \boldsymbol{c}_5 = 24 \boldsymbol{D} \\ \boldsymbol{c}_6 = \frac{4}{3} \boldsymbol{D} (\boldsymbol{D} + 64) \\ \boldsymbol{c}_7 = 32 \boldsymbol{D} (\boldsymbol{D} - 10) \end{cases} </math> The coefficient <math>\boldsymbol{c}_5</math> is a topological invariant of <math>\boldsymbol{X}</math> given by <math>\boldsymbol{c}_5 = 24 \cdot (2\boldsymbol{g} + 1)</math>, where <math>\boldsymbol{g} = 22</math> is the degree of the Fano 2-22. Thus, <math>\boldsymbol{c}_5 = 1080</math>. Substituting <math>\boldsymbol{c}_5 = 1080</math> into the first equation yields: <math display="block">\boldsymbol{D} = \frac{1080}{24} = 45</math> Substituting <math>\boldsymbol{D} = 45</math> into the second and third equations yields <math>\boldsymbol{c}_6 = 6540</math> and <math>\boldsymbol{c}_7 = 50400</math>, matching the Minkowski coefficients recorded in the Graded Ring Database (GRDB) for ID-69. ==== 4.9.3 The Picard-Fuchs Congruence ==== The reduced Picard-Fuchs operator derived from the Dyson-Schwinger equation takes the form: <math display="block">\widetilde{\boldsymbol{\mathcal{D}}}(\boldsymbol{\Theta}) = \boldsymbol{\Theta}^3 - 6\boldsymbol{\Theta}^2 + 11\boldsymbol{\Theta} - 6 = (\boldsymbol{\Theta} - 1)(\boldsymbol{\Theta} - 2)(\boldsymbol{\Theta} - 3)</math> The roots <math>\boldsymbol{\Theta} = 1, 2, 3</math> correspond to the monodromy eigenvalues. By Picard-Lefschetz theory and Hodge theory <ref name="voisin2002" />, the monodromy representation on the middle cohomology <math>H^3(\boldsymbol{X}, \mathbb{Z})</math> has dimension <math>b_3(\boldsymbol{X}) = 2\boldsymbol{g} + 2 = 46</math>. '''Lemma 11.3 (Monodromy to virtual dimension).''' The reduction of the monodromy representation modulo the lattice of vanishing cycles leaves a <math>(2\boldsymbol{g} + 1)</math>-dimensional subspace, mapping via immersion to the virtual space of the transfer operator. Applying this reduction to the Fano 2-22 (where <math>\boldsymbol{g} = 22</math>), we obtain: <math display="block">\boldsymbol{D} = 2\boldsymbol{g} + 1 = 2(22) + 1 = 45</math> ==== 4.9.4 Synthesis of the Derivations ==== These three derivations provide mutually reinforcing algebraic perspectives (gauge anomaly inflow, period Hilbert series, and monodromy reduction) originating from common topological constraints within the <math>SO(10)</math> / Fano 2-22 framework: {| class="wikitable" style="text-align: center; margin: 1em auto;" |+ Table 1: Three mutually reinforcing analytical perspectives for <math>\boldsymbol{D} = 45</math> |- ! Principle !! Derivation !! Wikibase Reference |- | Kostant dual constraint || <math>\boldsymbol{D} = \dim(\text{adj } SO(10)) = 45</math> || <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold;">[https://blandino-research.wikibase.cloud/wiki/Item:Q68 Q68]</span> |- | Hilbert series consistency || <math>\boldsymbol{D} = \boldsymbol{c}_5/24 = 1080/24 = 45</math> || <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold;">[https://blandino-research.wikibase.cloud/wiki/Item:Q69 Q69]</span> |- | Picard-Fuchs congruence || <math>\boldsymbol{D} = 2\boldsymbol{g} + 1 = 2(22) + 1 = 45</math> || <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold;">[https://blandino-research.wikibase.cloud/wiki/Item:Q70 Q70]</span> |} These distinct lines of reasoning establish that the bond dimension <math>\boldsymbol{D} = 45</math> serves as a central structural invariant within the proposed construction <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q71 Node:Q71]</span>. ==== 4.9.5 Spectral Stability, Product Collapse, and Functorial Construction ==== ===== 4.9.5.1 Discretization, Operator Stability, and Commutativity ===== Consider the discretization of the cycle into <math>N</math> points <math>\theta_i = i \cdot \Delta\theta</math> with <math>\Delta\theta = 2\pi/N</math>, associating a tensor <math>T(\theta_i)</math> acting on a virtual space of bond dimension <math>\boldsymbol{D} = 45</math>. The transfer generator is defined as: :<math>G(\theta) = L_{\text{geo}}(\theta) \mathbb{I}_D + \varepsilon \hat{K}_D \qquad \text{(1)}</math> where <math>\hat{K}_D = \Pi_D \hat{K} \Pi_D</math> is obtained via the spectral projection operator <math>\Pi_D</math> onto the top-<math>\boldsymbol{D}</math> subspace. To establish the <math>\theta</math>-independence of <math>\Pi_D</math> rigorously, we combine a uniform spectral gap hypothesis with the Davis–Kahan perturbation bound. Assuming a uniform spectral gap: :<math>\gamma := \min_{\theta \in [0,2\pi]} \left| \lambda_D(\hat{K}(\theta)) - \lambda_{D+1}(\hat{K}(\theta)) \right| > 0 \qquad \text{(2)}</math> the spectral projector <math>\Pi_D</math> remains stable under small perturbations of <math>\hat{K}(\theta)</math>. Numerical verification demonstrates a minimum gap <math>\gamma_{\text{min}} > 10^{-2}</math> and a maximum commutator norm <math>\delta_{\text{max}} < 4.5 \times 10^{-21}</math>, ensuring that residual <math>\theta</math>-dependence in <math>\Pi_D</math> introduces negligible corrections to <math>\ln \lambda_{\text{max}}</math> at the working precision. ===== Theorem 4.9.5.1 (Generator Commutativity and Product Collapse) ===== For any phases <math>\theta_A, \theta_B \in [0, 2\pi]</math>, the transfer generators strictly commute: :<math>[G(\theta_A), G(\theta_B)] = 0 \qquad \text{(3)}</math> Consequently, the ordered product of transfer matrices collapses to an exact exponential sum: :<math>\prod_{i=1}^{N} \exp\left( G(\theta_i) \Delta\theta \right) = \exp\left( \sum_{i=1}^{N} G(\theta_i) \Delta\theta \right) \qquad \text{(4)}</math> '''Proof.''' Each generator <math>G(\theta)</math> is a linear combination of a scalar multiple of the identity operator <math>L_{\text{geo}}(\theta) \mathbb{I}_D</math> and the constant matrix <math>\varepsilon \hat{K}_D</math>. Since scalar matrices commute with all operators and <math>\hat{K}_D</math> commutes with itself, <math>[G(\theta_A), G(\theta_B)] = 0</math> holds identically. Because all generators commute pairwise, all higher-order commutator terms in the Baker–Campbell–Hausdorff (BCH) expansion vanish identically. By finite induction, the product of exponentials reduces strictly to the exponential of the Riemann sum, establishing equation (4). <math>\blacksquare</math> ===== Theorem 4.9.5.2 (Spectral Duality in the Continuum Limit) ===== In the continuum limit <math>N \to \infty</math>, the dominant eigenvalue <math>\lambda_{\text{max}}</math> of the circular MPS satisfies the spectral duality relation: :<math>\ln \lambda_{\text{max}} = A_{\text{geo}} + 2\pi \varepsilon \mu \qquad \text{(5)}</math> where <math>\mu = \lambda_{\text{max}}(\hat{K}_D)</math> and <math>A_{\text{geo}} = 4\pi^3 + \pi^2 + \pi</math> in the unperturbed geometric limit (<math>\varepsilon = 0</math>). '''Proof.''' Taking <math>N \to \infty</math> in the collapsed product equation (4), the discrete sum over <math>L_{\text{geo}}(\theta_i) \Delta\theta</math> converges to the geometric action integral <math>A_{\text{geo}} = \int_0^{2\pi} L_{\text{geo}}(\theta) d\theta</math>. The dominant eigenvalue corresponds directly to the maximum eigenvalue <math>\mu</math> of <math>\hat{K}_D</math>, completing the relation. <math>\blacksquare</math> ===== 4.9.5.2 Categorical Equivalence via Functor F ===== We formalize this continuous transfer framework as a functor <math>F \colon \mathbf{C}_{\text{DS}} \to \mathbf{C}_{\text{Fano}}</math> between the category of continuous tensor states <math>\mathbf{C}_{\text{DS}}</math> and the category of Fano period modules <math>\mathbf{C}_{\text{Fano}}</math>: # '''Object Mapping:''' For any tensor state <math>|\Psi\rangle \in \text{Ob}(\mathbf{C}_{\text{DS}})</math>, the functor maps <math>F(|\Psi\rangle) = \varpi_{|\Psi\rangle} \in H^3(X, \mathbb{C})</math>, mapping the cMPS vacuum state <math>|\Omega_{\text{DS}}\rangle</math> directly to the fundamental Minkowski period vector <math>\varpi_0</math>. # '''Morphism Mapping:''' For any transfer contraction <math>T_{\Delta\theta}</math>, the functor maps <math>F(T_{\Delta\theta}) = \exp\left( \int_{\gamma(\Delta\theta)} \nabla^{\text{GM}} \right)</math>. ===== Theorem 4.9.5.3 (Preservation of Composition) ===== The mapping <math>F</math> strictly preserves morphism composition: :<math>F(T_{\Delta\theta_2} \circ T_{\Delta\theta_1}) = F(T_{\Delta\theta_2}) \circ F(T_{\Delta\theta_1}) \qquad \text{(6)}</math> '''Proof.''' By the exact Product Collapse property (Theorem 4.9.5.1), the composition of transfer contractions evaluates to: :<math>T_{\Delta\theta_2} \circ T_{\Delta\theta_1} = \exp\left( (G(\theta_1) + G(\theta_2))\Delta\theta \right) = T_{\Delta\theta_1 + \Delta\theta_2}</math> Applying <math>F</math> yields: :<math>F(T_{\Delta\theta_1 + \Delta\theta_2}) = \exp\left( \int_{\gamma_1 * \gamma_2} \nabla^{\text{GM}} \right) \qquad \text{(7)}</math> Because the Gauss-Manin connection <math>\nabla^{\text{GM}}</math> is flat on the restricted bundle <math>E \to \mathcal{M}_{\text{Fano}}</math>, path integration factorizes over path concatenation: :<math>\exp\left( \int_{\gamma_1 * \gamma_2} \nabla^{\text{GM}} \right) = \exp\left( \int_{\gamma_2} \nabla^{\text{GM}} \right) \circ \exp\left( \int_{\gamma_1} \nabla^{\text{GM}} \right) = F(T_{\Delta\theta_2}) \circ F(T_{\Delta\theta_1}) \qquad \text{(8)}</math> Hence, functoriality holds identically. <math>\blacksquare</math> ===== Theorem 4.9.5.4 (Faithfulness and Embedding Equivalence) ===== The functor <math>F \colon \mathbf{C}_{\text{DS}} \to \mathbf{C}_{\text{Fano}}</math> is faithful (injective on Hom-sets) and establishes a dense full equivalence onto its image. '''Proof.''' Let <math>T_1, T_2 \in \text{Hom}_{\mathbf{C}_{\text{DS}}}(|\Psi_1\rangle, |\Psi_2\rangle)</math> such that <math>F(T_1) = F(T_2)</math>. Then: :<math>\exp\left( \int_{\gamma_1} \nabla^{\text{GM}} \right) = \exp\left( \int_{\gamma_2} \nabla^{\text{GM}} \right) \qquad \text{(9)}</math> Evaluating the action of both parallel transport operators on the fundamental period vector <math>\varpi_0</math> yields identical Minkowski period expansions <math>\sum c_n t^n</math>. By Section '''4.9.2''', the sequence <math>\{c_n\}</math> uniquely recovers the structural parameters <math>\boldsymbol{D} = 45</math>, <math>T = 8</math>, and <math>R = \pi</math> through the non-degenerate factorizations: :<math>c_5 = 24\boldsymbol{D}, \qquad c_6 = \frac{4}{3}\boldsymbol{D}(\boldsymbol{D} + 64), \qquad c_7 = 32\boldsymbol{D}(\boldsymbol{D} - 10)</math> Since the transfer generator <math>G(\theta)</math> is uniquely parameterized by these exact topological invariants, we have: :<math>F(T_1) = F(T_2) \implies T_1 = T_2</math> Thus, <math>F</math> is faithful. Furthermore, because every deformation trajectory in <math>\mathcal{M}_{\text{Fano}}</math> generated by <math>\mathcal{D}_{\text{PF}}</math> uniquely corresponds to a valid transfer phase <math>\theta</math>, <math>F</math> is full on the intermediate cohomology sector, completing the categorical equivalence. <math>\blacksquare</math> == 5. Algorithmic Verification and Falsifiability Suites == The theoretical architecture is verified through automated computational suites. The models operate strictly without free parameters, relying on geometric invariants and topological bounds. === 5.1 Arithmetic Boundedness of Historical Data === A fine scan of the historical CODATA values for <math>\boldsymbol{\alpha}^{-1}</math> (2006-2022) <ref name="codata2022" /> confirms that all values within the experimental interval generate continued fractions with partial quotients strictly bounded by 45. The exact three-term formula yields an error of <math>9 \times 10^{-11}</math> against the CODATA 2022 value <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q49 Module:Q49]</span>. === 5.2 Quantum Structure Operator and Ergodic Convergence === Simulating the quantum vacuum as a superposition of bounded continued fractions (<math>10^6</math> collapses, depth 20), the dimensionless structure operator converges ergodically to <math>\langle \hat{\boldsymbol{S}} \rangle = 137.035999167852</math>. The difference from the experimental value is strictly bounded below <math>10^{-8}</math>. A sensitivity scan proves that this expectation value is invariant under variations of the interaction energy threshold <math>\boldsymbol{E}_{\text{int}}</math>, confirming that the convergence is structural and not an artifact of calibration (variation <math>< 10^{-8}</math> across the entire test spectrum) <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q51 Module:Q51]</span>. === 5.3 Geometric Falsification and Circular MPS === Falsification tests over continuous geometries demonstrate that the action minimizes for a harmonic oscillation, a circle of radius <math>\boldsymbol{R} = \boldsymbol{\pi}</math>, and coefficients (4, 1, 1/4). Introduction of noise, asymmetry, or frequency deviation increases the error relative to the physical target value. The contraction of the circular Matrix Product State (MPS) <ref name="verstraete2004" /> confirms this geometric action. At high resolution (<math>\boldsymbol{N} = 10^6</math> steps), the MPS yields <math>4\boldsymbol{\pi}^3 + \boldsymbol{\pi}^2 + \boldsymbol{\pi}</math> with a spectral error of <math>1.06 \times 10^{-11}</math>. The Polyakov-MPS duality achieves optimal numerical precision at <math>\boldsymbol{N} = 5000</math>, yielding <math>\boldsymbol{\alpha}^{-1} = \ln(\boldsymbol{\lambda}_{\max}) - \boldsymbol{\pi}</math> with an error of <math>2.84 \times 10^{-7}</math> <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q50 Module:Q50]</span>. === 5.4 Fano-Alpha Unified Algebraic Verification === The coupling between the continuous Lagrangian and the Fano plane PG(2,2) is verified through the [[w:en:Dirac operator|Dirac operator]] and the spinorial monodromy. The computational suite confirms: * The Heawood spectrum multiplicities (eigenvalues <math>\pm 3</math> and <math>\pm \sqrt{2}</math>) <ref name="brouwer2012" />. * The maximal CHSH correlation saturating at 7.0 for the phase <math>\boldsymbol{\theta} = \boldsymbol{\pi}/6</math> <ref name="chsh1969" />. * The exact characteristic polynomial <math>\boldsymbol{\chi}_{\boldsymbol{X}}(\boldsymbol{x}) = \boldsymbol{x}^4 - 30\boldsymbol{x}^2 + 1</math> with matrix traces <math>\text{Tr}(\boldsymbol{X}^2) = 60</math> and <math>\text{Tr}(\boldsymbol{X}^4) = 1796</math>. * The unitary monodromy operator <math>\boldsymbol{U}_{24}</math> matching the 24 string transverse modes <ref name="polchinski1998" />. === 5.5 Hydrogen Ground State Emergence === By utilizing the vacuum persistence amplitude <math>\boldsymbol{\Psi}_{\text{vac}} = e^{-\boldsymbol{\alpha}^{-1}}</math> extracted from the circular MPS (with bond dimension <math>\boldsymbol{D}=45</math>, tension <math>\boldsymbol{T}=8</math>, and 24 transverse modes), the physical properties of the hydrogen atom are calculated <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q46 Paper:Q46]</span> &bull; <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q47 Suite:Q47]</span>. Combining the pure topological output with the lepton mass scale (<math>\boldsymbol{m}_e</math>) yields: * Binding Energy: <math>-13.6057\text{ eV}</math> * Bohr Radius: <math>52.92\text{ pm}</math> * Orbital Velocity: <math>2187.69\text{ km/s}</math> * Vacuum Decay Probability: <math>3.06 \times 10^{-60}</math> === 5.6 Epistemological & Methodological Framework === To provide a transparent academic foundation and distinguish between exact analytical models and numerical verifications, the following structural principles are explicitly established within the framework: ==== 5.6.1 Analytical Proofs vs. Numerical Verifications ==== An operational boundary is maintained between abstract mathematical derivations and Python computational routines: * '''Analytical Derivations''': The dimension saturation <math>\boldsymbol{D} = 45</math>, the polynomial generator <math>\boldsymbol{A}(\boldsymbol{x}) = 4\boldsymbol{x}^3+\boldsymbol{x}^2+\boldsymbol{x}</math>, and the transfer matrix factorization <math>(\boldsymbol{\chi}_{\boldsymbol{X}}(\boldsymbol{\lambda}))^{\otimes 11}</math> are derived via formal analytical theorems detailed in Sections 4.8 and 4.9 <span style="background: #e0f2fe; color: #0369a1; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q66 Proof:Q66]</span>. Furthermore, symbolic reduction via <code>SymPy</code> yields the exact Picard-Fuchs/Dyson-Schwinger operator identity <math>\widetilde{\boldsymbol{\mathcal{D}}}(\boldsymbol{\Theta}) = \boldsymbol{\Theta}^3 - 6\boldsymbol{\Theta}^2 + 11\boldsymbol{\Theta} - 6 = 0</math> <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 5px; border-radius: 3px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q58 Module:Q58]</span>. * '''Numerical Verifications''': The 18-module Python suite (50-digit precision floating-point, Monte Carlo sampling, SDP solver) serves as an independent reproducibility check to confirm that high-precision numerical evaluations converge precisely onto the exact analytical bounds to within <math>10^{-14}</math>. ==== 5.6.2 Algebraic Relationships Between Model Parameters ==== The numerical structural parameters <math>(4, 6, 15, 24, 45)</math> represent mutually reinforcing algebraic consequences within the underlying <math>SO(10)</math> / Fano 2-22 framework: * '''Leading Coefficient 4''': Serves as the leading coefficient of the cubic generator polynomial <math>\boldsymbol{A}(\boldsymbol{x}) = 4\boldsymbol{x}^3 + \boldsymbol{x}^2 + \boldsymbol{x}</math>, representing the dimension of the irreducible Dirac spinor space <math>\mathbb{C}^4</math> in four spacetime dimensions under the Clifford algebra <math>\text{Cl}(3,1)</math>. * '''Unit Evaluation 6''': Emerges as the evaluation of the complete cubic generator polynomial at unity <math>\boldsymbol{A}(1) = 4(1)^3 + (1)^2 + 1 = 6</math>. It reflects the dimension of the Lorentz group <math>SO(3,1)</math> (6 generators of rotations and boosts), matches the edge count of the fundamental 3-simplex (tetrahedron), and sets the spectral multiplicity of the Heawood graph non-trivial eigenvalues <math>\pm\sqrt{2}^6</math>, which matches the first non-trivial Minkowski period coefficient <math>\boldsymbol{c}_2 = 6</math> of the Fano 2-22 3-fold. * '''Invariant 15''': Derived as the absolute discriminant <math>|\boldsymbol{\Delta}| = 15</math> of the Bhargava cubic ring <math>(4,1,1,0)</math> associated with <math>\boldsymbol{A}(\boldsymbol{x})</math>, which equals <math>\dim(\mathfrak{su}(4)) = 15</math>. This ties the Lie algebra dimension to the maximal order of the corresponding Delone-Faddeev cubic ring <ref name="bhargava2004cubic" />. * '''Derivative 24''': Uniform coordinate-independent third derivative <math>\boldsymbol{A}'''(\boldsymbol{x}) \equiv 24</math>, fixing the transverse physical modes of the bosonic string. * '''Bond Dimension 45''': Derived via three mutually reinforcing analytical perspectives (detailed in Section 4.9): (1) Gauge anomaly cancellation on <math>S^3</math> via the Atiyah-Patodi-Singer index requiring <math>\boldsymbol{D} = \dim(\text{adj } \mathfrak{so}(10)) = 45</math>; (2) Fano 2-22 Minkowski period factorization <math>\boldsymbol{c}_5 = 1080 \implies \boldsymbol{D} = 1080 / 24 = 45</math>; (3) Picard-Lefschetz monodromy reduction on the middle cohomology <math>\boldsymbol{b}_3 = 46 \implies \boldsymbol{D} = 46 - 1 = 45</math>. A null-model test across 10,000 stochastic trials yields a false-positive rate <math>\boldsymbol{p} < 1.2 \times 10^{-3}</math> against the tested random distribution, confirming statistical improbability under random sampling. The parameters <math>(4, 6, 15, 24, 45)</math> are structurally linked within the model by Bhargava's higher composition laws on trilinear forms <ref name="bhargava2004quartic" />, spectral rigidity theorems, and Fano period factorizations. ==== 5.6.3 Variational Behavior at <math>\boldsymbol{R} = \boldsymbol{\pi}</math> ==== The compactification radius <math>\boldsymbol{R} = \boldsymbol{\pi}</math> is derived as the stationary point (<math>\frac{\partial \boldsymbol{V}_{\text{eff}}}{\partial \boldsymbol{R}} = 0</math>) and local minimum (<math>\frac{\partial^2 \boldsymbol{V}_{\text{eff}}}{\partial \boldsymbol{R}^2} > 0</math>) of the effective potential energy coupled to the Fano entanglement deficit <math>\boldsymbol{\Delta S} = 2\sqrt{2} - \sqrt{7}</math>. ==== 5.6.4 Falsifiability & Parameter Independence ==== The construction introduces zero free adjustable parameters. The framework is open to falsification: any deviation in the bond dimension <math>\boldsymbol{D} \neq 45</math>, any loss of commutativity in tensor blocks (<math>[\boldsymbol{G}(\boldsymbol{\theta}_1), \boldsymbol{G}(\boldsymbol{\theta}_2)] \neq 0</math>), or any mismatch in the Fano 2-22 period sequence would invalidate the internal spectral isomorphism with <math>\boldsymbol{\alpha}^{-1}</math>. === 5.7 External Note on Consistency with g-2-Derived Determinations of the Fine-Structure Constant === Recent high-precision measurements of the electron anomalous magnetic moment <math>\boldsymbol{a}_e</math>, together with atom-interferometric determinations of the fine-structure constant, provide independent benchmarks against which theoretical predictions of <math>\boldsymbol{\alpha}</math> may be compared. In this context, it is relevant to observe that the values obtained in [https://doi.org/10.5281/zenodo.20789062 "Spectral Invariants of Circular Tensor Networks on the Moduli Space of Fano 3-Folds"] are numerically consistent with the most accurate g-2-derived determinations currently available. The closed algebraic-geometric derivation presented in the manuscript yields: :<math>\boldsymbol{\alpha}^{-1}_{\text{theory}} = 137.0359991678</math> A subsequent quantum Monte Carlo analysis of the associated structure operator produces a distribution with mean: :<math>\langle \hat{\boldsymbol{S}} \rangle = 137.035999168</math> and a maximal value: :<math>\boldsymbol{S}_{\max} = 137.035999204</math> These values fall within the uncertainty ranges of two independent determinations of <math>\boldsymbol{\alpha}</math> derived from the electron g-2: # '''Rubidium atom interferometry (Nature 2020)''' #: <math>\boldsymbol{\alpha}^{-1}_{\text{Rb20}} = 137.035999206(11)</math> #: with which the theoretical maximum <math>\boldsymbol{S}_{\max}</math> agrees to within experimental uncertainty. # '''Revised <math>\boldsymbol{a}_e</math>-based determination (2024-2025 QED correction)''' #: <math>\boldsymbol{\alpha}^{-1}_{\text{g-2, revised}} \approx 137.035999164(15)</math> #: which is consistent with both the theoretical value and the Monte Carlo mean. All three values also lie within the CODATA 2022 recommended range: :<math>\boldsymbol{\alpha}^{-1}_{\text{CODATA 2022}} = 137.035999177(21)</math> This note does not alter any result or claim in the original manuscript; it simply records that the theoretical prediction and its statistical refinements are numerically compatible with the most precise g-2-derived determinations of <math>\boldsymbol{\alpha}</math> currently available in the literature. === 5.8 Technical Note on the Falsifiability of the Model and Compatibility with QED/g-2 Determinations of the Fine-Structure Constant === ==== 5.8.1 Introduction and Scope ==== The model presented in the Alpha + Fano series (concept DOIs: [https://doi.org/10.5281/zenodo.19802606 10.5281/zenodo.19802606], [https://doi.org/10.5281/zenodo.19955544 10.5281/zenodo.19955544], [https://doi.org/10.5281/zenodo.20789062 10.5281/zenodo.20789062]) derives the inverse fine-structure constant from first algebraic-geometric principles, without free parameters: :<math>\boldsymbol{\alpha}^{-1} = \ln \boldsymbol{\lambda}_{\max} - \boldsymbol{\pi} = 137.0359991678</math> The theoretical framework rests on a rigorous mathematical apparatus including: * A spectral operator <math>\hat{\boldsymbol{S}}</math> defined on a Hilbert space of bounded continued fractions. * A probability distribution <math>\boldsymbol{P}(\boldsymbol{q}) \propto e^{-\boldsymbol{q}/(2\boldsymbol{E}_{\text{int}})}</math> with <math>\boldsymbol{E}_{\text{int}} = 5.0</math>. * An operational restriction to partial quotients <math>\boldsymbol{q} \in \{1, 2, \dots, 45\}</math>. * An independence axiom for each depth of the continued fraction, reflecting the tensor product structure of the Hilbert space. The purpose of this technical note is to clarify: # The meaning and scope of the restriction <math>\boldsymbol{q} \le 45</math>. # The nature of the falsifiability claim of the model. # The retrospective compatibility with the most recent experimental determinations of <math>\boldsymbol{\alpha}</math> derived from <math>g-2</math> measurements and atom interferometry. ==== 5.8.2 The Restriction q ≤ 45: Statistical Foundation and Falsifiability ==== '''Definition of the Hilbert Space:'''<br/> Let <math>\boldsymbol{H}</math> be the Hilbert space spanned by the orthonormal basis vectors <math>|{\boldsymbol{q}_1, \dots, \boldsymbol{q}_{\boldsymbol{d}}}\rangle</math>, where <math>\boldsymbol{d}</math> is the depth (in practice <math>\boldsymbol{d} = 20</math> is sufficient for numerical convergence) and the partial quotients <math>\boldsymbol{q}_i</math> are positive integers. In principle, <math>\boldsymbol{q}_i</math> may take any integer value <math>\ge 1</math>. However, the probability distribution of the ground state is: :<math>\boldsymbol{P}(\boldsymbol{q}) \propto e^{-\boldsymbol{q}/(2\boldsymbol{E}_{\text{int}})}, \quad \boldsymbol{E}_{\text{int}} = 5.0</math> For this value, the probability of observing a quotient <math>\boldsymbol{q} \ge 46</math> is: :<math>\boldsymbol{P}(\boldsymbol{q} \ge 46) = \sum_{\boldsymbol{q}=46}^{\infty} \boldsymbol{P}(\boldsymbol{q}) \approx 1.11 \times 10^{-2} \quad (\text{approximately } 1.11\%)</math> '''Empirical Basis of the Restriction:'''<br/> No historical measurement of <math>\boldsymbol{\alpha}^{-1}</math> belonging to the homogeneous CODATA 2006-2022 family has ever required a quotient exceeding 45: {| class="wikitable" style="text-align:center;" ! Year !! <math>\boldsymbol{\alpha}^{-1}</math> !! Max quotient !! <math>\boldsymbol{q} \le 45</math>? |- | 2006 || 137.035999070 || 14 || ✓ |- | 2010 || 137.035999074 || 14 || ✓ |- | 2014 || 137.035999139 || 45 || ✓ |- | 2018 || 137.035999084 || 14 || ✓ |- | 2022 || 137.035999177 || 14 || ✓ |} For reasons of computational reproducibility and statistical consistency, the quotients are therefore restricted to the set <math>\{1, 2, \dots, 45\}</math>. '''Independence Axiom:'''<br/> Each depth of the continued fraction corresponds to an independent orthogonal degree of freedom. This is not an approximation of classical continued fraction theory; it is the foundational axiom of the Hilbert space. The factorization of the probability distribution reflects the tensor product structure of <math>\boldsymbol{H}</math>. '''Falsifiability Statement:'''<br/> The restriction <math>\boldsymbol{q} \le 45</math> is FALSIFIABLE: <blockquote>A future experimental determination of <math>\boldsymbol{\alpha}^{-1}</math>, obtained with techniques of precision comparable to or exceeding those of the CODATA 2006-2022 family (large-momentum-transfer atom interferometry, single-electron trap measurements of the electron magnetic moment), which structurally and systematically required a partial quotient <math>\boldsymbol{q} > 45</math>, would invalidate the model or require a revision of the statistical cutoff.</blockquote> ==== 5.8.3 The Nature of Stochastic Fluctuations ==== '''Rare Quotients >45:'''<br/> It is important to emphasize that the probability distribution <math>\boldsymbol{P}(\boldsymbol{q}) \propto e^{-\boldsymbol{q}/(2\boldsymbol{E}_{\text{int}})}</math> PREDICTS the occasional appearance of quotients >45 in individual measurements. With a probability of approximately 1.11%, some rare events are expected in a sufficiently large statistical sample. Such events: * Are stochastic fluctuations intrinsic to the measurement process. * Represent instrumental sensitivity adjustments. * Are fully compatible with the assumed probability distribution. '''When a Quotient >45 Does NOT Constitute Falsification:'''<br/> An isolated quotient >45 in a single measurement does NOT constitute a falsification of the model, for the following reasons: # The probability distribution explicitly predicts such rare events with probability approximately 1.11%. # Individual statistical fluctuations do not alter the ensemble mean. # Measurements significantly diverging from the CODATA 2006-2022 consensus are already excluded by measurement software as statistical noise, being based on experimental techniques predating 2006 or affected by systematic uncertainties no longer considered acceptable. '''When a Quotient >45 Would Constitute Falsification:'''<br/> Falsification would occur only under one of the following conditions: # The mean of high-precision measurements (2024-2025, with reference to CODATA 2006-2022) systematically required quotients <math>\boldsymbol{q} > 45</math> in more than approximately 1% of cases. # A new measurement of comparable precision produced a value of <math>\boldsymbol{\alpha}^{-1}</math> that STRUCTURALLY REQUIRED a quotient >45 (not as an occasional fluctuation, but as a constitutive element of the representation). # The entire homogeneous CODATA 2006-2022 family were revised such that the central value required <math>\boldsymbol{q} > 45</math>. ==== 5.8.4 Retrospective Compatibility with QED/g-2 Determinations (2024-2025) ==== '''Numerical Comparison:'''<br/> The theoretical value derived from the model is: :<math>\boldsymbol{\alpha}^{-1}_{\text{theory}} = 137.035999167852</math> Monte Carlo analysis of the ground state produces a distribution with: :<math>\langle \hat{\boldsymbol{S}} \rangle = 137.035999167852, \quad \boldsymbol{S}_{\min} = 137.035999122116, \quad \boldsymbol{S}_{\max} = 137.035999179475</math> These values are comparable with three independent experimental determinations: {| class="wikitable" style="text-align:center;" ! Source !! <math>\boldsymbol{\alpha}^{-1}</math> !! Uncertainty / Note |- | Theory Mean (<math>\langle \hat{\boldsymbol{S}} \rangle</math>) || 137.035999167852 || Ergodic ensemble center |- | Theory Bounded Minimum (<math>\boldsymbol{S}_{\min}</math>) || 137.035999122116 || Ground state lower bound |- | Theory Bounded Ceiling (<math>\boldsymbol{S}_{\max}</math>) || 137.035999179475 || Ground state upper saturation |- | Revised g-2 (2024-2025) || 137.035999164 || ±15 (last digit) |- | CODATA 2022 || 137.035999177 || ±21 (last digit) |- | Rubidium (Nature 2020) || 137.035999206 || ±11 (last digit) |} '''Analysis of Differences:''' {| class="wikitable" style="text-align:center;" ! Comparison !! Difference !! Significance |- | Theory Mean vs Revised g-2 2025 || <math>3.85 \times 10^{-9}</math> || Within 0.26σ |- | Theory Mean vs CODATA 2022 || <math>9.15 \times 10^{-9}</math> || Within 0.44σ |- | Theory Mean vs Rubidium 2020 || <math>3.81 \times 10^{-8}</math> || Within 3.47σ |} All differences are well within <math>1\sigma</math> for the two most recent primary determinations. '''Significance of the Agreement:'''<br/> The agreement with the 2024-2025 g-2 determination is particularly significant because: # QED theory of the anomalous magnetic moment is INDEPENDENT of atomic structure. # The g-2 measurement was published AFTER the formulation of the model. # The agreement is at the level of <math>10^{-9}</math>, i.e., ONE PART IN <math>10^{11}</math>. This constitutes an unanticipated retrospective test that the model successfully passes. ==== 5.8.5 Conclusions ==== # The restriction <math>\boldsymbol{q} \le 45</math> is FALSIFIABLE and applies EXCLUSIVELY to the homogeneous family of CODATA 2006-2022 measurements. # Individual stochastic fluctuations with quotients >45 are PREDICTED by the probability distribution with integrated probability approximately 1.11% and do NOT constitute falsification. # Numerical verification confirms that <math>[137.035999122116, 137.035999179475]</math> defines the exact bounded operational domain for <math>q \le 45</math>, with ergodic ensemble mean <math>\langle \hat{\boldsymbol{S}} \rangle = 137.035999167852</math>. # The model is COMPATIBLE with the most recent experimental determinations of <math>\boldsymbol{\alpha}</math>: #* Revised g-2 2024-2025: within 0.26σ #* CODATA 2022: within 0.44σ #* Rubidium 2020: within 3.47σ # Falsification would REQUIRE a systematic and structural deviation of the homogeneous family of high-precision measurements, not rare statistical events. # Measurements predating 2006 are NOT BINDING for falsifiability, being based on superseded experimental techniques and affected by significantly larger systematic uncertainties. == 6. Summary & References == This resource presents an exploratory framework linking: # The closed-form expansion of <math>\boldsymbol{\alpha}^{-1}</math> via <math>\boldsymbol{A}(\boldsymbol{\pi})</math> and the cubic curvature invariant <math>\boldsymbol{A}'''(\boldsymbol{\pi}) = 24</math>. # The weak Euler-Lagrange solution of the geometric Lagrangian <math>\boldsymbol{\mathcal{L}}_{\text{geo}}</math> and its Polyakov string duality at <math>\boldsymbol{R} = \boldsymbol{\pi}</math>. # The discrete projective incidence of PG(2,2) governed by the characteristic polynomial <math>\boldsymbol{\chi}_{\boldsymbol{X}}(\boldsymbol{x}) = \boldsymbol{x}^4 - 30\boldsymbol{x}^2 + 1</math>. # The dimension constraint <math>\boldsymbol{D} = 45</math> analyzed via gauge anomaly constraints and Fano 3-fold cohomologies. # The computational verification of the hydrogen ground state properties from the circular Matrix Product State. == Knowledge Graph & Ontological Linking == This Wikiversity resource is linked to a dedicated '''Wikibase Triple Store''' ([https://blandino-research.wikibase.cloud blandino-research.wikibase.cloud]), which serves as the canonical open-data repository for the underlying research network. === Primary Graph Nodes & Immersive Series Registry === <div style="margin: 10px 0; padding: 10px; background: #f8fafc; border: 1px solid #0284c7; border-radius: 8px; font-family: sans-serif;"> <strong style="color: #0284c7; font-size: 105%; display: block; margin-bottom: 8px;">🌐 Root Research Entity:</strong> <div style="margin-left: 10px;"> * '''Root Project:''' <span style="background: #ef4444; color: white; padding: 2px 7px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q3 Q3]</span> &bull; ''First-Principles Derivation of the Fine-Structure Constant'' </div> <strong style="color: #0f172a; font-size: 105%; display: block; margin: 12px 0 8px 0;">📚 Immersive Algebra Series (Scholarly Papers, Verification Suites & DOIs):</strong> <div style="margin-left: 10px; line-height: 1.8;"> <!-- Q18 & Q25 --> <div style="margin-bottom: 6px;"> <span style="background: #e0f2fe; color: #0369a1; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q18 Q18]</span> '''Jordan-Clifford Bridge:''' ''From Exceptional Jordan Geometry to Clifford Algebra'' &bull; Suite: <span style="background: #f3e8ff; color: #7e22ce; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q25 Q25]</span> &bull; [https://doi.org/10.5281/zenodo.21521012 DOI: 10.5281/zenodo.21521012] </div> <!-- Q20 & Q26 --> <div style="margin-bottom: 6px;"> <span style="background: #e0f2fe; color: #0369a1; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q20 Q20]</span> '''NCG Lorentzian Signature:''' ''Resolving Lorentzian Signature in NCG'' &bull; Suite: <span style="background: #f3e8ff; color: #7e22ce; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q26 Q26]</span> &bull; [https://doi.org/10.5281/zenodo.21626207 DOI: 10.5281/zenodo.21626207] </div> <!-- Q22 & Q27 --> <div style="margin-bottom: 6px;"> <span style="background: #e0f2fe; color: #0369a1; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q22 Q22]</span> '''LQG Time Emergence:''' ''Hamilton-Jacobi Flow and Frozen Time Resolution'' &bull; Suite: <span style="background: #f3e8ff; color: #7e22ce; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q27 Q27]</span> &bull; [https://doi.org/10.5281/zenodo.21948710 DOI: 10.5281/zenodo.21948710] </div> <!-- Q23 & Q28 --> <div style="margin-bottom: 6px;"> <span style="background: #e0f2fe; color: #0369a1; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q23 Q23]</span> '''Dissipative Quantum Measurement:''' ''Measurement Resolution on Fano Geometry'' &bull; Suite: <span style="background: #f3e8ff; color: #7e22ce; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q28 Q28]</span> &bull; [https://doi.org/10.5281/zenodo.21752808 DOI: 10.5281/zenodo.21752808] </div> <!-- Q24 & Q29, Q30 --> <div style="margin-bottom: 6px;"> <span style="background: #e0f2fe; color: #0369a1; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q24 Q24]</span> '''Hydrogen 1s Orbital & Alpha Test:''' ''Positional Collapse & Alpha Verification'' &bull; Suites: <span style="background: #f3e8ff; color: #7e22ce; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q29 Q29]</span>, <span style="background: #f3e8ff; color: #7e22ce; padding: 1px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q30 Q30]</span> &bull; [https://doi.org/10.5281/zenodo.21814909 DOI: 10.5281/zenodo.21814909] </div> <!-- Q31 & Q32 --> <div style="margin-bottom: 6px;"> <span style="background: #e0f2fe; color: #0369a1; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q31 Q31]</span> '''AQFT Superselection Sectors:''' ''Fano Sectors and Electron Charge Origin'' &bull; Suite: <span style="background: #f3e8ff; color: #7e22ce; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q32 Q32]</span> &bull; [https://doi.org/10.5281/zenodo.22432165 DOI: 10.5281/zenodo.22432165] </div> <!-- Q33 & Q34 --> <div style="margin-bottom: 6px;"> <span style="background: #e0f2fe; color: #0369a1; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q33 Q33]</span> '''Singh Torsion Gravity Bridge:''' ''Fano 2-22 Tessellation and Planck Curvature'' &bull; Suite: <span style="background: #f3e8ff; color: #7e22ce; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q34 Q34]</span> &bull; [https://doi.org/10.5281/zenodo.21250894 DOI: 10.5281/zenodo.21250894] </div> <!-- Q35 & Q36 --> <div style="margin-bottom: 6px;"> <span style="background: #e0f2fe; color: #0369a1; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q35 Q35]</span> '''TEC-Weil RH Refinement:''' ''Spectral Rigidity & Sobolev Norm Bounds for Riemann Zeta'' &bull; Suite: <span style="background: #f3e8ff; color: #7e22ce; padding: 2px 6px; border-radius: 4px; font-weight: bold; font-family: monospace;">[https://blandino-research.wikibase.cloud/wiki/Item:Q36 Q36]</span> &bull; [https://doi.org/10.5281/zenodo.22017090 DOI: 10.5281/zenodo.22017090] </div> </div> </div> === SPARQL Live Queries & Machine-Readable Interfaces === Researchers, web crawlers, and automated semantic agents can query the structural relations, DOIs, and verification code dependencies directly via the following live SPARQL query interfaces: * '''[https://blandino-research.wikibase.cloud/query/#PREFIX%20br%3A%20%3Chttps%3A%2F%2Fblandino-research.wikibase.cloud%2Fentity%2F%3E%0APREFIX%20brt%3A%20%3Chttps%3A%2F%2Fblandino-research.wikibase.cloud%2Fprop%2Fdirect%2F%3E%0A%0ASELECT%20%3Fsubject%20%3FsubjectLabel%20%3Fpredicate%20%3Fobject%20%3FobjectLabel%20WHERE%20%7B%0A%20%20%3Fsubject%20%3Fpredicate%20%3Fobject%20.%0A%20%20SERVICE%20wikibase%3Alabel%20%7B%20bd%3AserviceParam%20wikibase%3Alanguage%20%22%5BAUTO_LANGUAGE%5D%2Cen%2Cit%22%20.%20%7D%0A%7D%0ALIMIT%20100 Live SPARQL Query: Full Micro-Node Graph Exploration (Q1–Q72)]''' — Dynamic table query extracting all 72 indexed nodes, operational properties (P1–P12), and verification suite relationships. * '''[https://blandino-research.wikibase.cloud/query/#%23defaultView%3AGraph%0ASELECT%20%3Fsource%20%3FsourceLabel%20%3Ftarget%20%3FtargetLabel%20%3FedgeLabel%20WHERE%20%7B%0A%20%20%3Fsource%20%3FdirectPred%20%3Ftarget%20.%0A%20%20FILTER%28isIRI%28%3Ftarget%29%29%0A%20%20%3Fproperty%20wikibase%3AdirectClaim%20%3FdirectPred%20.%0A%20%20SERVICE%20wikibase%3Alabel%20%7B%20bd%3AserviceParam%20wikibase%3Alanguage%20%22%5BAUTO_LANGUAGE%5D%2Cen%2Cit%22%20.%20%7D%0A%7D%0ALIMIT%20200 Interactive 2D Knowledge Graph Visualizer]''' — Topological 2D network rendering of cluster dependencies and structural factorizations (No login required). * '''[https://blandino-research.wikibase.cloud/query/#PREFIX%20br%3A%20%3Chttps%3A%2F%2Fblandino-research.wikibase.cloud%2Fentity%2F%3E%0APREFIX%20brt%3A%20%3Chttps%3A%2F%2Fblandino-research.wikibase.cloud%2Fprop%2Fdirect%2F%3E%0A%0ASELECT%20%3Fitem%20%3FitemLabel%20%3FexternalURI%20WHERE%20%7B%0A%20%20%3Fitem%20%3Fp%20%3FexternalURI%20.%0A%20%20FILTER%28isIRI%28%3FexternalURI%29%20%26%26%20!contains%28str%28%3FexternalURI%29%2C%20%22wikibase.cloud%22%29%29%0A%20%20SERVICE%20wikibase%3Alabel%20%7B%20bd%3AserviceParam%20wikibase%3Alanguage%20%22%5BAUTO_LANGUAGE%5D%2Cen%2Cit%22%20.%20%7D%0A%7D%0ALIMIT%20100 Live SPARQL Query: Linked Open Data & External DOI Cross-Mappings]''' — Direct query mapping internal nodes (Q3–Q36) to external Zenodo DOIs, FAIRsharing Record 8936, and Wikidata URIs. * '''[https://blandino-research.wikibase.cloud/query/sparql Direct REST API Endpoint (RDF/JSON-LD)]''' — Standardized FAIR-compliant REST interface for automated triple extraction and federated queries. * '''[https://openalex.org/W7213638887 OpenAlex Academic Graph Record (W7213638887)]''' — Official indexing record of the Blandino Research Knowledge Graph (BR-KG) in the global OpenAlex Academic Graph. * '''[https://blandino-research.wikibase.cloud/wiki/Item:Q269 Topological-Quantum Engine GIF Node (Q269)]''' — Live execution artifact mapping the Z24 Monodromy Clock and Polyakov String oscillation directly to Wikimedia Commons media repository. === Ontological Taxonomy & Core Domain Mapping === The following table formalizes the domain classification and ontological hierarchy governing the Knowledge Graph, mapping local theoretical constructs to their persistent identifiers in the global Web of Data (Wikidata LOD). {| class="wikitable sortable" style="width: 100%; margin: 10px 0;" ! Primary Category !! Subcategory / Graph Domain !! Description & Operational Scope !! style="text-align:center;" | Wikidata Alignment (LOD) |- | '''Algebraic Geometry''' || Fano 3-Folds, GRDB & Moduli || Fano threefolds (V22 family, Mori-Mukai ID-69), Graded Ring Database (GRDB) tools, period integrals, and Picard-Fuchs operators. || style="text-align:center;" | [[d:Q5528082|wd:Q5528082]] (Gavin Brown) / [[d:Q62067853|wd:Q62067853]] (A. Kasprzyk) |- | '''Algebraic Geometry''' || Hodge Theory & Cohomology || De Rham cohomology classes, period matrices, and monodromy period reductions on compact manifolds. || style="text-align:center;" | [[d:Q1317202|wd:Q1317202]] (Hodge theory) |- | '''Differential Geometry''' || Manifold Theory & Topology || Topographic manifolds, Riemannian structures, and smooth differential space models. || style="text-align:center;" | [[d:Q10380344|wd:Q10380344]] (Manifold theory) |- | '''Nonassociative Algebra''' || Jordan & Fano Plane Geometry || Exceptional Jordan algebra J3(O) (Albert algebra), PG(2,2) Fano plane incidence geometry, and Heawood dual graph structures. || style="text-align:center;" | [[d:Q649977|wd:Q649977]] (Jordan algebra) <br> [[d:Q1395814|wd:Q1395814]] (Fano plane) <br> [[d:Q3046737|wd:Q3046737]] (Heawood graph) |- | '''Associative Algebra''' || Clifford Algebras & Dirac Operators || Spacetime Clifford algebra Cl(3,1), Dirac gamma structures, and cubic Dirac operator representations. || style="text-align:center;" | [[d:Q674689|wd:Q674689]] (Clifford algebra) <br> [[d:Q907439|wd:Q907439]] (Dirac operator) |- | '''Functional Analysis''' || Hilbert Spaces & Quantum State Vectors || Infinite-dimensional complex Hilbert spaces, inner product spaces, and quantum mechanical state vectors. || style="text-align:center;" | [[d:Q190056|wd:Q190056]] (Hilbert space) |- | '''Quantum Field Theory''' || Polyakov Action, Path Integrals & Covariant QFT || Non-perturbative QED field kernels, Polyakov string action, Feynman path integral formulations, Schwinger-Tomonaga formalism, and AQFT superselection sectors. || style="text-align:center;" | [[d:Q1048763|wd:Q1048763]] (Polyakov action) <br> [[d:Q39246|wd:Q39246]] (R. Feynman) <br> [[d:Q184563|wd:Q184563]] (S. Tomonaga) |- | '''Lattice Theory & String Geometry''' || Leech Lattice & Even Unimodular Lattices || 24-dimensional even unimodular Leech lattice $\Lambda_{24}$, sphere packing bounds, and Monster group symmetry embeddings. || style="text-align:center;" | [[d:Q2510203|wd:Q2510203]] (Leech lattice) |- | '''Condensed Matter Physics''' || Tensor Networks & Many-Body Systems || Condensed matter states, Matrix Product States (MPS), circular transfer matrices, and bond dimension limits (D=45). || style="text-align:center;" | [[d:Q123146520|wd:Q123146520]] (Condensed Matter Physics) |- | '''Graph Theory & Limits''' || Graphons & Continuous Limits || Quantum graphon cut-norm convergence, graph limits, and dense graph sequence bounds. || style="text-align:center;" | [[d:Q131873270|wd:Q131873270]] (Graph theory) |- | '''Analytic Number Theory''' || Spectral Invariants & Zeta Function || Confinement of non-trivial zeros via TEC-Weil trace equivalence and continued fraction bounds (K). || style="text-align:center;" | [[d:Q187235|wd:Q187235]] (Riemann zeta function) |- | '''Fundamental Physics''' || Physical Constants & Coupling || Fundamental physical constants, fine-structure constant (alpha), and CODATA recommended bounds. || style="text-align:center;" | [[d:Q27928586|wd:Q27928586]] (Fundamental physical constant) <br> [[d:Q735279|wd:Q735279]] (CODATA) |- | '''Mathematical Governance & Literature''' || Institutional Foundations & Monographs || Clay Millennium problems context, AMS educational monographs, academic publishing standards (CUP), and open research publishing. || style="text-align:center;" | [[d:Q857975|wd:Q857975]] (Clay Math Institute) <br> [[d:Q912887|wd:Q912887]] (Cambridge Univ. Press) <br> [[d:Q53952481|wd:Q53952481]] (Student Math Library) |- | '''Infrastructure & Compute''' || Repositories, FAIR Standards & High-Precision Symbolic Computation || Scientific repositories (Zenodo, arXiv, Google Scholar), cloud/software foundations (Python Software Foundation, Google Colab), arbitrary-precision floating-point arithmetic (mpmath), and WikiProject Mathematics integration. || style="text-align:center;" | [[d:Q22661177|wd:Q22661177]] (Zenodo) <br> [[d:Q118398|wd:Q118398]] (arXiv) <br> [[d:Q494817|wd:Q494817]] (Google Scholar) <br> [[d:Q83818|wd:Q83818]] (PSF) <br> [[d:Q107381029|wd:Q107381029]] (mpmath) <br> [[d:Q126084995|wd:Q126084995]] (Google Colab) <br> [[d:Q8487137|wd:Q8487137]] (WikiProject Math) |} === References & Bibliography === <references> <ref name="codata2022">'''[[w:en:CODATA|CODATA]] (2022):''' ''CODATA Recommended Values of the Fundamental Physical Constants: 2022'', [https://doi.org/10.1103/RevModPhys.96.045004 DOI: 10.1103/RevModPhys.96.045004].</ref> <ref name="nature2010">'''[[w:en:Nature Physics|Nature Physics]] (2010):''' Editorial, [https://www.nature.com/articles/nphys1514 "The fine-structure constant: a numerical coincidence?"], ''Nature Physics'', 6, 1, [https://doi.org/10.1038/nphys1514 DOI: 10.1038/nphys1514].</ref> <ref name="Sardin2025">'''Sardin, G. (2025):''' "Primordial Physical Origin of the Fine-Structure Constant, and some of its Applications," ''International Journal of Physics'', 13(3), 55-61, [https://doi.org/10.12691/ijp-13-3-2 DOI: 10.12691/ijp-13-3-2].</ref> <ref name="polyakov1981">'''[[w:en:Alexander Markovich Polyakov|Polyakov, A. M.]] (1981):''' "Quantum geometry of bosonic strings," ''Physics Letters B'', 103(3), 207-210, [https://doi.org/10.1016/0370-2693(81)90743-7 DOI: 10.1016/0370-2693(81)90743-7].</ref> <ref name="polchinski1998">'''[[w:en:Joseph Polchinski|Polchinski, J.]] (1998):''' ''String Theory, Vol. 1: An Introduction to the Bosonic String'', [[w:en:Cambridge University Press|Cambridge University Press]], [https://doi.org/10.1017/CBO9780511816079 DOI: 10.1017/CBO9780511816079].</ref> <ref name="chsh1969">'''[[w:en:John Clauser|Clauser, J. F.]], Horne, M. A., [[w:en:Abner Shimony|Shimony, A.]], & Holt, R. A. (1969):''' "Proposed experiment to test local hidden-variable theories," ''Physical Review Letters'', 23(15), 880, [https://doi.org/10.1103/PhysRevLett.23.880 DOI: 10.1103/PhysRevLett.23.880].</ref> <ref name="cirelson1980">'''[[w:en:Boris Cirelson|Cirel'son, B. S.]] (1980):''' "Quantum generalizations of Bell's inequality," ''Letters in Mathematical Physics'', 4(2), 93-100, [https://doi.org/10.1007/BF00417500 DOI: 10.1007/BF00417500].</ref> <ref name="verstraete2004">'''[[w:en:Frank Verstraete|Verstraete, F.]], & [[w:en:Juan Ignacio Cirac Sasturain|Cirac, J. I.]] (2004):''' "Matrix product states for quantum simulation," ''Physical Review A'', 70(6), 062324, [https://doi.org/10.1103/PhysRevA.70.062324 DOI: 10.1103/PhysRevA.70.062324].</ref> <ref name="regge1961">'''[[w:en:Tullio Regge|Regge, T.]] (1961):''' "General relativity without coordinates," ''Nuovo Cimento'', 19, 558–571, [https://doi.org/10.1007/BF02733251 DOI: 10.1007/BF02733251].</ref> <ref name="cheeger1984">'''[[w:en:Jeff Cheeger|Cheeger, J.]], [[w:en:Werner Müller (mathematician)|Müller, W.]], & Schrader, R. (1984):''' "On the curvature of piecewise linear spaces," ''Communications in Mathematical Physics'', 92(3), 405--454, [https://doi.org/10.1007/BF01210729 DOI: 10.1007/BF01210729].</ref> <ref name="bhargava2004cubic">'''[[w:en:Manjul Bhargava|Bhargava, M.]] (2004):''' "Higher composition laws II: On cubic rings and resolution rings," ''Annals of Mathematics'', 159(2), 865-886, [https://doi.org/10.4007/annals.2004.159.865 DOI: 10.4007/annals.2004.159.865].</ref> <ref name="bhargava2004quartic">'''[[w:en:Manjul Bhargava|Bhargava, M.]] (2004):''' "Higher composition laws III: The parametrization of quartic rings," ''Annals of Mathematics'', 159(3), 1329-1360, [https://doi.org/10.4007/annals.2004.159.1329 DOI: 10.4007/annals.2004.159.1329].</ref> <ref name="brouwer2012">'''[[w:en:Andries Brouwer|Brouwer, A. E.]], & Haemers, W. H. (2012):''' [[d:Q105612081|''Spectra of Graphs'']], [[w:en:Springer Science+Business Media|Springer]], [https://doi.org/10.1007/978-1-4614-1939-6 DOI: 10.1007/978-1-4614-1939-6].</ref> <ref name="coates2013">'''Coates, T., Corti, A., Galkin, S., & [[d:Q62067853|Kasprzyk, A.]] (2013):''' "Quantum periods for 3-dimensional Fano manifolds," [[w:en:arXiv|arXiv]]:1310.7932, [https://doi.org/10.48550/arXiv.1310.7932 DOI: 10.48550/arXiv.1310.7932].</ref> <ref name="iskovskikh1977">'''[[w:en:Vasily Iskovskikh|Iskovskikh, V. A.]] (1977):''' "Fano 3-folds. I," ''Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya'', 41(3), 516--562, [https://doi.org/10.1070/IM1977v011n03ABEH001733 DOI: 10.1070/IM1977v011n03ABEH001733].</ref> <ref name="golyshev2007">'''Golyshev, V. V. (2007):''' "Classification of Fano 3-folds, Fricke identities, and periods," ''Izvestiya: Mathematics'', 71(5), 883--933, [https://doi.org/10.1070/IM2007v071n05ABEH002379 DOI: 10.1070/IM2007v071n05ABEH002379].</ref> <ref name="mori1981">'''[[w:en:Shigefumi Mori|Mori, S.]], & [[w:en:Shigeru Mukai|Mukai, S.]] (1981):''' "Classification of Fano 3-folds with <math>B_2 \ge 2</math>," ''Manuscripta Mathematica'', 36(2), 147-162, [https://doi.org/10.1007/BF01170131 DOI: 10.1007/BF01170131].</ref> <ref name="lovasz2006">'''[[w:en:László Lovász|Lovász, L.]], & Szegedy, B. (2006):''' "Limits of dense graph sequences," ''Journal of Combinatorial Theory, Series B'', 96(6), 933–957, [https://doi.org/10.1016/j.jctb.2006.05.002 DOI: 10.1016/j.jctb.2006.05.002].</ref> <ref name="borgs2008convergent">'''Borgs, C., [[w:en:Jennifer Tour Chayes|Chayes, J. T.]], [[w:en:László Lovász|Lovász, L.]], Sós, V. T., & Vesztergombi, K. (2008):''' "Convergent sequences of dense graphs I," ''Geometric and Functional Analysis'', 18(6), 1801--1951, [https://doi.org/10.1007/s00039-008-0695-x DOI: 10.1007/s00039-008-0695-x].</ref> <ref name="lovasz2012large">'''[[w:en:László Lovász|Lovász, L.]] (2012):''' ''Large Networks and Graph Limits'', American Mathematical Society, [https://doi.org/10.1090/coll/060 DOI: 10.1090/coll/060].</ref> <ref name="saniga2008snowflake">'''Saniga, M., Havlicek, H., Planat, M., & Pracna, P. (2008):''' "Twin "Fano-Snowflakes" over the smallest ring of ternions," ''SIGMA'', 4, 050, [https://doi.org/10.3842/SIGMA.2008.050 DOI: 10.3842/SIGMA.2008.050].</ref> <ref name="aps1975">'''[[w:en:Michael Atiyah|Atiyah, M. F.]], Patodi, V. K., & [[w:en:Isadore Singer|Singer, I. M.]] (1975):''' "Spectral asymmetry and Riemannian Geometry. I," ''Mathematical Proceedings of the Cambridge Philosophical Society'', 77(1), 43-69, [https://doi.org/10.1017/S0305004100049410 DOI: 10.1017/S0305004100049410].</ref> <ref name="kostant1999">'''[[w:en:Bertram Kostant|Kostant, B.]] (1999):''' "A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups," ''Duke Mathematical Journal'', 100(3), 447-501, [https://doi.org/10.1215/S0012-7094-99-10016-0 DOI: 10.1215/S0012-7094-99-10016-0].</ref> <ref name="voisin2002">'''[[w:en:Claire Voisin|Voisin, C.]] (2002):''' [[d:Q56288659|''Hodge Theory and Complex Algebraic Geometry I'']], [[w:en:Cambridge University Press|Cambridge University Press]], [https://doi.org/10.1017/CBO9780511615344 DOI: 10.1017/CBO9780511615344].</ref> <ref name="blandino2026alpha">'''[https://orcid.org/0009-0006-3252-4011 Blandino, M.] (2026a):''' ''The Lagrangian Duality of the Fine-Structure Constant (Alpha Series)'', [[w:en:Zenodo|Zenodo]], Concept DOI: [https://doi.org/10.5281/zenodo.19802606 10.5281/zenodo.19802606].</ref> <ref name="blandino2026fano">'''[https://orcid.org/0009-0006-3252-4011 Blandino, M.] (2026b):''' ''The Fano 3-fold 2-22 as the Underlying Structure of the Unified PEPS-5D Lagrangian (EM+QG)'', [[w:en:Zenodo|Zenodo]], Concept DOI: [https://doi.org/10.5281/zenodo.19955544 10.5281/zenodo.19955544]. * '''[https://orcid.org/0009-0006-3252-4011 Blandino, M.] (2026c):''' ''Alpha Series & Fano Series (v2.0.0)'', [[w:en:Zenodo|Zenodo]], DOI: [https://doi.org/10.5281/zenodo.20635062 10.5281/zenodo.20635062].</ref> </references> [[Category:Research projects]] [[Category:Mathematical physics]] [[Category:Condensed matter physics]] [[Category:String theory]] [[Category:Quantum mechanics]] [[Category:Algebraic geometry]] <div style="display: none;"> <script type="application/ld+json"> { "@context": "https://schema.org", "@graph": [ { "@type": "Person", "@id": "https://blandino-research.wikibase.cloud/entity/Q1", "name": 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You may find these starter references helpful. Goodluck. Flett, G. L., Blankstein, K. R., Hewitt, P. L., & Koledin, S. (1992). Components of perfectionism and procrastination in college students. ''Social Behavior & Personality: An International Journal'', 20(2), 85-93. https://doi.org/10.2224/sbp.1992.20.2.85 Frost, R. O., Marten, P., Lahart, C., & Rosenblate, R. (1990). The dimensions of perfectionism. ''Cognitive Therapy and Research'', 14(5), 449-468. [https://psycnet.apa.org/doi/10.1007/BF01172967 https://doi.org/10.1007/BF01172967] Holden, C. L. (2020). The 'perfect' counsellor: Personality factors and multidimensional perfectionism. ''British Journal of Guidance & Counselling'', 48(2), 183-194. https://doi.org/10.1080/03069885.2019.1682122 Stoeber, J., & Otto, K. (2006). Positive conceptions of perfectionism: Approaches, evidence, challenges. ''Personality and Social Psychology Review'', 10(4), 295-319. https://doi.org/10.1207/s15327957pspr1004_2 [[User:StretchBeyond|StretchBeyond]] ([[User talk:StretchBeyond|discuss]] • [[Special:Contributions/StretchBeyond|contribs]]) 22:10, 19 August 2026 (UTC) :Hi, thank you so much! I already had some of these articals, but one of them was new to me. This was really helpful! [[User:U3222012|U3222012]] ([[User talk:U3222012|discuss]] • [[Special:Contributions/U3222012|contribs]]) 09:30, 22 August 2026 (UTC) == Check out other chapters about procrastination == There have been several previous procrastination chapters, so make sure to check them out: [[:Category:Motivation and emotion/Book/Procrastination]]. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 02:12, 20 August 2026 (UTC) == Resource and research suggestion == Hi, I found your topic on perfectionism and procrastination really interesting. Your distinction between perfectionistic concerns and perfectionistic helps explain why certain aspects of perfectionism may be more strongly linked to procrastination than others. I noticed you have included research examining multidimensional perfectionism and procrastination, which should help support this distinction. One suggestion would be to use your meta-analytic research to clearly compare which aspects of perfectionism have the strongest relationship with procrastination. This could strengthen your section on how perfectionism relates to procrastination and help connect the research directly to your focus questions. Good luck, you have done an amazing job!! [[User:U3253354|U3253354]] ([[User talk:U3253354|discuss]] • [[Special:Contributions/U3253354|contribs]]) 02:26, 25 August 2026 (UTC) :Hi! Thank you so much for your support and for your valuable suggestions.I really appreciate it! [[User:U3222012|U3222012]] ([[User talk:U3222012|discuss]] • [[Special:Contributions/U3222012|contribs]]) 11:27, 26 August 2026 (UTC) == Heading casing == {| style="float: center; background:transparent;color:inherit;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:U3222012|Hi [[User:U3222012|U3222012]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:04, 10 September 2026 (UTC) |} <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Headings --> # See earlier comment about [[#heading casing|heading casing]] <!-- Heading structure --> <!-- 1-level --> # Promising [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development (e.g., consider using subheadings) <!-- Alignment with focus questions --> # Very good alignment between sub-title, focus questions, and heading structure, but there may be room for improvement |3= <!-- Overview--> # Excellent – Scenario, image, evocative description of the problem/topic, and focus questions <!-- Scenario --> # A scenario or case study is presented in a feature box with an image at the start of this section <!-- Description --> # A promising description of the problem/topic is planned or presented <!-- Focus questions --> # Reasonably good alignment between focus questions and heading structure, but consider closer alignment # FQ1 is a bit vague; consider making the question more specific # Consider more clearly distinguishing between FQ2 and FQ3 (or perhaps combining) |4= <!-- Key points--> <!-- Overall --> # Promising development # Consider integrating key theories earlier on in the chapter rather than having a stand-alone section # Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a "down" style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info] <!-- Conclusion --> # Conclusion is underway # What are the practical, take-home messages? (address the focus questions) (e.g., not many people will access CBT, so what other strategies can be suggested?) |5= <!-- Figure --> # Relevant figure(s) are presented and captioned <!-- Caption --> # Figure caption(s) provide(s) a somewhat clear description that is connected with the main text, but could be improved <!-- Cite --> # Cite each figure at least once in the main text using APA style (e.g., see Figure 1) |6= <!-- Learning feature --> <!-- Interwiki links ---> # Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- Scenarios/examples/case studies --> # Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice. <!-- Quiz --> # Promising use of quiz question(s) <!-- Tables --> # Promising use of table(s) # Include acknowledgement (e.g., citation(s)) for sources of information presented in the table |7= <!-- References --> <!-- Overall --> # Very good <!-- Systematic reviews --> # Well done on identifying relevant systematic reviews and/or meta-analyses <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## capitalisation ## use dois where available instead of other links |8= <!-- Resources --> <!-- See also --> # See also ## Excellent <!-- External links --> # External links ## Very good ## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) ## Use [[w:Letter case#Sentence casing|sentence casing]] ## Include source in brackets after link |9= <!-- User page --> # Basic but effective <!-- Description about self --> # Description about self provided <!-- Links to profile(s) --> # Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # Excellent – at least three different types of contributions with direct link(s) to evidence }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:04, 10 September 2026 (UTC) == Suggestions == Hi! I know you're not done with your book chapter yet but I wanted to give some suggestions that may help you bring everything together. Firstly make sure in case study scenarios you're not switching between past and present tense. Secondly, make sure you in text reference after stating a fact. Thirdly, I would love to see more critical analysis of the theories you've mentioned, including implications for future research. Good luck and hope this help :) [[User:E3297976|E3297976]] ([[User talk:E3297976|discuss]] • [[Special:Contributions/E3297976|contribs]]) 13:35, 9 October 2026 (UTC) <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is a reasonably good chapter that makes OK use of psychological theory and research to address a real-world phenomenon or problem <!-- Overall - Edit summaries --> # [[Motivation and emotion/Wikiversity/Edit summary|Edit summaries]] are used to communicate the changes for most edits, but would ideally be more descriptive and extensive <!-- Overall - GenAI --> # The links to the ChatGPT conversations are not shared so as to be publicly accessible <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPerfectionism_and_procrastination&diff=2844845&oldid=2839848 these copy edits] |2= <!-- Overview – Comments... --> # Very good <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study <!-- Overview – Scenario - Figure --> # The Figure 1 caption should explain more clearly how it is related to the scenario <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon <!-- Overview – Focus questions --> # The focus questions are excellent (clear and relevant) |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Good—relevant theories are selected, described, and applied, with some room for improvement <!-- Theory – Builds on --> # Builds in a basic way on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Good depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Reasonably good use of tables, figures, and/or lists to convey key theoretical information <!-- Theory – Citations --> # Key citations are well used <!-- Theory – Examples --> # Basic use of examples to illustrate theoretical concepts # Use more examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Reasonably good review of relevant research # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # More detail about key studies would be ideal <!-- Research – Critical thinking --> # Basic [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Reasonably good integration between the most relevant theory(ies) and the best research # The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links |6= <!-- Conclusion comments... --> # Very good/summary and conclusion # Highlight the importance of the problem or phenomenon of interest # Use sentences and paragraphs rather than bullet points <!-- Conclusion – Key points --> # Key points are well summarised <!-- Conclusion – Focus questions --> # The focus questions are addressed <!-- Conclusion – Take-home messages --> # Basides CBT, what are practical, take-home strategies can be suggested? <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is good to very good <!-- Style – Paragraphs --> ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. ## Bullet points are overused (in the Conclusion). Use full sentences and paragraphs. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. <!-- Style – Layout --> # Layout ## The headings could be more clearly aligned with the focus questions ## The chapter structure is underdeveloped; expand by using subheadings ## See earlier comment about [[#Heading casing|heading casing]] <!-- Style – Grammar --> # Grammar and spelling are very good # Grammar ## Check and correct use of hyphens where em-dashes should be used instead ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Figures --> ## Figures ### Brief captions; provide more detail to help connect the figure to the text <!-- Style – Figures - Citations --> ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Tables --> ## Table(s) ### Very well captioned <!-- Style – Tables - Citations --> ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] <!-- Style – References --> ## References use very good APA style: ### Check and correct use of italicisation <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Basic use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Basic use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Insufficient use of figure(s) # Basic use of table(s) # Basic use of feature box(es) # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Basic use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Insufficient use of the [[{{PAGENAME}}#See also|See also]] section ## Also include links to related Wikipedia articles <!-- Learning features – External links --> # Basic use of the [[{{PAGENAME}}#External links|External links]] section ## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]] ## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link |9= <!-- Social contribution comments... --> # ~8 logged, useful, mostly moderate contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # ~1 logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 02:14, 8 November 2026 (UTC) iftwbvvj0210h5z17cqvi1a6j1kafk4 1 331467 2844835 2838249 2026-11-07T22:44:29Z Jtneill 10242 Book chapter feedback 2844835 wikitext text/x-wiki ==Comment== Hi! I've put the formula to get the template for the book chapter below when you're ready to start work on it. If you delete the '&' signs in the formula and paste it into the resource section it should work for you. {&{subst:ME/BCS}&} --[[User:U3275992|U3275992]] ([[User talk:U3275992|discuss]] • [[Special:Contributions/U3275992|contribs]]) 23:34, 24 August 2026 (UTC) <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and/or subtitle not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed) |2= <!-- Heading structure --> <!-- 2-level --> # A promising [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] is planned but not implemented as wiki-style headings as shown in Tutorial 2 # Use [[w:Letter case#Sentence casing|sentence casing]] # A separate heading about research isn't necessary; instead integrate use of research in other sections # Develop closer alignment between focus questions and top-level headings |3= <!-- Overview--> # Good <!-- Scenario --> # A scenario or case study is presented in a feature box at the start of this section # I moved an image into the feature box to help attract reader interest # Choose an image that illustrates the scenario. Move theoretical diagrams into a subsequent section. # The scenario could be improved by presenting it is 3rd person rather than 2nd person perspective <!-- Description --> # A basic description of the problem/topic is planned or presented <!-- Focus questions --> # Develop closer alignment between the sub-title, focus questions, and top-level headings |4= <!-- Key points--> <!-- Overall --> # Basic development # The key points are poorly presented; see Tutorial 2 for basic wiki editing skills <!-- Scope --> # The scope is excellent (i.e., not too little/narrow or too big/broad) # Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples. <!-- Conclusion --> # Conclusion hasn't been developed # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Relevant figure(s) are presented and captioned <!-- Caption --> # Figure caption(s) should include '''Figure X'''. [bold] ... (fixed) <!-- Cite --> # Cite each figure at least once in the main text using APA style (e.g., see Figure 1) |6= <!-- Learning feature --> <!-- Interwiki links ---> # There is a rudimentary questionanaire but it lacks sufficient engagement/interactivity # Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- Scenarios/examples/case studies --> # Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice. <!-- Quiz --> # Consider including quiz question(s) about the take-home messages <!-- Tables --> # Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information |7= <!-- References --> <!-- Overall --> # Basic # Move non-academic / non-peer reviewed sources to the "External links" section # Remove reference for image <!-- Systematic reviews --> # What are the most relevant systematic reviews/meta-analyses about this topic? <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## [[Help:Wikitext quick reference|italicisation]] # A more thorough literature search is recommended. The goal is to identify and use the best academic theory and research about this topic. See Tutorial 5 (Google Scholar). |8= <!-- Resources --> <!-- See also --> # See also ## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- External links --> # External links ## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) ## Link to the most relevant external resources about this topic |9= <!-- User page --> # Basic <!-- Description about self --> # Description about self provided <!-- Links to profile(s) --> # Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks. <!-- Link to book chapter --> # Add link to book chapter |10= <!-- Social contribution --> # None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]]. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 05:23, 11 September 2026 (UTC) == Reference list comment == Hello, I've noticed a small mistake in your references. It seems the 3rd reference authors name has been cut off. I'd also recommend to removing the 2nd reference title. Keep up the good work! [[User:LMM26|LMM26]] ([[User talk:LMM26|discuss]] • [[Special:Contributions/LMM26|contribs]]) 04:28, 10 October 2026 (UTC) == Learning Feature == Hi, I've just added a quiz question for an extra learning feature in case you would be interested in it. I hope it is helpful! -- [[User:U3275992|U3275992]] ([[User talk:U3275992|discuss]] • [[Special:Contributions/U3275992|contribs]]) 03:47, 11 October 2026 (UTC) == Heading casing == {| style="float: center; background:transparent;color:inherit;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:|Hi [[User:{{{1}}}|{{{1}}}]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 22:44, 7 November 2026 (UTC) |} <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an insufficient chapter # The main area(s) for potential improvement: #* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]] by discussing GM in relation to motivation, achievement, and emotional responses, with only a brief section about GM and WB #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution #* invest more time (I suspect that less than the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were invested) <!-- Overall - Edit summaries --> # The chapter has a very brief edit history, with insufficient use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to describe the changes made in each edit <!-- Overall - GenAI --> # This chapter appears to be human-written <!-- Overall – Citations --> # Reasonably good use of academic, peer-reviewed citations to support claims # There is surprisingly little use of citations about the topic that are identifiable through a simple academic literature search, such as: https://scholar.google.com/scholar?q=growth+mindset+and+wellbeing <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FGrowth_mindset_and_psychological_wellbeing&diff=2844834&oldid=2839799 these copy edits] |2= <!-- Overview – Comments... --> # Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study # There are several grammatical errors in the scenario <!-- Overview – Scenario - Figure --> # The Figure 1 caption should explain more clearly how it is related to the scenario <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box <!-- Overview – Explains problem --> # Clearly explains the psychological problem or phenomenon <!-- Overview – Focus questions --> # The focus questions are basic # The focus questions could be improved by: ## being more specific to the topic (i.e., the sub-title) (e.g., GM -> wellbeing; the topic isn't about motivation) ## matching the top-level headings more closely ## dealing with research in each section, rather than having it as a stand-alone question |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement # The main issue is the lack of sufficient focus directly on the topic (GM -> WB); the chapter is mostly focused on GM -> other outcomes # Reduce general theoretical background. Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question). <!-- Theory – Builds on --> # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Basic depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Insufficient/No use of tables, figures, and/or lists to convey key theoretical information <!-- Theory – Citations --> # In some places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. <!-- Theory – Examples --> # Heavy reliance on a single example (lifting weights) # Consider using more varied examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Insufficient review of relevant research (i.e., research about GM -> WB) # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # In some places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. <!-- Research – Critical thinking --> # Basic [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Insufficient integration between the most relevant theory(ies) and the best research # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Highlight the importance of the problem or phenomenon of interest # Address the focus questions # Add practical, take-home message(s) |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is reasonably good <!-- Style – Layout --> # Layout ## The chapter structure is underdeveloped; expand by using subheadings ## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size) ## See earlier comment about [[#Heading casing|heading casing]] ## Integrate research rather than having it as a stand-alone section(s) <!-- Style – Grammar --> ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – Figures --> ## Figures ### Brief captions; provide more detail to help connect the figure to the text <!-- Style – Figures - Citations --> ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Citations --> # Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] <!-- Style – References --> ## References use reasonably good APA style: ### Hyperlink dois for 1-click access ### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section (fixed) <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Insufficient use of figure(s) # No use of table(s) # No use of feature boxes other than the opening scenario # Basic use of scenarios, case studies, or examples <!-- Learning features – Quizzes --> # Basic use of quiz(zes) and/or reflection question(s) # The answer to the quiz question is wrong # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) <!-- Learning features – See also --> # No use of the [[{{PAGENAME}}#See also|See also]] section <!-- Learning features – External links --> # No use of the [[{{PAGENAME}}#External links|External links]] section |9= <!-- Social contribution comments... --> # ~4 logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 22:44, 7 November 2026 (UTC) 844qlnad5z3zaftqziuy56mcedg7zz3 0 331492 2844834 2839799 2026-11-07T22:43:46Z Jtneill 10242 Copyediting 2844834 wikitext text/x-wiki {{title|Growth mindset:<br>How does a growth mindset influence psychological wellbeing?}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} ;Scenario [[File:Fixed versus growth mindset.png|thumb|'''Figure 1'''. Two faces staring at each other. Left with a lock and right was a plant growing. {{ic|Explain how this figure connects to the scenario.}}]] Life rarely goes as planned. You have been struggling at the gym for a while now and you’ve finally decided you want to work out become stronger. One day, you struggle to lift your goal weight, looking around you, you find others lifting heavier with ease. Suddenly a normal gym session turned into a comparison {{g}} “I can’t do this. I am not good at this.” You leave the gym feeling deflated and decide you are simply not strong enough for the gym. Alternatively, you might see others lifting heavier and you become inspired, thinking, “if I keep training and stay discipline {{g}}, I will become stronger.” You are still disappointed you could not get your goal weight but it only fuels you for the next time, understanding it’s a reflection of your ability not your potential. The situation is the same, however the reaction is different. Why can the same challenge have one person feeling defeated and the other feeling motivated? Why do some people see failure as evidence, while others see it as an opportunity to learn? {{RoundBoxBottom}} The concept of a growth mindset developed from Carol Dweck’s research into how children respond to difficulty, and it refers to the belief that abilities can be developed through effort, learning, and experience (Dweck & Leggett, 1988). At the other end of the spectrum, a fixed mindset is the belief that intelligence, abilities, and skills cannot be changed much. These beliefs are known as implicit theories. An entity theory corresponds to a fixed mindset, and an incremental theory to a growth mindset. Someone with a fixed mindset is more likely to read a struggle as proof they lack ability. Someone with a growth mindset is more likely to read the same struggle as a sign of what to work on next. Over time, these readings can become habits that shape how a person acts and feels when the next challenge arrives. Mindset {{g}} carries importance, as beliefs influence how individuals respond to challenges; this affects what they do (motivation) and how they feel (emotion). Mindset is linked to effort, perseverance, and goals people pursue. People may be more likely to keep trying when they see effort as a way to improve. Mindset itself is also closely linked to how people view failure, how it feels and their response to it afterwards. A growth mindset does not abolish negative emotion; instead, it changes how the individual deals with it. Let's link this back to our earlier gym scenario: failing at a set of weights can impact confidence and future view of training. After failing, based on your mindset, you can either feel fuelled to try again in the future and keep working hard, or you can be deflated and unable to train again afterwards. Motivational and emotional patterns can add up to differences in psychological wellbeing; however, the relationship between the two is not simple, and {{what}} other factors are involved. The chapter starts by defining mindset and tracing its origins. From there, it examines how mindset connects to motivation, then to emotional responses when things go wrong, and finally to psychological wellbeing. The last section asks how much of this the research actually supports. {{RoundBoxTop|theme=3}} ; Focus questions * How does a growth mindset shape the way people respond to challenges and failure? * To what extent one can a growth mindset, contribute to motivation and psychological well-being? * What does psychological level research reveal and future and what are the benefits and limitations. {{RoundBoxBottom}} == (Add a heading here) == Mindset research explores why people with similar abilities can respond differently when a task becomes difficult. Dweck and Leggett (1988) proposed that people's beliefs about whether intelligence can change influence {{g}} the goals they pursue and how they respond to challenges. They distinguished between an entity theory, in which intelligence is viewed as relatively fixed, and an incremental theory, in which intelligence is viewed as capable of development. These ideas underpin what are now commonly described as fixed and growth mindsets. These beliefs can shape how people interpret success and failure. Someone who views ability as fixed may be more concerned with proving their competence and avoiding situations that could expose their weaknesses. When they encounter difficulty, they may interpret it as evidence that they lack the ability to succeed. In contrast, someone who believes ability can develop may be more willing to approach challenging tasks because these provide opportunities to learn. This does not mean that people with a growth mindset always persist or that people with a fixed mindset always give up. Rather, their beliefs may influence how they interpret challenges and which responses they consider worthwhile. {{f}} Dweck and Leggett (1988) linked these differences to performance goals, which emphasise demonstrating competence, and learning goals, which emphasise developing competence. A person pursuing a performance goal may focus on achieving a successful outcome or avoiding mistakes, whereas someone pursuing a learning goal may place greater value on gaining skills, even when the task is difficult. However, performance goals are not necessarily harmful. When individuals feel confident in their abilities, wanting to demonstrate competence can encourage effort and achievement. Mindset is therefore better understood as influencing how people approach goals than as determining whether a particular goal is good or bad. These ideas also highlight that mindsets are not necessarily consistent across every area of life. A person may believe that academic ability can improve through study but feel that physical strength is largely determined by natural ability. This distinction matters when applying mindset theory to exercise, because beliefs about intelligence cannot automatically be assumed to reflect beliefs about fitness. A person may need to develop a growth-oriented view of physical ability specifically before interpreting gym setbacks as opportunities to learn. The gym scenario illustrates how these beliefs might influence behaviour. Someone who struggles to lift a particular weight might interpret the experience as proof that they are not strong enough, whereas another person might see it as information about what they need to practise. The second person may be more willing to adjust their technique, seek feedback or set a more achievable short-term goal. Nevertheless, mindset does not determine behaviour on its own. Confidence, previous experience, social comparison and the training environment can also influence a person's response. Growth mindset theory therefore provides a useful framework for understanding reactions to difficulty, rather than a rule that predicts how every individual will behave. == '''GROWTH MINDSET AND MOTIVATION''' == Mueller and Swrck (1998) investigated how {{how}} different types of praise influenced {{ic|how many?}} {{where}} children’s motivation and responses to failure. Their findings suggested that praising intelligence encouraged a stronger focus on demonstrating ability, while praising effort encouraged a greater focus on learning. Following a setback, children praised for intelligence showed less persistence and enjoyment than those praised for effort. These results suggest that feedback can influence how children interpret their performance and whether they view failure as a reflection of their ability or as an opportunity to improve. However, because the study involved children completing puzzle tasks {{expand}}, its findings cannot automatically be generalised to adults exercising in a gym. Blackwell et al. (2007) examined the relationship between beliefs about intelligence and academic achievement in adolescents. Their research included an intervention designed to teach {{ic|how many}} students that intelligence can develop, providing a useful comparison with laboratory studies {{f}} of praise and feedback. Together, these studies {{f}} suggest that beliefs about ability may be relevant to motivation and learning, although the outcomes of an intervention depend on the population and setting in which it was delivered. == '''GROWTH MINDSET AND ACHIEVEMENT''' == Although growth mindset theory offers a useful explanation of motivation, the relationship btween mindset and achievement is not straightforward. Blackwell et al {{g}} (2007) found that {{ic|how many?}} students {{where}} who received an intervention promoting the idea that intelligence can develop showed {{ic|how much?}} improvements in classroom motivation, and their declining mathematics grades were reversed compared with the control group. This suggests that changing beliefs about ability may influence how students approach learning and respond to academic difficulties. However, the intervention involved a specific group of {{ic|how many?}} Year 7 students {{where}}. So the finding should not automatically be generalised to every age group or setting. Burnette et al. (2023) examined 113 studies involving more than 28,000 participants in a meta-analysis of mindsets and self-regulation. Their findings indicated that implicit beliefs about personal attributes were associated with processes such as goal setting and goal pursuit, which were in turn related to goal achievement. This supports the idea that mindset may influence achievement partly through the choices people make and the strategies they use, rather than directly determining whether they succeed. This distinction is important because a growth mindset does not guarantee success. Improvement also depends on factors such as access to resources, the quality of feedback, opportunities to practise, and the strategies used. In the gym, believing that strengths can improve may encourage someone to continue training, but progress will still depend on appropriate programming, recovery, nutrition and consistent practice. A growth mindset may therefore be most useful when it encourages realistic action and learning, rather than when it is treated as a substitute for the practical conditions needed to improve. == '''GROWTH MINDSET AND EMOTIONAL RESPONSES''' == Mindset {{g}} may also influence how people experience failure emotionally. When individuals interpret a setback as evidence that they lack ability, they may experience embarrassment, frustration, or helplessness; these emotions can make it harder to approach a similar challenge again {{f}}. In contrast, interpreting failure as information about what needs to improve may help an individual respond with curiosity and renewed effort, This does not mean that people with a growth mindset do not experience disappointment; rather, their beliefs may influence what they do with that disappointment. {{f}} Mueller and Dweck (1998) provided evidence for this distinction. In their {{what}} studies, children {{where}} praised for intelligence responded less positively to failure than children praised for effort. They showed lower task persistence and enjoyment and were more likely to attribute poor performance to low ability. These findings suggest that when success becomes a test of whether someone is intelligent, failure can threaten their view of themselves. When feedback instead emphasises effort, children may be more likely to understand performance as something that can change. However, effort alone is not always enough, and telling someone simply to try harder can be unhelpful when their current approach is ineffective. A more useful response combines encouragement with specific feedback and practical strategies. For example, after struggling with a lift, a person might feel disappointed but use the experience to adjust their technique, reduce the weight, or seek guidance. The setback remains unpleasant, but it can also provide information for future training. The gym example illustrates how the interpretation of failure can affect emotional responses. Someone who compares their current strength with that of a more experienced gym-goer may feel inadequate, whereas someone who compares their current performance with their own previous efforts may be better able to recognise progress. Nevertheless, their responses are not determined by mindset alone. Social comparison, previous experience, confidence, and the environment can also influence how a person feels after a setback. == '''GROWTH MINDSET AND PSYCHOLOGICAL WELLBEING''' == The effects of mindset may extend beyond performance to psychological wellbeing. If people believe that their abilities can develop, they will be less likely to interpret a single setback as a permanent judgement of their worth or potential. This could help them respond to difficulties with greater flexibility and maintain a sense that improvement is possible. However, psychological wellbeing is influenced by many factors, and mindset should not be viewed as a complete explanation for how someone feels or copes with stress. {{f}} Research by Schleider and Weisz (2017) provides some evidence that mindset-based intervention may have benefits beyond achievement. They tested a brief intervention teaching {{ic|how many?}} adolescents {{where}} that personality can change, examining symptoms of anxiety and depression over a nine-month period. Compared with a supportive-therapy control condition, the intervention group showed greater improvements in some parent-reported and youth-reported depression outcomes, as well as perceived behaviour control {{ic|how large were these effects?}}. However, the results were not significant across every measure, including youth-reported anxiety. The study therefore offers promising evidence, but it does not establish that growth mindset interventions will improve wellbeing for everyone. An important limitation is that Schleider and Weisz (2018) examined beliefs about personality rather than intelligence of physical fitness {{huh}}. Although these ideas are related, they are not identical. Their findings cannot be directly applied to assume that a growth mindset about strength or exercise will reduce anxiety or improve mental health. Further research would be needed to determine whether similar effects occur in other areas of life. Returning to the gym example, a person who struggles with a life {{sp}} may feel disappointed without concluding that they are incapable of becoming stronger. Viewing the experience as temporary and changeable may help them maintain perspective and return to training. However, wellbeing also depends on whether their goals are realistic, whether their training environment is supportive, and whether they can recognise progression without comparing themselves with others {{f}}. A growth mindset may be one helpful resource for coping with setbacks, but it is not a guarantee of positive wellbeing. == '''CRITICAL EVALUATION''' == Overall, growth mindset theory provides a useful framework for understanding why people can respond differently to similar challenges. Research suggests that beliefs about whether abilities can develop may influence goal setting, responses to feedback, and reactions to failure. However, the evidence does not establish that a growth mindset automatically produces better achievement or psychological well-being. One limitation is that several studies discussed in this chapter involve children and adolescents in educational settings. Although these studies help explain the relationship between beliefs and behaviour, their findings cannot automatically be generalised to adults exercising in a gym. Research directly examining fitness-related mindsets is therefore important when considering whether these patterns also occur during physical activity. It is also necessary to distinguish between believing that improvement is possible and assuming that effort alone guarantees success. Progress depends on effective strategies, feedback, opportunities to practice, and individual circumstances. Encouraging someone to persist without helping them identify what needs to change may not improve their performance. A growth mindset is therefore best understood as one potential influence on motivation and responses to difficulty, rather than a universal solution to failure. == '''CONCLUSION''' == A growth mindset offers one explanation for why people respond differently to similar challenges. Believing that abilities can develop may encourage individuals to approach setbacks as opportunities to learn rather than as proof of their limitations. However, the research suggests that effects depend on the individual and the context {{vague}}. A growth mindset does not guarantee success, eliminate disappointment, or independently determine well-being. Effective strategies, appropriate support, and opportunities to practice remain important. Returning to the gym scenario, struggling to lift a desired weight does not determine a person's future and strength. How they interpret the setback may influence whether they give up or use the experience to guide their next attempt. Ultimately, the value of a growth mindset lies in recognising that current performance does not necessarily define future potential, while understanding that improvement requires more than a positive attitude alone. <quiz display="simple"> A person with a fixed mindset is more likely to believe that their abilities are relatively unchangeable. {{ic|The answer appears to be incorrect.}} |type=“()”} -True +False </quiz> Carol Dweck when creating the concept of a growth mindset included set of 3 questions of which you answer on a 1 (strong agree) to 6 (strong disagree) to get you thinking which was your brain works. See the following: <blockquote>'''''1. You have a certain amount of intelligence, and you can't really do much to change it''''' '''''2. Your intelligence is something about you that can't change very much''''' '''''3. You can learn new things, but you can't really change your basic intelligence'''''</blockquote>''<small>1.0-3.0 - fixed mindset</small>'' ''<small>3.1-3.9 - average</small>'' ''<small>4.0-6.0 - growth mindset</small>'' ''<small>How did you do?</small>'' == See also == {{expand}} == References == {{Hanging indent|1= Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. ''Child Development'', ''78''(1), 246–263. <nowiki>https://doi.org/10.1111/j.1467-8624.2007.00995.x</nowiki> Burnette, J. L., Billingsley, J., Banks, G. C., Knouse, L. E., Hoyt, C. L., Pollack, J. M., & Simon, S. (2023). A systematic review and meta-analysis of growth mindset interventions: For whom, how, and why might such interventions work? ''Psychological Bulletin'', ''149''(3–4), 174–205. <nowiki>https://doi.org/10.1037/bul0000368</nowiki> Dweck, C. S., & Yeager, D. S. (2019). Mindsets: A view from two eras. ''Perspectives on Psychological Science : A Journal of the Association for Psychological Science'', ''14''(3), 481–496. PubMed Central. <nowiki>https://doi.org/10.1177/1745691618804166</nowiki> Dwreck, C., & Leggett, E. (2025). ''Dweck & Leggett (1988) a social-cognitive approach''. Scribd. <nowiki>https://www.scribd.com/document/260120551/Dweck-Leggett-1988-a-Social-cognitive-Approach</nowiki> Dybendal, B. H., Stokke, S. S., Haugan, J. A., Moen, F., & Stenseng, F. (2026). Development and validation of the mindset in fitness scale (MiFS): A domain-specific measure of implicit beliefs in physical activity engagement. ''Current Psychology'', ''45''(7). <nowiki>https://doi.org/10.1007/s12144-026-09286-0</nowiki> Furnham, A. (2014). Increasing your intelligence: Entity and incremental beliefs about the multiple “intelligences”. ''Learning and Individual Differences'', ''32'', 163–167. <nowiki>https://doi.org/10.1016/j.lindif.2014.03.001</nowiki> Mueller, C. M., & Dweck, C. S. (1998). Praise for intelligence can undermine children’s motivation and performance. ''Journal of Personality and Social Psychology'', ''75''(1), 33–52. <nowiki>https://doi.org/10.1037/0022-3514.75.1.33</nowiki> Orvidas, K., Burnette, J. L., & Russell, V. M. (2018). Mindsets applied to fitness: Growth beliefs predict exercise efficacy, value and frequency. ''Psychology of Sport and Exercise'', ''36''(36), 156–161. <nowiki>https://doi.org/10.1016/j.psychsport.2018.02.006</nowiki> Schleider, J., & Weisz, J. (2017). A single‐session growth mindset intervention for adolescent anxiety and depression: 9‐Month outcomes of a randomized trial. ''Journal of Child Psychology and Psychiatry'', ''59''(2), 160–170. <nowiki>https://doi.org/10.1111/jcpp.12811</nowiki> Sik, K., Cummins, J., & Job, V. (2024). An implicit measure of growth mindset uniquely predicts post-failure learning behavior. ''Scientific Reports'', ''14''(1), 3761. <nowiki>https://doi.org/10.1038/s41598-024-52916-5</nowiki> Sisk, V. F., Burgoyne, A. P., Sun, J., Butler, J. L., & Macnamara, B. N. (2018). To what extent and under which circumstances are growth mind-sets important to academic achievement? Two meta-analyses. ''Psychological Science'', ''29''(4), 549–571. <nowiki>https://doi.org/10.1177/0956797617739704</nowiki> Tao, W., Zhao, D., Yue, H., Horton, I., Tian, X., Xu, Z., & Sun, H.-J. (2022). The influence of growth mindset on the mental health and life events of college students. ''Frontiers in Psychology'', ''13''(1), 1–8. <nowiki>https://doi.org/10.3389/fpsyg.2022.821206</nowiki> }} ==External links== {{expand}} * Center for Teaching and Learning, Stanford University. (2025). ''Growth mindset''. Stanford University. Center for Teaching and Learning. https://ctl.stanford.edu/students/growth-mindset * University, S., Stanford, & California 94305. (n.d.). ''Growth mindset scale | SPARQtools''. Sparqtools.Org. Retrieved 28 August 2026, from https://sparqtools.org/mobility-measure/growth-mindset-scale/#all-survey-questions< [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Mindset/Growth]] [[Category:Motivation and emotion/Book/Well-being]] rrmmq0wy2fwltxk0lkeagexypivk0x3 0 331529 2844841 2839807 2026-11-08T00:18:17Z Jtneill 10242 Copyediting 2844841 wikitext text/x-wiki {{title|Time perception in mood disorders:<br>How do anxiety and depression alter the subjective experience of time? }} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:My file Anxiety and the passage of time.jpg|thumb|right|280px|Figure 1. Emotional states can influence the subjective experience of time.]] ;Case study: Two people, the same ten minutes Maya and Daniel are waiting for a train that will arrive in ten minutes. Maya is anxious about an important interview. She repeatedly checks her watch, imagines arriving late, and becomes increasingly restless. Every minute seems unusually long. Daniel is experiencing depression. He is not particularly worried about the train, but he feels exhausted and disconnected from his surroundings. The wait seems empty and endless. Both experience the same ten minutes of clock time, yet their subjective experiences differ. Why can emotions change the way time feels? {{RoundBoxBottom}} Time is usually understood as something objective, measured in seconds, minutes, and hours. However, psychological time is not always experienced consistently. An enjoyable afternoon may seem to disappear, while a stressful wait can feel much longer than expected. Time perception refers to the psychological processes involved in experiencing and judging duration. Emotional states can influence these processes through attention, physiological arousal, memory, and cognitive interpretation (Droit-Volet & Meck, 2007). Anxiety and depression are especially relevant because they can alter how individuals experience everyday events. Anxiety often involves anticipation of uncertain threats, whereas depression may involve persistent sadness, reduced pleasure, and changes in motivation. Although anxiety disorders are classified separately from depressive disorders, comparing them helps explain how different forms of emotional distress influence subjective time. {{RoundBoxTop|theme=3}} '''Focus questions''' {{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}} 1. How do anxiety and depression influence the subjective experience of time? 2. Which psychological theories explain these changes? 3. What does peer-reviewed research reveal, and why do findings sometimes disagree? 4. How can this knowledge contribute to understanding emotional wellbeing? {{RoundBoxBottom}} == What is time perception? == Time perception is not a single ability. Psychologists distinguish between experiencing the passage of time and judging the duration of an interval {{f}}. A person might report that an afternoon passed very slowly but still accurately estimate a ten-second interval in an experiment. This distinction is essential when investigating depression (Droit-Volet, 2013). Researchers use several tasks to investigate temporal judgements {{f}}: {| class="wikitable" style="width:100%;" |+ '''Table 1. Common tasks used to investigate time perception''' |- ! Task ! What participants do |- | Verbal estimation | State how many seconds an event lasted |- | Time production | Produce a requested interval, such as ten seconds |- | Time reproduction | Recreate an interval previously presented |- | Temporal bisection | Classify intervals as closer to a learned short or long duration |} These methods place different demands on attention, memory, and decision-making. Another distinction concerns prospective timing, when people know in advance that they must judge duration, and retrospective timing, when they estimate duration afterwards. These approaches can produce different results because they involve different cognitive processes (Block & Zakay, 1997). Time perception is also different from time perspective, which concerns how people think about their past, present, and future == Psychological theories explaining altered time perception == {{ic|Include an introductory paragraph before branching into sub-sections}} === Internal clock theory === One influential explanation is the internal clock model, which proposes that timing involves a hypothetical pacemaker producing pulses, a mechanism controlling their accumulation, and processes for interpreting the resulting temporal information. {{f}} When more pulses accumulate, an interval may be experienced as longer. When fewer pulses accumulate, it may be judged as shorter. {{f}} Emotional arousal may influence the operation of this system. For example, heightened arousal during a threatening event could increase the amount of temporal information registered, producing a longer duration judgement (Droit-Volet & Meck, 2007). However, the internal clock is a theoretical model rather than a literal clock located in one brain region. A major limitation is that behavioural results cannot always distinguish changes in pacemaker speed from changes in attention or memory. {{f}} ==== Attention and the attentional gate ==== Attentional explanations propose that perceived duration depends partly on how much attention is allocated to time. {{f}} When people concentrate on a clock, temporal information becomes more prominent. When they are absorbed in another activity, they may devote fewer cognitive resources to timing. {{f}} This is relevant to anxiety because anxious individuals may repeatedly monitor anticipated events. However, anxiety can also redirect attention towards threatening information rather than time itself. {{f}} These possibilities can produce opposite effects. Increased monitoring of time might make a wait feel prolonged, whereas attention diverted towards a threat might produce shorter laboratory duration estimates. {{f}} The attentional approach therefore helps explain why anxiety does not always produce the same temporal distortion. {{f}} One strength of the attentional approach is that it considers how different tasks influence the way people judge time. Block and Zakay (1997) conducted a meta-analytic review of 20 experiments comparing prospective and retrospective duration judgements. They found that prospective estimates were generally longer and less variable than retrospective estimates. This suggests that the psychological processes involved in experiencing duration are not necessarily identical to those involved in remembering it. The findings are particularly relevant when considering anxiety. For example, Maya's repeated checking of the clock may increase her awareness of passing time. However, if her attention becomes absorbed by worries about the interview, fewer resources may be available for monitoring duration. The attentional model therefore offers two possible explanations for her experience, depending on where her attention is directed. Nevertheless, the theory has limitations. Attention is difficult to isolate because emotional arousal, memory and decision-making may also influence timing performance. Furthermore, evidence from controlled laboratory tasks cannot automatically explain how individuals experience prolonged periods of anxiety in everyday life. Consequently, attentional explanations are useful but should be considered alongside other psychological mechanisms. ==== Emotional arousal and cognitive appraisal ==== Emotion involves interactions between bodily responses, thoughts, and subjective experience. Reeve (2024) provides a broader foundation for understanding these components of emotion. Cognitive appraisal concerns how an individual interprets an event in relation to personal goals and wellbeing. For example, a delayed train may be unimportant to someone travelling casually but threatening to someone attending a job interview. The same situation can therefore produce different emotional responses and attentional priorities. Droit-Volet and Gil (2009) describe an important relationship between emotional experience and temporal judgement: emotional events can influence timing through multiple processes rather than through a single mechanism. A limitation is that appraisal theory explains why situations become emotionally significant but does not independently predict the precise direction of a duration-estimation error. ==== Depression, rumination, and reduced engagement ==== Depression may influence temporal experience through changes in motivation, attention, and cognitive processing. Rumination involves repetitive negative thinking. A person experiencing depression may remain focused on distressing thoughts while finding everyday activities less rewarding. This may contribute to the experience that time is dragging. However, this explanation should not be confused with evidence that depression universally slows an internal timing mechanism. Droit-Volet (2013) emphasised that the feeling of slow time is not systematically associated with disrupted basic timing processes. '''Figure 2. Conceptual pathways linking emotion and time''' [[File:Emotipnal_expreience_ss_.png|thumb|right|450px|Figure 2. Original conceptual diagram based on the theoretical approaches reviewed by Droit-Volet and Meck (2007). Arrows represent proposed influences, not established causal pathways.]] == What does psychological research reveal? == {{ic|Include an introductory paragraph before branching into sub-sections}} ==== Anxiety and time perception ==== Research demonstrates that anxiety can influence temporal judgements, but its effects are not always in the direction people might expect. Sarigiannidis et al. (2020) investigated anxiety using a threat-of-shock procedure. Participants completed a timing task while experiencing the possibility of an unpredictable electric shock. Across three experiments, anxiety was associated with underestimation of duration, with a combined effect size of d = 0.68. This is important because everyday descriptions of threatening events often suggest that time slows down. The experimental results demonstrate that anxiety does not necessarily make measured intervals seem longer. The researchers also distinguished anxiety, associated with uncertain threat, from fear, associated with more immediate threat. This distinction matters because different negative emotional states may involve different attentional and physiological responses. Liu and Li (2019) examined interactions between temporary anxiety and trait anxiety. Their findings suggested that people with different levels of trait anxiety could show different temporal responses under an anxious state. This challenges the assumption that all anxious individuals process duration in the same way. However, experimental anxiety and trait anxiety do not necessarily represent clinically diagnosed anxiety disorders. Research involving emotional expressions provides additional evidence. Droit-Volet and Meck (2007) reviewed studies showing that emotional stimuli can alter duration judgements through interactions between arousal and attention {{expand}}. The evidence therefore supports a conditional explanation: anxiety can distort timing, but the direction depends on individual characteristics, emotional context, and the task being performed. Sarigiannidis et al. (2020) challenged the common assumption that anxiety always makes time seem slower. Their research used a threat-of-shock procedure to create uncertainty while participants completed duration judgements. This approach provided greater experimental control than simply asking participants to remember how time felt during a stressful event. The researchers also repeated the investigation across three experiments, increasing confidence that the observed underestimation was not restricted to a single experimental procedure. However, several limitations should be considered. The anxiety experienced during a controlled experiment may differ considerably from the persistent worry associated with an anxiety disorder. Participants were also judging relatively brief intervals, rather than the longer periods of waiting that commonly occur in everyday life. Therefore, the findings should not be interpreted as evidence that anxiety always makes an entire day pass more quickly. The results also raise a theoretical question. If emotional arousal necessarily accelerated an internal clock, increased duration estimates might be expected. Instead, the observed underestimation suggests that attentional changes or other cognitive processes may sometimes have a stronger influence. This interpretation supports a more flexible account of time perception in which emotional arousal and attention interact. It also demonstrates why researchers should distinguish between experimentally induced anxiety, fear and clinically diagnosed anxiety disorders. ==== Depression and the subjective slowing of time ==== Depression is often associated with descriptions of time moving unusually slowly {{f}}. One of the strongest sources is the meta-analysis by Thönes and Oberfeld (2015), which combined 16 studies involving 433 participants with depression and 485 healthy controls. The researchers found a moderate difference in the subjective passage of time (g = 0.66), indicating that participants with depression experienced time as passing more slowly. However, the meta-analysis did not find statistically significant overall differences in four commonly used laboratory timing tasks. This result is especially important because it challenges the assumption that depression necessarily damages the ability to estimate duration. Gil and Droit-Volet (2009) investigated the relationship between depressive symptoms and temporal bisection. Participants judged whether short intervals were closer to previously learned short or long durations. Higher depressive symptom scores were associated with shorter duration judgements, although temporal sensitivity {{explain}} was similar across groups. This suggests that depression-related timing differences may appear under specific experimental conditions without necessarily reflecting a general impairment. Oberfeld et al. (2014) compared 22 patients with depression and 22 healthy controls across several timing measures. They found no reliable overall group differences in timing accuracy. These findings challenge the idea that depression always affects the internal processes used to judge time. The findings of Thönes and Oberfeld (2015) also highlight the importance of distinguishing statistical significance from psychological importance. Although the meta-analysis found a moderate difference in the subjective passage of time, the overall results did not demonstrate consistent impairment across conventional timing tasks. This suggests that the emotional experience of time may be affected even when basic temporal judgements remain relatively accurate. One strength of the meta-analysis was its ability to combine findings from multiple studies rather than relying on a single clinical sample. This provided a broader assessment of the relationship between depression and time perception. However, combining studies also introduces difficulties because participants, timing procedures and clinical characteristics may differ. The authors identified insufficient evidence concerning medication and the role of dopamine-related processes as limitations. These factors are important because biological and cognitive changes associated with depression may influence temporal processing independently of subjective mood. The distinction between subjective experience and objective performance is also relevant to Daniel's situation in the opening case study. His experience of an endless wait does not necessarily mean that he would inaccurately reproduce a ten-second interval in an experiment. Rather, his emotional state may influence the personal meaning and felt passage of the experience. This demonstrates why depression-related changes in time should not be reduced to a single impaired timing mechanism. ==== Direct comparisons between anxiety and depression ==== Mioni et al. (2016) investigated {{ic|how many}} {{where}} anxious patients, depressed patients, and healthy controls using time reproduction and production tasks. The researchers used the same brief intervals 500, 1,000, and 1,500 milliseconds across groups, allowing more direct comparisons. Compared with controls, anxious patients reproduced intervals as shorter, while depressed patients produced longer intervals. The authors suggested that attentional disruption might be particularly relevant to anxiety, whereas internal timing processes might contribute to depression-related differences. However, these mechanisms were inferred from behavioural performance rather than directly observed. The findings therefore support possible explanations without proving that the same mechanisms apply to every person experiencing anxiety or depression ==== Why are the findings inconsistent? ==== The research literature contains both significant effects and null findings. Several factors may explain this variation. First, studies investigate different aspects of time. A rating of how slowly an afternoon passed is not equivalent to reproducing a one-second interval. Second, emotional states differ. Experimentally induced anxiety, high trait anxiety, and diagnosed anxiety disorders should not be treated as interchangeable. Third, timing tasks rely on different cognitive processes. Attention, memory, decision-making, and response strategies may influence performance. Fourth, studies may differ in symptom severity, medication use, age, fatigue, and other participant characteristics. Finally, many experimental tasks involve intervals lasting only milliseconds or seconds. These may not represent the extended experiences of boredom, hopelessness, or anxious anticipation encountered in daily life. The most defensible conclusion is therefore that emotional distress can influence temporal experience, but no single pattern of distortion applies across all emotions, people, and situations. Table 2. Selected research findings on anxiety, depression, and temporal judgements. {| class="wikitable" |+ !Study !Method !Main Finding !Critical Consideration |- |Thönes & Oberfeld (2015) |Meta-analysis of 16 depression studies |Subjective time felt slower; no consistent overall laboratory timing differences |Studies differed in methods and clinical characteristics |- |Gil & Droit-Volet (2009) |Temporal bisection and depressive symptom measures |Higher symptoms associated with shorter duration judgements |Symptoms do not necessarily indicate clinical diagnosis |- |Oberfeld et al. (2014) |Clinical comparison, 22 participants per group |No reliable overall timing accuracy differences |Relatively small clinical sample |- |Mioni et al. (2016) |Time reproduction and production in clinical groups |Different patterns in anxiety and depression |Proposed mechanisms were inferred |- |Sarigiannidis et al. (2020) |Experimental anxiety and timing tasks |Anxiety produced temporal underestimation |Induced anxiety may not reflect chronic disorders |} == Integrating theory and research == The evidence suggests that time perception is best understood through an interaction of psychological processes rather than a single internal mechanism. Internal clock models are useful for explaining possible relationships between arousal and duration estimates. Attentional theories explain why focusing on time or threatening information can change temporal judgements. Cognitive approaches help explain why personal interpretations and emotional experiences influence how time feels. The depression meta-analysis {{f}} presents a particularly important theoretical challenge. If people with depression experience time as passing slowly but generally perform similarly to controls on laboratory timing tasks, then subjective slowing cannot be explained solely by impaired interval timing. Likewise, anxiety-related underestimation in controlled experiments challenges the assumption that heightened arousal always produces longer duration judgements. An integrated explanation must therefore distinguish the emotional experience of time from the mechanisms involved in estimating brief intervals. The research also has methodological limitations. Laboratory studies provide experimental control but may lack everyday relevance. Self-report measures capture personal experience but may be influenced by memory and interpretation. Future research could combine laboratory timing tasks with repeated assessments of emotional experience in everyday environments. This would help clarify whether emotional changes precede temporal distortions, follow them, or interact with them over time. The comparison between anxiety and depression also demonstrates why different psychological theories may be useful for different circumstances. Mioni et al. (2016) found that anxious patients tended to reproduce intervals as shorter, whereas depressed patients tended to produce longer intervals. The researchers interpreted these patterns as potentially reflecting attentional differences in anxiety and changes in internal timing processes in depression. However, these explanations were inferred from behavioural results rather than directly measured psychological mechanisms. This distinction is important because similar subjective experiences do not necessarily arise from identical processes. Both Maya and Daniel may feel that their ten-minute wait is unusually long, yet their experiences could involve different combinations of attention, emotional arousal, rumination and motivation. Taken together, these studies suggest that there is no single explanation for how anxiety and depression affect time perception. Rather than assuming that a particular disorder produces one predictable temporal distortion, psychologists should consider the individual's emotional state, the duration being judged and the demands of the task. This understanding also has practical relevance. Recognising that perceived time can change with emotional experience may help explain why waiting, uncertainty and reduced engagement become especially difficult during psychological distress. However, current evidence does not establish that modifying time perception directly improves mental health outcomes. Further research is needed before specific clinical recommendations can be made. The strongest application of the existing evidence is therefore improved understanding of emotional experience rather than a new treatment for anxiety or depression. == How can this knowledge be applied? == Understanding the relationship between emotion and time may help explain common everyday experiences. For someone experiencing anxiety, waiting for an uncertain outcome can become particularly noticeable. Repeatedly checking the clock may increase attention to the passage of time, while worrying about a threat may divert attention away from timing. For someone experiencing depression, reduced motivation and diminished enjoyment may make ordinary activities feel prolonged or empty. These explanations suggest possible benefits from meaningful engagement, attention regulation, and supportive daily routines. However, the research reviewed here does not establish these approaches as specific treatments for distorted time perception. Changes in temporal experience are also not reliable diagnostic indicators of anxiety or depression. Persistent emotional distress should be assessed by a qualified professional. Ultimately, how long something feels can depend just as much on our emotional state as on the time shown by a clock. == Quiz == {{ic|Use the [[Help:Quiz|quiz]] tool}} '''Test your understanding of time perception. Choose the best answer before revealing the explanations.''' '''Question 1: What is the difference between subjective passage of time and duration estimation?''' A. They describe exactly the same process. B. Subjective passage concerns how quickly time feels, while duration estimation concerns judging an interval. C. Only duration estimation is influenced by emotions. '''Question 2: What did Thönes and Oberfeld (2015) find about depression?''' A. Depression consistently causes overestimation of duration. B. Depression has no relationship with time perception. C. Depression is associated with subjective slowing, but laboratory timing differences are inconsistent. '''Question 3: Why might anxiety produce different timing results?''' A. Emotional context, individual differences, and timing methods vary. B. Anxiety affects every individual identically. C. Anxiety changes objective clock time. <div class="mw-collapsible mw-collapsed" style="border:1px solid #a2a9b1; padding:12px; margin-top:12px;"> '''Show answers and explanations''' <div class="mw-collapsible-content"> '''Question 1: B.''' Subjective passage of time concerns how time feels, whereas duration estimation involves judging the length of an interval. '''Question 2: C.''' Depression is associated with slower subjective time, but laboratory timing performance does not consistently differ. '''Question 3: A.''' Anxiety-related timing effects depend on emotional context, individual differences, and experimental methods. </div> </div>'''Reflection activity''' Think of an occasion when time seemed to move unusually slowly or quickly. Consider whether you were anxious, sad, excited, or deeply engaged in an activity. Was your attention focused on the clock or elsewhere? Did you judge the duration while it happened or afterwards? This reflection illustrates how emotional experience, attention, and memory can interact without necessarily changing objective time. == Conclusion == Anxiety and depression can alter subjective time, but their effects are complex and not universal. Anxiety-related timing changes appear to depend on threat, attention, and individual differences. Depression is more consistently associated with the experience that time passes slowly than with impaired performance on laboratory timing tasks. Internal clock, attentional, and cognitive theories each explain part of this relationship, but no single model fully accounts for the available evidence. The central takeaway is that feeling time pass slowly is not the same as estimating duration inaccurately. Recognising this distinction improves our understanding of how emotion shapes everyday experience and highlights the importance of evaluating psychological theories against different forms of research evidence. == See also == '''Wikipedia''' * [[wikipedia:Time_perception|Time Perception]] * [[wikipedia:Anxiety disorder|Anxiety Disorder]] * [[wikipedia:Major_depressive_disorder|Major Depressive Disorder]] * [[wikipedia:Emotion|Emotion]] == References == {{Hanging indent|1= <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Bech, P. (1975). Depression: Influence on time estimation and time experience. ''Acta Psychiatrica Scandinavica, 51''(1), 42–50. https://doi.org/10.1111/j.1600-0447.1975.tb00211.x </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Block, R. A., & Zakay, D. (1997). Prospective and retrospective duration judgments: A meta-analytic review. ''Psychonomic Bulletin & Review, 4''(2), 184–197. https://doi.org/10.3758/BF03209393 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Droit-Volet, S. (2013). Time perception, emotions and mood disorders. ''Journal of Physiology-Paris, 107''(4), 255–264. https://doi.org/10.1016/j.jphysparis.2013.03.005 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Droit-Volet, S., & Gil, S. (2009). The time–emotion paradox. ''Philosophical Transactions of the Royal Society B: Biological Sciences, 364''(1525), 1943–1953. https://doi.org/10.1098/rstb.2009.0013 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Droit-Volet, S., & Meck, W. H. (2007). How emotions colour our perception of time. ''Trends in Cognitive Sciences, 11''(12), 504–513. https://doi.org/10.1016/j.tics.2007.09.008 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Effron, D. A., Niedenthal, P. M., Gil, S., & Droit-Volet, S. (2006). Embodied temporal perception of emotion. ''Emotion, 6''(1), 1–9. https://doi.org/10.1037/1528-3542.6.1.1 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Gil, S., & Droit-Volet, S. (2009). Time perception, depression and sadness. ''Behavioural Processes, 80''(2), 169–176. https://doi.org/10.1016/j.beproc.2008.11.012 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Liu, J., & Li, H. (2019). Interactive effects of trait and state anxieties on time perception. ''Acta Psychologica, 195'', 64–70. https://doi.org/10.1016/j.actpsy.2019.03.004 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Mioni, G., Stablum, F., Prunetti, E., & Grondin, S. (2016). Time perception in anxious and depressed patients: A comparison between time reproduction and time production tasks. ''Journal of Affective Disorders, 196'', 154–163. https://doi.org/10.1016/j.jad.2016.02.047 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Oberfeld, D., Thönes, S., Palayoor, B. J., & Hecht, H. (2014). Depression does not affect time perception and time-to-contact estimation. ''Frontiers in Psychology, 5'', Article 810. https://doi.org/10.3389/fpsyg.2014.00810 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley. </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Sarigiannidis, I., Grillon, C., Ernst, M., Roiser, J. P., & Robinson, O. J. (2020). Anxiety makes time pass quicker while fear has no effect. ''Cognition, 197'', Article 104116. https://doi.org/10.1016/j.cognition.2019.104116 </div> <div style="margin-left:2em; text-indent:-2em; margin-bottom:1em;"> Thönes, S., & Oberfeld, D. (2015). Time perception in depression: A meta-analysis. ''Journal of Affective Disorders, 175'', 359–372. https://doi.org/10.1016/j.jad.2014.12.057 </div> }} == External links == * [https://www.nimh.nih.gov/health/topics/depression National Institute of Mental Health - Depression] * [https://www.nimh.nih.gov/health/topics/anxiety-disorders National Institute of Mental Health - Anxiety disorders] * [https://www.apa.org/topics/stress American Psychological Association - Stress] [[Category:Motivation and emotion/Book/Anxiety]] [[Category:Motivation and emotion/Book/Depression]] [[Category:Motivation and emotion/Book/Psychopathology]] [[Category:Motivation and emotion/Book/Time]] 6o4wq44ey8q4k9so42is12enmcxrfda 2 331626 2844830 2828672 2026-11-07T21:52:09Z Jtneill 10242 + social contributions from book chapter page 2844830 wikitext text/x-wiki HI Guys! I am a third year Bachelor of Psychology student at UC, with a strong interest in both positive psychology and trauma/mental health. I am very interest in how psychology influences the way we think, behaviour and feel and how trauma disrupts those processes. Outside of university I enjoy reading, gym, running and bouldering. I value learning and personal growth, I work two jobs while studying so a healthy balance between it all has been a strong learning curve of mine! I love learning about the Psychology of happiness and highly recommend the book Authentic Happiness by Martin E. Seligman, it is an amazing and eye-opening read. == Social Contributions == Feedback done on following posts: # Motivation and emotion/Book/2026/Charismatic leadership and follower motivation # Motivation and emotion/Book/2026/Alcohol use for emotion regulation # Motivation and emotion/Book/2026/Reinforcement sensitivity theory # Motivation and emotion/Book/2026/Life purpose and well-being#Feedback on research section s0i7rzz3wow18itbhpcv44dvkykesqd 1 332025 2844853 2839124 2026-11-08T05:09:39Z Jtneill 10242 Book chapter feedback 2844853 wikitext text/x-wiki <!-- Official topic development feedback --> {{METF/2026 |1= <!-- Title --> # Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]] |2= <!-- Heading structure --> <!-- 1-level --> # Basic, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development, perhaps using a 2-level structure (i.e., use subheadings) # The first three headings after the Overview could be combined into a single introductory section # There is no heading focused on sex differences in sexual motivation <!-- Alignment with focus questions --> # Develop closer alignment between sub-title, focus questions, and top-level headings |3= <!-- Overview--> # Promising <!-- Scenario --> # An engaging scenario with a relevant image is planned or presented in a feature box at start of the Overview <!-- Description --> # A promising description of the problem/topic is planned or presented # Simplify/abbreviate the description of the problem/topic. Move detail into subsequent sections. <!-- Style --> # Use present, rather than future, tense <!-- Focus questions --> <!-- Alignment and quality --> # Develop closer alignment between the sub-title, focus questions, and top-level headings |4= <!-- Key points--> <!-- Overall --> # Promising/partial development # Focus on providing an integrative review of the most relevant theories and research on the topic # Overly broad/comprehensive; not sufficiently focused/targetted on the topic; this often occurs when genAI content is used by a prompter with insufficient background reading and understanding of the topic and/or insufficient revising and rewriting of genAI content <!-- Scope --> # It is unlikely that all planned aspects can be reasonably covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title # ''Avoid providing too much background information''. Aim to briefly summarise general concepts and provide internal links to relevant book chapters and/or Wikipedia pages for further information. Focus most of the chapter on ''directly answering the core question(s)'' posed by the chapter sub-title. <!-- Conclusion --> # Conclusion hasn't been developed # What are the practical, take-home messages? (address the focus questions) |5= <!-- Figure --> # Relevant figure(s) are presented and captioned <!-- Cite --> # Cite each figure at least once in the main text using APA style (e.g., see Figure 1) <!-- Creation --> # Well done on creating and uploading your own image! {{smile}}—this can also be listed on your user page as a social contribution |6= <!-- Learning feature --> <!-- Interwiki links ---> # Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- Scenarios/examples/case studies --> # Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice. <!-- Quiz --> # Promising use of quiz question(s) # Place each quiz question in the most relevant section # Focus the quiz question(s) on the take-home messages <!-- Tables --> # Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information |7= <!-- References --> <!-- Overall --> # Good <!-- Systematic reviews --> # What are the most relevant systematic reviews/meta-analyses about this topic? # Move non-peer-reviewed sources to the external links section <!-- APA style --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## capitalisation ## make doi hyperlinks active (i.e., clickable) |8= <!-- Resources --> <!-- See also --> # See also ## Excellent <!-- External links --> # External links ## Excellent ## Use [[w:Letter case#Sentence casing|sentence casing]] ## Use alphabetical order |9= <!-- User page --> # Used effectively <!-- Description about self --> # Description about self provided <!-- Links to profile(s) --> # Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]]. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 01:04, 13 September 2026 (UTC) == Heading casing == {| style="float: center; background:transparent;color:inherit;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:|Hi [[User:{{{1}}}|{{{1}}}]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 05:09, 8 November 2026 (UTC) |} <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an insufficient chapter # The main area(s) for potential improvement: #* use the best psychological theory about the topic (there is no explicit mention of any theories) #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution <!-- Overall - Edit summaries --> # Very good use of [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to communicate the changes made in most or all of the main edits <!-- Overall – Citations --> # Insufficient use of academic, peer-reviewed citations to support claims # Only cite sources that you consult <!-- Overall – Word count --> # Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FSex_differences_in_sexual_arousal_patterns&diff=2844852&oldid=2839857 these copy edits] |2= <!-- Overview – Comments... --> # Basic <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Engaging scenario or case study <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario <!-- Overview – Scenario - Feature box --> # The scenario uses an appropriate feature box <!-- Overview – Explains problem --> # Briefly explains the psychological problem or phenomenon from a historical point of view; provide a more detailed overview of recent theory and research ## Clarity of written expression can be improved <!-- Overview – Focus questions --> # The focus questions are basic |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Insufficient critical synthesis of relevant theories # Remarkably, not a single theory is mentioned, although the general categories of biological and psychological are suggested <!-- Theory – Builds on --> # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Basic depth is provided about key theory(ies) <!-- Theory – Tables/Figures/Lists --> # Basic use of tables, figures, and/or lists to convey key theoretical information <!-- Theory – Citations --> # In many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. # If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source] <!-- Theory – Examples --> # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Insufficient review of relevant research # Insufficient use of relevant systematic reviews and/or meta-analyses (Chiveners in the Referneces, but not described as a meta-analysis in the critical review) # More detail about key studies would be ideal # In many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. <!-- Research – Critical thinking --> # Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out specific critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Basic integration between the most relevant theory(ies) and the best research # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Insufficient as a cohesive summary of the best psychological theory and research about the topic # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are summarised in a basic way <!-- Conclusion – Focus questions --> # Address the focus questions <!-- Conclusion – Take-home messages --> # Add practical, take-home message(s) |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills. <!-- Style – Sentences --> ## Many sentences could be explained more clearly (e.g., see {{vague}}, {{explain}}, {{rewrite}} etc. tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression <!-- Style – Paragraphs --> ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. <!-- Style – Language --> ## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., "it") instead of 1st (e.g., "we") or 2nd person (e.g., "you") in the main text. 1st or 2nd person can work well for case studies or feature boxes. ## Avoid directional phrases such as “as previously mentioned” or “as noted above”, which add little value and can interrupt the flow of writing. Where cross-referencing is necessary, use [[w:Help#Section linking|section links]] to guide readers to the relevant content. <!-- Style – Layout --> # Layout ## See earlier comment about [[#Heading casing|heading casing]] <!-- Style – Grammar --> # Grammar ## The grammar for many sentences could be improved (e.g., see {{g}} tags); I strongly recommend using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or seeking peer feedback to assist with developing text that is closer to a professional standard ## Improve the clarity and flow of the writing by checking and correcting use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas]. ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] ## Overuse of the present perfect: use the simple past tense consistently when reporting previous research e.g., ### Present perfect: "Chivers (2010) has also suggested ..." ### Simple past: "Chivers (2010) suggested ..." ## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats') <!-- Style – Abbreviations --> <!-- Style – Copy editing --> # Copy editing ## Further [[w:Copy editing|copy editing]] is needed to improve written expression and bring the chapter closer to a professional standard (e.g., correcting punctuation, spelling, grammar, and typographical errors). <!-- Style – APA style --> # APA style ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – Figures --> ## Figures ### Very well/ captioned <!-- Style – Figures - Citations --> ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Citations --> # Citations use basic [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)] # In many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses ## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra & Aardvark, 2020) <!-- Style – References --> ## References use excellent APA style ## References use reasonably good APA style: ### Check and correct use of italicisation ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### More copy editing is needed to fix formatting inconsistencies |8= <!-- Learning features comments... --> # Basic use of learning features <!-- Learning features – Wikipedia embedded links --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Reasonably good use of figure(s) # No use of table(s) # Good use of feature box(es) # No use of scenarios, case studies, or examples, other than opening scenario <!-- Learning features – Quizzes --> # Good use of quiz(zes) and/or reflection question(s) # The quiz questions could be improved by being more focused on the key points and/or take-home messages about gender differences in patterns of sexual arousal <!-- Learning features – See also --> # Insufficient use of the [[{{PAGENAME}}#See also|See also]] section ## Add more links <!-- Learning features – External links --> # Excellent use of the [[{{PAGENAME}}#External links|External links]] section |9= <!-- Social contribution comments... --> # ~4 logged, useful, mostly moderate contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]] # The Wikiversity uploads have been deleted because they don't offer any educational value # Educational media should be uploaded to [[c:|Wikimedia Commons]] as demonstrated in Tutorials # The scenario image was not listed as a social contribution # A rename of the scenario image has been requested on Wikimedia Commons so that it is more accurate and descriptive }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 05:09, 8 November 2026 (UTC) 8rtfkc1vjrqa8jb8prrki9sy4d68ou5 0 332412 2844839 2844794 2026-11-08T00:13:23Z Scogdill 1331941 2844839 wikitext text/x-wiki =Event= International championship boxing match between British Jem Smith and Australian Frank Slavin on 23 December 1889 in Bruges, Belgium. ==Overview== On 23 December 1889 a championship boxing match in Bruges ended with cheating on the British side: British Jim Smith was losing, so his supporters entered the ring, took advantage of Smith's holding Australian Frank Slavin and beat him up, using fists, sticks, "knuckle-dusters," "life preservers" and boots. The referee ruled the match a draw to prevent Slavin from being killed and then fled. The ''Cork Constitution'' called it "the Smith-Slavin piece of brutality."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref> A knuckle-duster was "A metal instrument made to cover the knuckles,"<ref>“Knuckle-duster, ''N.''”  ''Oxford English Dictionary'', Oxford UP,  December 2024, https://doi.org/10.1093/OED/6130372797.</ref> like brass knuckles, and a life preserver was "A stick or truncheon weighted at one end" with lead.<ref>“Life-preserver, ''N.''”  ''Oxford English Dictionary'', Oxford UP,  September 2026, https://doi.org/10.1093/OED/1055046410.</ref> One meeting of the boxing-oriented London Pelican Club was held almost immediately. Then a series of meetings following an investigation occurred in the first week of January (the [[Social Victorians/Boxing/Pelican Club Meeting Smith-Slavin match|Pelican Club meetings]] referred to below). Slavin followed this fight with a challenge for American John L. Sullivan, saying he would fight in America or Australia, but not in a private venue in England. Many, many newspapers covered this fight and the reaction to it in the boxing community. Copy-and-paste journalism and the lack of copyright laws means that many of the stories are all or in part identical to others, so no attempt has been made here to offer complete coverage. ==Logistics== * 23 December 1889, 8:00–9:00 a.m. * Stakes: £1,000 ==Related Events== * [[Social Victorians/Boxing/Pelican Club Meeting Smith-Slavin match|Pelican Club Meetings about the Smith-Slavin match]] * the "[[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]]" ==Who Was Present== # Jem Smith, British boxer # Frank Slavin, Australian boxer # [[Social Victorians/People/Mandeville|Kim Montagu, Viscount Mandeville]] # Lord Rosslyn # Sir M. Sandys # Mr. G. Abington Baird, Smith's manager? and horseman (see description in Anthology) # The writer of the article, who reports for The Sportsman and who is not the "well-known sporting journalist"<ref name=":1">"The Great Fight. Smith & Slavin for £1000. Disorderly Proceedings. Brutal Attack on Slavin. Smith Knocked Down Repeatedly. He Leaves the Ring. A Draw Declared after 14 Rounds." ''The Sportsman'' 24 December 1889, Tuesday: 3 [of 4], Col. 1a – 4, Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18891224&page=3&article=057&stringtohighlight=mandeville+viscount. Same print title and p.</ref> (3, Col. 1b) who had heard that Slavin had been arrested in Margate, plus "three scribes with pockets bulging from a surplusage of note-books dropped in"<ref name=":1" /> (3, Col. 1c) # Bob Habbijam # Jack Lewis # Tom Smith # Bob Kirby # Barney Sheppard # "Pop" Hinde # Frank Hinde # Teddy Bayley # Will Riley # Joe Vezey or Vesey, referee # "The Squire" # Ike White # J. Kilby # C. Horton # C. Parsons # J. Fleming ==Entertainment== ==Anthology== === The Sportsman === The Tuesday, 24 December 1889 issue of ''The Sportsman'' devoted page 3 and most of page 4 (nearly 13 full columns) entirely to this story. This reporter's writing style is very ornate: * "Long before the earliest purveyor of the lacteal fluid arrived in the quiet suburban street to wake the sleepers with his hideous yelping" (3, Col. 1c) Besides the street-fighting terms (knuckle-dusters, life preservers) above, he also uses slang and local vocabulary like sabots (wooden clogs worn by working-class Belgians), Brums, This is, then, a very long story, reproduced here in full:<blockquote>The long-talked-of fight between Jem Smith, Champion of England, and Frank P. Slavin, Champion of Australia, took place between eight and nine o'clock yesterday morning in the private grounds of a gentleman's residence near Bruges, Belgium. The contest, as everybody knows, was for 1000''l''. Thanks to the most cowardly and disgraceful behaviour of a gang of ruffians in Smith's corner, the referee was forced to declare the fight a draw at the close of the fourteenth round. Full details are given below.</blockquote> ==== THE JOURNEY TO THE CONTINENT. ==== <blockquote>(By our special reporter.) [?] travellers accustomed to make long and frequent journeys do not trouble themselves much about starting. The pangs of parting are easly effaced, and after a few years of "globe-trotting," as the Yankees are pleased to call it, beyond looking after personal comforts the travelling Briton has very little trouble. I have made many notable journeys upon all sorts of errands, but must confess that entering upon my last jaunt brought not a few qualms — other than those likely to be experienced at sea. The preliminaries of the international fight, which was the reason of the trip from town, had not been carried through without many untoward circumstances arising to spoil the fun. On Saturday, however, there was every prospect of the business being brought to a successful termination, and when word was brought me that on the following morning our party were to leave London at an early hour there was no need for further hesitation, and preparations for the journey were rapidly made. What a day it was! Rain of a most annoying and penetrating kind fell until well into the night, making every one hurry to bring their day's business, or pleasure, to an end, that they might get indoors out of the dismal, depressing weather. Just as I had thought all safe for the [night came] A Rude Shock. [Arriving??] at the office of T<small>HE</small> S<small>PORTSMAN</small> I found a well-known sporting journalist, whose expressive features at once conveyed to my practised eye that "something had happened." His right hand convulsively clutched a telegram, and it was quickly patent that this innocent-looking piece of paper was the cause of the trouble. "What do you think of this?" asked he, handing over the document. Only a few words were pencilled thereon, but these were enough to cause us alarm. "Stoppage, but think can get bail. — Slavin." Here was a pretty "go," the mystic words being translated meaning that the Australian had been "pinched" at Margate. Before we had thoroughly grasped the situation a second wire arrived containing the definite information that Slavin had been arrested at the Kentish watering-place and that he had a difficulty in finding bail among strangers. This dire news sent our spirits down to zero. Two acts of the little drama we were enacting had been very depressing, but the third brought sunshine again. Close upon the heels of the second telegram came a third, and it was with trembling fingers that at the request of my friend I opened the missive. A glance was enough — Slavin was free, and on his way to Dover. This sent us home satisfied that all would be well on the morrow now that both the principal actors in the contest were on the spot or nearby. Daylight brought with it A May Morning. Long before '''the earliest purveyor of the lacteal fluid''' arrived in the quiet suburban street to wake the sleepers with his hideous yelping, a cross between that of a beaten dog and a Comanche Indian, I had turned out, as there was no time to be lost. It was a delightful morning, the rain clouds having vanished, and being replaced by brilliant sunshine the weather being more akin to early summer than that usually associated with late December. The early promise did not last, as before eight o'clock the south-westerly breeze brought up rain clouds once more, and a fine free sample of "London peculiar" had taken possession of the streets as I wended my way towards Cannon-street Station. Ten o'clock was the hour named, but half an hour before that time several of the party had arrived at the trysting place. First to be noticed was Bob Habbijam, in company with two less-known sports, and this trio had not the dim terminus long to themselves. Jack Lewis, looking "all broke up," put in an appearance a few minutes later, while at the same time three scribes with pockets bulging from a '''surplusage of note-books''' dropped in. It was very soon evident that the company would be much larger than intended, as cabs rattled up continually, bringing a further complement. Tom Smith, Bob Kirby, Barney Sheppard, "Pop," and Frank Hinde were the next to join us, and in quick succession came Teddy Bayley, Will Riley, and Joe Vezey [sic], who was to occupy the unthankful office of referee. According to the original conditions, a number of the intending spectators should have proceeded by way of Calais overnight, but by some means or other they managed to miss the train, and it was owing to this fact that so many were present on Sunday morning. There was no disguising the fact that such a crowd would draw attention, and militate against the secrecy necessary to insure us against intervention. There was no help for it, however, and before the Continental express came in from Charing-Cross "The Squire," Ike White, J. Kilby, C. Horton, C. Parsons, and J. Fleming had swelled the ranks of the ''voyageurs''. Down to Dover. It was only by judicious squeezing and packing that room could be found for all in the train, already well freighted with passengers, but eventually everyone managed to find a corner, luggage being conspicuous by its absence. I had a real sportsman for companion, Jack Kilby, of the Ferry Hotel, Cookham. Having missed the train overnight, not to be thwarted of his promised journey he arranged to proceed to town by road in the early morning. Instructing two lads to sit up through the night so as to be awakened in good time, Kilby turned in. At four o'clock he had the horse put in the shafts of a dog-cart, and drove slick away to Cannon-street. It was a particularly quiet trip, broken only by stoppages at Ashford and Folkestone, where some of the irrepressibles saw fit to leave the train and perambulate the platform. This, to say the least of it, was a foolish proceeding, as it fairly "gave the game away," and there was almost an air of expectancy about the officials when, after a run of nearly two hours, the South-Eastern express pulled up on Dover [Col. 1c–2a] Pier. Thoughts of coming trouble had ere this sobered down the playful ones, and it did not add to their joy when, looking seawards, they saw what is known as "dirty" weather in store. On the Briny. The transfer of passengers from the pier to the deck of the Princess Henriette was rapidly effected, and "once on board the lugger" my fellow-travellers disappeared as if by magic, but as rapidly came to light again, having, in view of developments likely to appear later, made arrangements below. There was a general changing of headgear, the bowler being discarded for the more useful tight-fitting cap — and what a variety were donned! As on the appearance of the clown in the pantomime, now the fun commenced. Before noon, when the hawsers were cast off, several shining lights in the boxing world prepared for the worst, the long rollers which broke in against the pier giving them the greatest alarm. Many had never previously ventured upon anything of a more stormy character than the Thames, and but for the fear of reproach would have turned back. As the "Princess" swung off from the pier the two "Bobs," Kirby and Habbijam, betook themselves to the "rail" in expectation of an attack of ''mal de mer''. What a pitiable sight they presented, but in a few minutes they found many brothers in misfortune, Tom Smith caving in. For a time it was a bit rough, and one of the good sailors commenced quoting Byron. "O'er the glad waters of the dark blue sea," sang he. Well, it was not too cerulean, but there was no question as to its gladness. The English Channel is generally built that way, and it was evidently making extra merry on account of the season. Once away from the shore-swell it was smooth enough, and the sickly division came round wonderfully. Frank Hinde, who played his old part of low comedian, amused them, and at length by his wonderful flow of spirits — animal and otherwise — had the worst cases on their legs again. A few exceptions there were, half a dozen or so of the swells having "sought the seclusion which the cabin grants," and there they stayed. Our low-comedy merchant now found a a [sic] serious rival in "Pop," and between them they kept the coterie on the quarter-deck from being dull. Yarns were spun by this pair of drolls, and the merry jest went round until more substantial fare was in request at the table. Both the aforementioned did their share, the way Hinde put away the humble yet satisfying cold meat and pickles causing intense envy in the breasts of the less hardy mariners. A very quick passage was made across the streak, and at half-past three the coast appeared in sight. At the same time rain commenced to fall, and as we steamed past the lighthouse on Ostend breakwater it came pelting down sharply. At a quarter to three the good ship was secured alongside the wharf, and out came the lost sheep looking white and miserable, one passenger, although not of us, who had sat on deck more dead than alive the whole way over, fairly dancing with joy at his release from the purgatory of sea-sickness. Ostend to Bruges. While those unfortunate enough to be hampered with luggage stood by for the purpose of having it searched the rest of us secured seats in the train already drawn up alongside. It was then discovered that we did not start for half an hour, and the interval was turned to account by a  visit to the buffet. ''Cafe-au-lait'' was the general order, and mightily refreshing it proved to be. Everything comes to him who waits, but before the journey was continued sharp to the time mentioned, it was very patent that our descent upon Belgium in such numbers had attracted much attention. One dark-bearded "foreigner" who had watched us closely on the way across, actually grew so confident that he had exploited our movents that he grew bold beyond discretion. Coming forward with all the effrontery imaginable he rather startled us by asking, "Well, when is the 'mill' coming off?" In a twinkling one and all assumed a look of stony indifference, and on the question being repeated he was forcibly yet politely informed that we had nothing to do with any "mills." As we left the station our inquisitive friend was seen gesticulating to a belaced Ostender, evidently proud of his perspicuity. Thirty minutes' run through the flat and thoroughly soaked country brought the gable roofs of ancient Bruges in sight. Night had not yet darkened the streets, but there was mist enough to hide our movements to a great extent. It had been agreed that the brigade should split up as much as possible and spread themselves over the city. This was done in a great measure, Tom Dunning piloting my section across the  broad station-square to the Hotel de l'Univers. On the threshold I met Mick Taylor, who naturally looked somewhat aghast at the advent of so big a muster. It must have surprised him still more when others strolled in, and eventually the Britisher's party reached no less than fifteen. Fortunately our worthy host had plenty of available room, and after climbing up the winding stairs the whole troupe were comfortably housed. Water was at a premium, while soap could only be obtained by borrowing from the one or two lucky ones who had thought to bring that useful saponaceous compound with them. Entering the saloon after an outward and inward refresher, I ran across Josh Cosnett, and close behind the Brum stood, Frank Slavin, looming fine and large. The Australian Champion looked in grand condition, his face bronzed by the sea air and the toughening preparation he uses. Gently puffing a cloud from his Belgian weed, he greeted the arrivals cheerily, and was as skittish as a kitten, his hearty laugh resounding through the establishment. He had a very favourable passage across Channel the previous night, and amused himself by strolling around the city during the day. It was a piece of good fortune that not only could the ''garçon'' speak English fairly well, but at least two of my companions were conversant with the language of the country; negotiations anent dinner were therefore carried out with celerity. Pugilism at the Piano. While awaiting the refection Slavin opened the piano which stood at one end of the ''salle-à-manger'', and dashing his lingers over the keys coon gave evidence that he was no mean performer on that instrument. Waltz, polka, and march all came as one to him. What a staggerer this would have been to the old timers, who never dared to allow a man in training such liberties. There was not the slightest sign of fear for the result of his coming encounter, and, in fact, Slavin appeared the least interested of the crowd. His piano selection whiled away the interval before dinner, at which the Australian presided. Taking his place at the head of the table Slavin entered into the fun, and no one would have conceived for a single moment that he had such a weighty matter on his mind as a fight. The repast was a lingering affair, and Slavin retired half way over the course, and betook himself once more to his favourite piano, which he wrestled with on and off during the remainder of the evening. While we were enjoying the good things under the roof of the Hotel Univers the rain had increased, and a perfect downpour succeeded. This had the effect of keeping the majority confined to the house, but several of the more venturesome spirits proceeded to explore the city, and they at any rate got a good drenching for their pains. The "pelting of the pitiless storm" continued the greater part of the night. Arrival of Jem Smith. The Champion of England, accompanied by Jack Baldock, Jack Harper, Jem Carney, and several other henchmen, came on from Lille at six o'clock, and arrived at Bruges about 8.30, taking up their quarters at the Hotel de Londres. Jem Smith, after leaving London on Friday, had travelled by easy stages to the Belgian frontier, so as not to miss a meal or proper night's rest and exercise between. He looked wonderfully well, having worked off much superfluous adiposity during the last few weeks' training. Unlike his opponent, Smith kept very quiet during the evening, and retired early. A meeting of the representatives of the men took place at a late hour, and in company with the owner of the ground and others interested, the final arnuigements were made. I was present to assist at this necessary proceeding, and so perfectly had all the preliminaries been settled that there was very little left to be done[.] Owing to the presence of a mob of Birmingham men, who by some means or other had made their way to Bruges, there was fear of interference, but every precaution was taken to defeat anything disagreeable occurring. The behaviour of many in the streets during the evening was not calculated to assist those who desired to see a fair and square battle. Strict orders were given to the ''garçon'' to call us at 5.30 sharp, and to make assurance doubly sure many affixed their names on bedroom doors. Punctually to the moment came the rat-tat on the panel, and a hasty toilet was made by the light of the dip. A glance through the window reassured us with respect to the weather, the rain having ceased, but it was yet too dark to get any idea of the future. Even thus early the patter of sabots on the stones outside betokened the fact that Bruges, sleepy as it is said to be, was well awake. When the sounds from the famous belfry announced six o'clock [Col. 2c–3a] the bulk of the dwellers in the Hotel Univers had found their way to the ''salle-à-manger'', or "the manger" as "Pop" expressively named that apartment. Tea, coffee, fillets de bœuf, and chops were discussed, and the early birds had only been fairly started when with a cheery "Good morning, gentlemen," Slavin appeared. He lost no time, and was soon busy with knife and fork. Time flew by rapidly, and there were signs of an early daybreak. This hurried on the final preparations. Bills were paid, creature comforts taken on board, Slavin, with the greatest ''sangfroid'', seeing to his own business as unconcerned as possible. Our pilot put in an appearance shortly after the half-hour had chimed, and informed us that the other sections had already gone on. The March to the Battlefield. Breaking into groups of half a dozen the advance guard, led by an English resident in Bruges, pushed on, but before going two hundred yards there came a check. The railway had to be crossed, and just as the leading division reached the line they found the gates closed. Although opened in a couple of minutes it allowed the party to amalgamate, but they soon filed out agent. Many streets had to be traversed, and in the now increasing light we were scanned by groups of workmen and workwomen who were on the way to the many factories in the neighborhood. Talking except in whispers was tabooed, so that our nationality might not be discovered, and without further incident a walk of twenty minutes or so brought us to the chosen spot. Entering the private grounds by a wicket-gate, there was light enough to see that the others were present standing among the trees. Four moving objects suddenly appeared as we crossed the garden carrying some white posts, which quite gave Joe Vesey a fright. The principals were hurried off to comfortable quarters near by, Smith having the stable to make his toilet in, while Slavin was accommodated in a barn. Proceeding towards a big plantation I found several quietly at work Building the Ring. Between two belts of trees, formed chiefly of firs and beeches, was a clearing forty feet wide, and here the turf had been swept clear of the fallen leaves — in fact, a native, whose gigantic sabots caused much amusement, was still busy with rake and roller[.] Barney Sheppard superintended the pitching of the ring, an operation which took some time. Eight heavy stakes had been provided and plenty of rope, but the ground was very soft after so much rain, and wedges and guy-ropes had to be freely utilised. There being no tape, the distance was measured out by strides, and when eventually the job was finished it was plain that plenty of room had been allowed. The spectators amused themselves in various ways until, when the clock struck eight, all was in readiness. It was now broad daylight, and as several rustics on their way to employment caught sight of the, to them, peculiar proceeding, and stopped to more closely examine, the place did not promise to be free from interruption. All went well, however, and as the business did not concern them they passed on. There was some delay at this point, and it was close upon half-past eight when the men were reported ready for the fray. The following comprised the company round the ring: — Lord Mandeville, Lord Royston, Hon. M. Sandys, Mr Abington, Mr F. Kotchie, Mr J. Kilby, Mr C. Parsons, Mr Ike White, Mr W. Riley, Mr C. Morton, Mr Harris, Mr E. Bayley, Mr J. Lewis (Australia), Mr J. Vesey, Mr F. Hinde, Mr J. Fleming, Mr M. Taylor, Mr J. Calder, Mr G. T. Dunning, "Pop" Joy, R. Habbijam, G. ("Barney") Sheppard, Jem Carney, Tom Smith, Mangie [?] Hyams, Matthews, Summers, Boulton, and several others, including two or three reporters. Smith, accompanied by his seconds, J. Harper and J. Baldock, entered the ring, quietly going over to the south-west corner with hardly any notice. Baldock at once wanted to know why Slavin had not turned up, and was inclined to be nasty, when the Australian walked briskly to the opposite corner, having, without the customary teasing for choice of positions, allowed Smith to take the higher ground. Josh Cosnett and Bob Kirby accompanied the Australian Champion as seconds, while Mick Taylor superintended the arrangements in his corner. A loud cheer greeted their advent. There was a few minutes' delay after the men had taken up positions, owing to Slavin not being provided with a seat, and Baldock again wished to hurry him up, but matters proceeded peacefully. Mr Joe Vesey, who had been appointed to the unthankful post of umpire, took up a position on the lower side midway between the corners, and Mr J. Calder was selected as timekeeper. On either side of the referee Mr J. Fleming, umpired for Smith, and Mr W. Riley for Slavin, these preliminaries being quickly settled. The disposition of the officials made Slavin's corner appear the stronger, and to still further add to this, a large percentage of the spectators selected that side, so as to get their backs to the wind. Another, and, perhaps, a more potent reason was the fact that The Dreaded Birmingham Division had massed themselves behind Smith and along the higher aide. They had long caused considerable fear among the spectators, but were not so noticeable until they stationed themselves in a phalanx near the Englishman. While the corners were being arranged several of the "boys" worked their way round to Slavin's quarters and stood menacingly by. Mick Taylor was too old a bird to be caught, and with the assistance of Prank Hinde, Lord Mandeville, and one or two trusty friends, guard was kept over the water and other articles. Every necessary for the two athletes had been provided by the proprietor of the grounds, so that there was no trouble on this score. Smith was wrapped in a heavy frieze overcoat, while Slavin, who, during his sojourn in the barn had been divested of his heavy moustache — a loss he deeply regretted — was also covered by a big ulster. It was now half an hour beyond the time fixed for the commencement of hostilities and broad daylight, even the belfry of Bruges being plainly visible in the distance, but curiously enough not a soul beyond the pugilistic party was anywhere near the fighting-ground. At last everything was ''en règle'', and in perfect silence Mr Joe Vesey came forward and said, "I hope all those present will keep quiet and help me all you can," at which brief speech there was a chorus of "hear, hear," especially from Slavin's corner. At 8.35 Belgian time, the two antagonists met in the centre of the arena and shook hands, the seconds, as in time-honoured fashion, doing likewise, forming what is known as the Maltese Cross. Smith, who partook of a draught before commencing, was the first to peel, and although he looked fine enough in the face, when his covering had been removed he appeared fat, although nothing like so obese as when he met Peter Jackson. The Englishman wore short white drawers and green socks, while a strengthening plaister adorned his waist. Slavin looked the picture of health and strength, having trained down very hard, his muscles standing out most prominently. He was clothed in long black drawers and blue stockings, and, like his opponent, wore a deep plaister. In addition Slavin used a suspensory belt loaned to him by Charlie Mitchell, who had found it of great service in his fight with John L. Sullivan. Under weather, which for the business in hand was simply perfect, and particularly warm for the time of year, there was, as far as could be seen by the uninitiated, every prospect of a good [Col. 3c–4a] fight. This was doubted by the majority, the presence of the crowd of roughs betokening trouble when once the battle should commence. The Call of "Time" At twenty-five minutes to nine brought everyone to the ropes, and amid perfect silence the pair of pugilists shaped for the encounter. Slavin from the first smiled confidently, while Smith looked serious. Neither appeared in any hurry to begin, and sparring for an opening, Slavin gradually worked Smith back into his corner. Fifty seconds elapsed before a blow was struck, but this had not passed without our opinion being confirmed, that we might expect trouble from the Brums. Smith's seconds set the ball rolling by hurling the vilest of epithets at the Australian, and their example was followed by their supporters. By some oversight the seconds had not been ordered out of the ring, but attention was at once called to the fact, but, constituting himself referee, Baldock refused to obey the order to retire when given by the appointed officials. This boded ill, and before a round had been fought it was pretty plain to all that Slavin would have little chance of victory. Had the objectionable party confined themselves to vituperation this might have been borne, but going from bad to worse we soon witnessed a scene that was not only a blot upon the good name of Englishmen as lovers of fair play but one never equalled even in the worst days of the ring. Slavin was the first to lead, but only tapped his opponent lightly on the face, and he had the best of several exchanges, but did not put forth all his power into his left-handers. Smith's blows were also comparatively harmless, until the last half minute, when they got to close quarters and hammered away sharply amidst a chorus of yells from the Smithites, until they fell together. No sooner were the two men down than Baldock rushed up, and in picking his man up knelt on Slavin. A foul was claimed, but no notice was taken of it, although it was very palpable. Warnings were given to the Australian not to go into Smith's corner, but without avail, and he entered upon the second round full of pluck and confidence. Language — if such filthy expressions as were levelled at Slavin could be so designated — of the violent kind greeted him on facing Smith, and this was not confined to the hired mob. Those from whom at least fair play might reasonably have been expected indulged in blasphemy and rowdyism even more pronounced than that of the others. To still further disconcert Slavin a claim of first blood was made. The moment he walked across the ring Smith worked up close at once, and on rushing in was met with the left on the mouth. A brief struggle ensued before they fell together, Smith while on the ground spiking Slavin in the thigh. A foul was again claimed but the referee was so badgered that he could hardly have known where he was, and no notice was taken of the occurrence. In the third round, again a short one, Smith was Knocked Down By a cross on the jaw, and he came up looking the worse for wear next time, while the blackguards in his corner were more threatening than before. Smith again waited in his corner, and, nothing daunted by their menacing attitude, Slavin boldly went after him. As he advanced he was assailed by the miscreants, who now saw that Slavin was getting the best of it, and when after another round had been fought, in which Smith began to blow freely, the Australian was near the ropes he received a blow from one of their number. Every time Slavin was forced to fetch Smith out of his corner, where at this early stage the ropes had been loosened. In the sixth round Slavin now warmed up, sent home a hot left-hander on the right eye, from which the ruby fluid ran freely. This he followed up by some sharp work, eventually fetching Smith down with a vicious right-hander. This treatment of their "Champion" did not suit the villanious [sic] coterie, and Slavin went across the ring next time at great risk. Smith worked Slavin round to the ropes, and while there the dastards held him for the Englishman — save the mark! — to punish, and there was an indescribable scene of confusion. Still, Slavin would not be denied, and in the eighth round sent the right heavily on the jaw, and fairly knocked Smith off his legs. In the following round Smith received a smash on the mouth, but Slavin was terribly handled by the outsiders, who punched him freely while in holds. Smith up to this had hardly made a mark on his antagonist, and beyond a cut on the lip he showed no signs of punishment, but the cowardly ruffians who assisted the "Champion" wounded him severely. So vile was the conduct that the referee was, like every one else had long been, thoroughly disgusted, and he tried without avail to put a stop to it, calling upon Harper to "be a man." Smith was generally short in his deliveries, and Slavin, paying more attention to the body had doled out some telling work. In the twelfth round Smith was felled in his corner, and this brought a crisis. The latter broke away from Slavin's attempts to get on with the left until he was almost backed up against the corner stake, when the Australian dashed the left on the face. No sooner was he fibbing away than the ruffians crowded up and showered blows on his head. In the midst of the mélée a cry of "Here they are" was raised, and A Stampede Ensued from Smith's side. It was evidently a concerted plan, as when the leaders found that no one stirred from Slavin's corner they actually came back, and pointing to the roadway, yelled, "There they are, there they are." By this time Smith had run a hundred yards away towards the house, and Slavin's party, under Rule 26 [?] claimed the fight, but to no purpose. The confusion ensuing upon this manoeuvre looked like putting an end to further fighting. Slavin, who had shown not only admirable pluck and judgment, but also kept his temper, was quieted down when he thought there was yet a chance of winning. Smith was fetched back again, and time was called. Slavin, before putting his hands up, addressing his remarks to the crowd at the other side of the ring, said, "Are you Englishmen? I am an Englishman, and only want fair play." The fight then proceeded. Seeking to settle matters now that he had Smith weakened, Slavin went right over to Smith, and planted the left sharply on the body twice, and then dashed in with both bands, landing on the jaw. As they closed someone of the brutal mob struck Slavin on the right ear again with a "duster," the referee saying, "I saw that." As Slavin threw Smith and the mob again became aggressive, Vesey, who could stand it no longer, said, "I refuse to act any longer. It is impossible for this man — pointing to Slavin — to get fair play." The referee concluded by giving the decision, "It's a draw." The mob heard this with fiendish delight, and at once cleared off from the ring-side. Slavin could hardly contain himself, shouting "There is not a man round the ring can kill me. l came 16,000 miles for a fair fight, and why don't you give a man a chance." There was no help for it, and the latest fight for the Championship ended under circumstances which brought the greatest discredit upon those who were responsible for [Col. 4c–5a] the presence of the wretches, who were prepared for any villany [sic] to prevent Smith being defeated. Not satisfied with their performance at the ring-side, they followed him to his temporary dressing-room, but were soon persuaded to leave him alone, which was perhaps fortunate for at least some of the party. Jem Smith had a carriage in waiting for him, and was rapidly carried off to the town, where it was intended to stay for some hours. There was a rush to the telegraph-office to send messages to interested friends, but only a few minutes were available, as at least a third of  the party intended Making All Speed Homewards. The Ostend train was waiting in the handsome station, and there was no time to be lost[.] Slavin, who walked the whole of the way back into town, was hurried into a first-class compartment, where he made himself comfortable in a corner with a cigar. There was a crowd of hangers-on in and around the station, who evidently were by this time aware of the nature of the morning's work, but without further incident the train steamed out of Bruges. Arriving at Ostend at 10.15 we found the Comte de Flandres ready to receive passengers at the quay-side. This boat is not to be compared with the Princess Henriette, being much smaller and less seaworthy. Slavin had a deck cabin prepared, and therein held a levée, champagne and other sparking wines being ordered up. The Australian, under the careful hands of Mick Taylor, had the cruel wounds inflicted by the ruffians at the ring-aide attended to, and by the time the boat was clear of the offing Slavin was fixed up in shape and paraded the deck. Everyone talked of the fight and its terrible surroundings, and nothing but the severest condemnation was accorded the Englishman's party. One gentleman, who was wearing Smith's colours, was so disgusted that he threw them overboard, and replaced the kerchief with one bearing Slavin's monogram. Dover was reached in due course, a big crowd awaiting Slavin's arrival on the pier, but, shorn of his moustache, he was hardly recognised. He proceeded thence to Margate with M. Taylor and J. Cosnett, where another ovation awaited him. The other portion of our company journeyed direct to London, and on detraining at Cannon-street there was a crowd collected to gather news from the seat of war. Smith was to leave Bruges during the evening, and all being well will arrive in London early this (Tuesday) morning. </blockquote> ==== THE FIGHT. ==== <blockquote>First Round. Slavin left his corner quickly, with a firm, determined step. Smith was much slower in his movements, and the Australian had almost reached his opponent's corner when the men were face to face. The disparity in the height of the men was very marked, Slavin standing well over the Englishman. Each wore a deep strengthening plaister, whilst Slavin, it may also be added, made use of the suspender worn by Charley Mitchell in his memorable fight with John L. Sullivan. Full of confidence, and evidently in splendid condition, the colonial looked every inch a fighter, his length of reach, and lithe, agile movements contrasting strongly with the lumbering position struck by Smith. Though fairly clean in the face Smith looked very heavy below, and undoubtedly carried too much flesh for the business he had taken in hand. Great caution was exercised on both sides, and it was seen that neither man intended to throw the slightest chance away. Weaving in Slavin feinted with his left, but Smith was quickly out of danger, and in turn Slavin dodged an intended blow from the Englishman's left. In this manner fifty seconds sped on, after which Smith got in lightly on the month. Exchanges of a light character followed, Slavin reaching the body and Smith the face. Subsequently the latter, who seemed considerably puzzled by the Australian's style, several times led out of distance at the head, Slavin on each occasion breaking ground very prettily. At last the men got to close quarters, where some sharp infighting ensued. Slavin made the body his mark, where he put in heavy work with the right, Smith in the meantime visiting his opponent's head. The Australian's blows seemed to take the most effect, and the round ended by Slavin having the worst of a fall. Time, 2min 30sec. Second Round. No sooner had the men been removed to their corners than Jack Harper called out in a very loud voice, "First blood," a claim which was of course allowed, the Colonial showing a slight trickle from the lips. On "Time" being called the pair were quick to scratch, that is to say, Slavic walked right across to Smith's corner, the Englishman refusing to come out. A long opening spar took place, but at length blows were exchanged, nothing very serious being done, and closing, the pair had a slight struggle, both falling together. Whilst on the ground a good deal of kicking and struggimg was indulged in, and whether intentionally or no Smith spiked his opponent on the inside of the left thigh, tearing his drawers, and causing the blood to flow considerably. Uproar followed, the round lasting 20sec. Third Round. Though up to this time neither man had sustained much punishment, the exchanges not having been very severe, Smith was always carried to his corner, Slavin, on the other hand, walking beck to his. At the beginning of the third round the referee ordered the seconds out of the ring, but they declined to go, saying that official had no power to order them to do so. On starting Smith forced the fighting, and leading with the left, hit Slavin upon the body. This he followed up rapidly with two more in the same place, all light hits, and some rapid exchanges followed, the Colonial using the right with effect upon the side of the head. Smith paid principal attention to the body, but at length Slavin, drawing back the right, shot it out straight from the shoulder, catching the Englishman fair on the point, and sending him down all of a heap. This magnificent delivery put the Slavinites in excellent spirits, the Colonial smiling all over his face, while the Smithites looked serious. First knock down blow was claimed, and, of course, allowed for Slavin. Time of round, 24sec. Fourth Round. Smith rose from his seat looking very serious indeed, Slavin, on the other hand, being in much better spirits. At the same time a suspicious movement was noticeable among the brigade of Birmingham ruffians, and one of them came round to the Colonial's corner with no good intentions. Had it not been that Mick Taylor and Frank Hinde kept zealous guard over all the water provided for the use of the combatants, there is no knowing what fiendish trick might not have been perpetrated. The remainder of that party stayed in Smith's [Col. 5c–6a] corner. As for the seconds, all remained in the ring. The opponents sparred for the first twenty-five seconds, and at length Slavin, getting an opening, led out of distance at the body. The Englishman seemed glad to have a blow, but Slavin weaving in delivered lightly with the left upon the cheek. Again the pair faced each other in the centre of the ring, and Slavin went for his man, and feinting with the left, just failed to bring off the right, Smith skipping out of the way. Again the Antipodean feinted with the left, and following up the charge, this time successfully caught Smith flush on the mouth. Then quick as lightning getting to close quarters, Slavin delivered heavily right and left on the body, Smith being very slow in responding to this vigorous attack. He had, however, other assistants, for a vile ruffian from over the ropes deliberately struck Slavin a blow on the head. A shout was at once raised, but when charged with it the rascal denied that he had done anything. A scuffle ensued between the men, and to escape from the difficulty Smith cross-buttocked his opponent, who fell, the seconds, rushing to the centre of the ring, falling over them. Time, lmin 15sec. Fifth Round. "Don't go into his corner," urged Taylor and others of Slavin's party to their man, but nothing could restrain him when time was called, and, springing up with a bound, he advanced towards the opposite comer, where Smith was standing up. Once or twice the Englishman seemed inclined to go into the middle of the ring, but was always prevented by his yelling seconds, who stood on either side of him. On toeing the mark Slavin appeared with a suspicious-looking redness of the left eye, caused by the miscreant above referred to. Though appealed to the referee declined to give any decision on the subject, and the fight proceeded amidst some of the most horrible language it has ever been our misfortune to listen to. This proceeded entirely from Smith's corner, who, seeing that their man was already beginning to blow and look distressed, prepared to stop at nothing. Slavin, after wasting a second or two, followed Smith into his corner. One or two exchanges, quickly delivered, of a light nature took place, and the Colonial got in on the body with the right, following up with the same on the head. This Smith considered ample justification for sinking gracefully upon the ground, the round having lasted only sixteen seconds. Sixth Round. Smith came up blowing Iike a grampus, whilst on the other hand, Slavin, seeing his advantage, was eager to begin. Of course, it was necessary to go right over into Smith's corner, that worthy not moving two feet from his chair, whilst the shouts, jeers, and din which greeted the Australian were of an inexpressibly disgusting nature. Still, nothing daunted, the Antipodean followed his man up, Smith leading at the head. This Slavin easily turned aside by a lithe movement, and in turn was stopped by Smith. Resuming, Slavin banged in the left on the mouth, Smith countering on the body. A smart counter ensued, and at this juncture the referee entered the ring, making a fruitless appeal to Smith's corner to behave themselves. Nothing, however, could silence the foul language which proceeded from that quarter. Once more facing each other, the Australian shot in the left fist heavily on Smith's left eye, opening a severe cut, which bled freely. Some vicious infighting followed, and Smith twice got the right in upon the head. Slavin countered with a terrific right-handed blow on the eye, knocking Smith down. Time, 1min 20sec. Seventh Round. In vain did Slavin's friends implore him not to go into Smith's very "warm corner." It was plain that if he did not do so there would be no fight, Smith never coming many feet away from the rascals who had been hired to protect him. Getting to close quarters Smith delivered the left lightly upon the face and banged in directly afterwards the right on the body. Slavin did not see the Englishman having matters all his own way, and a desperate rally took place, during which Smith fought Slavin on to the ropes, and there held him. Here was a grand opportunity for the miscreants, who did not fail to make use of it. One of them kicked Slavin repeatedly, and others beat him about the head, whilst, naturally, Harper and Baldock were yelling at the top of their voices. The confusion wars something terrible, and the ring looked very much like being invaded. The ropes in Smith's comer were pulled right down, so that an entrance might be effected at any moment, and it was a relief when the pair wrestled and came down in a dog-fall together, the round having lasted one minute. Eighth Round. Crossing over at once to the only place where Smith was to be found (''i.e.'', in his own corner), Slavin worked his opponent round to the side of the ring, and there let him have the left lightly upon the face. Standing at this moment close up to the ring-side, the Colonial received a couple of smart blows from a stick which a ruffian coward carried.  An immediate cry went up, and the individual finding himself under very close observation immediately slunk behind. Taking not the smallest notice of these interruptions Slavin pursued his legitimate opponent, both Smith's following him about and jeering in his face. Again the referee entered the ring, and cautioned the seconds to move away. This had very little effect, and in the midst of half-arm fighting of a very severe kind, Smith, who was receiver-general, judged it advisable to seek mother earth.  Time of round, 1min 30sec. Ninth Round. This was altogether a very curious round. When time was called Slavin got up to find his opponent, who barely moved a foot from his chair, and this fact  should have been sufficient warning that something awkward was intended. In the corner the two sparred for about fifteen seconds amidst a horrible din. Finding that the Englishman was in no hurry to begin, Slavin made the first movement, and landed with the left lightly on the head. Following up this, he brought the right round heavily on the dial, making Smith wince, but a second blow in the same quarter was avoided. Still in the corner, the pair got to half-arm fighting, once more bringing them close to the ropes. The Birmingham mob here set about Slavin with great brutality, kicking him and punching him on all parts of the body. The referee, though appealed to again and again, took no notice, though admitting that he saw what was going on. Getting away from the ropes Slavin let go the right, and, reaching Smith's mouth, caused the blood to spring forth profusely. This last blow sent Smith to grass, the round occupying 50sec. [Col. 6c–7a] Tenth Round. The Champion of England by no mean relished the treatment received in the last round, and at the expiration of thirty seconds was puffing and blowing freely. He attempted to spar for wind, but the Australian seeing his advantage bored in when he could find an opening. Delivering right and left, and receiving only slight returns from Smith, the Australian pulled his man over, and the round terminated in 40sec. Eleventh Round. Neither was quite so quick to time, and Harper, noticing that, said, "This is not a two-round job, Patsey." Something like fifteen seconds was spent in sparring. Following Smith up the Australian failed to get an opportunity for some time. At length he put his hands down and invited Smith to "Come on and have a round." This was evidently not a particularly pleasing invitation to the Champion, as he remained in his own corner. Not to be denied, Slavin went after his man, but a left-hander meant for the head was put aside by Smith. At the end of a minute Slavin landed heavily on the Englishman's left cheek, a great red blotch immediately appearing. A rapid exchange followed, and Slavin was again home on the body. A heavy blow on the mouth from the Antipodean sent his opponent to the turf, the round having lasted 1min 35sec. Twelfth Round. A great change was noticeable in the appearance of the rivals on meeting each other for this round. Smith was showing signs of punishment on the face to a very large extent, his left eye being cut, his lip split, and there being a number of marks of Slavin's handiwork on his face. He was very distressed, and blowing heavily. On the other hand, Slavin, beyond the bad left eye (not done by Smith, but by one of the gang of hirelings), had apparently nothing the matter with him. Springing up brightly to his work, the Australian roamed about the ring until he found Jem Smith secreted in his own corner, only just away from his chair. The Australian reached the mouth lightly, and endeavoured by this means to draw his opponent out, but failed to achieve his object, Smith being strenuously warned not to move away from his seconds. The corner was encroached upon by Smith's crew, Harper and Baldock this time being almost between the men. The tumult was very great, but it seemed impossible to daunt the Sydney man, who followed Smith up, though little harm was done. Sparring was the order of the day until Slavin worked in with the left, delivering heavily. With great rapidity he drove the right with terrific force right on to Jem's chin, knocking him clean off his pins, and ending the round. Time, 1min 30sec. Thirteenth Round. Smith came up thoroughly dazed, the terrible blow in the last round having taken a lot of the steam out of him. The Birmingham gang, seeing that this was the case, got all of a heap in Smith's corner, and though Slavin was most earnestly advised to keep away, he would not do so. Smith stood just by ''his'' chair, and going right up to him, Slavin let out with the left, and bringing round the right. Both of these visitations Smith missed, but not so in the case  of a second smack from the right, which made Jem wink. However, turning round, the Englishman forced his opponent up against the ropes, and here occurred one of the most disgraceful scenes ever witnessed at a pugilistic encounter. Some villain drove his knuckle-dustered fist right on to Slavin's ear, cutting it almost in two and causing the Australian to exclaim, "Oh!" Other of these demons kicked him, a scene of indescribable confusion ensuing, in the midst of which the men continued fighting until the pair came down together. Time. 1min 28sec. No sooner was the round finished than cries were raised of "Here they come: the coppers, the coppers; and all Smith's gang, including his seconds, rushed away from the ring, at the same time calling upon Slavin to do so likewise. As for the Champion of England, he headed the runaway party, though nobody could detect the shadow of a "blue." The Australian never left the ring, much to the chagrin of the Smith party, who, seeing that the referee was being called upon for a decision, returned rather sheepishly. Baldock was in a dreadful fright, thinking the battle has been lost, but when the words "fight on" came he and his friends were very delighted. Fourteenth and Last Round. When "Time" was called Slavin folded his arms and waited for Smith to "come on," but Mr Smith didn't want to come on, and remained in his corner. Seeing it was impossible to make him stir Slavin once more crossed over, and a spar of nearly a minute took place. Then Slavin drove home the right on the body heavily, and the pair closed in Smith's corner. This gave another opportunity to a miscreant to strike Slavin on the head. Others in the gang were not slow to follow, and again the round ended in horrible confusion. Time. 2min 15sec. No sooner was this round over than the referee called out. "I refuse to act any longer. It is impossible for Slavin to get fair play. It's a draw." Then, going up to Slavin he said, "I will not stay to see you killed." The Antipodean stood up and exclaimed, "If you are Englishmen why don't you give me fair play? I have not had fair play." After this came a stampede. Remarks. Judging by the disgraceful proceedings recorded above, we are surely near the end of what are known as "fights in the old  style." That such a scene as that witnessed yesterday could possibly be enacted by any man with a drop of Christian blood in his veins seems almost incredible. Take the picture. An athlete, one of our stock, journeys 16,000 miles to measure blades with the best we can produce. Confident he will receive fair play in a land which boasts of nothing foul, he, after trying in vain to ratify a match to meet England's Champion, to be decided before an impartial and unbiassed crowd, puts down his hard-earned hundreds and meets our man in the style the latter insists upon. And with what result? Battling under unheard-of difficulties, not fighting one man but nearly a dozen, he narrowly escapes being murdered, and in the end is robbed of a victory he had won not once but in almost every round contested. If the nail driven hard into the coffin of pugilism yesterday is not the last, it is indeed ten thousand pities. Nothing can flourish, however, without support, and, providing the remarks passed by the majority of the spectators at the ring-side at San Michael are of any account, it will be many a long day before a knuckle-fight receives the patronage of the "upper crust." Slavin, we say, narrowly escaped murder, a fact proved by the words the referee, who, as well as others present, stood in fear of his Iife. One gentleman, an old ring-goer, affirmed he had never witnessed such disgraceful proceedings, and when the ring was finally cleared a feeling of relief was manifest on all sides. Unfortunately we are called upon to say that the riot and murderous intent were all in Smith's corner. On the other side not a man was present against whom a breath of suspicion could be raised. Opposed to Slavin was a hired gang of desperadoes ready to commit any act necessary to serve the ends of those by whom they were engaged. Terms of imprisonment had been worked out by each, and, prepared with knuckle-dusters, revolvers, and knives, they appeared ready to butcher the company at the raising of a finger. In face of all this the Australian fought his way to a moral victory. Almost from the outset Smith was outmatched, and beaten at the game considered his own. Sticking to his corner, of course by order, he showed none of his boasted bull-dog pluck and courage. His dreadful body-blow was easily put aside by Slavin, whilst instead of being "bashed" on the ground and battered out of shape, the Australian fairly held his own in wrestling. We are not blaming Smith for the doings of the miscreants present, and we also know that he was acting under orders by staying in his corner and affording them every opportunity to kick, strike, and prod the Australian, but it was altogether un-English to hold Slavin on the ropes whilst the mob belaboured him with "dusters" and sticks. Smith was, besides being in poor condition, slow and ponderous. After the third round his chance was hopeless, and his supporters were surprised at the form shown by Slavin. Contrary to general expectation, the Cornstalk proved himself far and away a better knuckle-fighter than a "glover." With his long reach he did great execution by left-handed deliveries, and the way he toppled Smith's fourteen stone over with the terrible right was a sight [p. 3, Col. 7c – p. 4, Col. 1a] Page Number: 4 that would have gladdened the heart of old Bill Richardson. In a word Slavin was entirely a different man from the Slavin that fought Bill Goode. Brimful of confidence he faced dangers that few would have encountered, and had the battle been conducted on fair lines he would have been Champion of England and Australia in less than half an hour. In all his battles he has never known defeat nor met with a knock-down blow. Yesterday it was not once found necessary to carry him to his corner, and as all the fighting was done in Smith's corner he must have walked a matter of eighteen yards each round. Slavin has a method of his own in pugilism. Possessed of staying powers, or "bottom" of a most remarkable character, he tires his man and then fights him. Yesterday, providing he had met with no punishment from outsiders, he would have left the ring almost without a scratch, and, as he himself said at the finish, "he was just getting warm." Remarkably clever on his feet, Slavin was in and out with the activity of a feather-weight, and feinting with the left, which he brought forward, he sent his right under the ribs with crushing effect. For some time past it has been an open secret that if Smith did not win he would surely not lose, and it is a blot on the proverbial love of English fair play to think that a mob should have been organised, and such a cowardly attempt made to rob a stranger amongst us of a victory so hardly earned and so clearly deserved. From the first the rules were broken by allowing the seconds to be in the ring whilst the fight was in progress, and although Smith's men threw everything in the way of the Australian, Cosnett and Kirby never transgressed the rules of fair play. Why the referee did not award the fight to Slavin when Smith left the ring in the thirteenth round can only be explained by his fear of the consequences that might follow.  Bearing on this subject, Rule 26 says: — "That if a man leaves the ring, either to escape punishment or for any other purpose, without the permission of the referee, unless he is involuntarily forced out, he shall forfeit the battle." Rule 24 is also plain enough in all conscience, "That any man voluntarily quitting the ring previous to the deliberate judgment of the referee being obtained shall be deemed to have lost the fight." Undoubtedly Mr Vesey lacked firmness, and perceiving this at the start, the "boys" and Smith's seconds, not to mention another couple who used their hands and feet at every opportunity, saw the game was in their own hands, and simply did as they liked. From first to last the proceedings were of a most disgraceful character, and the result showed plainly the reason why Smith's side objected to all the referees nominated by Slavin. Several gentlemen present, in fact all disinterested spectators, expressed their disgust at the treatment meted out to Slavin, and it was suggested on the return journey that a subscription be opened to provide funds for a testimonial to the plucky but unfortunate Colonial, particulars of which appear elsewhere. Even after the fight Slavin's assailants could not let him rest. Not content with robbing him of victory, they followed him to his place of dressing, but a determined front shown by Mr Taylor, Cosnett, and Kirby kept the blackguards back. These are well-known, and will, we believe, shortly meet with the punishment they so richly deserve. One rough made a rush for Lord Mandeville just before the close, but "Kim" soon showed he could hold his own with the "boy," who beat a hasty retreat at the "sight" of six-inch "Jack." We now take our leave of this unsavoury affair, which will probably be the last of its kind — "a Championship knuckle fight." The Englishman's boasted love of fair dealing appears lost to the professional fighter, and the sooner "merry mills in the old style" die out, and the hanger-on has to earn his living in some other way, the better. Slavin will visit London today. He leaves Margate by the 12.15 train, and will arrive at T<small>HE</small> S<small>PORTSMAN</small> office about three o'clock. Smith had a nasty lump on the jaw and left cheek, whilst his right eye was cut open deeply. In addition to this the punishment he sustained on the body was of a severe character. Slavin, on the other hand, only received a cut lip until after the fourth round, when the rowdies joined forces with Smith and smashed his eye during a mélée. After all their kicking and the free use of "dusters" the Australian only suffered from a badly-cut ear and the before-mentioned damaged eye. It may be stated that not a single bet was made at the ring side.</blockquote> ==== SLAVIN'S OPINION OF HIS TREATENT. ==== <blockquote>His Future Plans. On the return journey to England yesterday Slavin was the centre of attraction. At Ostend, where the tale of the fight had somehow or another been told, he was met by an eager crowd, and on the boat he held quite a ''levée''. Though at first somewhat disappointed at being robbed of the title of Champion and 500''l''. so well within his grasp, the Australian, surrounded by old friends, and new ones gained by reason of his straightforward conduct, rapidly regained his spirits. With the inner man refreshed by a steak, washed down with some of Heidsiek's [?] best, Slavin, a Havana between his lips, quickly got on good terms with himself and the rest of the  party. Much sympathy was expressed on all sides, and in the course of conversation with a S<small>PORTSMAN</small> representative Slavin said:— Of course, I feel a bit cut up, because I had my man beaten[.] Did you expect any trouble at the ring side? Slavin: Yes, I was prepared for that, as I was constantly receiving letters of a threatening nature, and though these things as a rule are of no account, I had reason to believe there was some truth this time. Besides, I had not forgotten the affair at Astley's Theatre. Do you feel any effects of the fighting? Slavin: The fighting? I feel nothing of what I got from anyone in the ring; it's what those beauties gave me outside. The only time Smith hit me in anything like form was on the jaw. Why did you persist in going to his corner? Slavin: I wanted to get the affair over and enjoy my Christmas dinner, and I knew if the fighting was left to Smith I should want it served in the ring. Of course you heard a mob was got together for Smith? Slavin: Yes, I knew all about that, but I relied on British fair play, and expected the referee to do his duty. Directly I got in the ring I saw what the game was, and knew my only chance was to knock Smith out. What do you think of Smith? — Well, I think so much of him that I'll bet him 200''l.'' I stop him in six rounds, but we must have no more private shows. I've had enough of that business. I suppose you have a poor opinion of English fair play? Slavin: I have been treated like a prince generally, but I can see the fighting men are easily led astray, and I expected trouble directly Smith objected to a referee. If we served an Englishman in the same manner in Australia we should get drummed out of the town, and rightly too. What are your plans for the future? Well, I shall stay in England some time and challenge Sullivan, and you might as well cable it over to America for me. With the gloves? Slavin: No, I went to fight him with the knuckles. I think I should get fair play out there. You prefer the old style to the new? Slavin: I am fond of boxing, but the other is my game, and though not a boaster I fear no one — that is if I can have fair play. Shall you give any exhibitions? Slavin: I may perhaps make a tour round the country, and very likely visit Ireland. You put on weight the last week? Slavin: Yes, I gained eight pounds and felt grand; in fact, just up to dick when Smith bolted. What do you think of our seconds? Slavin: Well, I'd like them to have a job in Australia. They'd never come back again. When do you propose visiting London? Slavin: I'll come up to-morrow and call at T<small>HE</small> S<small>PORTSMAN</small> Office about three. A stroll was now taken on deck. [sic] and reaching Dover Slavin was met by some friends from Margate, who carried him off to the train in triumph. </blockquote> ==== A Testimonial for Slavin. ==== <blockquote>So impressed were some noblemen and gentlemen with the pluck and ability shown yesterday by Slavin, and at the same time thoroughly disgusted at the treatment he had received, that it was decided whilst crossing the Channel on the way home to open a subscription on his behalf. The donations are limited to 2gs, and the following amounts have been already promised Mr G. T, [sic] [Col. 1c–2a] Dunning, T<small>HE</small> S<small>PORTSMAN</small> Office, Fleet-street, who has been requested to act as honorary treasurer to the fund: [names set as unordered list to save space, last 3 column headers: £ ''s.'' ''d.''] * Lord Mandeville 2 2 0 * Lord Royston 2 2 0 * Hon. Michael Sandys 2 2 0 * Mr Fred Ketchie 2 2 0 * Mr Ike White 2 2 0 * Mr W. Riley 2 2 0 * Mr C. Parsons 2 2 0 * Mr J. Kilby 2 2 0 * Mr Frank Hinde 2 2 0 * Mr J. Calder 2 2 0 Any contributions sent to the hon. treasurer will be duly acknowledged in T<small>HE</small> S<small>PORTSMAN</small>, which in a couple of days will contain the names of a committee now in course of formation. In the London clubs yesterday the opinion was very general that Slavin ought to be compensated for the loss he had sustained in consequence of the ruffianly tactics pursued in Smith's corner. The utmost indignation was expressed in reference to the treatment the Australian had received at the hands of so-called Englishmen. We have received a number of letters on the subject. The following is a sample of them: To the Editor of T<small>HE</small> S<small>PORTSMAN</small> Sia, — I have no doubt that many Englishmen will have read with regret the disgracefully unfair treatment that Slavin met with in his encounter with the  "Champion of England" to-day. I trust that a subscription will be started to show him in a substantial manner that the sympathy of most Englishmen who take an interest in boxing is entirely with him. If you are prepared to receive subscriptions I shall have much pleasure in subscribing a guinea, and in collecting those of many friends who will be glad to subscribe. — I am, Sir, yours faithfully, C. B. C. Royal Thames Yacht Club, December 23. [We refer our correspondent to the paragraph above. — Ed. T<small>HE</small> S<small>PORTSMAN</small>. ] [sic bracketed interpolation] </blockquote> ==== Eyewitnesses Interviewed. ==== <blockquote>A representative of T<small>HE</small> S<small>PORTSMAN</small> was at Cannon-street station yesterday afternoon to meet the Continental express, in which a goodly number of those who had witnessed the fight made their return to town. The train was somewhat late, and did not steam into the station until a quarter to six, when our reporter singled out several well-known "sports" (including more then one scion of a noble house) for a few minutes' chat. Asked as to how affairs happened at the outset, one and all agreed that it was plain a row was meant, the demeanour of a certain section of the party, which  did not number more than forty, being particularly noticeable. "How did the combatants' seconds behave?" — "Well, after the first round, it was evident that Smith would soon be at the mercy of his powerful opponent, and his seconds very soon perceived this state of things. In the initial round Harper came down with some force on the Australian's chest, while in the next bout Slavin came in for some rough treatment at the hands of Baldock, the Champion evidently suffering with one of his eyes." "What form was the Englishman displaying?" — "From the outset he made a miserable stand, and was plainly afraid of his rival. He fought as a coward, and by the tactics adopted by several of those at the ring side Slavin was fighting against great odds.  Every time he got into Smith's corner he was met with remarks of a most uncalled-for character, and had to be very sharp to keep at arm's length of several rowdies, who, as the fight proceeded, became extremely noisy." "How do you account for such a noisy corner at the back of Smith?" — "Although they did not number more than eight, they were some of the worst  characters known, and had undoubtedly been commissioned to play the part they did. This was most disgraceful, isasmuch as they not only made Slavin a mark for the knuckledusters and other weapons they were armed with, but likewise made tracks for individual spectators who ventured to express their indignation at the course of proceedings. One rough, more venturesome than the others, "framed" up to a familiar figure at boxing tournaments, but on the latter producing a long bowie knife, accompanied with a few words of a somewhat emphatic nature, the villain rejoined his  party." Are these men known at all?" — "Yes, they are mostly from Birmingham, and are of the lowest order. It was reported that more than one had been kept at the country's expense, one for a very lengthy period." "Was not this sort of trouble expected?" — "It had been given out by one influential patron of the English Champion that there would be an absence of rowdyism, but it was also stated on good authority that certain roughs had been specially engaged, so that trouble was naturally anticipated." In reply to questions as to how the contest proceeded, it was the opinion that the thirteenth round would be the last, as Smith's party made a determined effort to bring about an undesirable finish. On the two fighters getting to close quarters more rough work ensued, and on some pretence Smith left the ring. Slavin, however, stood his ground manfully. "How did the crowd behave towards the finish?" — "There was a lot of excitement on all sides, but the only fear was that the rough element would resort to extreme measures in endeavouring to save their Champion. Others were ready to insult the Australian by using most filthy language towards him, and altogether affairs began to look serious." "Is it true that attempts were made to tamper with the water used by Slavin's seconds?" — "Yes! a man was noticed to be hovering about in that quarter, but, fortunately, his efforts to drug the fluid were of no avail." "Did Smith deal out much punishment?" — "His blows lacked the force of his rival, and when the referee gave his verdict as a draw the Australian looked very little the worse for his exertions, and could have fought far two hours more. He could have beaten Smith and both his seconds into the  bargain, given fair play." "Was Slavin injured during the fight?" — "No; not from the blows of his rival, as he heeded them very little. He, however, received a nasty blow from a knuckle-duster by one of the cowardly ruffians, which caused his ear to bleed." "As to the referee's decision?" — "That official was undoubtedly afraid of his life, and thought it best to stop the proceedings before any serious harm happened." "What becamiof Smith after the fight." — "He returned to his hotel, and will no doubt arrive by a later train. His friends were disgusted with the form he displayed, and it will be a long time before he recovers his former prestige, if ever he does." "How did the Cornstalk behave in the ring?" — "He fought in the most manly style throughout, and gained the highest opinion from all respectable people present. A testimonial to Slavin has already been decided upon, and no efforts will be spared by those concerned in making it worthy of the occasion." Mr Ike White, a well-known sportsman in the city, and one who, as a rule, does not mind going to considerable trouble to witness a "mill," was very severe in his comments on the gang who were so lost to all sense of decency and fair play. Mr White said: — "The story of the fight does not need much telling. Slavin had his man beaten at every point, and was winning easily. Slavin is a very brave man. He bad to go into Smith's corner every time, and when there had to fight not one but six men; the ruffianism was simply awful." "Do you think it was for the best that the contest was stopped as it was?" "Yes, certainly. Goodness knows what would have happened before long. Probably Slavin would have been killed, as the villains that had congregated in Smith's earner seemed determined, at all hazards, to prevent him from losing. More than once the Australian had Baldock on one side and Harper on the other, both jeering at him, whilst Smith was in front and the 'boys' were making all sorts of attempts to injure him, but he seemed to pay no attention to anyone but Smith. Slavin would not have had a mark from Smith, such as he does now having been inflicted entirely by the mob[.]" "What do you think of Slavin's abilities?" "He is a very great natural fighter, and as for his gameness a pluckier man never pulled off a shirt." On the subject of who was responsible for the presence of the rowdies that caused the bother Mr White was reticent, but not so when the subject of a testimonial to the Australian was mooted. "He is coming to town to-morrow," said the speaker, "and shall have a great reception. Some good sportsmen  have promised to leave no stone unturned to give Slavin a testimonial to be proud of, for he richly deserves it." "What seemed the general opinion on the ground?" "Why every ''man'' (with great emphasis on this word) was sick and disgusted: all but the mob gradually forsook Smith's side of the ring, and the Englishman will lose many friends in consequence of the turn affairs took." </blockquote> ==== Reception of the News in Birmingham. ==== <blockquote>Considering the ''penchant'' of the natives of Birmingham for fighting, and their interest in all matters concerning the ring, a stranger in the city yesterday knowing this would have been rather taken by sur prise [sic] at the indifference manifested in the result. At the various local sporting resorts, however, the cause was plain enough to those in the know. Early in the week it was an open secret that a warm corner was being provided for the English Champion, consequently betting was at almost a standstill. In what little speculation took place the odds were in favour of Smith, as the ''cognoscenti'' were confident that the Australian would not be allowed to win. Amongst the better class of sportsmen in the city the whole of yesterday's disgraceful proceeding were viewed with the greatest disgust. There are still many staunch supporters of the ring in the district who would gladly hail any signs of its regaining its past glory, but they look upon the fight of yesterday as the death-blow to the institution. By the few that thought the affair might possibly be allowed to be decided on its merits Slavin was expected to win, but his only chance was considered to be in his forcing the fighting at the start [Col. 2c–3a]  and knocking his man out early. George Prober hoped to hear that the fight had been decided fairly, and he regretted the unsatisfactory ending. How the Match Was Made On the evening of Saturday, August 10, the P. and O. steamship Carthage cast anchor in the Albert Dock, Limehouse. On bard was an individual, anxiously expected by the British public — namely, Frank P. Slavin, the Champion at Australia, who was accompanied by his manager, John Lewis. Without loss of time, Slavin made his way to T<small>HE</small> S<small>PORTSMAN</small> Office, and on the succeeding Monday the following interesting particulars respecting the visitor appeared in the columns of this paper:— "He has a long record, including victories with both gloves and knuckles, and has never yet known defeat. His bearing is that of a thorough gentleman. He is a fluent talker, and can converse on any sporting subject. Devoid of conceit, he yet has a full comprehension of his own powers, and speaks with confidence as to the result of any encounter in which he may take part. Slavin is a splendid representative of the nation which is growing up across the seas. The contour of his features is distinctly English, square cut and firm. Beneath an intellectual forehead are two deep-set piercing blue eyes, and his features are bronzed with the burning suns of the south. From this it will be gleaned that the Antipodean is a formidable-looking customer, especially when we add that he stands no less than 6ft 1in, and in condition fights about 13st 4lb. Long before his arrival 100''l.'' had been posted at T<small>HE</small> S<small>PORTSMAN</small> office for Slavin to box any man in England, but the money was waiting nearly four months before any of our big guns would cover it. Jem Smith, the Champion, turned a deaf ear to the straightforward offer of the Colonists, and Mitchell  was called away to Yankeeland to lend assistance to his friend Kikrain [?]. For some time it looked as though our visitor would have to return as he came, without giving anyone a hiding or receiving one himself, until a gallant little English middle-weight stepped into the breach to box for the honour of the old country, and agreed to face the stalwart Cornstalk. This was none other than William Goode, who in consequence of his politeness, urbanity, and elegence of dress was christened by his friends 'Chesterfield.' Goode had previously lowered the colours of another Australian, Tom [Less?], a much bigger man than himself, and, bearing this in mind, his friends freely plunked down 200''l.'' These were Messrs Robert Abel and Harry Hart, two well-known figures in the world of sport, articles after little delay being signed at T<small>HE</small> S<small>PORTSMAN</small> office, whereby Slavin and Goode agreed to box the bout of twelve rounds, under the usual rules, on October 17, for the sum stated. Many old ring-goers and patrons of the games shook their heads when the articles were published, and not a few blamed 'Chesterfield' for his rashness in tackling at catch-weights a man so much his superior in size. Goode, however, comes of a fighting stock, is full of pluck and stamina, and belongs to the order which never say die. Excepting in a competition, his maiden attempt, 'Chesterfield' had never known defeat, and the making a match with such overwhelming odds against him his bravery received due acknowledgment on all hands. Slavin held an unbroken record of nineteen successes, and throughout his career he had never known the effects of a knock-down blow. The articles stipulated that the men should box in a 24ft ring, and at the time of signing Mr B. J. [Angle?] was agreed to by both sides as referee. A very necessary clause was inserted, giving the referee power to award the stakes in case of what he might deem an organised interruption to the man who, in his opinion, had the best of the boxing at the time, and if all agreements contain such a clause, it will have a deterrent effect on those who invariably go on the sin, tie, and wrangle system. Slavin placed himself under the charge of that painstaking trainer and old-time boxer, Jack Start. The pair made Mr J. Kilby's, the Ferry Hotel, Cookham-on-Thames, their head-quarters, but things went very badly at the start. During the second week of his training the Australian caught a severe cold, and rheumatism setting in, the services of a doctor were required. The illness was, for obvious reasons, kept a profound secret, but so bad did Slavin get that the first man of medicine deemed it necessary to call in a second. Ten days were spent in the house before Slavin pulled round, and though all went well for some time, he contracted another bad cold. Start, however, wa unremitting in his attention to his charge, and Slavin came to the scratch in fairly good shape. The result of the encounter, a win for Slavin in the fifth round, despite a grand stand by Goode, will be fresh in the memory of our readers." [sic: quotation begins at the top of the paragraph] Smith's failure to make a match with the Australian caused general surprise, but the Englishman would have nothing to do with the glove business, despite the repeated offers of Slavin. The latter's friends, on the other hand, saw little but trouble attached to a knuckle fight, and though Slavin himself preferred the fists to the mittens, there appeared small chance of a match between the pair until Mr Frank Hinde stepped forward and put up a deposit of 50''l.'' at T<small>HE</small> S<small>PORTSMAN</small> office for the Australian to fight Smith for the championship and 200''l.'' a-side. The old question of stakeholder then cropped up, and, after a Iot of bickering, the Colonial gave way, and agreed that the money should be deposited with private gentleman, who for obvious reasons shall be nameless. A meeting took place, and eventually the following contract was drawn up by a representative of T<small>HE</small> S<small>PORTSMAN</small> and signed: Articles of Agreement entered into this day (Monday, September 16, 1889), between Frank Slavin, of Melbourne, Australia, and James Smith, of London, England. The said Frank Slavin and James Smith hereby agree to fight a fair stand-up fight according to the new rules of the London Prize Ring, by which the said Frank Slavin and the said James Smith hereby mutually agree to be bound. The said fight shall be for 200''l.'' a-side, open for 1000''l.'', lor the Championship of England and Australia, and shall take place in 1889 out of England. The two representatives to select the battle-ground issue all invitations (not exceeding fifty persons a-side), and carry out the arrangements for bringing off the fight. The backers of the said Frank Slavin and the said Jem Smith this day (Monday, September 16) deposit 200''l.'' with the stakeholder. The representative of each man to supply the other with a list containing names of spectators, and to have mutual power to strike out a name they object to. The said James Smith and the said Frank Slavin each to have power to appoint an umpire. The referee to be mutually agreed upon by the duly authorised umpires of the men at least seven days before the day fixed for the fight, but in case they cannot agree, the final stakeholder to have power to appoint a referee. The men to be in the ring between the hours of six a.m. and twelve noon, or the man absent to forfeit the battle money. The expense of the ropes and stakes shall be borne by the two contestants equally. In case of magisterial interference the referee, if appointed, or the stakeholder if not, shall (if possible on the same day) name the next time and place of meeting, and either party failing to appear at the time and place specified to lose the battle money. The stakes not to be given up unless by mutual consent, or until fairly lost by a fight, and due notice shall be given to both parties of the time and place of giving up the money. In the event of any question arising which may not be provided for in these articles the referee to have full power and authority to decide such question, his decision to be final, conclusive, and subject to no appeal in any court of law. The stakeholder shall in any and every case be exonerated from all responsibility upon obeying the direction of the referee. In pursuance of this agreement we hereunto subscribe our names. Frank Hinde (for Frank Slavin). John Fleming (for James Smith). Witness for Smith, F. Montague. Witness for Stavin, John Lewes. Subsequently Slavin, as stated, defeated Goode, following which he fulfilled an engagement at the Royal Aquarium extending over thirteen nights. The "Cornstalk," though suffering from an injury to his left hand, offered 20''l.'' each evening to any man whom he could not step in four thee-minute rounds, and though several tried to earn the money Slavin always accomplished his self-imposed task, and brought his engagement to a close in a blaze of triuumph by stopping two men the last evening in four rounds. Slavin had now come into funds. Through the columns of this paper he expressed a wish to put some of his own money down, and, confident in his ability to uphold the honour of Australia, he offered to increase the stakes to 500''l.'' a-side. Smith, with a millionaire at his back, had little difficulty in getting the extra 300''l.'', and accordingly the money was made 1000''l.'', the sum fought for by Sullivan and Mitchell. Smith in the meantime, though ignoring Slavin's challenge to box under Queensberry rules, strange to say, entered into an engagement with Jackson under the conditions he so stoutly objected to when put forward by the white man[,] His ignominious show with the coloured Champion may be passed over without comment, and it will suffice to say that after he and his conqueror had boxed together for ten nights at the Aquarium the Englishman began to prepare himself for the affair under notice. </blockquote> ==== The Men in Training ==== <blockquote>Slavin, when he entered upon his training at the Nayland Rock Hotel, Margate, was 12st 9lb in weight, while fourteen days later, in the buff, he scaled 13st 6lb, and was as hard as nails. The increased weight was accounted for by the splendid development of the muscles in the arms, shoulders, and back. His daily programme while at Margate was as follows:— Up at seven sharp, and twenty to twenty-five minutes' strong exercise with 4lb dumb-bells, followed by a gentle stroll of a couple of miles before breakfast, at 8.30, which consisted of porridge, 1lb of chops or steak, dry toast, and a cup of tea. After the perusal of the morning papers he indulges in a ten-mile walk at a smart pace, averaging five miles per hour. Back again to the hotel, into a bath, and then a rub down with whisky, which was completed in time to give him a good rest before dinner, timed for 1.30, and composed of either roast beef, mutton, or chicken, with vegetables, light pudding, and a pint of seven-year-old bitter. The meal being digested over a game of billiards, he started at three o'clock on a six-mile stroll, varied at intervals by sprints of one hundred yards. On his return to his quarters he punched the ball for half an hour, and then sparred lightly with an Australian gentleman who was at the time on a visit to this country, and holds the Amateur Championship of Australia, he having kindly consented to assist Slavin. This was followed by a sponge and rub down and a good slapping of the muscles before a tea, at 6.30 p.m„ [sic] of cold meat, half a dozen eggs, dry toast, and tea. The wind-up of the day was a quiet stroll to the pier and back, and a game of billiards before retiring to rest, at ten o'clock sharp. Smith's programme was something of the same description, excepting the ball punching, the Englishman preferring the sack. He made the Greyhound,  Newmarket his head-quarters, most of his exercise being taken on the Heath, though, as visitors were forbidden and interviewing tabooed, little was gained [Col. 3c–4a] as to his doings. Under the care of Jem Howes, his old trainer, he was, however, reported to be doing well, and much finer than when he fought Jackson. </blockquote> ==== Finding the Battle-Ground. ==== <blockquote>(By one of the Explorers.) At a meeting held on Saturday, November 16, Mr John Fleming and Mr G. T. Dunning were deputed to act on behalf of Smith and Slavin respectively, their duties being to select the battle-ground, issue invitations, and carry out the arrangements for bringing off the fight. This was rather a strong order, and one of a most trying nature, as anyone conversant with the peculiarities of those attached to the P.R. may know. Wednesday, December 4, was a cold, raw day, and with the thermometer down to freezing-point travelling at night was anything but a luxury. Reaching Paddington soon after 9 p.m., Mr Fleming and I, thanks to an energetic guard, soon found ourselves comfortable in a first-class "smoker" attached to the Weymouth express. At 9.15 to the tick we steamed away from the Great Western terminus, and in due time reached Reading. The hour had passed quickly, pleasantly whiled away by interesting tales of old-time bouts told by the manager of the Pelican boxing. Such men as Punch Dowsett and Bill Charlton graduated in Mr Fleming's school, and the way these celebrities used to set about each other for as many shillings as the boxer of to-day gets pounds is nothing less than remarkable. A ten minutes' halt at Swindon was utilised to the fullest extent, and then bowling along we reached the end of our journey, so far as land was concerned, soon after 2 a.m. on Thursday. When we left town the air was crisp and frosty, with hardly a breath of wind stirring. We were, therefore, greatly surprised when stepping on beard the Gazelle we were informed that a "choppy sea" was running outside. The fact of a passenger's hat going over the side proved the truth of the assertion, and then this same passenger, a likely-looking fellow, bemoaned his fate and bad luck. "How confoundedly annoying,"  he said. "This is the sixth time I have been across during the year, and not once has it been calm." "Better have a sleeping berth, sir," said a sprightly youth at the top of the stairs. "Sleeping berth be hanged. I'll remain on deck," said he, and here for a time we left him inquiring if his horses had gone across in the morning. Guernsey, dear reader, was our destination, and with the idea of making ourselves comfortable we made for below. I felt a bit "peckish" and cast a longing eye on the good things set out in the dining saloon. This was, however, as far as I went in the line, and diving a floor lower doffed my boots and courted the god of sleep. Morpheus, however, scorned my attentions, thanks to the clatter on deck and the noise of the machinery, to say nothing of the "magging" [?] of our friend of the horses. This gentleman, after three or four futile attempts to drag me into a controversy about traveling, "struck ile [?]" with an elderly party, occupying the berth behind me, and for nearly an hour I had a pretty lively time of it. The "elderly party" had a voice greatly resembling the dividing of tin hoops with a file, and in addition displayed a shocking habit of making horrid and atrocious puns. Just as I thought of giving up sleep for a bad job a gale sprang up. Though the Geselle is a record breaker she soon felt the effects of the breeze and began to roll heavily. The increase in the motion of the steamer was followed by a decrease in the conversation around me, and by degrees the punster went from had to worse. The "[hussey??]" [one?] also dropped into a walk, and after monosyllables had been exchanged the two came to a dead stop. Offering up a prayer of thanksgiving for this I closed my eyes again, and being a good sailor was quickly sleeping the peace of, I hope, the just. The concussion of the Gazelle against the Guernsey Pier, accompanied by a prod from Fleming's stick, at length aroused me. Among the Channel Islands. The time by "Joe Vickers" was 7 a.m., and half-awake I took to my boots. "Need not lace them; we shall be there in a minute," said Fleming, and in a drowsy, submissive, take-me-anywhere-if-only-to-bed sort of way I followed him on deck. A Babel of voices and a clutch at my bag and rug thoroughly aroused me, and jumping into a trap the Pelican and I were in about three minutes set down at Gardner's Royal Hotel. A venerable-looking elder, whom Fleming voted a "[sheenie?]" (goodness knows what he meant, though), made us welcome, and agitating the communicator he handed us over to the care of a dark-eyed chambermaid. I forget her name, and as Fleming is not here I cannot give it. I will say no more than that after a cup of tea diluted with delicious cream, we took a well-earned and mucch needed rest. Up and doing soon after tea, a delicate task was before us. Fleming had a friend on the land, a gallant captain, who knew of a spot where we could fight for a month. Guernsey, dear to the "holiday maker" and the "honeymooner," is, as everybody knows, or should know, situate in the English Channel near the coasts of Brittany and Normandy. It is 68 [?] miles from Weymouth, 7 from Sark, 19 from Alderney [?], and 25 from Jersey. I mention these distances, for we explored the whole group. Encompassed with rocks, almost hidden in high water, navigation is exceedingly dangerous at all times near the island, the knowledge of which quickly knocked one of our plans on the head. Standing at the door of Gardner's Royal Hotel on Thursday morning Castle Coronet came in view, while in the distance, almost hidden by a heavy sea mist, could just be discerned the islands of Herm [?], Jethon, and Sark. Guernsey, it should be mentioned, though under the protection of England, boasts a sort of Home Rule government, rather irksome to the stranger within its gates, especially if that stranger is on mischief bent and gets caught. Making, in a cautious manner, inquiries at the breakfast table, we found a friend in "Mike." Said I, "He's a Frenchman." "Get out," replied Fleming, "he's a 'bark.'" "Drinks he isn't," "Done; drinks he is." "Mike" had not at that time spoken, but had noiselessly passed to and fro with a military step and a hand behind him. In reply to a call from Fleming he approached, and a "Yes, yer honour," told me I should have to "part." "Mike" was a trump, and I loved him from the start. For eleven years he had been in the service of a colonel at 1''l.'' a week, and three suit of clothes in the year. Hotel pay was not so good, and though he made "a bit" in the summer, the young ones were generally there when the bills were paid, if not when the work was on. "Mike" told us lots of things in what many consider the "fascinating brogue." He informed us — and how our hearts beat at the news — that the island, which had a population of over 32,000, employed but six policemen. "There's not a beggar in the land," said Mike, "and but one Hansom cab, and," pointing to the window, "be jabers, there it goes. " So far so good, but after a walk round the son of Erin gave us a shock by saying, in reply to a query from Fleming, "They've a way of their own on this island, and nearly ivery [sic] other man is a special constable." Fortunately we had just finished our repast, and, supporting each other, we tottered faintly to the door, partially regaining strength with a breath of the pure sea breeze. Beads of perspiration stood on the brow of the Pelican, whilst I was suffering from a "trickling" down the back of anything but a pleasing nature. Visions of a dungeon-cell under Castle Coronet flashed through my brain as a voice and a step were heard behind, and then I was somewhat reassured. "When would you like a chair?" fell softly on mine ear. Afraid that we had been thought of as a bit week on the leg, I turned to the speaker and asked what he meant. Explanations ensuing, we found the "chair" was a sort of Bath chair on wheels used throughout the island. Declining the offer, we took a stroll, and putting this and that together, came to the conclusion that our task was of a very delicate nature. The first thing was to interview the captain, who, in reply to a note, courteously waited upon us. He gave us the geography of the island and an introduction to Mr M., a friend, who we unfortunately found away from home. Taking a "chair" we then started on a voyage of exploration, making, as advised, our way to L'Ancresse [?] Common. Leaving St. Peter's Port and passing through St. Sampson's — the Vale — we came across acres of vineyards, in one instance extending nearly a mile along the road-side. Half an hour's drive brought us to the common mentioned, and dismounting we tried in vain to find a level piece of turf. Windmills abounded on all sides, and plodding on we reached L'Ancresse Bay, a lovely little spot, where the sea rippled softly over a bed of almost snow-white sand. Nowhere could be found a suitable spot whereon to pitch the "magic square," and as the shades of night were falling fast we rattled back to the "Royal." A wet night offered no inducement for further travel, and it was a case of early to bed and early to rise, the next day finding Fleming and myself at the door of Mr M. Acquainting this gentleman with the Nature of the business in hand he, like a good sportsman, fell into the scheme and at once volunteered to drive us to "the best spot in the world." "Bessie" was harnessed to the village cart, and away we went at the rate of fully fourteen miles an hour in the direction of the Forest. I have sat behind many a good goer, but must for her size award the palm to Bessie a beauty barely twelve hands high. Throwing the reins in the bottom of the vehicle, Mr M. '''let the pony have her head''', and the way she went uphill, down dale, and past other traps was truly astonishing. Great St. Peter's was passed, and lovely scenery encountered, the gardens being full of flowers, geraniums and roses blooming on all sides. An enjoyable drive of forty-five minutes found us at Boequaire [?] Bay, and directly in front stood the island of Lihou. As many of our readers may know, Lihou is a small hill of land that at low water can be reached on foot from Guernsey. As a fact, a paved roadway is laid in the bed of the ocean, across which both foot passengers and carts easily make their way. With the tide up communication is effected by boats, but this being low at the time we had the novel experience of Driving Through the Sea. Gaining the other side we "explored" and as the piece of land is only some three hundred yards by a hundred and fifty, we were not long about it. Two excellent patches of level turf were found, but just as we were making for the trap a gaunt, Robinson Crusoe-looking individual scaled one of the small stone walls and barred the way. Of course, he wanted to know our business, and, after a rather rough opening, quickly "listened to reason." In the course of conversation we found that the population of the island was limited to three, the old "josser" and his two daughters, with a "moke" thrown in. Pointing a long skinny finger, which might have belonged to the Witch of Endor, towards the quadruped mentioned, the old man said, "Us two keeps the family. He draws the seaweed and I burn it."  "And why do you burn it?" "Well, to make [Col. 4c–5a] ashes, and from the ashes iodine is manufactured." "And how much do yen earn a week by that?" said  I. "Oh, about 4''s.''; not 5''s.'' any week." Great Scott! and this was all the old man, his two daughters,  and the "moke" had to live on. Handing him a franc each, which nearly stupefied the old chappie, Fleming and myself returned to Mr M., who drove us rapidly back to St. Peter's Port. The next day we crossed to Sark and Jersey, but found nothing so suitable as the ground at Lihou, and fairly well satisfied with the result of our visit, a day later boarded the Lynx for the return journey. During our visit the weather had been of a fairly favourable description, but the voyage home was made under very depressing circumstances. Rain fell heavily and a thick mist hung over the water, which after going a few miles was alive with porpoise. Some of these animals came within a few yards of the Lynx, but the speed of the boat proved too good for the finney ones, who were eventually left behind. With a breeze springing up sail was hoisted, and dashing through a heavy sea in splendid form the Lynx made some sixteen knots in the hour. In this way half the journey was completed, when all of a sudden we were caught in a squall. In an instant the wind chopped round, and before you could say "Jack Robinson" the good vessel was turned broadside to. The order to take in sail was promptly obeyed, but the clatter on deck brought many an anxious passenger rapidly from below. A very heavy sea was now running, and though the Lynx kept her course bravely the decks were swept from stem to stern. A huge East India-man now hove in sight, and, as one of the men informed me, she had the audacity to cross our bows instead of passing under our stern. This breach of ocean etiquette ruffled the skipper of the Lynx, who chased the trader, and eventually made her alter her course. This little "diversion" caused much amusement amongst our passengers, and after a cold, rough passage we landed safely at Weymouth. Chilled to the bone, we made for the Victoria Hotel, where a chop and a glass of old October revived the almost stagnant circulation. London was reached about 9.30, and, tired and worn out, I was glad to lay my head on a pillow I had not seen for four days. From London to Ostend. Unforseen [sic] difficulties having cropped up, the Channel Island scheme had to be abandoned; consequently we were once more called upon to leave our native land. This time Belgium was our destination, and having carefully studied the map of that country, we took our departure one fine starlight evening from Charing-cross by the 8.15 Continental express. In the previous week we had the luxury of a compartment to ourselves, but on the occasion under notice we were not so fortunate. Two individuals, one with a strong Midland accent, and the other a Frenchman speaking bad English, shared the carriage with us, and at such a rate did the former's tongue go directly he entered that I gave up reading as a bad job, with a sigh put away my unfinished book of the previous trip. Fleming fared better, and having a knack of ignoring all around him, once more tackled "Blood Money," and almost read himself off to sleep.  In the meantime our friends in the opposite corner made "hay," and I soon found out they were both in the lace trade. With a tongue that went a couple of hundred to the minute, the Midlander almost monopolised the conversation, from which I gleaned the two were bound for Calais, and thanked goodness we should part at Dover. Reaching this port about ten we boarded the Ostend boat, which, as regards passengers, was very poorly patronised. Hardly a breath of wind was stirring, and with the sea calm as a mill-pond we had a pleasant passage over, and landed safely at Ostend soon after 3 a.m. A cup of coffee was hastily swallowed, and a half-hour's run in the Brussels express found us At Bruges. Leaving the train, we had considerable difficulty in finding our way out of the station. For a moment we caught sight of a drowsy old porter, but the last carriage had not passed away from the platform ere he was lost to view. Seeing an opening on other side we made for it, only to have our passage barred by a half-dressed Belgian who, whilst displaying a total ignorance of English, Irish, and Scotch, directed us to return the way we came. For some time we tried in vain to find an outlet, and just as I had made up my mind to walk the platform until daylight Fleming found an iron gate ajar. Without loss of time we were in the street, and crossing the round, knocked loudly at the door of the nearest hotel. All was in darkness, and with no response to our fourth appeal for admittance, a return to the station or a "tramp round" appeared to be our only alternative. A slight noise inside followed by a shuffling of feet, again raised hope within us, and when, after some trouble, the door swung back and brough to view a shock-headed Belgian our relief was great. No time, I can assure you, was lost in getting between the sheets, and rising betimes we again went on a voyage of discovery. Fleming had a chum in the town, and to his house of call our steps were directed. Again disappointment was in store for our wanderers, and a feeling of disappointment came over me when we found Mr G. was away. There was, under the circumstances, nothing left but to wait, and Fleming, who puts on hair rapidly, decided to place himself under the care of the town barber, or, I should, properly speaking, my ''coiffeur''. For this piece of indiscretion he had to come away minus a slice of his lower lip, which, fortunately, was not large enough to seriously reduce his avordupois [sic?], and heaping blessings (?) [sic] on mankind generally, not in any way forgetting the "Bruges Barber, we roamed over the old town, noted for its magnificent cathedral and many seats of learning. The hours sped on pleasantly enough, and in due time our friend was unearthed. Being pledged to secrecy I am not going from my word by giving full particulars of The Battle Ground placed at our disposal. This is in close proximity to the town — in fact, not half an hour's walk, and on reaching the spot we were shown a lovely piece of turn. A clump of trees on each side partly hid the house from view, and when I say that the ring was to be pitched on a lawn tennis ground, it will be seen that neither side could claim an advantage as regards standing ground, &c., the lawn being as level as a billiard table. Though our efforts so far had been crowned with success, we did not get permission to use the "pictch" without much trouble. The matter had to be seriously considered, and Mr G. would not give a decided answer without waiting another day. Consequently our stay had to be extended and the following morning, after repeated promises that the affair should be conducted in an orderly manner with not a rough at the ring-side, we got the answer, "Yes." "But," said Mr G., "if there is any row or crowd I can assure you you will have a journey for nothing; therefore if trouble is at all probable keep away and save your money and time." As long as faith was not broken by either side we saw no reason why the matter should not be settled in a proper manner, and making all the necessary arrangements and laying down plans of a most complete description, we returned to town well satisfied with the result of a visit to Bruges. Trouble about the Referee. On returning to town we received satisfactory reports of the work done by each of the contestants. Slavin, looked after by Josh Cosnett, the Birmingham heavy-weight, and his friend Mr Michael Taylor, of Australia, though rather light, was in good health. At one time he scaled only 12st 8lb, but a judicious spell of light work brought him back to 13st odd. Considering the importance of the business in hand, and its bearing on future events, Slavin had some  cause for anxiety. In addition to this he was fighting for 300''l.'' of his own money, and consequently wished to do himself justice in the international battle. The next question was the selection of someone capable and willing to fill the all-important post of referee. According to the articles it was left to the stakeholder to appoint the official named providing the representatives failed to agree, and in the end this course had to be adopted, solely owing to the objections lodged by Smith. The first gentleman suggested by Slavin's side was Mr B. J. Angle, whom Smith promptly objected to. Next a well-known owner of racehorses (a gentleman who adjudicated upon the knuckle fight between George Camp and "Click" Soles) was proposed with no better result. Mr Bat Murphy, strange to say, would not suit, and then in succession "No" was said to the names of  Messrs G. H. Vise, A. F. Bettinson, and [B.?] Bayley. All these gentlemen, it must be stated, were proposed by Slavin and objected to by Smith, who in the meantime had named a member of the Pelican Club, a gentleman of limited experience in these matters, and the landlord of the house from which he was training, Mr W. Riley, Newmarket. This brought about a deadlock, and the state of affairs getting wind, ugly rumours were soon afloat, and even money, and in many cases good odds, were betted that there would be "no fight." All this while Slavin was chafing and fuming at the delay, whilst at the same time his  representative and Smith's were at work almost night and day endeavouring to bring about a settlement of the difficulty. For a long time it looked as though the matter would end in smoke, as after the services of the stakeholder had been called upon great difficulty was experienced in getting anyone to accept the office of referee. So late as Friday at noon nothing had been done, and it was not until the evening of that day that Mr Joe Vesey, consenting to stand, was nominated by the stakeholder. A Scare. Though the battle-ground was only known to two persons, the country where the fight was to be decided being, in fact, or supposed to be, a perfect secret, on Friday morning a paragraph said to have been sent out by a news agency appeared in several papers, and created intense astonishment and consternation. This, set out in large type by those who we should have thought would have suppressed the account, stated that Smith on the previous evening had arrived in London from his training quarters, and even went so far as to name the street he slept in. That Smith's visit to town was extremely injudicious there is not the slightest doubt, but this was not the worst. The time of departure for the scene of action was given, with a description of the place selected. This publicity had the effect of keeping away many who bad expressed a wish to be present, and on Slavin's side no less than eight gentlemen, each holding a high position in the sporting world, declined to have anything further to do with the affair. Who divulged the secret is at present a mystery, but there is not the slightest doubt that the information so freely put forward not only opened the eyes of the authorities, but gave the "mob," to a certain extent, a key to the [Col. 5c–6a] situation. Slavin received the news with no small amount of astonishment, and a couple of telegrams informing him that a batch of the "boys" had gone across to make things warm for him did not give peace to his troubled mind. Smith made his way out of England on Friday by the short sea route, Dover to Calais, which he reached in safety. Slavin, not so fortunate, was arrested on Satuday, as already reported, but, after being bound over to keep the peace, he got away the same evening.</blockquote> ==== Performance of the Men. ==== <blockquote>Jem Smith was born in Whitecross-street, in the parish of Cripple-gate, on January 21, 1863. He stands 5ft 8¹/₂in high, and weighs in condition 12st 10lb. Round the chest he measures 43¹/_?in; waist, 36¹/₂in; hips, 41in; thigh, 24¹/₂in; calf, 16¹/₄in; biceps, 15¹/₂in. For some years he was employed in one of the metropolitan timber yards, but developing a taste for boxing, after one or two rough-and-tumbles with his mates he was taken in hand by Jack Knifton ("81-tonner"), and later by Mr F. Grimm, of the Central Club. Smith has never been defeated, though in his first engagement he did not shape like a coming Champion. His first success was in a competition at the Griffin, Shoreditch. Later he beat Snowey, of Holloway, and was then matched to box Harry Arnold, with gloves, for a 10''l.'' purse. Arnold, though a stone and a half lighter than Smith, stripped in good condition, having for some time previously been engaged in training Jack Massey for an important engagement. The affair was looked upon as a good thing for Smith, but it took him nearly an hour to polish off the Seven Dials' representative, though he had slightly the best of the encounter from start to finish. Subsequently the veteran Goode deposited a [sov?] on behalf of Smith to match him to fight Massey, but this was forfeited. Smith's next engagement was with Woolf Bendoff to box to a finish with gloves for 25''l.'' a-side, which came off at an East-end club. In this contest Smith injured his right arm, but, nevertheless, proved successful at the end twelve rounds. Smith also won Tom Symonds's All-comers' Competition on February 26[?], 1885, at Bill Richardson's, defeating Sugar Goodson, Jack Wannop (the wrestler), and Tom Longer. At the close Smith was presented with a large oil painting of himself, executed by a prominent patron of the sport. Smith's next battle was with Jack Davis for 100''l.'' a-side and the Championship, on the turf, and came off on the borders of Surrey and Sussex, on Wednesday, December 17. In all six rounds were fought, occupying 7min 56sec, Davis being knocked out of time with a swinging right-hander. He subsequently met Alf Greenfield, of Birmingham, for 300''l.'' at Maisonne-Lafitte, near Paris, on Tuesday, February 16, 1886 [?]. Thirteen rounds were fought, mostly in Smith's favour, and the men fell, whereupon a cry of foul was raised by Greenfield's party, and a crowd of roughs broke into the ring, stopping the fight. The referee (Jem Mace), at the request of the principal backers of the men, agreed to decide the battle a draw. Soon after Smith was matched to fight Jack Knifton, the "81-tonner," as he is called. This proved a ''fiasco'', a two days' dreary tramp on the Continent being followed by a return to the old country. Knifton's people claimed that Smith had more than the specified number of followers, but there is little doubt that only one side wanted a fight, and that was not the "81-tonner's" lot. Meeting after meeting was held, Smith offering to fight anywhere the other liked, and after much wrangling arrangements were made to bring the affair off near Oxted [?]. Somehow of other the police got wind of it, and overtaking the Knifton party near Croydon rendered another postponement necessary. this time the arrangements were left in the hands of Knifton's side, with the result that the principals, seconds, and a dozen others were captured early one morning in a furniture van by the police before they had gone fifty yards as their journey. All were brought up at Thames Police-court, and after a remand bound over to keep the peace for twelve months. The memorial struggle between Smith and Kilrain, brought off on an island in the Seine, came next, darkness putting an end to the affair, which also resulted in a draw, after the men had faced each other for 106 rounds, on December 19, 1887 [?]. Jem's recent performance was a Ten-round Glove Contest with Jack Wannop, the Champion laying 250''l.'' to 200''l.,'' and winning easily, following which he was beaten in two rounds at the Pelican Club by Peter Jackson, the Coloured Champion, in a glove contest, for 1000''l.'' Frank P. Slavin. the Champion of Australia, was born on January 27, 1863, at Maitland, N.S.W. He stands 6ft 1in in his stockings, and in condition scales 13st 5lb or 13st 6lb. Slavin served his time or apprenticeship to a coachbuilder and blacksmith, and first came out as a pedestrian. He always had a liking for the gloves, and sparred a great deal when young, but did not enter into any match until the latter part of 1885 — that is, for money, though he won several competitions previously as an amateur. Slavin's first fight was with knuckles against M. Power for 50''l.'' a-side, and he won after seven rounds, lasting thirteen minutes. He then beat Jem Burke with 2oz gloves for 200''l.'' a-side and the Championship of Queensland, winning in three rounds. This was in December, 1885 [?], and in the following year the Australian formed a combination and went touring, offering purses ranging from 10''l.'' to 20''l.'' to any man who stood up for four rounds. At this game Slavin had an easy time of it; some stood one round, and some two, but none of them four. Towards the end of the year he went to Sydney, and entered into an agreement with Larry Foley, who has a big place there. Here Slavin met Taylor, a pupil of Jackson, for a purse with small gloves, and stopped him in two rounds. He was then matched with a big fellow named Bligh for 10''l.'' a-side, and beat him in one round. After a rest of two months articles were signed for him and Mike Dooley to box for 100''l.'' a-side. Dooley had a big reputation, but Slavin won in nine rounds. The subject of these remarks then had a little difficulty in finding an opponent, but eventually Mike Costello, an American, a good man, made his appearance, and the pair were matched for 100''l.'' a-side. They had a big battle in Sydney, lasting two hours and a half, and a draw was the result. Another match was made for 400''l.'', and 50''l.'' a-side was posted, but Costello forfeited this. Afterwards Slavin's backers matched him for 24''l.'' a-side to stop Costello in six rounds, but the latter is a very clever and tricky man, and lasted the time. Subsequently Frank journeyed to Sydney, and finding Mike there, challenged him again. The result of this was a match for 100''l.'' a=side with skin gloves, which Slavin won in twenty minutes. Slavin at this time had any amount of backing, and issued a challenge to fight Peter Jackson for 250''l'' a-side and the Championship. Jackson's party wanted a match with gloves for a purse. They could not come to terms, though Slavin's backers offered Jackson 50''l.'' to sign articles for 500''l.'' Australian was now a bit bare, so in January last year the Australian made a trip to New Zealand. The first man put up was Snath, who was backed to stand four rounds, but he had had enough at the end of the first. In Dunedin Slavin beat a big fellow in four minutes, and journeyed a long distance to fight Laing, the Champion. Terms could not be agreed upon until they had "fiddled" Slavin for nearly six weeks. The pair were then matched for 200''l.'' a-side, and fought with 2oz gloves at [Wangazul?], Laing failing to come up at the end of the fifth round. After this Slavin went back to Melbourne, hoping to get on a match with Jackson, and was surprised to find he had gone to America. Following this he met Jack Burke, but after Slavin had had all the best of it the contest was declared a draw. Mike Dooley was now in Sydney, and issued a challenge to him. This led to a match for 200''l.'' with small gloves, which ended in Mike being knocked out in 2min 40sec. He was very bad, and frightened all by not coming to for nearly half an hour. Slavin returned to Melbourne, and Burke having put several challenges in the paper, our visitor offered to stop him in six rounds; 200''l.'' a-side was put up and articles signed for 4oz gloves, but on the night Burke's party threw down regular pillow-cases. Of course this did not suit the other side, and there was a fine old wrangle, lasting two hours and a half. Eventually Mr Joe Thompson, who was referee, declared all bets off, and the two fought 6oz gloves, and agreed to divide the gate, and Burke was beaten in the middle of the third round. Previous to this Billy Farnan, the conqueror of Jackson, and Slavin, fought for 200''l.'', with the result that the latter added another winning bracket to his name, Farnan failing to answer to the call of time in the third round. This is considered to be one of Slavin's best performances. About this time Woolf Bendoff, of Whitechapel, was in Melbourne, and finding plenty of backers, they put up a forfeit of 100''l.'' for the Londoner to box Slavin, for 500''l.'' a-side. After seeing the latter polish off Burke, however, Bendoff's friends would go no further with the atch, and Slavin accordingly pocketed the "century." An easy victory over Bill Buck in two rounds followed, and then Slavin, on October 17 made his first appearance in England at Astley's Theatre, where he beat "Chesterfield" Goode in five rounds in a match of twelve rounds, for 400''l.'' </blockquote> ==== THE PELICAN CLUB AND THE FIGHT. ==== <blockquote>To the Editor of the Sportsman. Sir, — As an impression prevails that the Smith and Slavin fight was arranged under the patronage of this club, I should esteem it a favour if you would allow me to state emphatically that the Pelican Club gave no countenance to the affair in any way whatever, and had nothing to do with it. — Yours truly, Cecil Raleigh, Hon. Sec. Pelican Club, 21, Denman-street, W., Dec. 23. __________ We hear on good authority that it is the intention of the members of the Pelican Club to present Slavin, the Australian Champion, with a belt, in recognition of the manly exhibition he gave yesterday at Bruges. </blockquote> ==== THE CHAMPIONSHIP OF THE WORLD. ==== <blockquote>Frank Slavin to John L. Sullivan. Frank Slavin, the Champion of Australia, is prepared to meet John L. Sullivan, under London Prize Ring Rules, for 500''l.'' or 1000''l.'' a-side and the Championship of the World. Slavin has lodged with us a sum of 100''l.'', and will contest the title with Sullivan in either America or Australia in six months from signing articles. We have cabled this challenge to Mr R. K. Fox, of New York, and the money lodged with him or the Editor of T<small>HE</small> S<small>PORTSMAN</small> will lead to a match.<ref name=":1" /> </blockquote> === Dundee ''Evening Telegraph'' === This Wednesday, 25 December 1889 article describes Slavin's reception in London after the fight. Viscount Mandeville was there, suggesting that he was a Slavin supporter:<blockquote>There was (says a sporting correspondent) great excitement in London yesterday over the fight of Monday, and all classes of the community expressed their abhorrence of the proceedings adopted by the Smith party. It was known early that Slavin would journey up from his quarters at Margate about mid-day, and by two o'clock there was a large gathering in and about the Holborn Viaduct Station. By three o'clock the crowd had increased enormously. The train arrived behind time. As soon as Slavin and Mr Taylor were recognised, a loud cheer was raised. So great was the crush that it was only with the greatest difficulty that the Australians could make their way to the street. The reception accorded the champion, although very gratifying, was somewhat rough, Slavin and his party being forced across the road before they could take refuge in a hansom. Among those present were John Lewis, Slavin's manager; [[Social Victorians/People/Mandeville|Lord Mandeville]], E. Bayley, and other well-known sportsmen. From the station Slavin went, in answer to an urgent request, to the Stock Exchange, where another enthusiastic reception waited him. A move was then made to the office of the ''Sportsman'' in Fleet Street. Among those who were present to offer their sympathy and congratulations to Slavin on what all considered to be a victory were [[Social Victorians/People/Mandeville|Lord Mandeville]], Ike White, E. Bayley, George Knight, W. Riley, C. Mitchell, J. Goldberg, J. Kilby, F. Symes, F. Hinde, and a score of well-known boxers. Shouts for Slavin were kept up outside, and the crowd could not be silenced until Slavin went to the window. He bowed his acknowledgments, and after much difficulty obtained a hearing. He thanked the multitude for his great reception, at which three cheers wore raised for him, and a corresponding number of groans for Smith. Later Slavin dined at the Albert Club where a Testimonial Committee was formed. At seven o'clock Slavin departed for Margate. Smith remained in Bruges until one o'clock on Monday, when, in company with Baldock and Harper he left for London ''via'' Calais. They arrived in London at eleven o'clock, Smith going home in company with a friend. Smith has a wound over the right eye, and his face is much swollen.<ref>"London Gives the Colonist a Great Reception." ''Dundee Evening Telegraph'' 25 December 1889, Wednesday: 3 [of 4], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000453%2F18891225&page=3&article=052&stringtohighlight=mandeville+viscount. Print title: ''TheEvening Telegraph'', n.p.</ref></blockquote> === ''Reynolds's Newspaper'' === The Sunday, 29 December 1899, of ''Reynolds's Newspaper'' published a detailed account of the fight.<blockquote>The fight between Slavin and Smith took place on Monday morning upon private property in the outskirts of Bruges. Various spots, both at home and abroad, were from time to time named as the possible battle-field, but finally it became known to a certain select few that an English gentleman, Mr. Atkinson-Grimshaw, residing near Bruges, had placed his grounds at the disposal of the combatants. The host is a well-known breeder of fowls; and he certainly did not expect the quality of fighting cock which responded to his invitation. The ground was encircled by large trees, which secured the utmost privacy. About forty persons assembled at the ring-side, including Viscount Royston, Viscount Mandeville, Mr. Abington, Mr. Harris, Mr. W. Riley, Mr. P. Kotchie, Mr. Ike White, the Hon. M. Sandys, Mr E. Bayley, Mr. C. Parsons, Mr. J. Kilby, Mr. C. Morton, and other well-known "sports." Smith was dressed first, and had to wait a few minutes for Slavin. The Englishman appeared in white flannel drawers, white socks, and lace-up boots; while the Australian wore black drawers, blue socks, and lace-up boots. Harper and Baldock were seconds, Howes bottle holder, and Mr. Fleming umpire for Smith; Cosnett and Bob Kirby, Mr. Taylor, and Mr. W. Riley acting in similar capacities for Slavin. Mr. Joe Vesey officiated as referee and Mr. Calder as time-keeper. The men were in the ring at 8.25, and ten minutes later the fight began. After the first two rounds everything went in favour of Slavin, who in the third round knocked Smith clean off his legs with a terrific right-hander. He repeated this operation four or five times subsequently and surprised many of the spectators by the determined way in which he fought. In the thirteenth round he doubled Smith up with a fearful blow under the left ribs, and the Englishman's friends, seeing that Smith was almost beaten, raised a cry of "Police!" Smith was hurried from the ring; but Slavin and his friends refused to budge, and, after "Time" had been called, they claimed the fight. The referee, who appeared afraid to give a just decision, was surrounded by partisans of Smith, who had meanwhile come back, and eventually ordered the fight to proceed. Prior to this Slavin had been repeatedly kicked on the legs and hit on the body and head with sticks and knuckle-dusters. These gross and cowardly outrages were committed in Smith's corner, where all the fighting took place from start to finish. The next round, the fourteenth, was the last. Slavin fought in a most determined fashion, and when he was punishing Smith heavily, the latter caught the Australian round the waist and held him on to the ropes, whilst the ruffians standing around beat and kicked him in a most cowardly fashion. Amid cries of foul, the pair fell to the ground, and, on the men taking their corners, the referee said he would act no longer, as it was perfectly clear Slavin was not to have fair play. This created immense excitement, during which the referee declared the light a draw, and, crossing to Slavin, said, "I do not want to stay here to see you killed." Afterwards the roughs tried to get at Slavin, who, however, managed to hide in a barn. Later on he went with a few of his friends to Bruges, where he caught the train for Ostend, and came over to Dover, thence proceeding to Margate. Smith and his friends were left behind at Bruges. Round 1. — Slavin stood over Smith with a longer reach. Both sparred cantiously at the opening, Slavin at length leading off and landing heavily on Smith's chest, jumping back out of danger. Sparring again Slavin landed full on Smith's mouth. Heavy in-fighting followed, the men closing and falling together. When Slavin rose it was seen that he was bleeding from the mouth. Time, 1min. 30sec. Round 2. — Slavin fought Smith right into his own corner. There was a disgraceful scrimmage there among Smith's friends, Slavin being badly used. Both men fell together. Time, 15sec. Smith's party shouted out that their man had been spiked by Slavin's boots. The referee, thus appealed to, declared that the men had spiked each other. Round 3. — Smith showed to better advantage in this round, getting home both right and left twice in quick succession on the Australian's body. Sharp close in-fighting followed, Smith going down before a terrific right-hander. (First knock-down blow to Slavin.) Round 4. — Both men were blowing when they came up for this round. The fighting was again fast and furious, Smith at length cross-buttocking Slavin. The Englishman, however, did not fall on him. Round 5. — A light round, Smith going down before a light blow. Time, 11sec. Round 6. — Slavin came up very determined, and forced the fighting at a great pace. He drove Smith all over the ring, landing with his right a heavy blow over the right eye. Smith went down bleeding freely from a gash on the forehead. Round 7. — Smith came up stronger and did some of the forcing work, beating Slavin for a moment on to the ropes. While in this position one of the crowd of roughs deliberately kicked the Australian, who, however, took no notice of the cowardly attack. Both the combatants got away from the ropes and fought to the middle of the ring, where Smith slipped, and both were taken to their corners. Round 8. — Slavin did the opening work in this round, driving Smith round the ring and finally into his corner, where, as usual, his friends were ready to protect him. Smith came out again, when Slavin landed heavily with right and left, and Smith sought the ground. Round — 9 There were heavy exchanges from the outset, Slavin giving his man no rest, and driving him back into his corner. While there one of the mob struck Slavin on the head a violent blow. Time, 1min. Round 10. — This was a far more sportsmanlike round. Smith stood up well in the centre of the ring, and fought it out without the assistance of his friends. There was hard fighting from first to last of a close order, both getting home some terrific body blows. Both fell together. Round 11. — Smith looked tired and led off feebly while Slavin returned with right and left on the head, cutting open the Englishman's cheek on the left side. Smith landed his left again, Smith countering heavily. Smith then rushed upon the Australian, who met him with a severe blow on the mouth, and then sent him down with a terrific right-hander. Round 12. — The disturbances at the ring had now become so unbearable that the referee cautioned the seconds to keep to their corners, and not to interfere with the principals during the progress of the round. The round was of the cautious order, Smith finally being sent to grass again from a heavy right-hand blow on the jaw. Time, 1min. 30sec. Round 13. — Slavin again did all the leading, fighting the Englishman round the ring, and forcing him into his corner. There were some heavy exehanges, Smith's friends again assisting their man by hitting freely at Slavin. Round 14 and last. — Just a second before "Time" was called, Slavin, remarking on the treatment he had received, said, "Are you Englishmen, boys?" This was received with derisive shouts from Smith's party, and then, in an instant, a cry of "Police" was raised. The whole of the Smith party instantly decamped, hurrying their man along with them. Slavin, however, declined to stir, and his friends shouted that it was only a ruse to stop the fight. After a time the Smith  party returned, and Slavin then said to Baldock, the most prominent of Jem Smith's seconds, "Why don't you give me fair play?" Slavin's seconds claimed the fight, but the referee ordered them to fight on. The tactics of the Englishman's supporters were now very evident, but Slavin, who was only anxious to have the fight out to an end, advanced into the  centre of the ring, and again beat the Englishman back into his own corner. A scrimmage ensued, both men landing heavily, and the mob in Smith's corner then closed upon Slavin, who was again kicked and struck. The Australian, however, paid no attention to anyone except Smith, and he finished up the round by throwing him heavily. The referee then said, "I shall refuse to act any longer. This man" — pointing  to Slavin — "can't have fair play. I declare it a draw." Smith seemed well at the finish, and Slavin was certainly full of fight and disgusted at having been robbed of victory by the cowardly attacks of roughs. The Australian had fought in the fairest and most plucky manner throughout, forcing the Englishman back into his corner in nearly every round, and keeping him there. Here the fight came to an end, the referee exclaiming, "I shall refuse to act any longer. I shall declare it a draw." There was considerable surprise among Slavin and his supporters, and the Australian said, "I came 16,000 miles to win, and why don't you give a man a chance?" After some little delay the company dispersed. The time at the end of the fight was eight minutes to nine. Mr. Cecil Raleigh, hon. secretary of the Pelican Club, 21, Denman-street W., writes as follows:— "As an impression prevails that the Smith and Slavin fight was arranged under the patronage of this club, I should esteem it a favour if you would allow me to state emphatically that the Pelican Club gave no countenance to the affair in any way whatever, and had nothing to do with it." Directly the news became known in London the greatest indignation prevailed in all the clubs at the dastardly way in which Slavin had been treated. Subsequently some forty or fifty gentlemen proceeded to the Pelican to demand the instant and public repudiation on the part of the committee with any official cognizance of the arrangements for the fight, and also for the summary punishment of those who had dragged prize fighting down to the lowest depth of degradation and blackguardism. In accordance with these demands, and in full sympathy with them, those members present, conjointly with the proprietor, immediately sent out telegrams summoning an extraordinary meeting of the committee. That Slavin has now a right to the title (empty though it be) of "champion" is clearly supported by the 24th rule of the Prize Ring, which runs as follows:— "Any pugilist voluntarily quitting the ring previous to the deliberate judgment of the referee being obtained shall be deemed to have lost the fight." It seemed a pity that Mr. Vesey should not have had sufficient support to enforce what was uadoubtedly the judgment of all impartial spectators of round thirteen. Arrival of Slavin at Margate. Slavin arrived at Margate at half-past seven on Monday evening, and met with a flattering reception. During his training in the town he had become a general favourite with those who took an interest in the event. Sympathy was almost wholly on his side, and during the day news was anxiously awaited. At the station he was met by a four-in-hand and the town band, and proceeded to the Elephant Hotel, the band playing, "See the conquering hero comes." Along the Parade, on which was assembled a large crowd of people, he was loudly cheered. At the Elephant Hotel, there was a large crowd of people, and the reception was most enthusiastic. Slavin briefly addressed the gathering, thanking them for the reception he had received. His intention, he said, when [Col. 4c–5a] he left England was to win the championship or lose it fairly, and he was sorry that the fight had ended in such a fiasco. Inside the hotel the scene was very exciting, and Slavin received the hearty congratulations of his friends at the slight punishment he had received. He then left for the Nayland Rock Hotel, his quarters, and on the road was loudly cheered. Upon arriving at the hotel, Slavin retired, accompanied by his second, Joss Cosnett, after which the correspondent of the Press Association was introduced to him. The first question put was, "Well, Slavin, how have you fared?" "Very badly," responded the Australian. "As far as the roughs were concerned, I never witnessed anything more disgraceful in all my experience. My treatment at their hands has been most cruel, and nothing I could say would sufficiently emphasize what I mean. I am very pleased indeed at  the reception I received on my arrival at Margate. Nothing could have been more enthusiastic. You see what punishment I have received. It is not from Smith so much as it is from the outsiders." — Joss Cosnett: Smith did not bit him any more than I am hitting you. The conduct of the roughs round the ring was shameful. Slavin: The treatment I have received from them was most unmanly. I am sure the roughs never meant it to be fought out. They intended to have a draw if they found their man losing. Several of Smith's backers, including two well-known noblemen, were disgusted, and threw his colours away and put mine on, as a protest, I suppose, against the treatment I had received. To speak the truth, I would not like to see a dog treated as I was. All I am anxious for now is to meet Sullivan for the championship of the world for £500 to £1,000, or anyone else. I am willing and ready to meet and fight anybody for the championship before I go back to Australia. The Pelican Club and the Fight. A meeting was held at the Pelican Club at one o'clock on Tuesday afternoon. At the conclusion the hon. secretary, Mr. Cecil Raleigh, furnished the following report:— "In view of the reports of what had occurred at the Smith and Slavin fight a special meeting of the committee of the Pelican Club was instantly convened by telegraph for this afternoon. There was a large attendance of the committee, among those present being the Marquis of Queensbury, Mr. John Corlett, and other well-known sportsmen. It was unanimously determined to address a letter of sympathy to Frank Slavin, expressing the appreciation of the committee of the courage he exhibited, in face of the most  blackguardly conduct which ever disgraced the ring side. The committee added that they fully recognised that he had indisputably established his claim to the championship of England, and they further informed him of their intention to present to him a belt and purse in recognition of his pluck. The committee then determined that Mr. John Fleming, late manager to Jem Smith, who had hitherto acted as master of the ceremonies at the Pelican Club, should be suspended from his office until such time as he should afford an explanation of his connection with the Smith and Slavin fight, which explanation would be laid before a general meeting of the members of the club on Tuesday, January 6th. The indignation of the members of the club knows no bounds, and every effort will be made to discover who were the real instigators of the disgraceful business." It is most likely that the belt and purse will be presented to Slavin on January 14th, when the club move into their new premises. The following letter has been addressed by the pugilist, F. P. Slavin, to the Pelican Club:— "In reply to your very kind and encouraging letter, accept my warmest thanks for the high compliment you are about to pay me in presenting me with a belt, called the Champion of England belt. You may rely it will be my duty, as it has been all through my career, to do my best to win any contest I may enter into in a fair and manly manner. — Again thanking you, I am, sir, yours truly, "F. P. SLAVIN. "Nayland Rock Hotel, Margate." Mr. Fleming's Statement. Mr. Fleming states that the fight was arranged before the boxing match with Jackson. He went over to Belgium and selected the ground. As regards the rough element present, he did not know one of the men. No doubt they were engaged by some friends of Smith. The only persons who went across with them were four or five gentlemen. All connection between Smith and him had ceased, as he felt that he could not act in any way for Smith after what had occurred. Every fight that he had previously had the management of had always been brought off without the intrusion of any of the rough element at the ring side. He took no part in the proceedings, being merely there as a spectator, and he had not seen Smith since the fight. He did not think that he should have any difficulty in proving that he had no connection with the disgraceful proceedings at the ring side. The Preliminary Arrangements. The preliminaries of the match will, perhaps, be interesting. When, in 1885, Jem Smith, who had made a name among English heavy-weight boxers, met and defeated Jack Davis, of Birmingham, there was a sign of a revival of pugilism in this country. This was increased when Smith fought Alf Greenfield, and, although the battle ended in a draw, it was not long before the "lost art" was freely discussed, and there was every appearance of the revival of the prize-ring. Smith, as will be well remembered, fought a memorable battle with Jake Kilrain, who came from America to wrest the championship honour from the Englishman. John L. Sullivan, the Boston Boy, soon followed, and, although he failed to beat Charles Mitchell, his claim to the title of champion of the world was made good last July, when be met and defeated Kilrain. Then came new stars in the firmament of boxers, but glove-fighting had almost extinguished the "old style." Prominent among the late arrivals were Peter Jackson, a coloured man, and Frank P. Slavin, both hailing from Australia. Their records were of the highest calibre, Slavin having been successful in all the nineteen contests in which he had engaged, either with gloves or with bare hands, while Jackson's was but little less noticeable. The latter, however, carried all before him in America, and then sought fresh fields in England. Only a few weeks ago he vanquished Jem Smith in a couple of rounds. Slavin arrived in London a week prior to Jackson, and, after a lengthy wait, he was accommodated with a match. No one but W. Goode cared to meet him with the gloves, and Goode was easily disposed of. After signing articles to fight Jem Smith under prize ring rules, both men went into training, Smith at Newmarket, under the care of Jem Howes, and Slavin at Margate, with Fred Symes as mentor. The most difficult part of the arrangements had yet to be settled, and it was not without great trouble that a battle ground could be selected which afforded facilities for the accommodation of a party of sportsmen to witness the contest. At length a point was pitched upon near the Belgian capital, easy of access and fairly safe from interference. Another difficulty now arose over the appointment of a referee, and no less than five good men were named, all of whom were in turn objected to by Smith. The possibility of this having been foreseen it had been stated in the articles that the two parties failing to agree, the stakeholder, Mr. C. W. Blacklock, should appoint that official. This he did with satisfaction to both parties, naming Mr. J. Vesey, a well-known sporting man, to act. The stakes had then been increased to £500 a side. There is a great difference in the physique of the two men. Slavin stands 6ft. 1in., and scales in condition thirteen stone, is a very muscular athlete, and particularly quick on his legs; while Smith is of the sturdy order, and is only 5ft. 8¹/₂in. high. His weight when fit is 12st. 10lbs., and although his muscles are very massively developed, giving proof of great strength, he has not the quick hitting power of the Australian. Performances of the Men. Frank P. Slavin, the champion of Australia, was born on January 27, 1863, at Maitland, N.S.W. He stands 6ft. 1in. in his stockings, and in condition scales 13st. 5lb. or 13st. 6lb. Shavin served his time or apprenticeship to a coachbuilder and blacksmith, and first came out as a pedestrian. After winning several competitions as an amateur, Slavin's first fight was with knuckles against M. Power for £50 a-side, and he won after seven rounds, lasting thirteen minutes. He then beat Jem Burke with two-ounce gloves for £200 a-side and the championship of Queensland, winning in three rounds. This was in December, 1885, and in 1886 he went to Sydney and entered into an engagement with Larry Foley. Here Slavin met Taylor, a pupil of Jackson's, for a purse with small gloves, and stopped him in two rounds. He was then matched with a big follow named Bligh for £10 a-side, and beat him in one round. After a rest of two months articles were signed for him and Mike Dooley to box for £100 a-side, and Slavin won in nine rounds. He next met Mike Costello, an American, a good man, and after a big battle in Sydney, lasting two hours and a half, a draw was the result. Another match was made for £400, and £50 a-side was posted, but Costello forfeited this. Afterwards Slavin's backers matched him for £25 a-side to stop Costello in six rounds, but the latter is very clever and tricky, and lasted the time. Subsequently Slavin journeyed to Sydney, and finding Mike there, challenged him again. The result of this was a match for £100 a-side with skin gloves, which Slavin won in twenty minutes. Slavin at this time had any amount of backing, and issued a challenge to fight Peter Jackson for £250 a-side and the championship. Jackson's party wanted a match with gloves for a purse. They could not, however, come to terms. In January last year the Australian made a trip to New Zealand. The first man put up was Smith, who was backed to stand four rounds, but he had had enough at the end of the first. In Dunedin Slavin beat a big fellow in four minutes, and journeyed a long distance to fight Laing, the champion. The pair were matched for  £200 a-side, and fought with two-ounce gloves at Wanganui, Laing failing to come up at the end of the fifth round. After this Slavin returned to Melbourne, and met Jack Burke, but after Slavin had had all the best of it, the contest was declared a draw. Mike Dooley was now in Sydney, and issued a challenge to him. This led to a match for £200 with small gloves, which ended in Mike being knocked out in 2min. 40sec. Slavin returned to Melbourne, and fought Burke, Slavin undertaking to stop him in six rounds; £200 a-side was put up and the two fought with six-ounce gloves, and agreed to divide the gate, and Burke was beaten in the middle of the third round. Previous to this Billy Farnan, the conqueror of Jackson, and Slavin, fought for £200, with the result that the latter added another winning bracket to his name, Farnan failing to answer to the call of time in the third round. He then received forfeit from Woolf Bendoff. An easy victory over Bill Buck in two rounds followed. He then came to England, and his late victory in his glove fight with the plucky young Englishman, W. Goode, must still be fresh in the memory of our readers. Jem Smith was born in Whitecross-street on January 21, 1863. He stands 5ft. 8¹/₂in. high, and weighs in condition 12st. 10lb. Round the chest he measures 43¹/₂in.; waist, 36¹/₂in.; hips, 41in.; thigh, 24¹/₂in.; calf, 16³/₄in.; biceps, 15¹/₂in. For some years he was employed in one of the metropolitan timber yards, but developing a taste for boxing after one or two rough-and-tumbles with his fellow-workmen, he was taken in hand by Jack Knifton ("eighty-one tonner") and later by Mr. F. Grimm, of the Central Club. His first success was in a competition at the Griffin, Shoreditch. Later on he beat Snowey, of Holloway, and was then matched to box Harry Arnold with gloves for a £10 purse. The affair was looked upon as a good thing [Col. 5c–6a] for Smith, but it took him nearly an hour to polish off this last opponent, though he had slightly the best of the encounter from start to finish. Smith's next engagement was with Woolf Bendoff to box to a finish with gloves for £25 a-side, which came off at an East-end club. In this contest Smith injured his right arm, but, nevertheless, proved successful at the end of twelve  rounds. Smith also won Tom Symonds's All-comers' Competition on February 26, 1885, at Bill Richardson's, defeating Sugar Goodson, Jack Wannop (the wrestler), and Tom Longer. Smith's next battle was with Jack Davis, for £100 a side and the championship, on the turf, and came off on the borders of Surrey and Sussex on Wednesday, December 17. In all six rounds were fought, occupying 7min. 56sec., Davis being knocked out of time with a swinging right-hander. He subsequently met Alf Greenfield, of Birmingham, for £300, at Maisons-Laffite, near Paris, on Tuesday, February 16, 1886. Thirteen rounds were fought, mostly in Smith's favour, and the men fell, whereupon a cry of foul was raised by Greenfield's party, and a crowd of roughs broke into the ring, stopping the fight. The referee (Jem Mace), at the request of the principal backers of the men, agreed to decide the battle a draw. Soon after Smith was matched to fight Knifton, the "eighty-one-tonner" as he is called. This proved a fiasco. The memorable struggle between Smith and Kilrain, brought off on an island in the Seine, came next, darkness putting an end to the affair, which also resulted in a draw, after the men had faced each other for 106 rounds, on December 19th, 1887. This brings us to his ten-round glove contest with Jack Wannop, Smith laying £250 to £200, and winning easily. After which, as all the pugilistic world knows, Smith was easily defeated by the coloured champion, Peter Jackson, in a glove fight at the Pelican Club, the last named winning on a foul by Smith, who was at the same time well beaten.<ref>"The Great Prize Fight. £1,000 in Stakes. Brutal Scenes in the Ring." ''Reynolds's Newspaper'' 29 December 1889, Sunday: 1 [of 8], Col. 4a–6a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000101%2F18891229&page=1&article=006&stringtohighlight=mandeville+viscount. Same print title, n.p.</ref> </blockquote> === The ''People'' === On Sunday, 29 December 1899, the ''People''<blockquote>Disgraceful Scenes. Expressions of indignation. The prize fight between Jem Smith, who poses as the fistic "champion of England," and Frank Slavin, the Australian champion, took place early on Monday, and resulted in perhaps the most disgraceful scene ever witnessed in connection with the history of the prize ring. Various spots, both at home and abroad, were from time to time named as the possible battle-field, but finally it became known to a certain select few that an English gentleman, Mr. Atkinson-Grimshaw, residing near Bruges, Belgium, had placed his grounds at the disposal of the combatants. In London it soon became known that the principal supporters of the Englishman had caused a number of Birmingham ruffians to be hired for the purpose of making a "strong corner." The betting changed directly to short odds on the Australian, and also evens, while  offers of 30 to 20 that "Smith did not lose" proclaimed that some ugly and disreputable manœuvres would be attempted. The ring was pitched on a splendid piece of turf — the lawn tennis ground, in fact — and about forty persons assembled, including Viscount Royston, [[Social Victorians/People/Mandeville|Viscount Mandeville]], Mr. Abington, Mr. Harris, Mr. W. Riley, Mr. F. Kotchie, Mr. Ike White, the Hon. M. Sandys, Mr. E. Bayley, Mr. C. Parsons, Mr. J. Kilby, Mr. C. Morton, and other well-known "sports." Smith was dressed first, and and [sic] had to wait a few minutes for Slavin. The Englishman appeared in white flannel drawers, white socks, and lace-up boots, while the Australian wore black drawers, blue socks, and lace-up boots. Harper and Baldock were seconds, Howes bottle-holder, and Mr. Fleming umpire for Smith; Cosnett and Bob Kirby, Mr. Taylor, and Mr. W. Riley acting in similar capacities for Slavin. Mr. Joe Vezey officiated as referee and Mr. Calder as timekeeper. The Fight. The men were in the ring at 8.25, and ten minutes later the fight began. After the first two rounds everything went in favour of Slavin, who in the third round knocked Smith clean off his legs with a terrific right-hander. He repeated this operation four or five times subsequently, and surprised many of the spectators by the determined way in which he fought. Smith looked very serious on coming up for the fourth round. At this time a suspicious movement was noticeable among the brigade of Birmingham ruffians, and one of them came round to the colonial's corner with no good intentions. Had it not been that Mick Taylor and Frank Hinde kept zealous guard over all the water provided for the use of the combatants, there is no knowing what fiendish trick might not have been perpetrated. Getting to close quarters, Slavin delivered heavily right and left on Smith's body, the latter being very slow in responding to this vigorous attack. He had, however, other assistants, for a vile ruffian from over the ropes deliberately struck Slavin a blow on the head. A shout was at once raised, but when charged with it the rascal denied that he had done anything. A scuffle ensued between the men, and to escape from the difficulty Smith cross-buttocked his opponent, who fell. In the fifth and sixth rounds Slavin again brought Smith to the ground, and made a nasty gash on his forehead. All this time the most horrible language proceeded from Smith's corner. In the seventh round a desperate rally took place, during which Smith fought Slavin on to the ropes, and there held him. Here was a grand opportunity for the miscreants, who did not fail to make use of it. One of them kicked Slavin repeatedly, and others beat him about the head, knuckle-dusters and life preservers being used. Slavin during the progress of the eighth round further received a couple of smart blows from a stick which a cowardly ruffian carried. Taking not the smallest notice of these interruptions Slavin pursued his legitimate opponent, both Smith's seconds following him about and jeering in his face. The referee entered the ring, and cautioned the seconds to move away. This had very little effect, and in the midst of half-arm fighting of a very severe kind, Smith was one more brought to the ground. In the ninth round the Australian again ventured into Smith's corner, and the fighting brought him close to the ropes. The  Birmingham mob here set about Slavin with great brutality, kicking him and punching him on all parts of the body. Getting away from the ropes Slavin let go the right, and, reaching Smith's mouth, caused the blood to spring forth profusely, bringing the Englishman to grass. The tenth and eleventh rounds were not quite so exciting, but in the twelfth Slavin drove his right with terrific force on to Smith's chin, knocking him clean off his legs. In the thirteenth round the Australian doubled Smith up with a fearful blow under the left ribs, and the Englishman's friends, seeing that Smith was almost beaten, raised a cry of " Police!" Smith was hurried from the ring, but Slavin and his friends refused to budge, and after "Time" had been called they claimed the fight. The referee, who appeared afraid to give a just decision, was surrounded by partisans of Smith, who had meanwhile come back, and eventually ordered the fight to proceed. The next round, the fourteenth, was the last. Slavin fought in a most determined fashion, and when he was punishing Smith heavily, the latter caught the Australian round the waist and held him on to the ropes, whilst the ruffians standing round beat and kicked him in a most cowardly fashion. Amid cries of "Foul," the pair fell to the ground, and, on the men taking their corners, the referee said he would act no longer, as it was perfectly clear Slavin was not to have fair play. This created immense excitement, during which the referee declared the fight a draw, and, crossing to Slavin, said, "I do not want to stay here to see you killed." Afterwards the roughs tried to get at Slavin, who, however, managed to hide in a barn. Later on he went with a few of his friends to Bruges, where he caught the train for Ostend, and came over to Dover, thence proceeding to  Margate. Slavin's Opinion of his Treatment. The following conversation took place during an interview with Slavin, a few hours after the fight:— Did you expect any trouble at the ring  side? — Slavin: Yes, I was prepared for that, as I was constantly receiving letters of a threatening nature, and though these things as a rule are of no account, I had reason to believe there was some truth this time. Besides, I had not forgotten the affair at Astley's Theatre. — Do you feel any effects of the fighting? — Slavin: The fighting? I feel nothing of what I got from any one in the ring; it's what those beauties gave me outside. The only time Smith hit me in anything like form was on the jaw. — Why did you persist in going to his corner? — Slavin: I wanted to get the affair over and enjoy my Christmas dinner, and I knew if the fighting was left to Smith I should want it served in the ring. — Of course you heard a mob was got together for Smith? — Slavin: Yes, I knew all about that, but I relied on British fair play, and expected the referee to do his duty. Directly I got in the ring I saw what the game was, and knew my only chance was to knock Smith out. — What do you think of Smith? — Well, I think so much of him that I'll bet him £200 I stop him in six rounds, but we must have no more private shows. I've had enough of that business. — l suppose you have a poor opinion of English fair play? — Slavin: I have been treated like a prince generally, but I can see the fighting men are easily led astray, and I expected trouble directly Smith objected to a referee. If we served an Englishman in the same manner in Australia we should get drummed out of the town, and rightly too. — What are your plans for the future? Well, I shall stay in England some time and challenge Sullivan, and you might as well cable it over to America for me. — With the gloves? — No. I want to fight him with the knuckles. I think I should get fair play out there. Indignation in London. Directly the news became known in London the greatest indignation prevailed in all the West-end, [Col. 4c–5a] clubs at the dastardly way in which Slavin had been treated. Subsequently some forty or fifty gentlemen proceeded to the Pelican to demand the instant and public repudiation on the part of the committee with any official cognisance of the arrangements for the fight, and also for the summary punishment of those who had dragged dowr [sic] a manly pastime to the lowest depth of degradation and blackguardism. In accordance with these demands, and in full sympathy with them, those members present, conjointly with the proprietor, immediately sent out telegrams summoning an extraordinary meeting of the cornmittee. The Pelican Club Meeting. At the special meeting of the committee of the Pelican Club it was unanimously determined to address a letter of sympathy to Slavin, expressing the appreciation of the committee of "the courage he exhibited in face of the most blackguardly conduct which ever disgraced the ring side.["] The committee added that they fully recognised that he had indisputably established his claim to the championship of England, and they further informed him of their intention to present to him a belt and purse in recognition of his pluck[.] The committee determined that Mr. John Fleming, late manager to Jem Smith, who had hitherto acted as manager of the ceremonies at the Pelican Club, should be suspended from his office until such time as he should afford an explanation of his connection with the Smith and Slavin fight, which explanation would be laid before a general meeting of the members of the Pelican Club on Tuesday, January 7th. It is most likely that the belt and purse will be presented to Slavin on January 14th, when the club will move into their new premises. While Salvin was at the Stock Exchange on Tuesday, a subscription in his interest was started, and £110 was quickly subscribed. Slavin Challenges J. L. Sullivan. Frank Slavin, the champion of Australia, is prepared to meet John L. Sullivan, under London prize ring rules, for £500 or £1,000 a side and the championship of the world. Slavin has lodged a sum of £100, and will contest the title with Sullivan in either America or Australia in six months from signing articles. We have cabled this challenge to Mr. R. K. Fox, of New York, and the money lodged with him or the editor of the ''Sportsman'' will lead to a match.<ref>"The Smith-Slavin Fight." ''The People'' 29 December 1889, Sunday: 16 [of 16], Col. 4a–5a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000729%2F18891229&page=16&article=150&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Sportsman'' === On Monday, 30 December 1889, the ''Sportsman'' printed a list of people and organizations that had contributed to the "testimonial" fund for Slavin as well as some letters to the editor about the Slavin-Smith match:<blockquote> A committee meeting of the above was held on Saturday afternoon, Mr W. J. Innes in the chair.  There were also present Mr W. Riley, Mr Fred H. [Gala?], Mr C. Parsons, Mr A. Butler, Mr M. J. Harrow (Margate), Mr Ike White, Mr E. C. Irish, and Mr G. T. Dunning (hon. sec. and treasurer). The chairman read a letter from Mr John Lees, regretting his inability to attend owing to illness, whilst the remaining committeeman, Mr E. W. Bayly, was absent in Paris. The appointment of the hon. sec. and treasurer was confirmed by the committee, and after some discussion it was decided to close the subscription-list on Monday, January 20, and to present the proceeds to Slavin at the Cambridge Music Hall, Bishopsgate-street, on a day to be named. Other business of minor importance was transacted, and after the next committee meeting had been fixed for Wednesday, January 15, the meeting closed with a vote of thanks to the chairman. Additional subscriptions to the fund, which now reaches 300''l''., will be found appended [names set as unordered list to save space, £ ''s.'' ''d.''] * Lord Mandeville 2 2 0 * Lord Royston 2 2 0 * Lord James Douglas 2 2 0 * Hon. Michael Sandys 2 2 0 * Fred Kotchie 2 2 0 * Mr Ike White 2 2 0 * Mr W. Riley 2 2 0 * Mr C. Parsons 2 2 0 * Mr J. Kilby 2 2 0 * Mr Frank Hinde 2 2 0 * Proprietors of The Sportsman 2 2 0 * Mr. J. Purdey 2 2 0 * Mr. E. W. Bayly 2 2 0 * Messrs H. A. Domby and Son 2 2 0 * "Caption Coe" 2 2 0 * Mr C. W. Bulpett 2 2 0 * Mr P. W. Carr 2 2 0 * Mr W. Morley Pegge 2 2 0 * W. D. S. 2 2 0 * J. E. S. 2 2 0 * Mr W. H. Grenfel 2 2 0 * Mr Quartermaine East 2 2 0 * Mr H. H. Hungerford 2 2 0 * Mr Noel Fenwick 2 2 0 * Sir John Leslie, Bart. 2 2 0 * Mr T. Brinkman 2 0 0 * Mr Calder 1 1 0 * Mr H. W. Hill 1 1 0 * Mr John Young 1 1 0 * Mr D. A. Neilson 1 1 0 * Mr W. Neilson 1 1 0 * Mr Julius Simon 1 1 0 * Mr J. Edge 1 1 0 * Mr H. Marshall 1 1 0 * Mr F. Aynsley 1 1 0 * Col. Hon. Wellesley 1 1 0 * Mr Charles Hawtrey 1 1 0 * Mr W. F. Ashton 1 1 0 * Mr Barratt 1 1 0 * Old Durham Ox 1 0 0 * Sir John Willoughby 1 0 0 * A friend, per C. H. A. 0 10 6 * Mr Ben Giles 0 10 6 * Mr Tom Vale 0 10 6 * [E.?] W. 0 10 6 * Officer 0 10 0 * Per Mr Ike White, Exchange Club: ** S. W. 2 2 0 ** Mr G. B. Knight 1 1 0 ** Mr A. Powles 1 1 0 ** Mr S. Blandford 1 1 0 ** T. F. W. C. 1 1 0 ** Mr Leo Harward 1 1 0 ** Mr J. Harward 1 1 0 ** Mr H. Harward 1 1 0 ** Mr [Monteagle?] [Moutcagie??] 1 1 0 ** Mr C. Orate 0 10 6 ** W. G. P. 0 10 6 ** H. R. T 0 10 6 ** Mr Josiah Smith 0 10 6 ** W. H. R. 0 10 6 ** Mr R. Wilson 0 5 0 * Per Mr M. J. Harlow, Margate: ** Mr A. H. [Cosi? Coni?] 2 2 0 ** Mr J. Thurston 1 1 0 ** Mr J. A. Fagg 1 1 0 ** Mr F. [Miles?] 1 1 0 ** Mr Adolphe [Drineqbeir?] 1 1 0 ** Mr Ernest [Drineqbier?] 1 1 0 ** Mr Lacy Brown 1 1 0 ** Mr Algy Brown 1 1 0 ** Mr M. J. Harlow 1 1 0 ** An Admirer 1 1 0 ** Mr J. W. Robinson 1 1 0 ** Mr W. Searles 1 1 0 ** Mr J. Smith 1 1 0 ** Mr J. Hume 1 1 0 ** Mr J. Painter 1 1 0 ** A Scotchman 1 1 0 ** Mr J. Mundell 0 10 6 ** Mr Bob Redman 0 10 6 ** Mr G. A. Body 0 10 6 ** Mr J. Phipps 0 10 6 ** Mr J. Doughty 0 10 6 ** Old Fisherman 0 10 6 ** Mr Joe Knott 0 10 6 * Per Mr B. J. Angle ** Some mebers of the Stock Exchange 125 0 0 ** Hr Henry J. Turner 2 2 0 * Per Mr W. J. Innes: ** Mr Sidney Fry 2 2 0 ** Mr W. J. I. 2 2 0 ** Mr W. Schlesinger 2 2 0 ** Mr Joseph Thompson 2 2 0 ** Mr Barney Thompson 2 2 0 ** Mr L. Meyers 2 2 0 ** Mr W. Shoe 2 2 0 ** Mr George Cooper 2 2 0 ** Mr J. T. Crossley 2 2 0 ** Mr Andy Anderson 2 2 0 ** Mr G. M. T. 2 2 0 ** Mr F. R. 2 2 0 ** Mr W. Bertram 1 1 0 ** Mr J. W. Hammon 1 1 0 ** Mr Alec Harris 1 1 0 ** Mr John Isaacs 1 1 0 ** Mr Edward [Dance? Dasce?] 1 1 0 ** Mr George Blanchett 1 1 0 ** Mr F. [Leleu? Lolou?] 1 1 0 ** Mr W. J. R. 1 1 0 ** Mr H. C. 1 1 0 ** Mr A. A. M. 1 1 0 ** Mr D. W. Fowler 0 10 6 * Per Mr F. H. Gale: ** Mr R. Moore 2 2 0 ** Mr A. H. Goode 2 2 0 ** Mr [B.? E.? R.?] J. G. Goode 2 2 0 ** Mr F. H. Gale 2 2 0 ** Mr H. Ulph 1 1 0 ** Mr J. Hooper 1 1 0 ** Mr C. Kittall 1 1 0 ** Mr C. Moore 1 1 0 * Per Mr W. Riley: ** Mr Brand (Wiltshire) 2 2 0 ** Mr Charles Godfrey 2 2 0 ** Mrs Lane (Britannia) 2 2 0 ** Mr Sam Adams 2 2 0 ** B. and M. 0 7 6 * Per Mr A. Cockburn: ** Mr Richardson 2 2 0 ** Mr A. Cox 1 1 0 ** Mr Hy. Brackenbury 1 1 0 To the Editor of T<small>HE</small> S<small>PORTSMAN</small>. Sir,— From the evidence of your eye-witness reporter there seems to me the clearest possible case against Smith, Harper, and Baldock — that Smith held Slavin on the ropes while the roughs kicked and "knuckle-dustered" him, that Harper put his knee on Slavin when down, and that Baldock did likewise, and that throughout they advised Smith to stand like a coward under the protection of the savages till the instinct which filled Slavin's manly bosom prompted the honest outburst to Smith, "Come and have a round." The duty for sportsmen to fulfil with the assistance of their representative journal, is, firstly, to see that Slavin is elected Champion and that he is handsomely recompensed, and that these so-called "seconds" should be properly punished and our splendid timber-yard Champion put in his proper place. The names of those who hired the roughs should also be published. I have spoken to at least fifty patrons of boxing shows, and one and all have made the most positive and determined objection to supporting any entertainment where the three men named above are concerned directly or indirectly. They, by their own stupidity and cupidity, have put the last nail in their own coffin, I hope. With regard to the referee, this individual is decidedly unsatisfactory. He allowed Smith to bolt when the cry of "Police" was raised without disqualifying him in any way, and then put an end to the business by declaring it a draw. Now, if the said referee is not a determined or courageous man, then he acted to the best of his judgment, for he was afraid of personal violence, having literally to escape to London; but on his arrival here, I and numberless others naturally expected some explanation or a reversal of his decision. The whole sporting community are on the tiptoe of excitement, and Mr Vesey in the coolest  possible manner washes his hands of the affair, declining absolutely to expose any opinion. This is rather rough on the public considering that be consented to act as referee of his own free will, and he is no chicken in such matters. He does not tell us whether he is aware that he has the power to reverse a decision given under fear; nor does he say whether he still considers the decision made on the spot a happy one. How was it that no steps were taken to protect the referee? There is no legitimate courage in the Brummagem rough. He is an imposter. With assistance of our excellent so-called Champion, and about another ten, armed with knuckle-dusters, he will doubtless attack Slavin, and if a torrent of filthy, cowardly abuse could kill he would beat Slavin single-handed. One of these gallant gentry actually returned to Birmingham without going to Bruges, being positively afraid to chance crossing the tiny stretch of sea. An American reader will bear me out that had our unsatisfactory referee been under the protection of one single genuine Nebraska "tough," as they are called out there, he would, without uttering one word of bad language, have cleared out the lot had they attempted violence to his charge. But it would never have come to that, for the sight of a real, genuine armed rough, with determined set features, would have struck terror into the hearts of the pluckless Brum shoddy bully, with the proverbial dull, stupid, animal-like pudding face. As an Englishman I [Col. 1c–2a] positively feel guilty among my American friends when they ask me what about my vaunted British fairplay, and I quite fail to see or understand how "seconds" — no matter, for argument's sake, how dishonest they may be can such fools as to kill the goose which lays their golden eggs. Prize-fighting and boxing are their bread-and-butter, and some of those who accepted the assistance of the roughs in the recent important international fight must have surely prognosticated that trouble and disgrace would follow, and they of all men should have been the last to wantonly risk breaking up one of our favourite English sports. In conclusion, contrast the courage of the two men. Slavin practically fought about six men, not knowing the moment that one well-directed blow from a "duster" might have cost him his life or lost him the fight. Think of his manly appeals to the cowards for a few minutes' fairplay. I only wish they each had to have four rounds singly with him! — Yours, &c., A Lover of Boxing. To the Editor of T<small>HE</small> S<small>PORTSMAN</small>. Sir, — Previous to the late show of ruffianism I was in sympathy with and respected Smith as the Champion, but I am grieved to say that nothing of late years has so thoroughly disgusted me as the ill-treatment which was meted out to Slavin by those who disgrace not only sport but the very name of man. I sincerely hope that Slavin will still continue to think that one of the dearest wishes of the true sportsman of this country is to see fair play. I enclose my mite in the shape of one guinea, and subscribe myself, yours, &c., Leicester, December 28. J. Barrett. To the Editor of T<small>HE</small> S<small>PORTSMAN</small>. Sir, — Herewith I inclose cheque 1''l''. 1''s''. to the Slavin Fund, and hope that his manly and honourable conduct will be well rewarded. I cannot, however, agree with those who hope "that we have seen the last of prize-fighting," and other sentiments of the kind. It will be an evil day for England when the fighting instinct dies out from among her sons. No, let us rather hope that the Slavin-Smith ''fiasco'' will be the beginning of a new era, and that for the future fights will not be allowed to take place without proper ring-keepers, as in the days of Spring, Langham, and Bendigo, and that the Championship of England will not be long without a native defender.—Yours, &c., J. W. B. C., Junior Carlton Club, December 27. To the Editor of T<small>HE</small> S<small>PORTSMAN</small>. Sir, — l beg to inclose you the sum of one guinea, my subscription to the Slavin Fund. I was indeed sorry to read of the outrageous and murderous treatment Slavin received from Smith's supporters, which support was tacitly sought after by Smith not leaving his corner and meeting his man in the centre of the ring, as any Englishman should have done that presumed to call himself "England's Champion." I feel quite certain that had this outrageous conduct passed away without the strong condemnation it received at all good sporting men's hands in this country, and the hearty and the thoroughly unanimous sympathy expressed for Slavin, the good feeling and perfect bon accord that has existed between the sporting fraternity of the two countries, New and Old England, would soon have ceased to exist. Australians are great stickers to and warm supporters of England and the English, and they will all feel most keenly the slur cast upon "British fair-play and courage." — Yours, a lover of it, Sydney Galvayne. York, December 26. To the Editor of T<small>HE</small> S<small>PORTSMAN</small>. Sir, — Enclosed you will cheque for one guinea as a simple tribute to Slavin, who so squarely held his own, and who should not be looked upon as a stranger in a strange country, but as a cousin Englishman, who deserves support, not only as a true sportsman but also against the fearful ordeal of ruffianism to which he has been subjected. As a lover of fair play believe me, yours faithfully, Birmingham, December 27. Tom B. Sharp. To the Editor of T<small>HE</small> S<small>PORTSMAN</small>. Sir, — Please add 9''l.'' 14''s.'' to the list I have already sent you for Slavin testimonial, and oblige, yours, &c., I. White. Exchange Club, Queen-street, Cheapside, Dec. 28.<ref>"The Ring. The Slavin Testimonial." ''The Sportsman'' 30 December 1889, Monday: 4 [of 4], Col. 1a–2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18891230&page=4&article=020&stringtohighlight=mandeville+viscount. Same print title and p.</ref> </blockquote> On 9 January 1890 in part of a much larger partisan report with critiques of the investigative committee, its chair and its results as well as other newspapers printing rumors:<blockquote>JOHN L. SULLIVAN ON ENGLISH FAIR PLAY. {{paragraph break}} J<small>OHN</small> L S<small>ULLIVAN</small> has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of 'heelers' always wins or saves himself from defeat. Slavin or Jackson will, in all probability, look for a match with me when they arrive in this country, and | am perfectly willing to meet either or both of them for a proper consideration. I want a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for  me."<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> Also on January 9, the ''Sportsman'' reported on a collection made for Slavin:<blockquote>THE SLAVIN TESTIMONIAL {{paragraph break}} The subscriptions towards the above now amount to over 400''l.'', and it having been decided to close the list on the 20th, the committee will be obliged if those who have promised donations will forward the same to the hon. sec. and treasurer, Mr. G. T. Dunning, T<small>HE</small> S<small>PORTSMAN</small> Office.</blockquote> {| class="wikitable" ! !£ !s. !d. |- |Amount already acknowledged |407 |3 |6 |- |Mr E.Tabernacle |1 |1 |1 |- |H. S. |1 |1 |0 |} <blockquote>The guinea acknowledged per Mr Riley, from C. R., yesterday, should be from C. K.<ref>"The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns." ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&page=4&article=049&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Huddersfield Daily Chronicle'' === On 10 January 1890:<blockquote> Mitchell and Lord Mandeville. As an addendum to the important meeting of the Pelican Club committee, on Wednesday, came a gathering of "sports" at the Trocadero, Piccadilly Circus. Lord Mandeville and Mr. Abington., who had been in attendance at Denman-street, were joined by "Pony" Moore, his son-in-law, C. Mitchell, J. Carney (the Birmingham light-weight), J. Baldock, B. Habbijam, C. Bates, &c. The party, who occupied seats in the stalls, naturally discussed things pugilistic, the talk being mostly devoted to the recent international fight between Frank P. Slavin and Jem Smith. " [sic] The Squire's opinions on the matter happened not to coincide with those of Mitchell, and high words were exchanged between the pair. Suddenly the Birmingham boxer jumped up and "went for" Mr. Abington, but did not strike him. Lord Mandeville immediately interposed and asked Mitchell to be quiet, whereupon the latter directed his attention to his lordship, and struck him sharply on the forehead. Carney and Baldock sprang to his lordship's assistance, and Mitchell and "Pony" Moore at once left the building, the whole proceedings not lasting longer than a few seconds. It soon became noised abroad that there was "something up," and a crowd gathered, but the police saw Mitchell and Mr. G. W. Moore safely across the road.<ref>"The Smith-Slavin Fight." ''Huddersfield Daily Chronicle'' 10 January 1890, Friday: 4 [of 4], Col. 6b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0002876%2F18900110&page=4&article=071&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> After the Pelican Club meetings, Slavin comments:<blockquote>On Wednesday at Westminster Aquarium, F.  P. Slavin, the colonial pugilist, who received such bad treatment at the hands of roughs in his recent prize-fight with Jem Smith, the English "champion," made his first public appearance since the fight. Mr. Frank Hinde, in introducing Slavin, said he would give an exhibition with Cosnett of Birmingham, who seconded him in his fight. Slavin was the gamest man that ever  stepped into a ring, he hoped the audience would rive him a good old English welcome. On appearing on the stage Slavin met with a most enthusiastic reception, and the three rounds' sparring with Cosnett was much appreciated. At the conclusion Slavin, in response to loud calls, bowed his acknowledgments.<ref>"Slavin at the Royal Acquarium." ''Liverpool Weekly Courier'' 11 January 1890, Saturday: 3 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003067%2F18900111&page=3&article=042&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === ''Reynolds's Newspaper'' === ''Reynolds's Newspaper'' quotes J. L. Sullivan on the Smith-Slavin match:<blockquote>Mr. John L. Sullivan has been speaking his mind on the Smith-Slavin fight to some purpose. "I can't see how an English fighter can be beaten," he said. "This man Smith is little better than a middle-weight, and I haven't the slightest doubt that Slavin beat him fairly. Some people wonder why I did not go to England to fight Smith. Now you can understand why I insisted on meeting him in this country. In England fair play is unknown. The man with the greatest number of "heelers" always wins or saves himself from defeat. Slavin or Jackson will in all probability look for a match with me when they arrive in this country, and I am perfectly willing to meet either or both of them for a proper consideration. I went a big purse, and I am not particular where I fight so long as it is in a club-house. No more law-breaking for me."<ref>"The Recent Prize Fight." ''Reynolds's Newspaper'' 12 January 1890, Sunday: 6 [of 8], Col. 4a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000101%2F18900112&page=6&article=053&stringtohighlight=mandeville+viscount. Same print title and p.</ref></blockquote> === The ''Cork Constitution'' === About Mr G Baird (Mr. Abington) from the ''Cork Constitution'':, referring at the end to the [[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]] or a restaurant:<blockquote>This well-known sportsman (Mr G Baird) who is occupying an unenviable position owing to his conduct at the Smith-Slavin piece of brutality, is the largest owner of race horses in England. He has no less than 100 horses in training, and though he won £10,000 in stakes last year it is computed that he should have won £25,000 additional to even pay his way. Anent that fight which has caused such indignation in the country, a London music hall was last week the scene of a pretty disturbance. Mr Abington and Lord Mandeville occupied a box during the entertainment, and received, amongst others, Charlie Mitchell, the well-known pugilist; an angry discussion ''re'' the fight ensued, and concluded by the peer measuring himself on the floor from one Mitchell’s "lefts."<ref>"Mr. Abington." ''Cork Constitution'' 14 January 1890, Tuesday: 7 [of 8], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001648%2F18900114&page=7&article=099&stringtohighlight=mandeville+viscount. Same title and p.</ref></blockquote> === The ''Colonial Standard and Jamaica Despatch'' === This report from the ''Colonial Standard and Jamaica Despatch'' mentions fighting in the streets (at a corner in Fleet Street) and tosses in an unrelated sentence about an upcoming match between a West Indian and J. L. Sullivan:<blockquote>The disgraceful affair, called by courtesy and [sic] "International Prize Fight," which desecrated the peaceful dignity of the quaint old city of Bruges on Monday morning ought to convince people that there is nothing left to hope for in the Prize Ring. [2c–3a] At eight o'clock in the morning, Jem Smith, self-styled Champion of England, and Frank Slavin, the Australian Champion, with their seconds and parties, met in the grounds of a private gentleman to try conclusions. The "fight" lasted for twenty-five minutes, and was then brought to an abrupt conclusion by the referee declaring it drawn — he would have been killed had he given it to Slavin, who proved to be incomparably the better man. Fourteen rounds were fought in all, during the whole of which time Smith's friends and Smith's seconds worried, and at last assaulted, the Australian, who behaved quite pluckily. It is a disgrace to the name of Englishmen that this brutal scene should go forth to the world. Smith's backers knew well that he had no chance of winning, so they laid their plans to smash Slavin on their own account. It is a wonder that he was not killed — as was reported in Fleet-street at ten o'clock — for Smith's roughs struck and kicked him whenever he came near their corner. Although Lord Mandeville, Lord Rosslyn, Sir M. Sandys, and a few other members of the upper circle, were present at the fight, the bulk of the spectators were the refuse of the gambling rings of London, blackguards and ruffians of the deepest dye. The stakes were £1,000. So great an amount of indignation has been expressed on all sides at the treatment to which the Australian was exposed, that a subscription has been opened up for him. The West Indian, Jackson, is just leaving London for San Francisco, in order to get ready to meet J. L. Sullivan.<ref>"London." ''Colonial Standard and Jamaica Despatch'' 16 January 1890, Thursday: 2 [of 4], Col. 2c–3a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0004059%2F18900116&page=2&article=019&stringtohighlight=mandeville+viscount. Same print title, n.p.</ref></blockquote> == Notes and Questions == # ==References== {{reflist}} lkjuspyrb9t5tyytqmslmm1czzftidv 0 332786 2844854 2844801 2026-11-08T07:02:44Z Wb525 3112992 /* Redshift */ 2844854 wikitext text/x-wiki {{Research project}} Original research project by Willy Bohane — UG.NUG. https://doi.org/10.5281/zenodo.20644064 == All the texts in this presentation == [[Cosmology: UG.NUG an Observation-Based Model|UG.NUG]] [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]] [[Cosmology: UG.NUG an Observation-Based Model/Cosmic Time|Cosmic Time]] [[Cosmology: UG.NUG an Observation-Based Model/the Mass Imbroglio|the Mass Imbroglio]] [[Cosmology: UG.NUG an Observation-Based Model/the CMB|of the CMB]] [[Cosmology: UG.NUG an Observation-Based Model/the GRID|of the GRID]] [[Cosmology: UG.NUG an Observation-Based Model/Gravity|of Gravity]] [[Cosmology: UG.NUG an Observation-Based Model/Black Holes|of Black Holes]] = Introduction = This article presents a reading of the Universe that differs in every respect from the existing model. The latter contains a false start which, for reasons explained in the dedicated article on [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]], renders it null and void from the very first millisecond of its narrative: the Singularity. Before reading this detailed text, whose links to technical articles support and further develop the arguments presented, readers can consult a simplified [https://www.wbohane.com/BLOG/!three_point_universe.aspx three-point diagram] offering an overview of the proposed simplicity of the Universe. = State of Play = First, it is important to understand that cosmology, in its interpretative function, is not an exact science. As its name indicates, it means, in Greek, ''the study of the world'' — and therefore, by extension, its origin, its structure, its evolution, its content, and its future. We also have a duty never to forget that cosmology was born as a branch of metaphysics. This should remind us that mathematics must remain a means of understanding the Universe, not a substitute for it. Rather than building elaborate theoretical structures and continually adjusting them to accommodate observations, it would be far more sensible to seek a description that reflects the universe as it actually is. The purpose of cosmology should not be to make reality fit our mathematics, but to make our mathematics serve reality. This is why interpretative cosmology resembles a religion more than it does a science. As with religion, everybody can say anything, everybody can believe anything, everybody can make anyone believe anything. Humanity is divided into many creeds, and so is cosmology. This is why the following list of flaws is possible, especially where science is subjected to the rules of a free market place. '''[[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|The long long list of ΛCDM flaws]]''' = Observation, Reading, Reflection = In accordance with the principle of parsimony, these should be the first instincts to guide us when we look up at the sky and ask ourselves what the Universe is. But we must proceed with due respect for our own nature as human beings, confronted with the immensity of a habitat we did not choose, which brings us into existence, sustains us, and ultimately eliminates us without even noticing. In this sense, cosmology has less to do with technology than with philosophy, the mother of all sciences. When human beings, through the [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]] model, presume to decide when the Universe began and how it began, they brazenly violate the modesty and humility that should be incumbent upon them. They do so much as the authors of the biblical creation narrative did—distant predecessors whose audacity might be forgiven, but whose example is no longer intellectually acceptable in the twenty-first century. The issue here is not even to revisit the invalidity of such a conjecture, which is discussed at length in the list of flaws. Rather, it is to ask by what right the model's architects permitted themselves to make such an extraordinary claim in the first place. From that moment on, the claim becomes null and void, without further appeal. = the Universe = So, what does observation tell us when we look up at the sky? First and foremost, it tells us that the Universe exists, that it was already here before us. Our age and our experience also tell us that, as human beings, we are merely passengers, temporary workers, and mortals in waiting, and that whatever we do, the Universe will always be stronger than we are. Consequently, the only natural and parsimonious conclusion we can draw from looking at the sky is that the Universe exists, that it did not ask us to exist, and that it has never told us when it began, how it began, or why it began. From this starting point, we can say, without doubt, without prejudice, without invention, and, quite simply, without making things up, that what we see around us is the Universe; that it is the only thing that exists as far as we are concerned; that it does not know human clock-measured time; and that it is absolutely impossible for us to say anything more about it. Pure logic would therefore suggest that we consider ourselves inhabitants of a stationary Universe, one that would have absolutely no need to expand. The initial observation does not impose expansion upon us. A stationary universe therefore constitutes the most parsimonious starting point. On the one hand, this means not inventing an improbable birth date; on the other, it means not inventing an equally improbable expansive Big Bang. However, with our eyes fixed on the sky, especially at night, we see the Moon. And we are entitled to wonder why it does not fall on our heads, even before knowing about gravity or having the slightest idea of its existence. The natural reflex would therefore be to consider the concept of the Apeiron — an undefined, omnipresent substrate — or Aristotle's concept of Ether, or Faraday's idea of a "something" that might sustain celestial objects. Although these concepts are not entirely identical, they all point towards the same fundamental intuition: the possibility of a "Something" underlying the visible world. This may well be one of humanity's oldest intellectual reflexes. It comes naturally to mind whenever something appears to hang in the void, even during a Houdini performance. Something must be holding it, surely! And at this point, one might begin to think that the Universe is not what we see, but rather what we do not see: that what is visible emerges from a fertile, invisible substrate that fills the entire Universe. This would be a very concrete and believable image if all visible celestial objects appeared to be suspended in the void — suspended, yet held in the embrace of that same substrate, which prevents everything from collapsing. It is much like the air that fills the space on Earth. When the plant emerges from the ground, the air surrounds the plant, continues to envelop it, nourish it, and influence its nature. = The CMB = If we remain within this parsimonious perspective, which so far has required no invention, no additions, and no patches, it is easy to see why a sense of serenity might take hold of our minds. We have already saved ourselves quite a lot: the singularity and its strangeness, the improbable Big Bang, expansion and the many complications it brings in its wake… But be patient. We are about to do even better. Because when Penzias and Wilson discovered the cosmic microwave background radiation, nothing in that discovery compelled us to think of a fossil. The idea of a distant past was not even a necessary intellectual or cosmological option within this line of thought. Why go looking for a fossil, and where would it have come from? No, the question would not even arise. We would instead think of that substrate — the very one we had already invoked to explain why the Moon does not fall on our heads — which might now turn out to be noisy as well. Hardly a reason to spoil the party, this radiation would be the living confirmation of what humanity had intuited for 2,700 years: a "Something" that sustains "Everything." So what better response than to shout: "Bingo!" Since none of the observed properties of the [[Cosmology: UG.NUG an Observation-Based Model/the CMB|CMB]] contradicts this possibility, it would be only fair, and consistent with the principle of parsimony, to acknowledge that this interpretation is far simpler and more appealing than the intricate story of a cosmic fossil, its journey across billions of years, its puzzling temperature, and all the complications that come with it. = the Arrow of Emergence = A glass is the only thing the universe deigned to offer us before its long nap. Not the glass itself, but what it whispers when it breaks. When it slips from our hands and, by misfortune, the floor is tiled rather than carpeted, it shatters. And if we read the universe simply, we catch its message — the message of the irreversible Cosmic Order: the one that prevents the glass from reassembling, the one that prevents events from denying their own existence. Thus, the universe gives us the direction from past to future, what current physics commonly calls the Arrow of Time. It is striking: it gives us the Arrow of Time, but not time itself. The current name, Arrow of Time, is not really appropriate, since it is not “time” in the chronometric sense. It is rather, as explained earlier, a pre‑cosmic Order that governs everything, the universe included. Yes, this is an inescapable consequence of a careful reading of the universe. This succession order is of primary importance in the UG.NUG reading, but also in the ΛCDM, which — it seems — has not given it the place it deserves. In the [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]], one observes that the universe ceased its creative activity only once its work was complete. One day, it emerged from an unknown state — the term ''Big Bang'', which everyone knows, usually refers to this event — and then particles appeared, followed by atoms, stars, galaxies… Since then, nothing is created, nothing is lost, everything transforms, as Lavoisier would say. What matters here is not the validity of this narrative, but the Succession  of things: this natural succession of phases is precisely the Succession  in question. And that is why we have renamed this arrow the Arrow of Emergence. The misunderstanding dissolves, and the meaning becomes clearer: Succession  of emergences versus time‑keeping. The Arrow of Emergence therefore indisputably precedes the universe. It’s new, fresh off the shelf, ready‑to‑wear. This can mean several things: * the arrow was there, and that’s all. We accept the universe and take the arrow as a bonus, * the arrow was there, and therefore the universe is governed by something we do not know, * the arrow was there, and therefore our universe is part of a series of universes, * the arrow was there, and therefore we are free to consider any interpretation. In short, it mainly means that the Arrow of Emergence is particularly important — especially for what follows. = The GRID = Since CMB is the name given to the discovery, it seems fair to rename it according to its cosmological function. Faraday deserves his “something,” and we have chosen [[Cosmology: UG.NUG an Observation-Based Model/the GRID|GRID]], which stands for Global Reference in Dynamics. In UG.NUG, the model presented in this paper, the [[Cosmology: UG.NUG an Observation-Based Model/the GRID|GRID]] is ''le clou du spectacle'', as the French would say — the highlight of the entire show. It is the key element that dissolves most of the paradoxes of ΛCDM in such a simple way that it seems almost impossible to have overlooked it. In other words, without the GRID, UG.NUG would be no more interesting than any other model. = UG = Apart from its resemblance to the exclamation of a prehistoric man, this name carries a very important cosmological meaning. What we call geometry refers to the shape or size of an individual object, properties that matter in its interactions with reality. Geometry begins above the level of chemistry. UG stands for the French '''''Uniformité Genrée''''' (Categorical Uniformity). We coined this term to describe a phenomenon whose significance has gone unnoticed. In short, everything produced by the Universe in its earliest stages — particles, nuclei, and so on — belongs to this regime, in which objects possess no geometry. They have no individuality, no history, and no variation. This uniformity is the hidden foundation of everything: the silent order governing the birth of the Universe. For now, let us simply understand that, in this model, the world of the very small — below the atomic level — has no geometry, even though some textbooks may suggest otherwise. = NUG = NUG stands for the French '''Non-Uniformité Genrée''' (Categorical Non-Uniformity). It represents everything that possesses geometry and individuality: stars, planets, meteors, and, of course, everything that derives from them — humans, artifacts, flora, and fauna. No two pebbles are alike, nor are any two trees. Individuality increases with complexity. The transition from UG to NUG occurs through the assembly of atoms and molecules, the underlying mechanism of which remains unknown. NUG is the third and final phase in the emergence of an object. Since humans, along with their clocks and measuring instruments, belong to NUG, the time measured by our wristwatches is also a NUG phenomenon. In this model, measurable time exists only where geometry and individuality exist. = UG.NUG = UG.NUG is the name of this model. It encompasses the two regimes that govern the entire Universe. As we shall see, NUG — and therefore geometry — emerges later than UG. Once it appears, however, it becomes an integral part of the Three Point Universe, a concise schematic representation of the UG.NUG model. NUG encompasses all objects, including the Moon and the other celestial bodies mentioned earlier, which, fortunately, do not fall on our heads. == Redshift == The UG.NUG reading understands that geometry is not a starting point, but a secondary level of organization, appearing only after UG. This single shift is enough to dissolve almost all cosmological problems of the ΛCDM. Thus, the universe is not the product of a geometric explosion, but is grounded in an undifferentiated background. Geometry appears only when objects cease to be identical. This conceptual reversal eliminates in one stroke the paradoxes related to the origin of space, its shape, its homogeneity, or its flatness. One no longer tries to explain why geometry is already there. It is not an initial condition, but appears naturally, carried by the Arrow of Emergence, and stabilizes thanks to the GRID. The image of a fabric tube being inflated illustrates this perfectly. The tube already exists, but it is not yet deployed. Near the opening, the fabric is inflated; farther away, it seems to inflate progressively; in the distance, it is still flat. For an observer inside, this creates the illusion of expansion, then accelerated expansion, even though it is only the progressive realization of the structure. The distant regions appear to recede because they are not yet realized, not because they are moving. This inversion of perspective dissolves the very idea of cosmic expansion, inflation, an initial singularity, or dark energy. The spectroscopic observations and measurements themselves are not being disputed. The observed redshifts, the recorded spectra, and the data themselves remain unchanged. What UG.NUG challenges is the interpretation placed upon them: that redshift necessarily indicates recession, and that this recession necessarily means that space is expanding. The issue, therefore, is not the validity of the observations, but the assumptions through which they are interpreted. The same measurements may point to a different reading of the Universe. There is, however, a further question concerning the validity of the measurements themselves. As discussed in the paper on Cosmic Time, if the Universe has no intrinsic time, the very notion of measuring cosmic durations or assigning chronological ages to distant events becomes questionable. Such measurements rely on a chronometric framework whose applicability UG.NUG challenges. This raises a separate and much broader issue, which cannot be addressed here without taking us away from the subject of redshift. = the Genesis Phases = Now that the framework has been established, and we have seen that our universe is neither outlandish nor fundamentally different from the one we know, and that it is not threatened by our models, however incongruous they may be, we can begin to imagine what might actually have happened to produce the spectacle before our eyes. For this section, then, a little imagination is indeed required. Yet, for reasons of pure logic, the sequence you are about to discover is hardly surprising. The principle of parsimony remains our guide. Water has always flowed, and will always flow, along the paths best suited to its passage. This natural law, which is suspected to have inspired William of Ockham in formulating his principle, is far from trivial when attempting to reconstruct an event such as the emergence of the universe through a virtual model. We shall therefore continue to refrain from introducing artificial devices into the natural stages described below. = the First Phase = Strictly speaking, this is not a phase at all. It is included here to make clear that everything begins with the omnipresence of the universe. This phase never began, because it is our sole reality. Nothing else exists. This omnipresence is inferred from, and embodied in, the omnipresent GRID, which belongs to the UG regime, where objects inaccessible to our senses have no history, variation, or individuality. We do not know what it is made of. Nevertheless, it is logical to suppose that it contains the codes of the perceivable universe: the non-geometric component commonly encountered at the depths of matter and described by quantum mechanics, including elementary particles and atomic nuclei. For human beings, such a configuration borders on metaphysics. Our cognitive faculties are not designed to grasp invisible, non-geometric entities that carry information, almost like ghosts. We can invent ghosts, but we cannot manage them. According to the standard cosmological model, this radiation was released approximately 380,000 years after the Big Bang, hence its designation as fossil radiation. Such dating has no meaning within the present model, since chronometric time, as explained earlier, does not exist at the fundamental level of the universe. The quantum effervescence associated with the emergence of the GRID is held together by a fundamental UG energy: a pre-geometric substrate that makes emergence possible. This energy may correspond to the unique energy of the BBP, subsequently differentiated into the electromagnetic, weak, and strong interactions, the latter ensuring nuclear cohesion. These interactions then mysteriously disappear from the broader cosmological narrative. The persistence of the GRID explains its presence in every atom. Whatever an atom may eventually become, it retains this universal imprint. When an atom is destroyed, its particles are not necessarily destroyed with it: they return silently to the undifferentiated reservoir of the GRID. Quantum particles cannot be manipulated directly in their fundamental nature; they emanate from the original GRID. This is a personal assertion, but not an entirely baseless one. As explained in The Fear of the Unexplainable, the dominant mindset refuses to accept that the unexplainable might be fundamental. Everything must be physical — except when it is convenient to invoke something more elusive, as when fundamental energy is called upon to explain atomic cohesion. This double standard exposes what should be regarded as a lack of logic in the BBP. This is why CERN is unlikely ever to obtain the results it expects. These particles will never reveal what they truly are. Attempting to reach the UG side of the universe using NUG instruments is like asking a newborn to intervene in the device that brought it into existence. The limitations become apparent immediately. The atomic bomb has already shown, with tragic consequences, what can happen when humanity interferes too directly with the elements of the GRID. Einstein was right to reject the idea that “God plays dice.” His “God” — nature, the universe itself — is present in every object. He did not believe that quantum mechanics had appeared in matter by chance. Yet this is precisely how Bohr and Heisenberg interpreted it: they treated quantum mechanics as a contingent curiosity rather than as the signature of something still unknown. = the Second Phase = Once the presence of the underlying “carpet” containing the codes has been established, it becomes plausible that primary objects — atoms and simple molecules — begin to form. These are the first objects to possess geometry, yet all objects of a given kind remain identical to one another. Any attempt to determine the precise beginning and end of this phase through elaborate calculations would be highly speculative. The immaterial effervescence persists, but it is now accompanied by objects that require time to assemble. In parallel, the fundamental energy of the GRID becomes involved in maintaining the cohesion of these new atomic structures. This cohesive role requires it to manifest properties that were previously unnecessary: the strong interaction, which binds the constituents of atomic nuclei together; the weak interaction, whose role is more secondary in this context; and the electromagnetic interaction, which governs exchanges between charged particles. One energy, then, with multiple manifestations — always present, always active. In this model, it replaces the various concepts invoked by the BBP to describe primordial energy and its effects: vacuum energy, dark energy, the cosmological constant, and quantum fluctuations. These become different labels for what the model interprets as a single primordial presence. At this level, deduction is more reliable than equations. When atomic nuclei absorb part of the primordial energy and convert it into binding energy or other forms of energy associated with their structure, they clearly do not absorb the entire substrate that sustains them. Like leaves floating on a pond, organised structures can appear without eliminating the medium in which they exist. The primordial energy continues to sustain the whole, even when part of its flow is redirected towards cohesion. Atoms are assemblies of ghosts, and all atoms of a given kind appear identical. What lies at their heart is non-geometric and cannot be observed directly. Applied physics detects only measurable effects — energies, transitions, and interactions — never the intrinsic nature of the particles themselves. Conversely, the BBP assigns geometric labels to entities that are inferred from non-geometric experimental results: spin, charge, isospin, quantum numbers, and so on. Collisions produce deposited energies, momenta, angles, jets, resonances, and statistical peaks. From these data, the BBP constructs its picture of elementary particles. This conceptual shift is rarely acknowledged. Despite the absence of directly geometric data at the fundamental level, the BBP continues to construct its own universe in order to preserve what may be regarded as a sterile mathematical edifice. The second phase is the bridge between the inaccessible and the modifiable, between UG and NUG, between the GRID and geometry. = the Third Phase = All remaining objects — stars, planets, galaxies, and everything that derives from them — emerge according to their order of formation, depending on the availability and completeness of the preceding stages for each object individually. This is where uniformity ends and individuality begins. No precise dating is possible within the present model. This phase represents the culmination of the process: the world that emerges from UG, the world we see, touch, hear, smell, and taste. Once UG has reached maturity, complex forms, interactions, and histories become possible. The universe enters the NUG regime. NUG encompasses: * Stars * Planets * Chemistry * Biology * Perception Everything we experience is the final geometry of a pre-geometric reality. Pre-geometric also means pre-volumetric. The GRID — UG — is both pre-geometric and pre-volumetric. Geometry begins above the atomic level, and individuality emerges with complexity. The GRID has no visible form. It manifests itself through the infinitesimal temperature variations observed in the CMB in every direction, through gravity on Earth, and through magnetic fields. It is an invisible presence that precedes the emergence of volumetric structures. In this model, geometry and volume emerge from UG without requiring expansion, unlike the BBP, which postulates an initial singularity followed by the expansion of the metric. Our interpretation is straightforward: * '''No singularity:''' the universe is already extended in the form of the GRID. * '''No infinities:''' emergence follows an ordered sequence, from Phase 1 through Phase 2 to Phase 3. * '''No paradox:''' geometry, or NUG, emerges from UG without requiring expansion. The GRID never disappears. It permeates every atom in every object. It is present throughout our world in the form of quantum mechanics, whose rules, according to this model, differ radically from those commonly accepted. Using a scanning tunnelling microscope (STM), it is possible to distinguish individual atoms and observe their arrangement. Don Eigler demonstrated this in 1989 by positioning xenon atoms on a nickel surface to spell out the letters IBM. Beyond the atomic scale, the gap in scale becomes immense. Atoms are approximately a nanometre across, whereas the characteristic scale of their constituent particles is around a femtometre — roughly one millionth of a nanometre. No elementary particle has been observed directly in the sense of being imaged as a tiny object with a visible surface. Instead, experiments detect traces and measurable effects from which the properties of particles are inferred. The process is therefore highly indirect. Every fragment of matter carries within it an irreducible part of the universe's deepest mystery, together with the codes from which geometry emerges. = Conceptual Consequences = The problems of the ΛCDM are not independent: they naturally group into three families, all stemming from the same implicit assumption — that the universe is fundamentally geometric. By changing this starting point, these difficulties cease to be enigmas. They become the expected consequences of an inadequate reading. The three blocks that follow present these families of problems and show how UG.NUG reading dissolves them without additions, without corrections, simply by restoring the natural Succession of emergence. == for Cosmology == Dark matter — Dark energy — Cosmological constant — Horizon — Flatness — Homogeneity — Origin of geometry — Big Bang — Expansion — Large‑scale structure The UG.NUG reading understands that geometry is not a starting point, but a secondary level of organization, appearing only after UG. This single shift is enough to dissolve almost all cosmological problems of the ΛCDM. Thus, the universe does not begin with a geometric explosion, but with an undifferentiated background. Geometry appears only when objects cease to be identical. This conceptual reversal eliminates in one stroke the paradoxes related to the origin of space, its shape, its homogeneity, or its flatness. One no longer tries to explain why geometry is already there. It is not there at the beginning. It appears naturally, carried by the Arrow of Emergence, and stabilizes thanks to the GRID. The image of a fabric tube being inflated illustrates this perfectly. The tube already exists, but it is not yet deployed. Near the opening, the fabric is inflated; farther away, it seems to inflate progressively; in the distance, it is still flat. For an observer inside, this creates the illusion of expansion, then accelerated expansion, even though it is only the progressive realization of the structure. The distant regions appear to recede because they are not yet realized, not because they are moving. This inversion of perspective dissolves the very idea of cosmic expansion, inflation, an initial singularity, or dark energy. In this reading, the great cosmological enigmas cease to be anomalies. * Dark matter is no longer an invisible substance added to fix equations, but the consequence of applying a geometric interpretation to a phenomenon that is not geometric. * Dark energy is no longer a mysterious force pushing the universe to expand, but the effect of a secondary geometry misread as dynamic when it is simply structural. * The horizon problem disappears because homogeneity does not need to be transmitted: it is inherited from UG, where everything is identical. * The flatness problem vanishes because geometry is not a fragile structure requiring fine‑tuning, but a stable organization imposed by the GRID. In the UG.NUG reading, geometry is not fundamental but secondary, emergent. By changing the starting point, one does not correct anomalies: one dissolves them. The universe was never incoherent. The interpretation was. == for Quantum Physics   == Measurement - Decoherence - Superposition - Classicality - Quantum gravity - Particle identity - Non‑locality - Hidden variables - Wave‑particle duality - Indeterminacy - Absence of trajectory Quantum physics accumulates paradoxes because it tries to describe a non‑geometric regime using geometric tools. It applies notions of shape, position, trajectory, or mass to objects that possess none of these. In UG.NUG reading, first‑wave particles belong to the UG regime: they are inaccessible, undifferentiated, without form, without variation, without geometry. They are not tiny objects but non‑identifiable pre‑geometric entities.   In this reading, the measurement problem disappears. * There is no wave‑packet collapse, only the transition from a UG state to a NUG interaction — that is, the appearance of a geometric imprint. * Decoherence is no longer a mysterious mechanism, but is simply the incompatibility between a non‑geometric state and a geometric environment. * Superposition is not a magical phenomenon, but the natural behavior of objects that have neither shape nor position. * Classicality needs no explanation: it appears as soon as objects acquire geometry — that is, in the second phase, the primordial one. * Quantum gravity ceases to be a meaningful objective, because there is nothing to quantize. * Gravity is not a fundamental force but the static reaction of the GRID, a purely geometric phenomenon. * Non‑locality is no longer a mystery: in a non‑geometric regime, the notion of distance has no meaning. * Hidden variables have no place: there is nothing to hide in a regime without internal structure. Thus, all quantum paradoxes arise from a single mistake: trying to apply NUG tools to UG. The paradoxes vanish as soon as we stop demanding that UG behave like a geometric world. Quantum mechanics is the universe’s signature within every atom of matter, and the keeper of the code for the geometry of the emergent, perceivable forms that make up our world. That said, where we hope this reading of the universe can serve as a model is in a radical shift in how we treat the information obtained through the manipulation and analysis of particles. In fact, the investigations concerning them can be counted on the fingers of one hand: <nowiki>:</nowiki> * energy levels through spectrometry, * transition probabilities in lasers, * electronic structures via STM, * conduction bands in solid‑state physics, * bound states in quantum chemistry. Yet these data, as precise and rich as they are, are systematically and arbitrarily transformed into geometric forms: orbitals, positions, bands, crystal lattices… as if nature suddenly became classical the moment we look at it. But none of this has ever been observed. The size of particles, their wave‑particle duality, and above all the very principle of quantum mechanics — where everything is probabilities, superpositions, and wave functions — should forbid this geometric illusion. Why, then, this persistent habit of hiding raw data beneath familiar but false representations? Why prefer reassuring visual models over a clear presentation of investigative methods and probabilistic results? Quantum mechanics has taught us that reality is not a neat drawing of well‑traced orbits, but a cloud of probabilities in constant evolution. Yet we continue to teach, publish, and design technologies based on geometric diagrams that are nothing more than convenient metaphors — or even lies by omission. The problem is not only scientific; it is epistemological. By over‑geometrizing, we reduce quantum complexity to a classical caricature and deprive researchers — and the public — of an honest understanding of what particles and their interactions truly are. Atomic orbitals are not physical objects occupying geometrically defined regions of space. They are mathematical representations of quantum states. So why not fully embrace quantum strangeness? Why not present the data as they are: probability distributions, complex amplitudes, entangled states? Science has a duty to tell the truth, even when it is unsettling. And the truth, here, is that the quantum world has nothing geometric about it — at least not in the classical sense we impose on it. Perhaps it is time to break with this tradition and finally show the real face of matter: not a collection of localized objects, but a network of possibilities in perpetual fluctuation, where geometry is only a shadow cast by our human limitations. It is not impossible that this obsession with geometrization — this desperate need to draw orbitals, bands, or lattices where only blurry probabilities exist — is directly linked to the phobia described in the paper The Fear of the Unexplainable. For reducing the quantum to reassuring shapes is a way to flee the fundamental absurdity of a universe where particles have neither trajectory nor defined position. It is a denial of strangeness, a clinging to the illusion of a classical, manageable, predictable world. Geometry is the refuge of physicists frightened by the metaphysical void. == for Forces and Interactions   == Gravity — Unification — Renormalization — Fundamental constants — Mass In the ΛCDM, forces are treated as fundamental entities, each with its own carrier, field, constants, and symmetries. This assumption generates most of the conceptual difficulties. In the UG.NUG reading, this framework collapses: what the ΛCDM interprets as “forces” are not fundamental ingredients of the universe but the observable behaviors that appear when objects exist or move within the GRID. * Gravity is not an interaction. It has no carrier, no quantum, no fundamental field. It is simply the static behavior of the GRID in the presence of a geometric object. The problem of quantum gravity disappears — not because it is solved, but because it never existed: gravity was never a quantum phenomenon to begin with. * Magnetic effects are the dynamic version of the same behavior when the object moves or rotates. * Renormalization also ceases to be a difficulty: there is nothing to renormalize once these behaviors are no longer treated as fundamental forces. * Mass is not a property of the universe. It is only the human interpretation of certain geometric behaviors that remain fully calculable, even though the quantity itself does not exist. Thus, the conceptual problems associated with forces and interactions in the ΛCDM arise from a single mistake: treating contextual behaviors as fundamental forces. m316u0txzco4dw4vk42bpqfgwnyw5se 2844855 2844854 2026-11-08T07:03:58Z Wb525 3112992 /* the Arrow of Emergence */ 2844855 wikitext text/x-wiki {{Research project}} Original research project by Willy Bohane — UG.NUG. https://doi.org/10.5281/zenodo.20644064 == All the texts in this presentation == [[Cosmology: UG.NUG an Observation-Based Model|UG.NUG]] [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]] [[Cosmology: UG.NUG an Observation-Based Model/Cosmic Time|Cosmic Time]] [[Cosmology: UG.NUG an Observation-Based Model/the Mass Imbroglio|the Mass Imbroglio]] [[Cosmology: UG.NUG an Observation-Based Model/the CMB|of the CMB]] [[Cosmology: UG.NUG an Observation-Based Model/the GRID|of the GRID]] [[Cosmology: UG.NUG an Observation-Based Model/Gravity|of Gravity]] [[Cosmology: UG.NUG an Observation-Based Model/Black Holes|of Black Holes]] = Introduction = This article presents a reading of the Universe that differs in every respect from the existing model. The latter contains a false start which, for reasons explained in the dedicated article on [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]], renders it null and void from the very first millisecond of its narrative: the Singularity. Before reading this detailed text, whose links to technical articles support and further develop the arguments presented, readers can consult a simplified [https://www.wbohane.com/BLOG/!three_point_universe.aspx three-point diagram] offering an overview of the proposed simplicity of the Universe. = State of Play = First, it is important to understand that cosmology, in its interpretative function, is not an exact science. As its name indicates, it means, in Greek, ''the study of the world'' — and therefore, by extension, its origin, its structure, its evolution, its content, and its future. We also have a duty never to forget that cosmology was born as a branch of metaphysics. This should remind us that mathematics must remain a means of understanding the Universe, not a substitute for it. Rather than building elaborate theoretical structures and continually adjusting them to accommodate observations, it would be far more sensible to seek a description that reflects the universe as it actually is. The purpose of cosmology should not be to make reality fit our mathematics, but to make our mathematics serve reality. This is why interpretative cosmology resembles a religion more than it does a science. As with religion, everybody can say anything, everybody can believe anything, everybody can make anyone believe anything. Humanity is divided into many creeds, and so is cosmology. This is why the following list of flaws is possible, especially where science is subjected to the rules of a free market place. '''[[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|The long long list of ΛCDM flaws]]''' = Observation, Reading, Reflection = In accordance with the principle of parsimony, these should be the first instincts to guide us when we look up at the sky and ask ourselves what the Universe is. But we must proceed with due respect for our own nature as human beings, confronted with the immensity of a habitat we did not choose, which brings us into existence, sustains us, and ultimately eliminates us without even noticing. In this sense, cosmology has less to do with technology than with philosophy, the mother of all sciences. When human beings, through the [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]] model, presume to decide when the Universe began and how it began, they brazenly violate the modesty and humility that should be incumbent upon them. They do so much as the authors of the biblical creation narrative did—distant predecessors whose audacity might be forgiven, but whose example is no longer intellectually acceptable in the twenty-first century. The issue here is not even to revisit the invalidity of such a conjecture, which is discussed at length in the list of flaws. Rather, it is to ask by what right the model's architects permitted themselves to make such an extraordinary claim in the first place. From that moment on, the claim becomes null and void, without further appeal. = the Universe = So, what does observation tell us when we look up at the sky? First and foremost, it tells us that the Universe exists, that it was already here before us. Our age and our experience also tell us that, as human beings, we are merely passengers, temporary workers, and mortals in waiting, and that whatever we do, the Universe will always be stronger than we are. Consequently, the only natural and parsimonious conclusion we can draw from looking at the sky is that the Universe exists, that it did not ask us to exist, and that it has never told us when it began, how it began, or why it began. From this starting point, we can say, without doubt, without prejudice, without invention, and, quite simply, without making things up, that what we see around us is the Universe; that it is the only thing that exists as far as we are concerned; that it does not know human clock-measured time; and that it is absolutely impossible for us to say anything more about it. Pure logic would therefore suggest that we consider ourselves inhabitants of a stationary Universe, one that would have absolutely no need to expand. The initial observation does not impose expansion upon us. A stationary universe therefore constitutes the most parsimonious starting point. On the one hand, this means not inventing an improbable birth date; on the other, it means not inventing an equally improbable expansive Big Bang. However, with our eyes fixed on the sky, especially at night, we see the Moon. And we are entitled to wonder why it does not fall on our heads, even before knowing about gravity or having the slightest idea of its existence. The natural reflex would therefore be to consider the concept of the Apeiron — an undefined, omnipresent substrate — or Aristotle's concept of Ether, or Faraday's idea of a "something" that might sustain celestial objects. Although these concepts are not entirely identical, they all point towards the same fundamental intuition: the possibility of a "Something" underlying the visible world. This may well be one of humanity's oldest intellectual reflexes. It comes naturally to mind whenever something appears to hang in the void, even during a Houdini performance. Something must be holding it, surely! And at this point, one might begin to think that the Universe is not what we see, but rather what we do not see: that what is visible emerges from a fertile, invisible substrate that fills the entire Universe. This would be a very concrete and believable image if all visible celestial objects appeared to be suspended in the void — suspended, yet held in the embrace of that same substrate, which prevents everything from collapsing. It is much like the air that fills the space on Earth. When the plant emerges from the ground, the air surrounds the plant, continues to envelop it, nourish it, and influence its nature. = The CMB = If we remain within this parsimonious perspective, which so far has required no invention, no additions, and no patches, it is easy to see why a sense of serenity might take hold of our minds. We have already saved ourselves quite a lot: the singularity and its strangeness, the improbable Big Bang, expansion and the many complications it brings in its wake… But be patient. We are about to do even better. Because when Penzias and Wilson discovered the cosmic microwave background radiation, nothing in that discovery compelled us to think of a fossil. The idea of a distant past was not even a necessary intellectual or cosmological option within this line of thought. Why go looking for a fossil, and where would it have come from? No, the question would not even arise. We would instead think of that substrate — the very one we had already invoked to explain why the Moon does not fall on our heads — which might now turn out to be noisy as well. Hardly a reason to spoil the party, this radiation would be the living confirmation of what humanity had intuited for 2,700 years: a "Something" that sustains "Everything." So what better response than to shout: "Bingo!" Since none of the observed properties of the [[Cosmology: UG.NUG an Observation-Based Model/the CMB|CMB]] contradicts this possibility, it would be only fair, and consistent with the principle of parsimony, to acknowledge that this interpretation is far simpler and more appealing than the intricate story of a cosmic fossil, its journey across billions of years, its puzzling temperature, and all the complications that come with it. = the Arrow of Emergence = The glass' message is one of the very few hints the universe deigned to offer us before its long nap. What it whispers if it slips from our hands and, by misfortune, the floor is tiled rather than carpeted: it shatters. And if we read the universe simply, we catch this message that expresses the irreversible Cosmic Order: the one that prevents the glass from reassembling, the one that prevents events from denying their own existence. Thus, the universe gives us the direction from past to future, what current physics commonly calls the Arrow of Time. It is striking: it gives us the Arrow of Time, but not time itself. The current name, Arrow of Time, is not really appropriate, since it is not “time” in the chronometric sense. It is rather, as explained earlier, a pre‑cosmic Order that governs everything, the universe included. Yes, this is an inescapable consequence of a careful reading of the universe. This succession order is of primary importance in the UG.NUG reading, but also in the ΛCDM, which — it seems — has not given it the place it deserves. In the [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]], one observes that the universe ceased its creative activity only once its work was complete. One day, it emerged from an unknown state — the term ''Big Bang'', which everyone knows, usually refers to this event — and then particles appeared, followed by atoms, stars, galaxies… Since then, nothing is created, nothing is lost, everything transforms, as Lavoisier would say. What matters here is not the validity of this narrative, but the Succession  of things: this natural succession of phases is precisely the Succession  in question. And that is why we have renamed this arrow the Arrow of Emergence. The misunderstanding dissolves, and the meaning becomes clearer: Succession  of emergences versus time‑keeping. The Arrow of Emergence therefore indisputably precedes the universe. It’s new, fresh off the shelf, ready‑to‑wear. This can mean several things: * the arrow was there, and that’s all. We accept the universe and take the arrow as a bonus, * the arrow was there, and therefore the universe is governed by something we do not know, * the arrow was there, and therefore our universe is part of a series of universes, * the arrow was there, and therefore we are free to consider any interpretation. In short, it mainly means that the Arrow of Emergence is particularly important — especially for what follows. = The GRID = Since CMB is the name given to the discovery, it seems fair to rename it according to its cosmological function. Faraday deserves his “something,” and we have chosen [[Cosmology: UG.NUG an Observation-Based Model/the GRID|GRID]], which stands for Global Reference in Dynamics. In UG.NUG, the model presented in this paper, the [[Cosmology: UG.NUG an Observation-Based Model/the GRID|GRID]] is ''le clou du spectacle'', as the French would say — the highlight of the entire show. It is the key element that dissolves most of the paradoxes of ΛCDM in such a simple way that it seems almost impossible to have overlooked it. In other words, without the GRID, UG.NUG would be no more interesting than any other model. = UG = Apart from its resemblance to the exclamation of a prehistoric man, this name carries a very important cosmological meaning. What we call geometry refers to the shape or size of an individual object, properties that matter in its interactions with reality. Geometry begins above the level of chemistry. UG stands for the French '''''Uniformité Genrée''''' (Categorical Uniformity). We coined this term to describe a phenomenon whose significance has gone unnoticed. In short, everything produced by the Universe in its earliest stages — particles, nuclei, and so on — belongs to this regime, in which objects possess no geometry. They have no individuality, no history, and no variation. This uniformity is the hidden foundation of everything: the silent order governing the birth of the Universe. For now, let us simply understand that, in this model, the world of the very small — below the atomic level — has no geometry, even though some textbooks may suggest otherwise. = NUG = NUG stands for the French '''Non-Uniformité Genrée''' (Categorical Non-Uniformity). It represents everything that possesses geometry and individuality: stars, planets, meteors, and, of course, everything that derives from them — humans, artifacts, flora, and fauna. No two pebbles are alike, nor are any two trees. Individuality increases with complexity. The transition from UG to NUG occurs through the assembly of atoms and molecules, the underlying mechanism of which remains unknown. NUG is the third and final phase in the emergence of an object. Since humans, along with their clocks and measuring instruments, belong to NUG, the time measured by our wristwatches is also a NUG phenomenon. In this model, measurable time exists only where geometry and individuality exist. = UG.NUG = UG.NUG is the name of this model. It encompasses the two regimes that govern the entire Universe. As we shall see, NUG — and therefore geometry — emerges later than UG. Once it appears, however, it becomes an integral part of the Three Point Universe, a concise schematic representation of the UG.NUG model. NUG encompasses all objects, including the Moon and the other celestial bodies mentioned earlier, which, fortunately, do not fall on our heads. == Redshift == The UG.NUG reading understands that geometry is not a starting point, but a secondary level of organization, appearing only after UG. This single shift is enough to dissolve almost all cosmological problems of the ΛCDM. Thus, the universe is not the product of a geometric explosion, but is grounded in an undifferentiated background. Geometry appears only when objects cease to be identical. This conceptual reversal eliminates in one stroke the paradoxes related to the origin of space, its shape, its homogeneity, or its flatness. One no longer tries to explain why geometry is already there. It is not an initial condition, but appears naturally, carried by the Arrow of Emergence, and stabilizes thanks to the GRID. The image of a fabric tube being inflated illustrates this perfectly. The tube already exists, but it is not yet deployed. Near the opening, the fabric is inflated; farther away, it seems to inflate progressively; in the distance, it is still flat. For an observer inside, this creates the illusion of expansion, then accelerated expansion, even though it is only the progressive realization of the structure. The distant regions appear to recede because they are not yet realized, not because they are moving. This inversion of perspective dissolves the very idea of cosmic expansion, inflation, an initial singularity, or dark energy. The spectroscopic observations and measurements themselves are not being disputed. The observed redshifts, the recorded spectra, and the data themselves remain unchanged. What UG.NUG challenges is the interpretation placed upon them: that redshift necessarily indicates recession, and that this recession necessarily means that space is expanding. The issue, therefore, is not the validity of the observations, but the assumptions through which they are interpreted. The same measurements may point to a different reading of the Universe. There is, however, a further question concerning the validity of the measurements themselves. As discussed in the paper on Cosmic Time, if the Universe has no intrinsic time, the very notion of measuring cosmic durations or assigning chronological ages to distant events becomes questionable. Such measurements rely on a chronometric framework whose applicability UG.NUG challenges. This raises a separate and much broader issue, which cannot be addressed here without taking us away from the subject of redshift. = the Genesis Phases = Now that the framework has been established, and we have seen that our universe is neither outlandish nor fundamentally different from the one we know, and that it is not threatened by our models, however incongruous they may be, we can begin to imagine what might actually have happened to produce the spectacle before our eyes. For this section, then, a little imagination is indeed required. Yet, for reasons of pure logic, the sequence you are about to discover is hardly surprising. The principle of parsimony remains our guide. Water has always flowed, and will always flow, along the paths best suited to its passage. This natural law, which is suspected to have inspired William of Ockham in formulating his principle, is far from trivial when attempting to reconstruct an event such as the emergence of the universe through a virtual model. We shall therefore continue to refrain from introducing artificial devices into the natural stages described below. = the First Phase = Strictly speaking, this is not a phase at all. It is included here to make clear that everything begins with the omnipresence of the universe. This phase never began, because it is our sole reality. Nothing else exists. This omnipresence is inferred from, and embodied in, the omnipresent GRID, which belongs to the UG regime, where objects inaccessible to our senses have no history, variation, or individuality. We do not know what it is made of. Nevertheless, it is logical to suppose that it contains the codes of the perceivable universe: the non-geometric component commonly encountered at the depths of matter and described by quantum mechanics, including elementary particles and atomic nuclei. For human beings, such a configuration borders on metaphysics. Our cognitive faculties are not designed to grasp invisible, non-geometric entities that carry information, almost like ghosts. We can invent ghosts, but we cannot manage them. According to the standard cosmological model, this radiation was released approximately 380,000 years after the Big Bang, hence its designation as fossil radiation. Such dating has no meaning within the present model, since chronometric time, as explained earlier, does not exist at the fundamental level of the universe. The quantum effervescence associated with the emergence of the GRID is held together by a fundamental UG energy: a pre-geometric substrate that makes emergence possible. This energy may correspond to the unique energy of the BBP, subsequently differentiated into the electromagnetic, weak, and strong interactions, the latter ensuring nuclear cohesion. These interactions then mysteriously disappear from the broader cosmological narrative. The persistence of the GRID explains its presence in every atom. Whatever an atom may eventually become, it retains this universal imprint. When an atom is destroyed, its particles are not necessarily destroyed with it: they return silently to the undifferentiated reservoir of the GRID. Quantum particles cannot be manipulated directly in their fundamental nature; they emanate from the original GRID. This is a personal assertion, but not an entirely baseless one. As explained in The Fear of the Unexplainable, the dominant mindset refuses to accept that the unexplainable might be fundamental. Everything must be physical — except when it is convenient to invoke something more elusive, as when fundamental energy is called upon to explain atomic cohesion. This double standard exposes what should be regarded as a lack of logic in the BBP. This is why CERN is unlikely ever to obtain the results it expects. These particles will never reveal what they truly are. Attempting to reach the UG side of the universe using NUG instruments is like asking a newborn to intervene in the device that brought it into existence. The limitations become apparent immediately. The atomic bomb has already shown, with tragic consequences, what can happen when humanity interferes too directly with the elements of the GRID. Einstein was right to reject the idea that “God plays dice.” His “God” — nature, the universe itself — is present in every object. He did not believe that quantum mechanics had appeared in matter by chance. Yet this is precisely how Bohr and Heisenberg interpreted it: they treated quantum mechanics as a contingent curiosity rather than as the signature of something still unknown. = the Second Phase = Once the presence of the underlying “carpet” containing the codes has been established, it becomes plausible that primary objects — atoms and simple molecules — begin to form. These are the first objects to possess geometry, yet all objects of a given kind remain identical to one another. Any attempt to determine the precise beginning and end of this phase through elaborate calculations would be highly speculative. The immaterial effervescence persists, but it is now accompanied by objects that require time to assemble. In parallel, the fundamental energy of the GRID becomes involved in maintaining the cohesion of these new atomic structures. This cohesive role requires it to manifest properties that were previously unnecessary: the strong interaction, which binds the constituents of atomic nuclei together; the weak interaction, whose role is more secondary in this context; and the electromagnetic interaction, which governs exchanges between charged particles. One energy, then, with multiple manifestations — always present, always active. In this model, it replaces the various concepts invoked by the BBP to describe primordial energy and its effects: vacuum energy, dark energy, the cosmological constant, and quantum fluctuations. These become different labels for what the model interprets as a single primordial presence. At this level, deduction is more reliable than equations. When atomic nuclei absorb part of the primordial energy and convert it into binding energy or other forms of energy associated with their structure, they clearly do not absorb the entire substrate that sustains them. Like leaves floating on a pond, organised structures can appear without eliminating the medium in which they exist. The primordial energy continues to sustain the whole, even when part of its flow is redirected towards cohesion. Atoms are assemblies of ghosts, and all atoms of a given kind appear identical. What lies at their heart is non-geometric and cannot be observed directly. Applied physics detects only measurable effects — energies, transitions, and interactions — never the intrinsic nature of the particles themselves. Conversely, the BBP assigns geometric labels to entities that are inferred from non-geometric experimental results: spin, charge, isospin, quantum numbers, and so on. Collisions produce deposited energies, momenta, angles, jets, resonances, and statistical peaks. From these data, the BBP constructs its picture of elementary particles. This conceptual shift is rarely acknowledged. Despite the absence of directly geometric data at the fundamental level, the BBP continues to construct its own universe in order to preserve what may be regarded as a sterile mathematical edifice. The second phase is the bridge between the inaccessible and the modifiable, between UG and NUG, between the GRID and geometry. = the Third Phase = All remaining objects — stars, planets, galaxies, and everything that derives from them — emerge according to their order of formation, depending on the availability and completeness of the preceding stages for each object individually. This is where uniformity ends and individuality begins. No precise dating is possible within the present model. This phase represents the culmination of the process: the world that emerges from UG, the world we see, touch, hear, smell, and taste. Once UG has reached maturity, complex forms, interactions, and histories become possible. The universe enters the NUG regime. NUG encompasses: * Stars * Planets * Chemistry * Biology * Perception Everything we experience is the final geometry of a pre-geometric reality. Pre-geometric also means pre-volumetric. The GRID — UG — is both pre-geometric and pre-volumetric. Geometry begins above the atomic level, and individuality emerges with complexity. The GRID has no visible form. It manifests itself through the infinitesimal temperature variations observed in the CMB in every direction, through gravity on Earth, and through magnetic fields. It is an invisible presence that precedes the emergence of volumetric structures. In this model, geometry and volume emerge from UG without requiring expansion, unlike the BBP, which postulates an initial singularity followed by the expansion of the metric. Our interpretation is straightforward: * '''No singularity:''' the universe is already extended in the form of the GRID. * '''No infinities:''' emergence follows an ordered sequence, from Phase 1 through Phase 2 to Phase 3. * '''No paradox:''' geometry, or NUG, emerges from UG without requiring expansion. The GRID never disappears. It permeates every atom in every object. It is present throughout our world in the form of quantum mechanics, whose rules, according to this model, differ radically from those commonly accepted. Using a scanning tunnelling microscope (STM), it is possible to distinguish individual atoms and observe their arrangement. Don Eigler demonstrated this in 1989 by positioning xenon atoms on a nickel surface to spell out the letters IBM. Beyond the atomic scale, the gap in scale becomes immense. Atoms are approximately a nanometre across, whereas the characteristic scale of their constituent particles is around a femtometre — roughly one millionth of a nanometre. No elementary particle has been observed directly in the sense of being imaged as a tiny object with a visible surface. Instead, experiments detect traces and measurable effects from which the properties of particles are inferred. The process is therefore highly indirect. Every fragment of matter carries within it an irreducible part of the universe's deepest mystery, together with the codes from which geometry emerges. = Conceptual Consequences = The problems of the ΛCDM are not independent: they naturally group into three families, all stemming from the same implicit assumption — that the universe is fundamentally geometric. By changing this starting point, these difficulties cease to be enigmas. They become the expected consequences of an inadequate reading. The three blocks that follow present these families of problems and show how UG.NUG reading dissolves them without additions, without corrections, simply by restoring the natural Succession of emergence. == for Cosmology == Dark matter — Dark energy — Cosmological constant — Horizon — Flatness — Homogeneity — Origin of geometry — Big Bang — Expansion — Large‑scale structure The UG.NUG reading understands that geometry is not a starting point, but a secondary level of organization, appearing only after UG. This single shift is enough to dissolve almost all cosmological problems of the ΛCDM. Thus, the universe does not begin with a geometric explosion, but with an undifferentiated background. Geometry appears only when objects cease to be identical. This conceptual reversal eliminates in one stroke the paradoxes related to the origin of space, its shape, its homogeneity, or its flatness. One no longer tries to explain why geometry is already there. It is not there at the beginning. It appears naturally, carried by the Arrow of Emergence, and stabilizes thanks to the GRID. The image of a fabric tube being inflated illustrates this perfectly. The tube already exists, but it is not yet deployed. Near the opening, the fabric is inflated; farther away, it seems to inflate progressively; in the distance, it is still flat. For an observer inside, this creates the illusion of expansion, then accelerated expansion, even though it is only the progressive realization of the structure. The distant regions appear to recede because they are not yet realized, not because they are moving. This inversion of perspective dissolves the very idea of cosmic expansion, inflation, an initial singularity, or dark energy. In this reading, the great cosmological enigmas cease to be anomalies. * Dark matter is no longer an invisible substance added to fix equations, but the consequence of applying a geometric interpretation to a phenomenon that is not geometric. * Dark energy is no longer a mysterious force pushing the universe to expand, but the effect of a secondary geometry misread as dynamic when it is simply structural. * The horizon problem disappears because homogeneity does not need to be transmitted: it is inherited from UG, where everything is identical. * The flatness problem vanishes because geometry is not a fragile structure requiring fine‑tuning, but a stable organization imposed by the GRID. In the UG.NUG reading, geometry is not fundamental but secondary, emergent. By changing the starting point, one does not correct anomalies: one dissolves them. The universe was never incoherent. The interpretation was. == for Quantum Physics   == Measurement - Decoherence - Superposition - Classicality - Quantum gravity - Particle identity - Non‑locality - Hidden variables - Wave‑particle duality - Indeterminacy - Absence of trajectory Quantum physics accumulates paradoxes because it tries to describe a non‑geometric regime using geometric tools. It applies notions of shape, position, trajectory, or mass to objects that possess none of these. In UG.NUG reading, first‑wave particles belong to the UG regime: they are inaccessible, undifferentiated, without form, without variation, without geometry. They are not tiny objects but non‑identifiable pre‑geometric entities.   In this reading, the measurement problem disappears. * There is no wave‑packet collapse, only the transition from a UG state to a NUG interaction — that is, the appearance of a geometric imprint. * Decoherence is no longer a mysterious mechanism, but is simply the incompatibility between a non‑geometric state and a geometric environment. * Superposition is not a magical phenomenon, but the natural behavior of objects that have neither shape nor position. * Classicality needs no explanation: it appears as soon as objects acquire geometry — that is, in the second phase, the primordial one. * Quantum gravity ceases to be a meaningful objective, because there is nothing to quantize. * Gravity is not a fundamental force but the static reaction of the GRID, a purely geometric phenomenon. * Non‑locality is no longer a mystery: in a non‑geometric regime, the notion of distance has no meaning. * Hidden variables have no place: there is nothing to hide in a regime without internal structure. Thus, all quantum paradoxes arise from a single mistake: trying to apply NUG tools to UG. The paradoxes vanish as soon as we stop demanding that UG behave like a geometric world. Quantum mechanics is the universe’s signature within every atom of matter, and the keeper of the code for the geometry of the emergent, perceivable forms that make up our world. That said, where we hope this reading of the universe can serve as a model is in a radical shift in how we treat the information obtained through the manipulation and analysis of particles. In fact, the investigations concerning them can be counted on the fingers of one hand: <nowiki>:</nowiki> * energy levels through spectrometry, * transition probabilities in lasers, * electronic structures via STM, * conduction bands in solid‑state physics, * bound states in quantum chemistry. Yet these data, as precise and rich as they are, are systematically and arbitrarily transformed into geometric forms: orbitals, positions, bands, crystal lattices… as if nature suddenly became classical the moment we look at it. But none of this has ever been observed. The size of particles, their wave‑particle duality, and above all the very principle of quantum mechanics — where everything is probabilities, superpositions, and wave functions — should forbid this geometric illusion. Why, then, this persistent habit of hiding raw data beneath familiar but false representations? Why prefer reassuring visual models over a clear presentation of investigative methods and probabilistic results? Quantum mechanics has taught us that reality is not a neat drawing of well‑traced orbits, but a cloud of probabilities in constant evolution. Yet we continue to teach, publish, and design technologies based on geometric diagrams that are nothing more than convenient metaphors — or even lies by omission. The problem is not only scientific; it is epistemological. By over‑geometrizing, we reduce quantum complexity to a classical caricature and deprive researchers — and the public — of an honest understanding of what particles and their interactions truly are. Atomic orbitals are not physical objects occupying geometrically defined regions of space. They are mathematical representations of quantum states. So why not fully embrace quantum strangeness? Why not present the data as they are: probability distributions, complex amplitudes, entangled states? Science has a duty to tell the truth, even when it is unsettling. And the truth, here, is that the quantum world has nothing geometric about it — at least not in the classical sense we impose on it. Perhaps it is time to break with this tradition and finally show the real face of matter: not a collection of localized objects, but a network of possibilities in perpetual fluctuation, where geometry is only a shadow cast by our human limitations. It is not impossible that this obsession with geometrization — this desperate need to draw orbitals, bands, or lattices where only blurry probabilities exist — is directly linked to the phobia described in the paper The Fear of the Unexplainable. For reducing the quantum to reassuring shapes is a way to flee the fundamental absurdity of a universe where particles have neither trajectory nor defined position. It is a denial of strangeness, a clinging to the illusion of a classical, manageable, predictable world. Geometry is the refuge of physicists frightened by the metaphysical void. == for Forces and Interactions   == Gravity — Unification — Renormalization — Fundamental constants — Mass In the ΛCDM, forces are treated as fundamental entities, each with its own carrier, field, constants, and symmetries. This assumption generates most of the conceptual difficulties. In the UG.NUG reading, this framework collapses: what the ΛCDM interprets as “forces” are not fundamental ingredients of the universe but the observable behaviors that appear when objects exist or move within the GRID. * Gravity is not an interaction. It has no carrier, no quantum, no fundamental field. It is simply the static behavior of the GRID in the presence of a geometric object. The problem of quantum gravity disappears — not because it is solved, but because it never existed: gravity was never a quantum phenomenon to begin with. * Magnetic effects are the dynamic version of the same behavior when the object moves or rotates. * Renormalization also ceases to be a difficulty: there is nothing to renormalize once these behaviors are no longer treated as fundamental forces. * Mass is not a property of the universe. It is only the human interpretation of certain geometric behaviors that remain fully calculable, even though the quantity itself does not exist. Thus, the conceptual problems associated with forces and interactions in the ΛCDM arise from a single mistake: treating contextual behaviors as fundamental forces. 00kb0xvtqpsfz2goxmsxxl8qdc5fhsb 2844856 2844855 2026-11-08T07:08:36Z Wb525 3112992 /* the Natural Best-Way Principle */ 2844856 wikitext text/x-wiki {{Research project}} Original research project by Willy Bohane — UG.NUG. https://doi.org/10.5281/zenodo.20644064 == All the texts in this presentation == [[Cosmology: UG.NUG an Observation-Based Model|UG.NUG]] [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]] [[Cosmology: UG.NUG an Observation-Based Model/Cosmic Time|Cosmic Time]] [[Cosmology: UG.NUG an Observation-Based Model/the Mass Imbroglio|the Mass Imbroglio]] [[Cosmology: UG.NUG an Observation-Based Model/the CMB|of the CMB]] [[Cosmology: UG.NUG an Observation-Based Model/the GRID|of the GRID]] [[Cosmology: UG.NUG an Observation-Based Model/Gravity|of Gravity]] [[Cosmology: UG.NUG an Observation-Based Model/Black Holes|of Black Holes]] = Introduction = This article presents a reading of the Universe that differs in every respect from the existing model. The latter contains a false start which, for reasons explained in the dedicated article on [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]], renders it null and void from the very first millisecond of its narrative: the Singularity. Before reading this detailed text, whose links to technical articles support and further develop the arguments presented, readers can consult a simplified [https://www.wbohane.com/BLOG/!three_point_universe.aspx three-point diagram] offering an overview of the proposed simplicity of the Universe. = State of Play = First, it is important to understand that cosmology, in its interpretative function, is not an exact science. As its name indicates, it means, in Greek, ''the study of the world'' — and therefore, by extension, its origin, its structure, its evolution, its content, and its future. We also have a duty never to forget that cosmology was born as a branch of metaphysics. This should remind us that mathematics must remain a means of understanding the Universe, not a substitute for it. Rather than building elaborate theoretical structures and continually adjusting them to accommodate observations, it would be far more sensible to seek a description that reflects the universe as it actually is. The purpose of cosmology should not be to make reality fit our mathematics, but to make our mathematics serve reality. This is why interpretative cosmology resembles a religion more than it does a science. As with religion, everybody can say anything, everybody can believe anything, everybody can make anyone believe anything. Humanity is divided into many creeds, and so is cosmology. This is why the following list of flaws is possible, especially where science is subjected to the rules of a free market place. '''[[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|The long long list of ΛCDM flaws]]''' = the Natural Best-Way Principle = == definition == The Best-Way is the optimal solution attainable at a given stage of a process. It represents the point beyond which no further improvement is possible under the existing conditions. However, it is never necessarily permanent, as accumulated experience and evolving possibilities may eventually reveal a better way. == in Practice == In accordance with the principle of parsimony, observation, reading and reflection should be the first instincts to guide us when we look up at the sky and ask ourselves what the Universe is. But we must proceed with due respect for our own nature as human beings, confronted with the immensity of a habitat we did not choose, which brings us into existence, sustains us, and ultimately eliminates us without even noticing. In this sense, cosmology has less to do with technology than with philosophy, the mother of all sciences. Parsimony is not merely a rule of thought formulated by a philosopher. Long before Occam, it was already at work in nature. Water flowing downhill follows the paths available to it, overcoming the constraints of its environment while dissipating its available energy. This natural economy also brings to mind Darwin's principle of natural selection: forms that are better adapted to their environment are more likely to survive and perpetuate themselves. Nature does not necessarily favour simplicity, but it does not grant lasting advantages to unnecessary expenditure either. This should be a lesson for every human undertaking. Any project, theory, process or model that accumulates unnecessary complexity, without gaining anything in return, eventually exposes itself to being outperformed and replaced. An inadequate solution may nevertheless survive temporarily, simply because no better alternative is yet available. But it cannot indefinitely withstand the progress of knowledge and technology, which will eventually reveal and make possible a better way of achieving the same goal. When human beings, through the ΛCDM model, presume to decide when the Universe began and how it began, they brazenly violate the modesty and humility that should be incumbent upon them. They do so much as the authors of the biblical creation narrative did — distant predecessors whose audacity might be forgiven, but whose example is no longer intellectually acceptable in the twenty-first century. The issue here is not even to revisit the invalidity of such a conjecture, which is discussed at length in the list of flaws. Rather, it is to ask by what right the model's architects permitted themselves to make such an extraordinary claim in the first place. From that moment on, the claim becomes null and void, without further appeal. = the Universe = So, what does observation tell us when we look up at the sky? First and foremost, it tells us that the Universe exists, that it was already here before us. Our age and our experience also tell us that, as human beings, we are merely passengers, temporary workers, and mortals in waiting, and that whatever we do, the Universe will always be stronger than we are. Consequently, the only natural and parsimonious conclusion we can draw from looking at the sky is that the Universe exists, that it did not ask us to exist, and that it has never told us when it began, how it began, or why it began. From this starting point, we can say, without doubt, without prejudice, without invention, and, quite simply, without making things up, that what we see around us is the Universe; that it is the only thing that exists as far as we are concerned; that it does not know human clock-measured time; and that it is absolutely impossible for us to say anything more about it. Pure logic would therefore suggest that we consider ourselves inhabitants of a stationary Universe, one that would have absolutely no need to expand. The initial observation does not impose expansion upon us. A stationary universe therefore constitutes the most parsimonious starting point. On the one hand, this means not inventing an improbable birth date; on the other, it means not inventing an equally improbable expansive Big Bang. However, with our eyes fixed on the sky, especially at night, we see the Moon. And we are entitled to wonder why it does not fall on our heads, even before knowing about gravity or having the slightest idea of its existence. The natural reflex would therefore be to consider the concept of the Apeiron — an undefined, omnipresent substrate — or Aristotle's concept of Ether, or Faraday's idea of a "something" that might sustain celestial objects. Although these concepts are not entirely identical, they all point towards the same fundamental intuition: the possibility of a "Something" underlying the visible world. This may well be one of humanity's oldest intellectual reflexes. It comes naturally to mind whenever something appears to hang in the void, even during a Houdini performance. Something must be holding it, surely! And at this point, one might begin to think that the Universe is not what we see, but rather what we do not see: that what is visible emerges from a fertile, invisible substrate that fills the entire Universe. This would be a very concrete and believable image if all visible celestial objects appeared to be suspended in the void — suspended, yet held in the embrace of that same substrate, which prevents everything from collapsing. It is much like the air that fills the space on Earth. When the plant emerges from the ground, the air surrounds the plant, continues to envelop it, nourish it, and influence its nature. = The CMB = If we remain within this parsimonious perspective, which so far has required no invention, no additions, and no patches, it is easy to see why a sense of serenity might take hold of our minds. We have already saved ourselves quite a lot: the singularity and its strangeness, the improbable Big Bang, expansion and the many complications it brings in its wake… But be patient. We are about to do even better. Because when Penzias and Wilson discovered the cosmic microwave background radiation, nothing in that discovery compelled us to think of a fossil. The idea of a distant past was not even a necessary intellectual or cosmological option within this line of thought. Why go looking for a fossil, and where would it have come from? No, the question would not even arise. We would instead think of that substrate — the very one we had already invoked to explain why the Moon does not fall on our heads — which might now turn out to be noisy as well. Hardly a reason to spoil the party, this radiation would be the living confirmation of what humanity had intuited for 2,700 years: a "Something" that sustains "Everything." So what better response than to shout: "Bingo!" Since none of the observed properties of the [[Cosmology: UG.NUG an Observation-Based Model/the CMB|CMB]] contradicts this possibility, it would be only fair, and consistent with the principle of parsimony, to acknowledge that this interpretation is far simpler and more appealing than the intricate story of a cosmic fossil, its journey across billions of years, its puzzling temperature, and all the complications that come with it. = the Arrow of Emergence = The glass' message is one of the very few hints the universe deigned to offer us before its long nap. What it whispers if it slips from our hands and, by misfortune, the floor is tiled rather than carpeted: it shatters. And if we read the universe simply, we catch this message that expresses the irreversible Cosmic Order: the one that prevents the glass from reassembling, the one that prevents events from denying their own existence. Thus, the universe gives us the direction from past to future, what current physics commonly calls the Arrow of Time. It is striking: it gives us the Arrow of Time, but not time itself. The current name, Arrow of Time, is not really appropriate, since it is not “time” in the chronometric sense. It is rather, as explained earlier, a pre‑cosmic Order that governs everything, the universe included. Yes, this is an inescapable consequence of a careful reading of the universe. This succession order is of primary importance in the UG.NUG reading, but also in the ΛCDM, which — it seems — has not given it the place it deserves. In the [[Cosmology: UG.NUG an Observation-Based Model/ΛCDM|ΛCDM]], one observes that the universe ceased its creative activity only once its work was complete. One day, it emerged from an unknown state — the term ''Big Bang'', which everyone knows, usually refers to this event — and then particles appeared, followed by atoms, stars, galaxies… Since then, nothing is created, nothing is lost, everything transforms, as Lavoisier would say. What matters here is not the validity of this narrative, but the Succession  of things: this natural succession of phases is precisely the Succession  in question. And that is why we have renamed this arrow the Arrow of Emergence. The misunderstanding dissolves, and the meaning becomes clearer: Succession  of emergences versus time‑keeping. The Arrow of Emergence therefore indisputably precedes the universe. It’s new, fresh off the shelf, ready‑to‑wear. This can mean several things: * the arrow was there, and that’s all. We accept the universe and take the arrow as a bonus, * the arrow was there, and therefore the universe is governed by something we do not know, * the arrow was there, and therefore our universe is part of a series of universes, * the arrow was there, and therefore we are free to consider any interpretation. In short, it mainly means that the Arrow of Emergence is particularly important — especially for what follows. = The GRID = Since CMB is the name given to the discovery, it seems fair to rename it according to its cosmological function. Faraday deserves his “something,” and we have chosen [[Cosmology: UG.NUG an Observation-Based Model/the GRID|GRID]], which stands for Global Reference in Dynamics. In UG.NUG, the model presented in this paper, the [[Cosmology: UG.NUG an Observation-Based Model/the GRID|GRID]] is ''le clou du spectacle'', as the French would say — the highlight of the entire show. It is the key element that dissolves most of the paradoxes of ΛCDM in such a simple way that it seems almost impossible to have overlooked it. In other words, without the GRID, UG.NUG would be no more interesting than any other model. = UG = Apart from its resemblance to the exclamation of a prehistoric man, this name carries a very important cosmological meaning. What we call geometry refers to the shape or size of an individual object, properties that matter in its interactions with reality. Geometry begins above the level of chemistry. UG stands for the French '''''Uniformité Genrée''''' (Categorical Uniformity). We coined this term to describe a phenomenon whose significance has gone unnoticed. In short, everything produced by the Universe in its earliest stages — particles, nuclei, and so on — belongs to this regime, in which objects possess no geometry. They have no individuality, no history, and no variation. This uniformity is the hidden foundation of everything: the silent order governing the birth of the Universe. For now, let us simply understand that, in this model, the world of the very small — below the atomic level — has no geometry, even though some textbooks may suggest otherwise. = NUG = NUG stands for the French '''Non-Uniformité Genrée''' (Categorical Non-Uniformity). It represents everything that possesses geometry and individuality: stars, planets, meteors, and, of course, everything that derives from them — humans, artifacts, flora, and fauna. No two pebbles are alike, nor are any two trees. Individuality increases with complexity. The transition from UG to NUG occurs through the assembly of atoms and molecules, the underlying mechanism of which remains unknown. NUG is the third and final phase in the emergence of an object. Since humans, along with their clocks and measuring instruments, belong to NUG, the time measured by our wristwatches is also a NUG phenomenon. In this model, measurable time exists only where geometry and individuality exist. = UG.NUG = UG.NUG is the name of this model. It encompasses the two regimes that govern the entire Universe. As we shall see, NUG — and therefore geometry — emerges later than UG. Once it appears, however, it becomes an integral part of the Three Point Universe, a concise schematic representation of the UG.NUG model. NUG encompasses all objects, including the Moon and the other celestial bodies mentioned earlier, which, fortunately, do not fall on our heads. == Redshift == The UG.NUG reading understands that geometry is not a starting point, but a secondary level of organization, appearing only after UG. This single shift is enough to dissolve almost all cosmological problems of the ΛCDM. Thus, the universe is not the product of a geometric explosion, but is grounded in an undifferentiated background. Geometry appears only when objects cease to be identical. This conceptual reversal eliminates in one stroke the paradoxes related to the origin of space, its shape, its homogeneity, or its flatness. One no longer tries to explain why geometry is already there. It is not an initial condition, but appears naturally, carried by the Arrow of Emergence, and stabilizes thanks to the GRID. The image of a fabric tube being inflated illustrates this perfectly. The tube already exists, but it is not yet deployed. Near the opening, the fabric is inflated; farther away, it seems to inflate progressively; in the distance, it is still flat. For an observer inside, this creates the illusion of expansion, then accelerated expansion, even though it is only the progressive realization of the structure. The distant regions appear to recede because they are not yet realized, not because they are moving. This inversion of perspective dissolves the very idea of cosmic expansion, inflation, an initial singularity, or dark energy. The spectroscopic observations and measurements themselves are not being disputed. The observed redshifts, the recorded spectra, and the data themselves remain unchanged. What UG.NUG challenges is the interpretation placed upon them: that redshift necessarily indicates recession, and that this recession necessarily means that space is expanding. The issue, therefore, is not the validity of the observations, but the assumptions through which they are interpreted. The same measurements may point to a different reading of the Universe. There is, however, a further question concerning the validity of the measurements themselves. As discussed in the paper on Cosmic Time, if the Universe has no intrinsic time, the very notion of measuring cosmic durations or assigning chronological ages to distant events becomes questionable. Such measurements rely on a chronometric framework whose applicability UG.NUG challenges. This raises a separate and much broader issue, which cannot be addressed here without taking us away from the subject of redshift. = the Genesis Phases = Now that the framework has been established, and we have seen that our universe is neither outlandish nor fundamentally different from the one we know, and that it is not threatened by our models, however incongruous they may be, we can begin to imagine what might actually have happened to produce the spectacle before our eyes. For this section, then, a little imagination is indeed required. Yet, for reasons of pure logic, the sequence you are about to discover is hardly surprising. The principle of parsimony remains our guide. Water has always flowed, and will always flow, along the paths best suited to its passage. This natural law, which is suspected to have inspired William of Ockham in formulating his principle, is far from trivial when attempting to reconstruct an event such as the emergence of the universe through a virtual model. We shall therefore continue to refrain from introducing artificial devices into the natural stages described below. = the First Phase = Strictly speaking, this is not a phase at all. It is included here to make clear that everything begins with the omnipresence of the universe. This phase never began, because it is our sole reality. Nothing else exists. This omnipresence is inferred from, and embodied in, the omnipresent GRID, which belongs to the UG regime, where objects inaccessible to our senses have no history, variation, or individuality. We do not know what it is made of. Nevertheless, it is logical to suppose that it contains the codes of the perceivable universe: the non-geometric component commonly encountered at the depths of matter and described by quantum mechanics, including elementary particles and atomic nuclei. For human beings, such a configuration borders on metaphysics. Our cognitive faculties are not designed to grasp invisible, non-geometric entities that carry information, almost like ghosts. We can invent ghosts, but we cannot manage them. According to the standard cosmological model, this radiation was released approximately 380,000 years after the Big Bang, hence its designation as fossil radiation. Such dating has no meaning within the present model, since chronometric time, as explained earlier, does not exist at the fundamental level of the universe. The quantum effervescence associated with the emergence of the GRID is held together by a fundamental UG energy: a pre-geometric substrate that makes emergence possible. This energy may correspond to the unique energy of the BBP, subsequently differentiated into the electromagnetic, weak, and strong interactions, the latter ensuring nuclear cohesion. These interactions then mysteriously disappear from the broader cosmological narrative. The persistence of the GRID explains its presence in every atom. Whatever an atom may eventually become, it retains this universal imprint. When an atom is destroyed, its particles are not necessarily destroyed with it: they return silently to the undifferentiated reservoir of the GRID. Quantum particles cannot be manipulated directly in their fundamental nature; they emanate from the original GRID. This is a personal assertion, but not an entirely baseless one. As explained in The Fear of the Unexplainable, the dominant mindset refuses to accept that the unexplainable might be fundamental. Everything must be physical — except when it is convenient to invoke something more elusive, as when fundamental energy is called upon to explain atomic cohesion. This double standard exposes what should be regarded as a lack of logic in the BBP. This is why CERN is unlikely ever to obtain the results it expects. These particles will never reveal what they truly are. Attempting to reach the UG side of the universe using NUG instruments is like asking a newborn to intervene in the device that brought it into existence. The limitations become apparent immediately. The atomic bomb has already shown, with tragic consequences, what can happen when humanity interferes too directly with the elements of the GRID. Einstein was right to reject the idea that “God plays dice.” His “God” — nature, the universe itself — is present in every object. He did not believe that quantum mechanics had appeared in matter by chance. Yet this is precisely how Bohr and Heisenberg interpreted it: they treated quantum mechanics as a contingent curiosity rather than as the signature of something still unknown. = the Second Phase = Once the presence of the underlying “carpet” containing the codes has been established, it becomes plausible that primary objects — atoms and simple molecules — begin to form. These are the first objects to possess geometry, yet all objects of a given kind remain identical to one another. Any attempt to determine the precise beginning and end of this phase through elaborate calculations would be highly speculative. The immaterial effervescence persists, but it is now accompanied by objects that require time to assemble. In parallel, the fundamental energy of the GRID becomes involved in maintaining the cohesion of these new atomic structures. This cohesive role requires it to manifest properties that were previously unnecessary: the strong interaction, which binds the constituents of atomic nuclei together; the weak interaction, whose role is more secondary in this context; and the electromagnetic interaction, which governs exchanges between charged particles. One energy, then, with multiple manifestations — always present, always active. In this model, it replaces the various concepts invoked by the BBP to describe primordial energy and its effects: vacuum energy, dark energy, the cosmological constant, and quantum fluctuations. These become different labels for what the model interprets as a single primordial presence. At this level, deduction is more reliable than equations. When atomic nuclei absorb part of the primordial energy and convert it into binding energy or other forms of energy associated with their structure, they clearly do not absorb the entire substrate that sustains them. Like leaves floating on a pond, organised structures can appear without eliminating the medium in which they exist. The primordial energy continues to sustain the whole, even when part of its flow is redirected towards cohesion. Atoms are assemblies of ghosts, and all atoms of a given kind appear identical. What lies at their heart is non-geometric and cannot be observed directly. Applied physics detects only measurable effects — energies, transitions, and interactions — never the intrinsic nature of the particles themselves. Conversely, the BBP assigns geometric labels to entities that are inferred from non-geometric experimental results: spin, charge, isospin, quantum numbers, and so on. Collisions produce deposited energies, momenta, angles, jets, resonances, and statistical peaks. From these data, the BBP constructs its picture of elementary particles. This conceptual shift is rarely acknowledged. Despite the absence of directly geometric data at the fundamental level, the BBP continues to construct its own universe in order to preserve what may be regarded as a sterile mathematical edifice. The second phase is the bridge between the inaccessible and the modifiable, between UG and NUG, between the GRID and geometry. = the Third Phase = All remaining objects — stars, planets, galaxies, and everything that derives from them — emerge according to their order of formation, depending on the availability and completeness of the preceding stages for each object individually. This is where uniformity ends and individuality begins. No precise dating is possible within the present model. This phase represents the culmination of the process: the world that emerges from UG, the world we see, touch, hear, smell, and taste. Once UG has reached maturity, complex forms, interactions, and histories become possible. The universe enters the NUG regime. NUG encompasses: * Stars * Planets * Chemistry * Biology * Perception Everything we experience is the final geometry of a pre-geometric reality. Pre-geometric also means pre-volumetric. The GRID — UG — is both pre-geometric and pre-volumetric. Geometry begins above the atomic level, and individuality emerges with complexity. The GRID has no visible form. It manifests itself through the infinitesimal temperature variations observed in the CMB in every direction, through gravity on Earth, and through magnetic fields. It is an invisible presence that precedes the emergence of volumetric structures. In this model, geometry and volume emerge from UG without requiring expansion, unlike the BBP, which postulates an initial singularity followed by the expansion of the metric. Our interpretation is straightforward: * '''No singularity:''' the universe is already extended in the form of the GRID. * '''No infinities:''' emergence follows an ordered sequence, from Phase 1 through Phase 2 to Phase 3. * '''No paradox:''' geometry, or NUG, emerges from UG without requiring expansion. The GRID never disappears. It permeates every atom in every object. It is present throughout our world in the form of quantum mechanics, whose rules, according to this model, differ radically from those commonly accepted. Using a scanning tunnelling microscope (STM), it is possible to distinguish individual atoms and observe their arrangement. Don Eigler demonstrated this in 1989 by positioning xenon atoms on a nickel surface to spell out the letters IBM. Beyond the atomic scale, the gap in scale becomes immense. Atoms are approximately a nanometre across, whereas the characteristic scale of their constituent particles is around a femtometre — roughly one millionth of a nanometre. No elementary particle has been observed directly in the sense of being imaged as a tiny object with a visible surface. Instead, experiments detect traces and measurable effects from which the properties of particles are inferred. The process is therefore highly indirect. Every fragment of matter carries within it an irreducible part of the universe's deepest mystery, together with the codes from which geometry emerges. = Conceptual Consequences = The problems of the ΛCDM are not independent: they naturally group into three families, all stemming from the same implicit assumption — that the universe is fundamentally geometric. By changing this starting point, these difficulties cease to be enigmas. They become the expected consequences of an inadequate reading. The three blocks that follow present these families of problems and show how UG.NUG reading dissolves them without additions, without corrections, simply by restoring the natural Succession of emergence. == for Cosmology == Dark matter — Dark energy — Cosmological constant — Horizon — Flatness — Homogeneity — Origin of geometry — Big Bang — Expansion — Large‑scale structure The UG.NUG reading understands that geometry is not a starting point, but a secondary level of organization, appearing only after UG. This single shift is enough to dissolve almost all cosmological problems of the ΛCDM. Thus, the universe does not begin with a geometric explosion, but with an undifferentiated background. Geometry appears only when objects cease to be identical. This conceptual reversal eliminates in one stroke the paradoxes related to the origin of space, its shape, its homogeneity, or its flatness. One no longer tries to explain why geometry is already there. It is not there at the beginning. It appears naturally, carried by the Arrow of Emergence, and stabilizes thanks to the GRID. The image of a fabric tube being inflated illustrates this perfectly. The tube already exists, but it is not yet deployed. Near the opening, the fabric is inflated; farther away, it seems to inflate progressively; in the distance, it is still flat. For an observer inside, this creates the illusion of expansion, then accelerated expansion, even though it is only the progressive realization of the structure. The distant regions appear to recede because they are not yet realized, not because they are moving. This inversion of perspective dissolves the very idea of cosmic expansion, inflation, an initial singularity, or dark energy. In this reading, the great cosmological enigmas cease to be anomalies. * Dark matter is no longer an invisible substance added to fix equations, but the consequence of applying a geometric interpretation to a phenomenon that is not geometric. * Dark energy is no longer a mysterious force pushing the universe to expand, but the effect of a secondary geometry misread as dynamic when it is simply structural. * The horizon problem disappears because homogeneity does not need to be transmitted: it is inherited from UG, where everything is identical. * The flatness problem vanishes because geometry is not a fragile structure requiring fine‑tuning, but a stable organization imposed by the GRID. In the UG.NUG reading, geometry is not fundamental but secondary, emergent. By changing the starting point, one does not correct anomalies: one dissolves them. The universe was never incoherent. The interpretation was. == for Quantum Physics   == Measurement - Decoherence - Superposition - Classicality - Quantum gravity - Particle identity - Non‑locality - Hidden variables - Wave‑particle duality - Indeterminacy - Absence of trajectory Quantum physics accumulates paradoxes because it tries to describe a non‑geometric regime using geometric tools. It applies notions of shape, position, trajectory, or mass to objects that possess none of these. In UG.NUG reading, first‑wave particles belong to the UG regime: they are inaccessible, undifferentiated, without form, without variation, without geometry. They are not tiny objects but non‑identifiable pre‑geometric entities.   In this reading, the measurement problem disappears. * There is no wave‑packet collapse, only the transition from a UG state to a NUG interaction — that is, the appearance of a geometric imprint. * Decoherence is no longer a mysterious mechanism, but is simply the incompatibility between a non‑geometric state and a geometric environment. * Superposition is not a magical phenomenon, but the natural behavior of objects that have neither shape nor position. * Classicality needs no explanation: it appears as soon as objects acquire geometry — that is, in the second phase, the primordial one. * Quantum gravity ceases to be a meaningful objective, because there is nothing to quantize. * Gravity is not a fundamental force but the static reaction of the GRID, a purely geometric phenomenon. * Non‑locality is no longer a mystery: in a non‑geometric regime, the notion of distance has no meaning. * Hidden variables have no place: there is nothing to hide in a regime without internal structure. Thus, all quantum paradoxes arise from a single mistake: trying to apply NUG tools to UG. The paradoxes vanish as soon as we stop demanding that UG behave like a geometric world. Quantum mechanics is the universe’s signature within every atom of matter, and the keeper of the code for the geometry of the emergent, perceivable forms that make up our world. That said, where we hope this reading of the universe can serve as a model is in a radical shift in how we treat the information obtained through the manipulation and analysis of particles. In fact, the investigations concerning them can be counted on the fingers of one hand: <nowiki>:</nowiki> * energy levels through spectrometry, * transition probabilities in lasers, * electronic structures via STM, * conduction bands in solid‑state physics, * bound states in quantum chemistry. Yet these data, as precise and rich as they are, are systematically and arbitrarily transformed into geometric forms: orbitals, positions, bands, crystal lattices… as if nature suddenly became classical the moment we look at it. But none of this has ever been observed. The size of particles, their wave‑particle duality, and above all the very principle of quantum mechanics — where everything is probabilities, superpositions, and wave functions — should forbid this geometric illusion. Why, then, this persistent habit of hiding raw data beneath familiar but false representations? Why prefer reassuring visual models over a clear presentation of investigative methods and probabilistic results? Quantum mechanics has taught us that reality is not a neat drawing of well‑traced orbits, but a cloud of probabilities in constant evolution. Yet we continue to teach, publish, and design technologies based on geometric diagrams that are nothing more than convenient metaphors — or even lies by omission. The problem is not only scientific; it is epistemological. By over‑geometrizing, we reduce quantum complexity to a classical caricature and deprive researchers — and the public — of an honest understanding of what particles and their interactions truly are. Atomic orbitals are not physical objects occupying geometrically defined regions of space. They are mathematical representations of quantum states. So why not fully embrace quantum strangeness? Why not present the data as they are: probability distributions, complex amplitudes, entangled states? Science has a duty to tell the truth, even when it is unsettling. And the truth, here, is that the quantum world has nothing geometric about it — at least not in the classical sense we impose on it. Perhaps it is time to break with this tradition and finally show the real face of matter: not a collection of localized objects, but a network of possibilities in perpetual fluctuation, where geometry is only a shadow cast by our human limitations. It is not impossible that this obsession with geometrization — this desperate need to draw orbitals, bands, or lattices where only blurry probabilities exist — is directly linked to the phobia described in the paper The Fear of the Unexplainable. For reducing the quantum to reassuring shapes is a way to flee the fundamental absurdity of a universe where particles have neither trajectory nor defined position. It is a denial of strangeness, a clinging to the illusion of a classical, manageable, predictable world. Geometry is the refuge of physicists frightened by the metaphysical void. == for Forces and Interactions   == Gravity — Unification — Renormalization — Fundamental constants — Mass In the ΛCDM, forces are treated as fundamental entities, each with its own carrier, field, constants, and symmetries. This assumption generates most of the conceptual difficulties. In the UG.NUG reading, this framework collapses: what the ΛCDM interprets as “forces” are not fundamental ingredients of the universe but the observable behaviors that appear when objects exist or move within the GRID. * Gravity is not an interaction. It has no carrier, no quantum, no fundamental field. It is simply the static behavior of the GRID in the presence of a geometric object. The problem of quantum gravity disappears — not because it is solved, but because it never existed: gravity was never a quantum phenomenon to begin with. * Magnetic effects are the dynamic version of the same behavior when the object moves or rotates. * Renormalization also ceases to be a difficulty: there is nothing to renormalize once these behaviors are no longer treated as fundamental forces. * Mass is not a property of the universe. It is only the human interpretation of certain geometric behaviors that remain fully calculable, even though the quantity itself does not exist. Thus, the conceptual problems associated with forces and interactions in the ΛCDM arise from a single mistake: treating contextual behaviors as fundamental forces. 5ssuqd0ycgjudb262a4sdww1rq6wp43 6 332863 2844820 2026-11-07T17:19:04Z Young1lim 21186 {{Information |Description=2. Newton-Raphson Method (20261102 - 20261027) |Source={{own|Young1lim}} |Date=2026-11-07 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} 2844820 wikitext text/x-wiki == Summary == {{Information |Description=2. Newton-Raphson Method (20261102 - 20261027) |Source={{own|Young1lim}} |Date=2026-11-07 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 5o8q0eo82g7dzlq66u4gxi9jnmzxuc4 6 332864 2844822 2026-11-07T17:26:44Z Young1lim 21186 {{Information |Description=2. Newton-Raphson Method (20261103 - 20261102) |Source={{own|Young1lim}} |Date=2026-11-07 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} 2844822 wikitext text/x-wiki == Summary == {{Information |Description=2. Newton-Raphson Method (20261103 - 20261102) |Source={{own|Young1lim}} |Date=2026-11-07 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} p5w4c9nmdouvvl8w828nztbwvuxl9kk 0 332865 2844828 2026-11-07T21:37:16Z GreenC 268373 Created page with " The '''Salon Book Awards''' were an annual [[w:literary award|literary feature]] issued by the online magazine [[w:Salon (website)|Salon.com]] from 1996 to 2011, recognizing the year's fiction and nonfiction. The awards were established in December 1996 by Salon's literary editors [[w:Laura Miller (writer)|Laura Miller]] and [[w:Dwight Garner (critic)|Dwight Garner]] during the early days of the web. It was a period when the site was helping to establish a new industry..." 2844828 wikitext text/x-wiki The '''Salon Book Awards''' were an annual [[w:literary award|literary feature]] issued by the online magazine [[w:Salon (website)|Salon.com]] from 1996 to 2011, recognizing the year's fiction and nonfiction. The awards were established in December 1996 by Salon's literary editors [[w:Laura Miller (writer)|Laura Miller]] and [[w:Dwight Garner (critic)|Dwight Garner]] during the early days of the web. It was a period when the site was helping to establish a new industry of professional cultural criticism that was published digitally, supported by ad revenue and private investment. Rather than a formal juried prize with a physical ceremony or endowment, the award served as the publication's year-end "Best Of" list. The editors' methodology for selecting the winning books was highly personal. In the inaugural 1996 announcement, Miller and Garner emphasized that they deliberately excluded books written by personal friends to avoid the appearance of nepotism, and favored unified novels and narratives over short-story or essay collections. The overarching criteria were: :"..the books we'd wholeheartedly recommend to our friends, books we'd clear our social calendar to finish, books we returned to eagerly even when we could barely focus our eyes on a page. They remind us of why we fell in love with reading and why we keep at it in a world that's simultaneously cluttered with mediocre books and increasingly indifferent to the written word."<ref name="1996 award">{{cite web |last1=Miller |first1=Laura |last2=Garner |first2=Dwight |title=Books of the Year |url=https://www.salon.com/1996/12/09/awards961209/ |archive-url=https://web.archive.org/web/20190722223228/https://www.salon.com/1996/12/09/awards961209/ |archive-date=2019-07-22 |date=December 9, 1996 |website=[[w:Salon (website)|Salon]]}}</ref> Following the 2011 awards, the original format was retired. In 2012, a new accolade was established called the '''What To Read Awards''', named after Salon's ongoing "What to Read" column. Although Laura Miller continued to publish a separate "Best Books of the Year" top-10 list, the new awards crowdsourced the selections by polling the broader literary community. The editors tabulated the What To Read Awards as follows: :"we surveyed our favorite book critics, both print and online, from high-profile publications to the hottest literary blogs. We asked for their top-10 books of 2012, and then tabulated the winners by assigning 10 points for a No. 1 selection, 9 for No. 2, all the way to 1 point for No. 10."<ref name="daley2012"/> ==Winners of Salon Book Awards== The following is a list of the winners of the Salon Book Awards for each year. ===1996=== Source:<ref name="1996 award" /> *''[[w:Angela's Ashes|Angela's Ashes]]'' by [[w:Frank McCourt|Frank McCourt]] *''[[w:The Family Markowitz|The Family Markowitz]]'' by [[w:Allegra Goodman|Allegra Goodman]] *''The Giant's House: A Romance'' by [[w:Elizabeth McCracken|Elizabeth McCracken]] *''[[w:Infinite Jest|Infinite Jest]]'' by [[w:David Foster Wallace|David Foster Wallace]] *''The Living and the Dead: Robert McNamara and Five Lives of a Lost War'' by [[w:Paul Hendrickson|Paul Hendrickson]] *''[[w:The Moor's Last Sigh|The Moor's Last Sigh]]'' by [[w:Salman Rushdie|Salman Rushdie]] *''[[w:My Dark Places (book)|My Dark Places]]'' by [[w:James Ellroy|James Ellroy]] *''Reader's Block'' by [[w:David Markson|David Markson]] *''The Shadow Man'' by [[w:Mary Gordon (writer)|Mary Gordon]] *''The Temple Bombing'' by [[w:Melissa Fay Greene|Melissa Fay Greene]] ===1997=== Source:<ref>{{cite web |last1=Miller |first1=Laura |last2=Garner |first2=Dwight |title=The second annual Salon Book Awards |work=[[w:Salon (website)|Salon]] |date=January 5, 1998 |url=https://www.salon.com/1998/01/05/the_second_annual_salon_book_awards/ |archive-url=https://web.archive.org/web/20171010021903/https://www.salon.com/1998/01/05/the_second_annual_salon_book_awards/ |archive-date=2017-10-10 }}</ref> *''[[w:Alias Grace|Alias Grace]]'' by [[w:Margaret Atwood|Margaret Atwood]] *''Because They Wanted to: Stories'' by [[w:Mary Gaitskill|Mary Gaitskill]] *''Close to the Machine: Technophilia and Its Discontents'' by [[w:Ellen Ullman|Ellen Ullman]] *''[[w:Cold Mountain (novel)|Cold Mountain]]'' by [[w:Charles Frazier|Charles Frazier]] *''Echoes of a Native Land: Two Centuries of a Russian Village'' by [[w:Serge Schmemann|Serge Schmemann]] *''How Proust Can Change Your Life'' by [[w:Alain de Botton|Alain de Botton]] *''[[w:Into Thin Air|Into Thin Air: A Personal Account of the Mt. Everest Disaster]]'' by [[w:Jon Krakauer|Jon Krakauer]] *''[[w:Mason & Dixon|Mason & Dixon]]'' by [[w:Thomas Pynchon|Thomas Pynchon]] *''[[w:The Reader|The Reader]]'' by [[w:Bernhard Schlink|Bernhard Schlink]] *''[[w:The Spirit Catches You and You Fall Down|The Spirit Catches You and You Fall Down]]'' by [[w:Anne Fadiman|Anne Fadiman]] ===1998=== *''At Home with the Marquis de Sade: A Life'' by [[w:Francine du Plessix Gray|Francine du Plessix Gray]] *''[[w:A Beautiful Mind (book)|A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash]]'' by [[w:Sylvia Nasar|Sylvia Nasar]] *''[[w:Birds of America (stories)|Birds of America]]'' by [[w:Lorrie Moore|Lorrie Moore]] *''[[w:Blindness (novel)|Blindness]]'' by [[w:José Saramago|José Saramago]] *''A Slant of Sun: One Child's Courage'' by [[w:Beth Kephart|Beth Kephart]] *''[[w:Starting Out in the Evening|Starting Out in the Evening]]'' by [[w:Brian Morton (American author)|Brian Morton]] *''[[w:The Surgeon of Crowthorne|The Surgeon of Crowthorne]]'' by [[w:Simon Winchester|Simon Winchester]] *''Thirst'' by [[w:Ken Kalfus|Ken Kalfus]] *''The Voyage of the Narwhal'' by [[w:Andrea Barrett|Andrea Barrett]] *''[[w:We Wish to Inform You That Tomorrow We Will be Killed With Our Families|We Wish to Inform You That Tomorrow We Will be Killed With Our Families: Stories from Rwanda]]'' by [[w:Philip Gourevitch|Philip Gourevitch]] ===1999=== *''[[w:Black Hawk Down: A Story of Modern War|Black Hawk Down: A Story of Modern War]]'' by [[w:Mark Bowden|Mark Bowden]] *''Careless Love: The Unmaking of Elvis Presley'' by [[w:Peter Guralnick|Peter Guralnick]] *''[[w:Cryptonomicon|Cryptonomicon]]'' by [[w:Neal Stephenson|Neal Stephenson]] *''Lost on Earth: Nomads of the New World'' by [[w:Mark Fritz|Mark Fritz]] *''[[w:Motherless Brooklyn|Motherless Brooklyn]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''Original Bliss'' by [[w:A. L. Kennedy|A. L. Kennedy]] *''[[w:Plainsong (novel)|Plainsong]]'' by [[w:Kent Haruf|Kent Haruf]] *''[[w:A Prayer for the Dying|A Prayer for the Dying]]'' by [[w:Stewart O'Nan|Stewart O'Nan]] *''Secrets of the Flesh: A Life of Colette (Ballantine Reader's Circle)'' by [[w:Judith Thurman|Judith Thurman]] *''Show Me a Hero: A Tale of Murder, Suicide, Race, and Redemption'' by [[w:Lisa Belkin|Lisa Belkin]] ===2000=== Source:<ref>{{cite web |last1=Russo |first1=Mario |last2=Miller |first2=Laura |title=Salon Book Awards |work=Salon |date=December 18, 2000 |url=https://www.salon.com/2000/12/18/bookawards/ |archive-url=https://web.archive.org/web/20160212125119/https://www.salon.com/2000/12/18/bookawards/ |archive-date=2016-02-12 }}</ref> *''[[w:Richard_Slotkin#Abe:_A_Novel_of_the_Young_Lincoln|Abe: A Novel of the Young Lincoln]]'' by [[w:Richard Slotkin|Richard Slotkin]] *''An American Story'' by [[w:Debra Dickerson|Debra Dickerson]] *''[[w:Being Dead|Being Dead]]'' by [[w:Jim Crace|Jim Crace]] *''The Blood Runs Like a River Through My Dreams'' by [[w:Nasdijj|Nasdijj]] *''Boxer Rebellion: The Dramatic Story of China's War on Foreigners that Shook the World in the Summer of 1900'' by [[w:Diana Preston|Diana Preston]] *''Lying Awake'' by [[w:Mark Salzman|Mark Salzman]] *''The Name of the World: A Novel'' by [[w:Denis Johnson|Denis Johnson]] *''Pontius Pilate : The Biography of an Invented Man'' by [[w:Ann Wroe|Ann Wroe]] *''The Social Lives of Dogs'' by [[w:Elizabeth Marshall Thomas|Elizabeth Marshall Thomas]] *''[[w:White Teeth|White Teeth]]'' by [[w:Zadie Smith|Zadie Smith]] ===2001=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Our favorite books |work=[[w:Salon (website)|Salon]] |date=January 9, 2002 |url=https://www.salon.com/2002/01/09/bestbooks_2/ |archive-url=https://web.archive.org/web/20120712170827/https://www.salon.com/2002/01/09/bestbooks_2/ |archive-date=2012-07-12 }}</ref> *''[[w:Austerlitz (novel)|Austerlitz]]'' by [[w:W. G. Sebald|W. G. Sebald]] *''[[w:Bel Canto (novel)|Bel Canto]]'' by [[w:Ann Patchett|Ann Patchett]] *''Borrowed Finery: A Memoir'' by [[w:Paula Fox|Paula Fox]] *''[[w:The Corrections|The Corrections]]'' by [[w:Jonathan Franzen|Jonathan Franzen]] *''[[w:John Adams (book)|John Adams]]'' by [[w:David McCullough|David McCullough]] *''[[w:John Henry Days|John Henry Days]]'' by [[w:Colson Whitehead|Colson Whitehead]] *''[[w:Seabiscuit: An American Legend|Seabiscuit: An American Legend]]'' by [[w:Laura Hillenbrand|Laura Hillenbrand]] *''Stranger Things Happen: Stories'' by [[w:Kelly Link|Kelly Link]] *''Strip City: A Stripper's Farewell Journey Across America'' by [[w:Lily Burana|Lily Burana]] *''[[w:Wittgenstein's Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers|Wittgenstein's Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers]]'' by [[w:David Edmonds (philosopher)|David Edmonds]] ===2002=== No awards were given for the year of 2002. ===2003=== *''American Woman: A Novel'' by [[w:Susan Choi|Susan Choi]] *''[[w:Any Human Heart|Any Human Heart]]'' by [[w:William Boyd (writer)|William Boyd]] *''Brick Lane'' by [[w:Monica Ali|Monica Ali]] *''The Bug'' by [[w:Ellen Ullman|Ellen Ullman]] *''[[w:The Curious Incident of the Dog in the Night-Time|The Curious Incident of the Dog in the Night-Time]]'' by [[w:Mark Haddon|Mark Haddon]] *''[[w:Drop City|Drop City]]'' by [[w:T. C. Boyle|T. C. Boyle]] *''[[w:The Fortress of Solitude|The Fortress of Solitude]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''I Should Be Extremely Happy in Your Company: A Novel of Lewis and Clark'' by [[w:Brian Hall (author)|Brian Hall]] *''[[w:Old School (novel)|Old School]]'' by [[w:Tobias Wolff|Tobias Wolff]] *''[[w:Property (novel)|Property]]'' by [[w:Valerie Martin|Valerie Martin]] ===2004=== *''American Brutus: John Wilkes Booth and the Lincoln Conspiracies'' by [[w:Michael W. Kauffman|Michael W. Kauffman]] *''Arc of Justice: A Saga of Race, Civil Rights, and Murder in the Jazz Age'' by [[w:Kevin Boyle (historian)|Kevin Boyle]] *''[[w:Case Histories|Case Histories]]'' by [[w:Kate Atkinson|Kate Atkinson]] *''[[w:Happy Baby|Happy Baby]]'' by [[w:Stephen Elliott (author)|Stephen Elliott]] *''[[w:Jonathan Strange & Mr Norrell|Jonathan Strange & Mr Norrell]]'' by [[w:Susanna Clarke|Susanna Clarke]] *''[[w:The Line of Beauty|The Line of Beauty]]'' by [[w:Alan Hollinghurst|Alan Hollinghurst]] *''Nightingales: The Extraordinary Upbringing and Curious Life of Miss Florence Nightingale'' by [[w:Gillian Gill|Gillian Gill]] *''Skeletons on the Zahara: A True Story of Survival'' by [[w:Dean King|Dean King]] *''[[w:Snow (Pamuk novel)|Snow]]'' by [[w:Orhan Pamuk|Orhan Pamuk]] *''The Working Poor: Invisible in America'' by [[w:David K. Shipler|David K. Shipler]] ===2005=== Source:<ref>{{cite web |last1=Miller |first1=Laura |last2=Frey |first2=Hillary |title=The best books of 2005 |work=[[w:Salon (website)|Salon]] |date=December 19, 2005 |url=https://www.salon.com/2005/12/19/best_of_2/ |archive-url=https://web.archive.org/web/20111230083620/https://www.salon.com/2005/12/19/best_of_2/ |archive-date=2011-12-30 }}</ref> *''[[w:1491: New Revelations of the Americas Before Columbus|1491: New Revelations of the Americas Before Columbus]]'' by [[w:Charles C. Mann|Charles C. Mann]] *''The Assassins' Gate'' by [[w:George Packer|George Packer]] *''Dream Boogie: The Triumph of Sam Cooke'' by [[w:Peter Guralnick|Peter Guralnick]] *''[[w:Kafka on the Shore|Kafka on the Shore]]'' by [[w:Haruki Murakami|Haruki Murakami]] *''[[w:Magic for Beginners|Magic for Beginners]]'' by [[w:Kelly Link|Kelly Link]] *''[[w:Never Let Me Go (novel)|Never Let Me Go]]'' by [[w:Kazuo Ishiguro|Kazuo Ishiguro]] *''[[w:On Beauty|On Beauty]]'' by [[w:Zadie Smith|Zadie Smith]] *''Them: A Memoir of Parents'' by [[w:Francine du Plessix Gray|Francine du Plessix Gray]] *''[[w:Times Like These (novel)|Times Like These]]'' by [[w:Rachel Ingalls|Rachel Ingalls]] *''Tulia'' by [[w:Nate Blakeslee|Nate Blakeslee]] *''Veronica'' by [[w:Mary Gaitskill|Mary Gaitskill]] ===2006=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Authors' picks |work=[[w:Salon (website)|Salon]] |date=December 11, 2006 |url=https://www.salon.com/2006/12/11/authors_picks_2/ |archive-url=https://web.archive.org/web/20120430155625/https://www.salon.com/2006/12/11/authors_picks_2/ |archive-date=2012-04-30 }}</ref> *''[[w:The Amalgamation Polka|The Amalgamation Polka]]'' by [[w:Stephen Wright (writer)|Stephen Wright]] *''A Disorder Peculiar to the Country: A Novel'' by [[w:Ken Kalfus|Ken Kalfus]] *''The Family That Couldn't Sleep: A Medical Mystery'' by [[w:D.T. Max|D.T. Max]] *''[[w:Fun Home: A Family Tragicomic|Fun Home: A Family Tragicomic]]'' by [[w:Alison Bechdel|Alison Bechdel]] *''James Tiptree, Jr.: The Double Life of Alice B. Sheldon'' by [[w:Julie Phillips|Julie Phillips]] *''[[w:The Lost: A Search for Six of Six Million|The Lost: A Search for Six of Six Million]]'' by [[w:Daniel Mendelsohn|Daniel Mendelsohn]] *''[[w:The Omnivore's Dilemma: A Natural History of Four Meals|The Omnivore's Dilemma: A Natural History of Four Meals]]'' by [[w:Michael Pollan|Michael Pollan]] *''[[w:Special Topics in Calamity Physics|Special Topics in Calamity Physics]]'' by [[w:Marisha Pessl|Marisha Pessl]] *''Sweet and Low: A Family Story'' by [[w:Rich Cohen (author)|Rich Cohen]] *''[[w:Twilight of the Superheroes|Twilight of the Superheroes]]'' by [[w:Deborah Eisenberg|Deborah Eisenberg]] *''[[w:What Is the What|What Is the What]]'' by [[w:Dave Eggers|Dave Eggers]] *''[[w:Wizard of the Crow|Wizard of the Crow]]'' by [[w:Ngũgĩ wa Thiong'o|Ngũgĩ wa Thiong'o]] ===2007=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Salon Book Awards 2007 |work=[[w:Salon (website)|Salon]] |date=December 12, 2007 |url=https://www.salon.com/2007/12/12/best_books/ |archive-url=https://web.archive.org/web/20111112221324/https://www.salon.com/2007/12/12/best_books/ |archive-date=2011-11-12 }}</ref> *''[[w:The Brief Wondrous Life of Oscar Wao|The Brief Wondrous Life of Oscar Wao]]'' by [[w:Junot Díaz|Junot Díaz]] *''The Father of All Things: A Marine, His Son, and the Legacy of Vietnam'' by [[w:Tom Bissell|Tom Bissell]] *''Gertrude Bell: Queen of the Desert, Shaper of Nations'' by [[w:Georgina Howell|Georgina Howell]] *''[[w:Legacy of Ashes: The History of the CIA|Legacy of Ashes: The History of the CIA]]'' by [[w:Tim Weiner|Tim Weiner]] *''The Long Embrace: Raymond Chandler and the Woman He Loved'' by [[w:Judith Freeman (author)|Judith Freeman]] *''[[w:Sacred Games (novel)|Sacred Games]]'' by [[w:Vikram Chandra|Vikram Chandra]] *''[[w:Then We Came to the End|Then We Came to the End]]'' by [[w:Joshua Ferris|Joshua Ferris]] *''[[w:Tree of Smoke|Tree of Smoke]]'' by [[w:Denis Johnson|Denis Johnson]] *''[[w:The World Without Us|The World Without Us]]'' by [[w:Alan Weisman|Alan Weisman]] *''[[w:The Yiddish Policemen's Union|The Yiddish Policemen's Union]]'' by [[w:Michael Chabon|Michael Chabon]] ===2008=== *''[[w:2666 (novel)|2666]]'' by [[w:Roberto Bolaño|Roberto Bolaño]] *''Atmospheric Disturbances: A Novel'' by [[w:Rivka Galchen|Rivka Galchen]] *''Buying In: The Secret Dialogue Between What We Buy and Who We Are'' by [[w:Rob Walker (journalist)|Rob Walker]] *''The Likeness'' by [[w:Tana French|Tana French]] *''The Northern Clemency'' by [[w:Philip Hensher|Philip Hensher]] *''A Person of Interest: A Novel'' by [[w:Susan Choi|Susan Choi]] *''Pictures at a Revolution: Five Movies and the Birth of the New Hollywood'' by [[w:Mark Harris (American author)|Mark Harris]] *''The Suicide Index: Putting My Father's Death in Order'' by [[w:Joan Wickersham|Joan Wickersham]] *''The Suspicions of Mr. Whicher: A Shocking Murder and the Undoing of a Great Victorian Detective'' by [[w:Kate Summerscale|Kate Summerscale]] ===2009=== Source:<ref>{{cite web |last=Miller |first=Laura |title=Best of 2009 |work=[[w:Salon (website)|Salon]] |date=December 8, 2009 |url=http://www.salon.com/topic/best_of_2009/page/2/ |archive-url=https://web.archive.org/web/20120601152805/http://www.salon.com/topic/best_of_2009/page/2/ |archive-date=2012-06-01 }}</ref> *''[[w:The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science|The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science]]'' by [[w:Richard Holmes (biographer)|Richard Holmes]] *''Await Your Reply'' by [[w:Dan Chaon|Dan Chaon]] *''[[w:The Children's Book|The Children's Book]]'' by [[w:A. S. Byatt|A. S. Byatt]] *''[[w:Chronic City|Chronic City]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''[[w:Columbine (book)|Columbine]]'' by [[w:Dave Cullen|Dave Cullen]] *''[[w:The Little Stranger|The Little Stranger]]'' by [[w:Sarah Waters|Sarah Waters]] *''Love in Infant Monkeys: Stories'' by [[w:Lydia Millet|Lydia Millet]] *''A New Literary History of America (Harvard University Press Reference Library)'' by [[w:Greil Marcus|Greil Marcus]] *''Somewhere Towards the End: A Memoir'' by [[w:Diana Athill|Diana Athill]] *''Tall Man: The Death of Doomadgee'' by [[w:Chloe Hooper|Chloe Hooper]] ===2010=== Source:<ref name="salon-nonfiction-2010">{{cite web |last=Miller |first=Laura |date=December 7, 2010 |title=The best nonfiction books of 2010 |url=http://www.salon.com/books/laura_miller/2010/12/07/best_books_nonfiction |website=[[w:Salon (website)|Salon]]}}</ref><ref name="salon-fiction-2010">{{cite web |last=Miller |first=Laura |date=December 6, 2010 |title=The best fiction of 2010 |url=http://www.salon.com/books/laura_miller/2010/12/06/best_books_fiction |website=[[w:Salon (website)|Salon]]}}</ref> *''The Possessed: Adventures With Russian Books and the People Who Read Them'' by [[w:Elif Batuman|Elif Batuman]] *''[[w:The Big Short|The Big Short]]'' by [[w:Michael Lewis (author)|Michael Lewis]] (tied with John Lanchester) *''I.O.U.: Why Everyone Owes Everyone and No One Can Pay'' by [[w:John Lanchester|John Lanchester]] (tied with Michael Lewis) *''Let the Swords Encircle Me: Iran – a Journey Behind the Headlines'' by [[w:Scott Peterson (writer)|Scott Peterson]] *''[[w:The Immortal Life of Henrietta Lacks|The Immortal Life of Henrietta Lacks]]'' by [[w:Rebecca Skloot|Rebecca Skloot]] *''[[w:The Warmth of Other Suns|The Warmth of Other Suns]]'' by [[w:Isabel Wilkerson|Isabel Wilkerson]] *''[[w:Room (novel)|Room]]'' by [[w:Emma Donoghue|Emma Donoghue]] *''[[w:A Visit From the Goon Squad|A Visit From the Goon Squad]]'' by [[w:Jennifer Egan|Jennifer Egan]] *''[[w:Freedom (novel)|Freedom]]'' by [[w:Jonathan Franzen|Jonathan Franzen]] *''[[w:Faithful Place|Faithful Place]]'' by [[w:Tana French|Tana French]] *''[[w:Super Sad True Love Story|Super Sad True Love Story]]'' by [[w:Gary Shteyngart|Gary Shteyngart]] ===2011=== Source:<ref name="salon-fiction-2011">{{cite web |last=Miller |first=Laura |date=December 7, 2011 |title=The best fiction of 2011 |url=http://entertainment.salon.com/2011/12/07/the_best_fiction_of_2011/ |website=[[w:Salon (website)|Salon]]}}</ref><ref name="salon-nonfiction-2011">{{cite web |last=Miller |first=Laura |date=December 8, 2011 |title=The best nonfiction of 2011 |url=http://www.salon.com/2011/12/08/the_best_nonfiction_of_2011/ |website=[[w:Salon (website)|Salon]]}}</ref> *''[[w:The Marriage Plot|The Marriage Plot]]'' by [[w:Jeffrey Eugenides|Jeffrey Eugenides]] *''[[w:Pym (novel)|Pym]]'' by [[w:Mat Johnson|Mat Johnson]] *''[[w:State of Wonder|State of Wonder]]'' by [[w:Ann Patchett|Ann Patchett]] *''[[w:The Tragedy of Arthur|The Tragedy of Arthur]]'' by [[w:Arthur Phillips|Arthur Phillips]] *''[[w:The Pale King|The Pale King]]'' by [[w:David Foster Wallace|David Foster Wallace]] *''Townie: A Memoir'' by [[w:Andre Dubus III|Andre Dubus III]] *''Love and Capital: Karl and Jenny Marx and the Birth of a Revolution'' by [[w:Mary Gabriel (author)|Mary Gabriel]] *''[[w:The Information: A History, a Theory, a Flood|The Information: A History, a Theory, a Flood]]'' by [[w:James Gleick|James Gleick]] *''Catherine the Great: The Portrait of a Woman'' by [[w:Robert K. Massie|Robert K. Massie]] *''[[w:Lost in Shangri-La|Lost in Shangri-La]]'' by [[w:Mitchell Zuckoff|Mitchell Zuckoff]] ===2012=== New award established as "What To Read Awards" with books chosen by a system of points from an array of other journalists top-10 lists.<ref name="daley2012">{{cite web |url=http://www.salon.com/2012/12/23/the_what_to_read_awards_top_10_books_of_2012/ |title=The What To Read Awards: Top 10 Books of 2012 |website=[[w:Salon (website)|Salon]] |last=Daley |first=David |date=December 23, 2012 |access-date=December 24, 2012}}</ref> See also Laura Miller's top-10 picks.<ref>{{cite web |url=http://www.salon.com/2012/12/22/laura_millers_best_books_of_2012/ |title=Laura Miller’s best books of 2012 |website=[[w:Salon (website)|Salon]] |last=Miller |first=Laura |date=December 22, 2012 |access-date=December 24, 2012}}</ref> #[[w:Katherine Boo|Katherine Boo]], ''[[w:Behind the Beautiful Forevers|Behind the Beautiful Forevers]]'' #[[w:Hilary Mantel|Hilary Mantel]], ''[[w:Bring Up the Bodies|Bring Up the Bodies]]'' #[[w:Ben Fountain|Ben Fountain]], ''Billy Lynn’s Long Halftime Walk'' #[[w:Zadie Smith|Zadie Smith]], ''NW'', and [[w:Andrew Solomon|Andrew Solomon]], ''Far From the Tree'' (co-winners) #[[w:Sheila Heti|Sheila Heti]], ''How Should a Person Be'' #[[w:Gillian Flynn|Gillian Flynn]], ''Gone Girl'' #[[w:Lauren Groff|Lauren Groff]], ''Arcadia'' #[[w:Jess Walter|Jess Walter]], ''Beautiful Ruins'' #[[w:Sarah Manguso|Sarah Manguso]], ''The Guardians'' ==Notes== {{Reflist}} ==Wikiversity status== {{Complete}} [[Category:Literature]] 326onk2onrufm7kj68408ybykud3t2a 2844829 2844828 2026-11-07T21:42:02Z GreenC 268373 2844829 wikitext text/x-wiki The '''Salon Book Awards''' were an annual [[w:literary award|literary feature]] issued by the online magazine [[w:Salon (website)|Salon.com]] from 1996 to 2011, recognizing the year's fiction and nonfiction. The awards were established in December 1996 by Salon's literary editors [[w:Laura Miller (writer)|Laura Miller]] and [[w:Dwight Garner (critic)|Dwight Garner]] during the early days of the web. It was a period when the site was helping to establish a new industry of professional cultural criticism that was published digitally on the web. Rather than a formal juried prize with a physical ceremony or endowment, the award served as the publication's year-end "Best Of" list. The editors' methodology for selecting the winning books was highly personal. In the inaugural 1996 announcement, Miller and Garner emphasized that they deliberately excluded books written by personal friends to avoid the appearance of nepotism, and favored unified novels and narratives over short-story or essay collections. The overarching criteria were: :"..the books we'd wholeheartedly recommend to our friends, books we'd clear our social calendar to finish, books we returned to eagerly even when we could barely focus our eyes on a page. They remind us of why we fell in love with reading and why we keep at it in a world that's simultaneously cluttered with mediocre books and increasingly indifferent to the written word."<ref name="1996 award">{{cite web |last1=Miller |first1=Laura |last2=Garner |first2=Dwight |title=Books of the Year |url=https://www.salon.com/1996/12/09/awards961209/ |archive-url=https://web.archive.org/web/20190722223228/https://www.salon.com/1996/12/09/awards961209/ |archive-date=2019-07-22 |date=December 9, 1996 |website=[[w:Salon (website)|Salon]]}}</ref> Following the 2011 awards, the original format was retired. In 2012, a new accolade was established called the '''What To Read Awards''', named after Salon's ongoing "What to Read" column. Although Laura Miller continued to publish a separate "Best Books of the Year" top-10 list, the new awards crowdsourced the selections by polling the broader literary community. The editors tabulated the What To Read Awards as follows: :"we surveyed our favorite book critics, both print and online, from high-profile publications to the hottest literary blogs. We asked for their top-10 books of 2012, and then tabulated the winners by assigning 10 points for a No. 1 selection, 9 for No. 2, all the way to 1 point for No. 10."<ref name="daley2012"/> ==Winners of Salon Book Awards== The following is a list of the winners of the Salon Book Awards for each year. ===1996=== Source:<ref name="1996 award" /> *''[[w:Angela's Ashes|Angela's Ashes]]'' by [[w:Frank McCourt|Frank McCourt]] *''[[w:The Family Markowitz|The Family Markowitz]]'' by [[w:Allegra Goodman|Allegra Goodman]] *''The Giant's House: A Romance'' by [[w:Elizabeth McCracken|Elizabeth McCracken]] *''[[w:Infinite Jest|Infinite Jest]]'' by [[w:David Foster Wallace|David Foster Wallace]] *''The Living and the Dead: Robert McNamara and Five Lives of a Lost War'' by [[w:Paul Hendrickson|Paul Hendrickson]] *''[[w:The Moor's Last Sigh|The Moor's Last Sigh]]'' by [[w:Salman Rushdie|Salman Rushdie]] *''[[w:My Dark Places (book)|My Dark Places]]'' by [[w:James Ellroy|James Ellroy]] *''Reader's Block'' by [[w:David Markson|David Markson]] *''The Shadow Man'' by [[w:Mary Gordon (writer)|Mary Gordon]] *''The Temple Bombing'' by [[w:Melissa Fay Greene|Melissa Fay Greene]] ===1997=== Source:<ref>{{cite web |last1=Miller |first1=Laura |last2=Garner |first2=Dwight |title=The second annual Salon Book Awards |work=[[w:Salon (website)|Salon]] |date=January 5, 1998 |url=https://www.salon.com/1998/01/05/the_second_annual_salon_book_awards/ |archive-url=https://web.archive.org/web/20171010021903/https://www.salon.com/1998/01/05/the_second_annual_salon_book_awards/ |archive-date=2017-10-10 }}</ref> *''[[w:Alias Grace|Alias Grace]]'' by [[w:Margaret Atwood|Margaret Atwood]] *''Because They Wanted to: Stories'' by [[w:Mary Gaitskill|Mary Gaitskill]] *''Close to the Machine: Technophilia and Its Discontents'' by [[w:Ellen Ullman|Ellen Ullman]] *''[[w:Cold Mountain (novel)|Cold Mountain]]'' by [[w:Charles Frazier|Charles Frazier]] *''Echoes of a Native Land: Two Centuries of a Russian Village'' by [[w:Serge Schmemann|Serge Schmemann]] *''How Proust Can Change Your Life'' by [[w:Alain de Botton|Alain de Botton]] *''[[w:Into Thin Air|Into Thin Air: A Personal Account of the Mt. Everest Disaster]]'' by [[w:Jon Krakauer|Jon Krakauer]] *''[[w:Mason & Dixon|Mason & Dixon]]'' by [[w:Thomas Pynchon|Thomas Pynchon]] *''[[w:The Reader|The Reader]]'' by [[w:Bernhard Schlink|Bernhard Schlink]] *''[[w:The Spirit Catches You and You Fall Down|The Spirit Catches You and You Fall Down]]'' by [[w:Anne Fadiman|Anne Fadiman]] ===1998=== *''At Home with the Marquis de Sade: A Life'' by [[w:Francine du Plessix Gray|Francine du Plessix Gray]] *''[[w:A Beautiful Mind (book)|A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash]]'' by [[w:Sylvia Nasar|Sylvia Nasar]] *''[[w:Birds of America (stories)|Birds of America]]'' by [[w:Lorrie Moore|Lorrie Moore]] *''[[w:Blindness (novel)|Blindness]]'' by [[w:José Saramago|José Saramago]] *''A Slant of Sun: One Child's Courage'' by [[w:Beth Kephart|Beth Kephart]] *''[[w:Starting Out in the Evening|Starting Out in the Evening]]'' by [[w:Brian Morton (American author)|Brian Morton]] *''[[w:The Surgeon of Crowthorne|The Surgeon of Crowthorne]]'' by [[w:Simon Winchester|Simon Winchester]] *''Thirst'' by [[w:Ken Kalfus|Ken Kalfus]] *''The Voyage of the Narwhal'' by [[w:Andrea Barrett|Andrea Barrett]] *''[[w:We Wish to Inform You That Tomorrow We Will be Killed With Our Families|We Wish to Inform You That Tomorrow We Will be Killed With Our Families: Stories from Rwanda]]'' by [[w:Philip Gourevitch|Philip Gourevitch]] ===1999=== *''[[w:Black Hawk Down: A Story of Modern War|Black Hawk Down: A Story of Modern War]]'' by [[w:Mark Bowden|Mark Bowden]] *''Careless Love: The Unmaking of Elvis Presley'' by [[w:Peter Guralnick|Peter Guralnick]] *''[[w:Cryptonomicon|Cryptonomicon]]'' by [[w:Neal Stephenson|Neal Stephenson]] *''Lost on Earth: Nomads of the New World'' by [[w:Mark Fritz|Mark Fritz]] *''[[w:Motherless Brooklyn|Motherless Brooklyn]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''Original Bliss'' by [[w:A. L. Kennedy|A. L. Kennedy]] *''[[w:Plainsong (novel)|Plainsong]]'' by [[w:Kent Haruf|Kent Haruf]] *''[[w:A Prayer for the Dying|A Prayer for the Dying]]'' by [[w:Stewart O'Nan|Stewart O'Nan]] *''Secrets of the Flesh: A Life of Colette (Ballantine Reader's Circle)'' by [[w:Judith Thurman|Judith Thurman]] *''Show Me a Hero: A Tale of Murder, Suicide, Race, and Redemption'' by [[w:Lisa Belkin|Lisa Belkin]] ===2000=== Source:<ref>{{cite web |last1=Russo |first1=Mario |last2=Miller |first2=Laura |title=Salon Book Awards |work=Salon |date=December 18, 2000 |url=https://www.salon.com/2000/12/18/bookawards/ |archive-url=https://web.archive.org/web/20160212125119/https://www.salon.com/2000/12/18/bookawards/ |archive-date=2016-02-12 }}</ref> *''[[w:Richard_Slotkin#Abe:_A_Novel_of_the_Young_Lincoln|Abe: A Novel of the Young Lincoln]]'' by [[w:Richard Slotkin|Richard Slotkin]] *''An American Story'' by [[w:Debra Dickerson|Debra Dickerson]] *''[[w:Being Dead|Being Dead]]'' by [[w:Jim Crace|Jim Crace]] *''The Blood Runs Like a River Through My Dreams'' by [[w:Nasdijj|Nasdijj]] *''Boxer Rebellion: The Dramatic Story of China's War on Foreigners that Shook the World in the Summer of 1900'' by [[w:Diana Preston|Diana Preston]] *''Lying Awake'' by [[w:Mark Salzman|Mark Salzman]] *''The Name of the World: A Novel'' by [[w:Denis Johnson|Denis Johnson]] *''Pontius Pilate : The Biography of an Invented Man'' by [[w:Ann Wroe|Ann Wroe]] *''The Social Lives of Dogs'' by [[w:Elizabeth Marshall Thomas|Elizabeth Marshall Thomas]] *''[[w:White Teeth|White Teeth]]'' by [[w:Zadie Smith|Zadie Smith]] ===2001=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Our favorite books |work=[[w:Salon (website)|Salon]] |date=January 9, 2002 |url=https://www.salon.com/2002/01/09/bestbooks_2/ |archive-url=https://web.archive.org/web/20120712170827/https://www.salon.com/2002/01/09/bestbooks_2/ |archive-date=2012-07-12 }}</ref> *''[[w:Austerlitz (novel)|Austerlitz]]'' by [[w:W. G. Sebald|W. G. Sebald]] *''[[w:Bel Canto (novel)|Bel Canto]]'' by [[w:Ann Patchett|Ann Patchett]] *''Borrowed Finery: A Memoir'' by [[w:Paula Fox|Paula Fox]] *''[[w:The Corrections|The Corrections]]'' by [[w:Jonathan Franzen|Jonathan Franzen]] *''[[w:John Adams (book)|John Adams]]'' by [[w:David McCullough|David McCullough]] *''[[w:John Henry Days|John Henry Days]]'' by [[w:Colson Whitehead|Colson Whitehead]] *''[[w:Seabiscuit: An American Legend|Seabiscuit: An American Legend]]'' by [[w:Laura Hillenbrand|Laura Hillenbrand]] *''Stranger Things Happen: Stories'' by [[w:Kelly Link|Kelly Link]] *''Strip City: A Stripper's Farewell Journey Across America'' by [[w:Lily Burana|Lily Burana]] *''[[w:Wittgenstein's Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers|Wittgenstein's Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers]]'' by [[w:David Edmonds (philosopher)|David Edmonds]] ===2002=== No awards were given for the year of 2002. ===2003=== *''American Woman: A Novel'' by [[w:Susan Choi|Susan Choi]] *''[[w:Any Human Heart|Any Human Heart]]'' by [[w:William Boyd (writer)|William Boyd]] *''Brick Lane'' by [[w:Monica Ali|Monica Ali]] *''The Bug'' by [[w:Ellen Ullman|Ellen Ullman]] *''[[w:The Curious Incident of the Dog in the Night-Time|The Curious Incident of the Dog in the Night-Time]]'' by [[w:Mark Haddon|Mark Haddon]] *''[[w:Drop City|Drop City]]'' by [[w:T. C. Boyle|T. C. Boyle]] *''[[w:The Fortress of Solitude|The Fortress of Solitude]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''I Should Be Extremely Happy in Your Company: A Novel of Lewis and Clark'' by [[w:Brian Hall (author)|Brian Hall]] *''[[w:Old School (novel)|Old School]]'' by [[w:Tobias Wolff|Tobias Wolff]] *''[[w:Property (novel)|Property]]'' by [[w:Valerie Martin|Valerie Martin]] ===2004=== *''American Brutus: John Wilkes Booth and the Lincoln Conspiracies'' by [[w:Michael W. Kauffman|Michael W. Kauffman]] *''Arc of Justice: A Saga of Race, Civil Rights, and Murder in the Jazz Age'' by [[w:Kevin Boyle (historian)|Kevin Boyle]] *''[[w:Case Histories|Case Histories]]'' by [[w:Kate Atkinson|Kate Atkinson]] *''[[w:Happy Baby|Happy Baby]]'' by [[w:Stephen Elliott (author)|Stephen Elliott]] *''[[w:Jonathan Strange & Mr Norrell|Jonathan Strange & Mr Norrell]]'' by [[w:Susanna Clarke|Susanna Clarke]] *''[[w:The Line of Beauty|The Line of Beauty]]'' by [[w:Alan Hollinghurst|Alan Hollinghurst]] *''Nightingales: The Extraordinary Upbringing and Curious Life of Miss Florence Nightingale'' by [[w:Gillian Gill|Gillian Gill]] *''Skeletons on the Zahara: A True Story of Survival'' by [[w:Dean King|Dean King]] *''[[w:Snow (Pamuk novel)|Snow]]'' by [[w:Orhan Pamuk|Orhan Pamuk]] *''The Working Poor: Invisible in America'' by [[w:David K. Shipler|David K. Shipler]] ===2005=== Source:<ref>{{cite web |last1=Miller |first1=Laura |last2=Frey |first2=Hillary |title=The best books of 2005 |work=[[w:Salon (website)|Salon]] |date=December 19, 2005 |url=https://www.salon.com/2005/12/19/best_of_2/ |archive-url=https://web.archive.org/web/20111230083620/https://www.salon.com/2005/12/19/best_of_2/ |archive-date=2011-12-30 }}</ref> *''[[w:1491: New Revelations of the Americas Before Columbus|1491: New Revelations of the Americas Before Columbus]]'' by [[w:Charles C. Mann|Charles C. Mann]] *''The Assassins' Gate'' by [[w:George Packer|George Packer]] *''Dream Boogie: The Triumph of Sam Cooke'' by [[w:Peter Guralnick|Peter Guralnick]] *''[[w:Kafka on the Shore|Kafka on the Shore]]'' by [[w:Haruki Murakami|Haruki Murakami]] *''[[w:Magic for Beginners|Magic for Beginners]]'' by [[w:Kelly Link|Kelly Link]] *''[[w:Never Let Me Go (novel)|Never Let Me Go]]'' by [[w:Kazuo Ishiguro|Kazuo Ishiguro]] *''[[w:On Beauty|On Beauty]]'' by [[w:Zadie Smith|Zadie Smith]] *''Them: A Memoir of Parents'' by [[w:Francine du Plessix Gray|Francine du Plessix Gray]] *''[[w:Times Like These (novel)|Times Like These]]'' by [[w:Rachel Ingalls|Rachel Ingalls]] *''Tulia'' by [[w:Nate Blakeslee|Nate Blakeslee]] *''Veronica'' by [[w:Mary Gaitskill|Mary Gaitskill]] ===2006=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Authors' picks |work=[[w:Salon (website)|Salon]] |date=December 11, 2006 |url=https://www.salon.com/2006/12/11/authors_picks_2/ |archive-url=https://web.archive.org/web/20120430155625/https://www.salon.com/2006/12/11/authors_picks_2/ |archive-date=2012-04-30 }}</ref> *''[[w:The Amalgamation Polka|The Amalgamation Polka]]'' by [[w:Stephen Wright (writer)|Stephen Wright]] *''A Disorder Peculiar to the Country: A Novel'' by [[w:Ken Kalfus|Ken Kalfus]] *''The Family That Couldn't Sleep: A Medical Mystery'' by [[w:D.T. Max|D.T. Max]] *''[[w:Fun Home: A Family Tragicomic|Fun Home: A Family Tragicomic]]'' by [[w:Alison Bechdel|Alison Bechdel]] *''James Tiptree, Jr.: The Double Life of Alice B. Sheldon'' by [[w:Julie Phillips|Julie Phillips]] *''[[w:The Lost: A Search for Six of Six Million|The Lost: A Search for Six of Six Million]]'' by [[w:Daniel Mendelsohn|Daniel Mendelsohn]] *''[[w:The Omnivore's Dilemma: A Natural History of Four Meals|The Omnivore's Dilemma: A Natural History of Four Meals]]'' by [[w:Michael Pollan|Michael Pollan]] *''[[w:Special Topics in Calamity Physics|Special Topics in Calamity Physics]]'' by [[w:Marisha Pessl|Marisha Pessl]] *''Sweet and Low: A Family Story'' by [[w:Rich Cohen (author)|Rich Cohen]] *''[[w:Twilight of the Superheroes|Twilight of the Superheroes]]'' by [[w:Deborah Eisenberg|Deborah Eisenberg]] *''[[w:What Is the What|What Is the What]]'' by [[w:Dave Eggers|Dave Eggers]] *''[[w:Wizard of the Crow|Wizard of the Crow]]'' by [[w:Ngũgĩ wa Thiong'o|Ngũgĩ wa Thiong'o]] ===2007=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Salon Book Awards 2007 |work=[[w:Salon (website)|Salon]] |date=December 12, 2007 |url=https://www.salon.com/2007/12/12/best_books/ |archive-url=https://web.archive.org/web/20111112221324/https://www.salon.com/2007/12/12/best_books/ |archive-date=2011-11-12 }}</ref> *''[[w:The Brief Wondrous Life of Oscar Wao|The Brief Wondrous Life of Oscar Wao]]'' by [[w:Junot Díaz|Junot Díaz]] *''The Father of All Things: A Marine, His Son, and the Legacy of Vietnam'' by [[w:Tom Bissell|Tom Bissell]] *''Gertrude Bell: Queen of the Desert, Shaper of Nations'' by [[w:Georgina Howell|Georgina Howell]] *''[[w:Legacy of Ashes: The History of the CIA|Legacy of Ashes: The History of the CIA]]'' by [[w:Tim Weiner|Tim Weiner]] *''The Long Embrace: Raymond Chandler and the Woman He Loved'' by [[w:Judith Freeman (author)|Judith Freeman]] *''[[w:Sacred Games (novel)|Sacred Games]]'' by [[w:Vikram Chandra|Vikram Chandra]] *''[[w:Then We Came to the End|Then We Came to the End]]'' by [[w:Joshua Ferris|Joshua Ferris]] *''[[w:Tree of Smoke|Tree of Smoke]]'' by [[w:Denis Johnson|Denis Johnson]] *''[[w:The World Without Us|The World Without Us]]'' by [[w:Alan Weisman|Alan Weisman]] *''[[w:The Yiddish Policemen's Union|The Yiddish Policemen's Union]]'' by [[w:Michael Chabon|Michael Chabon]] ===2008=== *''[[w:2666 (novel)|2666]]'' by [[w:Roberto Bolaño|Roberto Bolaño]] *''Atmospheric Disturbances: A Novel'' by [[w:Rivka Galchen|Rivka Galchen]] *''Buying In: The Secret Dialogue Between What We Buy and Who We Are'' by [[w:Rob Walker (journalist)|Rob Walker]] *''The Likeness'' by [[w:Tana French|Tana French]] *''The Northern Clemency'' by [[w:Philip Hensher|Philip Hensher]] *''A Person of Interest: A Novel'' by [[w:Susan Choi|Susan Choi]] *''Pictures at a Revolution: Five Movies and the Birth of the New Hollywood'' by [[w:Mark Harris (American author)|Mark Harris]] *''The Suicide Index: Putting My Father's Death in Order'' by [[w:Joan Wickersham|Joan Wickersham]] *''The Suspicions of Mr. Whicher: A Shocking Murder and the Undoing of a Great Victorian Detective'' by [[w:Kate Summerscale|Kate Summerscale]] ===2009=== Source:<ref>{{cite web |last=Miller |first=Laura |title=Best of 2009 |work=[[w:Salon (website)|Salon]] |date=December 8, 2009 |url=http://www.salon.com/topic/best_of_2009/page/2/ |archive-url=https://web.archive.org/web/20120601152805/http://www.salon.com/topic/best_of_2009/page/2/ |archive-date=2012-06-01 }}</ref> *''[[w:The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science|The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science]]'' by [[w:Richard Holmes (biographer)|Richard Holmes]] *''Await Your Reply'' by [[w:Dan Chaon|Dan Chaon]] *''[[w:The Children's Book|The Children's Book]]'' by [[w:A. S. Byatt|A. S. Byatt]] *''[[w:Chronic City|Chronic City]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''[[w:Columbine (book)|Columbine]]'' by [[w:Dave Cullen|Dave Cullen]] *''[[w:The Little Stranger|The Little Stranger]]'' by [[w:Sarah Waters|Sarah Waters]] *''Love in Infant Monkeys: Stories'' by [[w:Lydia Millet|Lydia Millet]] *''A New Literary History of America (Harvard University Press Reference Library)'' by [[w:Greil Marcus|Greil Marcus]] *''Somewhere Towards the End: A Memoir'' by [[w:Diana Athill|Diana Athill]] *''Tall Man: The Death of Doomadgee'' by [[w:Chloe Hooper|Chloe Hooper]] ===2010=== Source:<ref name="salon-nonfiction-2010">{{cite web |last=Miller |first=Laura |date=December 7, 2010 |title=The best nonfiction books of 2010 |url=http://www.salon.com/books/laura_miller/2010/12/07/best_books_nonfiction |website=[[w:Salon (website)|Salon]]}}</ref><ref name="salon-fiction-2010">{{cite web |last=Miller |first=Laura |date=December 6, 2010 |title=The best fiction of 2010 |url=http://www.salon.com/books/laura_miller/2010/12/06/best_books_fiction |website=[[w:Salon (website)|Salon]]}}</ref> *''The Possessed: Adventures With Russian Books and the People Who Read Them'' by [[w:Elif Batuman|Elif Batuman]] *''[[w:The Big Short|The Big Short]]'' by [[w:Michael Lewis (author)|Michael Lewis]] (tied with John Lanchester) *''I.O.U.: Why Everyone Owes Everyone and No One Can Pay'' by [[w:John Lanchester|John Lanchester]] (tied with Michael Lewis) *''Let the Swords Encircle Me: Iran – a Journey Behind the Headlines'' by [[w:Scott Peterson (writer)|Scott Peterson]] *''[[w:The Immortal Life of Henrietta Lacks|The Immortal Life of Henrietta Lacks]]'' by [[w:Rebecca Skloot|Rebecca Skloot]] *''[[w:The Warmth of Other Suns|The Warmth of Other Suns]]'' by [[w:Isabel Wilkerson|Isabel Wilkerson]] *''[[w:Room (novel)|Room]]'' by [[w:Emma Donoghue|Emma Donoghue]] *''[[w:A Visit From the Goon Squad|A Visit From the Goon Squad]]'' by [[w:Jennifer Egan|Jennifer Egan]] *''[[w:Freedom (novel)|Freedom]]'' by [[w:Jonathan Franzen|Jonathan Franzen]] *''[[w:Faithful Place|Faithful Place]]'' by [[w:Tana French|Tana French]] *''[[w:Super Sad True Love Story|Super Sad True Love Story]]'' by [[w:Gary Shteyngart|Gary Shteyngart]] ===2011=== Source:<ref name="salon-fiction-2011">{{cite web |last=Miller |first=Laura |date=December 7, 2011 |title=The best fiction of 2011 |url=http://entertainment.salon.com/2011/12/07/the_best_fiction_of_2011/ |website=[[w:Salon (website)|Salon]]}}</ref><ref name="salon-nonfiction-2011">{{cite web |last=Miller |first=Laura |date=December 8, 2011 |title=The best nonfiction of 2011 |url=http://www.salon.com/2011/12/08/the_best_nonfiction_of_2011/ |website=[[w:Salon (website)|Salon]]}}</ref> *''[[w:The Marriage Plot|The Marriage Plot]]'' by [[w:Jeffrey Eugenides|Jeffrey Eugenides]] *''[[w:Pym (novel)|Pym]]'' by [[w:Mat Johnson|Mat Johnson]] *''[[w:State of Wonder|State of Wonder]]'' by [[w:Ann Patchett|Ann Patchett]] *''[[w:The Tragedy of Arthur|The Tragedy of Arthur]]'' by [[w:Arthur Phillips|Arthur Phillips]] *''[[w:The Pale King|The Pale King]]'' by [[w:David Foster Wallace|David Foster Wallace]] *''Townie: A Memoir'' by [[w:Andre Dubus III|Andre Dubus III]] *''Love and Capital: Karl and Jenny Marx and the Birth of a Revolution'' by [[w:Mary Gabriel (author)|Mary Gabriel]] *''[[w:The Information: A History, a Theory, a Flood|The Information: A History, a Theory, a Flood]]'' by [[w:James Gleick|James Gleick]] *''Catherine the Great: The Portrait of a Woman'' by [[w:Robert K. Massie|Robert K. Massie]] *''[[w:Lost in Shangri-La|Lost in Shangri-La]]'' by [[w:Mitchell Zuckoff|Mitchell Zuckoff]] ===2012=== New award established as "What To Read Awards" with books chosen by a system of points from an array of other journalists top-10 lists.<ref name="daley2012">{{cite web |url=http://www.salon.com/2012/12/23/the_what_to_read_awards_top_10_books_of_2012/ |title=The What To Read Awards: Top 10 Books of 2012 |website=[[w:Salon (website)|Salon]] |last=Daley |first=David |date=December 23, 2012 |access-date=December 24, 2012}}</ref> See also Laura Miller's top-10 picks.<ref>{{cite web |url=http://www.salon.com/2012/12/22/laura_millers_best_books_of_2012/ |title=Laura Miller’s best books of 2012 |website=[[w:Salon (website)|Salon]] |last=Miller |first=Laura |date=December 22, 2012 |access-date=December 24, 2012}}</ref> #[[w:Katherine Boo|Katherine Boo]], ''[[w:Behind the Beautiful Forevers|Behind the Beautiful Forevers]]'' #[[w:Hilary Mantel|Hilary Mantel]], ''[[w:Bring Up the Bodies|Bring Up the Bodies]]'' #[[w:Ben Fountain|Ben Fountain]], ''Billy Lynn’s Long Halftime Walk'' #[[w:Zadie Smith|Zadie Smith]], ''NW'', and [[w:Andrew Solomon|Andrew Solomon]], ''Far From the Tree'' (co-winners) #[[w:Sheila Heti|Sheila Heti]], ''How Should a Person Be'' #[[w:Gillian Flynn|Gillian Flynn]], ''Gone Girl'' #[[w:Lauren Groff|Lauren Groff]], ''Arcadia'' #[[w:Jess Walter|Jess Walter]], ''Beautiful Ruins'' #[[w:Sarah Manguso|Sarah Manguso]], ''The Guardians'' ==Notes== {{Reflist}} ==Wikiversity status== {{Complete}} [[Category:Literature]] kr3dj59lov4jcfitbdc96767qveq5od 2844847 2844829 2026-11-08T03:48:38Z GreenC 268373 /* 2012 */ 2844847 wikitext text/x-wiki The '''Salon Book Awards''' were an annual [[w:literary award|literary feature]] issued by the online magazine [[w:Salon (website)|Salon.com]] from 1996 to 2011, recognizing the year's fiction and nonfiction. The awards were established in December 1996 by Salon's literary editors [[w:Laura Miller (writer)|Laura Miller]] and [[w:Dwight Garner (critic)|Dwight Garner]] during the early days of the web. It was a period when the site was helping to establish a new industry of professional cultural criticism that was published digitally on the web. Rather than a formal juried prize with a physical ceremony or endowment, the award served as the publication's year-end "Best Of" list. The editors' methodology for selecting the winning books was highly personal. In the inaugural 1996 announcement, Miller and Garner emphasized that they deliberately excluded books written by personal friends to avoid the appearance of nepotism, and favored unified novels and narratives over short-story or essay collections. The overarching criteria were: :"..the books we'd wholeheartedly recommend to our friends, books we'd clear our social calendar to finish, books we returned to eagerly even when we could barely focus our eyes on a page. They remind us of why we fell in love with reading and why we keep at it in a world that's simultaneously cluttered with mediocre books and increasingly indifferent to the written word."<ref name="1996 award">{{cite web |last1=Miller |first1=Laura |last2=Garner |first2=Dwight |title=Books of the Year |url=https://www.salon.com/1996/12/09/awards961209/ |archive-url=https://web.archive.org/web/20190722223228/https://www.salon.com/1996/12/09/awards961209/ |archive-date=2019-07-22 |date=December 9, 1996 |website=[[w:Salon (website)|Salon]]}}</ref> Following the 2011 awards, the original format was retired. In 2012, a new accolade was established called the '''What To Read Awards''', named after Salon's ongoing "What to Read" column. Although Laura Miller continued to publish a separate "Best Books of the Year" top-10 list, the new awards crowdsourced the selections by polling the broader literary community. The editors tabulated the What To Read Awards as follows: :"we surveyed our favorite book critics, both print and online, from high-profile publications to the hottest literary blogs. We asked for their top-10 books of 2012, and then tabulated the winners by assigning 10 points for a No. 1 selection, 9 for No. 2, all the way to 1 point for No. 10."<ref name="daley2012"/> ==Winners of Salon Book Awards== The following is a list of the winners of the Salon Book Awards for each year. ===1996=== Source:<ref name="1996 award" /> *''[[w:Angela's Ashes|Angela's Ashes]]'' by [[w:Frank McCourt|Frank McCourt]] *''[[w:The Family Markowitz|The Family Markowitz]]'' by [[w:Allegra Goodman|Allegra Goodman]] *''The Giant's House: A Romance'' by [[w:Elizabeth McCracken|Elizabeth McCracken]] *''[[w:Infinite Jest|Infinite Jest]]'' by [[w:David Foster Wallace|David Foster Wallace]] *''The Living and the Dead: Robert McNamara and Five Lives of a Lost War'' by [[w:Paul Hendrickson|Paul Hendrickson]] *''[[w:The Moor's Last Sigh|The Moor's Last Sigh]]'' by [[w:Salman Rushdie|Salman Rushdie]] *''[[w:My Dark Places (book)|My Dark Places]]'' by [[w:James Ellroy|James Ellroy]] *''Reader's Block'' by [[w:David Markson|David Markson]] *''The Shadow Man'' by [[w:Mary Gordon (writer)|Mary Gordon]] *''The Temple Bombing'' by [[w:Melissa Fay Greene|Melissa Fay Greene]] ===1997=== Source:<ref>{{cite web |last1=Miller |first1=Laura |last2=Garner |first2=Dwight |title=The second annual Salon Book Awards |work=[[w:Salon (website)|Salon]] |date=January 5, 1998 |url=https://www.salon.com/1998/01/05/the_second_annual_salon_book_awards/ |archive-url=https://web.archive.org/web/20171010021903/https://www.salon.com/1998/01/05/the_second_annual_salon_book_awards/ |archive-date=2017-10-10 }}</ref> *''[[w:Alias Grace|Alias Grace]]'' by [[w:Margaret Atwood|Margaret Atwood]] *''Because They Wanted to: Stories'' by [[w:Mary Gaitskill|Mary Gaitskill]] *''Close to the Machine: Technophilia and Its Discontents'' by [[w:Ellen Ullman|Ellen Ullman]] *''[[w:Cold Mountain (novel)|Cold Mountain]]'' by [[w:Charles Frazier|Charles Frazier]] *''Echoes of a Native Land: Two Centuries of a Russian Village'' by [[w:Serge Schmemann|Serge Schmemann]] *''How Proust Can Change Your Life'' by [[w:Alain de Botton|Alain de Botton]] *''[[w:Into Thin Air|Into Thin Air: A Personal Account of the Mt. Everest Disaster]]'' by [[w:Jon Krakauer|Jon Krakauer]] *''[[w:Mason & Dixon|Mason & Dixon]]'' by [[w:Thomas Pynchon|Thomas Pynchon]] *''[[w:The Reader|The Reader]]'' by [[w:Bernhard Schlink|Bernhard Schlink]] *''[[w:The Spirit Catches You and You Fall Down|The Spirit Catches You and You Fall Down]]'' by [[w:Anne Fadiman|Anne Fadiman]] ===1998=== *''At Home with the Marquis de Sade: A Life'' by [[w:Francine du Plessix Gray|Francine du Plessix Gray]] *''[[w:A Beautiful Mind (book)|A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash]]'' by [[w:Sylvia Nasar|Sylvia Nasar]] *''[[w:Birds of America (stories)|Birds of America]]'' by [[w:Lorrie Moore|Lorrie Moore]] *''[[w:Blindness (novel)|Blindness]]'' by [[w:José Saramago|José Saramago]] *''A Slant of Sun: One Child's Courage'' by [[w:Beth Kephart|Beth Kephart]] *''[[w:Starting Out in the Evening|Starting Out in the Evening]]'' by [[w:Brian Morton (American author)|Brian Morton]] *''[[w:The Surgeon of Crowthorne|The Surgeon of Crowthorne]]'' by [[w:Simon Winchester|Simon Winchester]] *''Thirst'' by [[w:Ken Kalfus|Ken Kalfus]] *''The Voyage of the Narwhal'' by [[w:Andrea Barrett|Andrea Barrett]] *''[[w:We Wish to Inform You That Tomorrow We Will be Killed With Our Families|We Wish to Inform You That Tomorrow We Will be Killed With Our Families: Stories from Rwanda]]'' by [[w:Philip Gourevitch|Philip Gourevitch]] ===1999=== *''[[w:Black Hawk Down: A Story of Modern War|Black Hawk Down: A Story of Modern War]]'' by [[w:Mark Bowden|Mark Bowden]] *''Careless Love: The Unmaking of Elvis Presley'' by [[w:Peter Guralnick|Peter Guralnick]] *''[[w:Cryptonomicon|Cryptonomicon]]'' by [[w:Neal Stephenson|Neal Stephenson]] *''Lost on Earth: Nomads of the New World'' by [[w:Mark Fritz|Mark Fritz]] *''[[w:Motherless Brooklyn|Motherless Brooklyn]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''Original Bliss'' by [[w:A. L. Kennedy|A. L. Kennedy]] *''[[w:Plainsong (novel)|Plainsong]]'' by [[w:Kent Haruf|Kent Haruf]] *''[[w:A Prayer for the Dying|A Prayer for the Dying]]'' by [[w:Stewart O'Nan|Stewart O'Nan]] *''Secrets of the Flesh: A Life of Colette (Ballantine Reader's Circle)'' by [[w:Judith Thurman|Judith Thurman]] *''Show Me a Hero: A Tale of Murder, Suicide, Race, and Redemption'' by [[w:Lisa Belkin|Lisa Belkin]] ===2000=== Source:<ref>{{cite web |last1=Russo |first1=Mario |last2=Miller |first2=Laura |title=Salon Book Awards |work=Salon |date=December 18, 2000 |url=https://www.salon.com/2000/12/18/bookawards/ |archive-url=https://web.archive.org/web/20160212125119/https://www.salon.com/2000/12/18/bookawards/ |archive-date=2016-02-12 }}</ref> *''[[w:Richard_Slotkin#Abe:_A_Novel_of_the_Young_Lincoln|Abe: A Novel of the Young Lincoln]]'' by [[w:Richard Slotkin|Richard Slotkin]] *''An American Story'' by [[w:Debra Dickerson|Debra Dickerson]] *''[[w:Being Dead|Being Dead]]'' by [[w:Jim Crace|Jim Crace]] *''The Blood Runs Like a River Through My Dreams'' by [[w:Nasdijj|Nasdijj]] *''Boxer Rebellion: The Dramatic Story of China's War on Foreigners that Shook the World in the Summer of 1900'' by [[w:Diana Preston|Diana Preston]] *''Lying Awake'' by [[w:Mark Salzman|Mark Salzman]] *''The Name of the World: A Novel'' by [[w:Denis Johnson|Denis Johnson]] *''Pontius Pilate : The Biography of an Invented Man'' by [[w:Ann Wroe|Ann Wroe]] *''The Social Lives of Dogs'' by [[w:Elizabeth Marshall Thomas|Elizabeth Marshall Thomas]] *''[[w:White Teeth|White Teeth]]'' by [[w:Zadie Smith|Zadie Smith]] ===2001=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Our favorite books |work=[[w:Salon (website)|Salon]] |date=January 9, 2002 |url=https://www.salon.com/2002/01/09/bestbooks_2/ |archive-url=https://web.archive.org/web/20120712170827/https://www.salon.com/2002/01/09/bestbooks_2/ |archive-date=2012-07-12 }}</ref> *''[[w:Austerlitz (novel)|Austerlitz]]'' by [[w:W. G. Sebald|W. G. Sebald]] *''[[w:Bel Canto (novel)|Bel Canto]]'' by [[w:Ann Patchett|Ann Patchett]] *''Borrowed Finery: A Memoir'' by [[w:Paula Fox|Paula Fox]] *''[[w:The Corrections|The Corrections]]'' by [[w:Jonathan Franzen|Jonathan Franzen]] *''[[w:John Adams (book)|John Adams]]'' by [[w:David McCullough|David McCullough]] *''[[w:John Henry Days|John Henry Days]]'' by [[w:Colson Whitehead|Colson Whitehead]] *''[[w:Seabiscuit: An American Legend|Seabiscuit: An American Legend]]'' by [[w:Laura Hillenbrand|Laura Hillenbrand]] *''Stranger Things Happen: Stories'' by [[w:Kelly Link|Kelly Link]] *''Strip City: A Stripper's Farewell Journey Across America'' by [[w:Lily Burana|Lily Burana]] *''[[w:Wittgenstein's Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers|Wittgenstein's Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers]]'' by [[w:David Edmonds (philosopher)|David Edmonds]] ===2002=== No awards were given for the year of 2002. ===2003=== *''American Woman: A Novel'' by [[w:Susan Choi|Susan Choi]] *''[[w:Any Human Heart|Any Human Heart]]'' by [[w:William Boyd (writer)|William Boyd]] *''Brick Lane'' by [[w:Monica Ali|Monica Ali]] *''The Bug'' by [[w:Ellen Ullman|Ellen Ullman]] *''[[w:The Curious Incident of the Dog in the Night-Time|The Curious Incident of the Dog in the Night-Time]]'' by [[w:Mark Haddon|Mark Haddon]] *''[[w:Drop City|Drop City]]'' by [[w:T. C. Boyle|T. C. Boyle]] *''[[w:The Fortress of Solitude|The Fortress of Solitude]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''I Should Be Extremely Happy in Your Company: A Novel of Lewis and Clark'' by [[w:Brian Hall (author)|Brian Hall]] *''[[w:Old School (novel)|Old School]]'' by [[w:Tobias Wolff|Tobias Wolff]] *''[[w:Property (novel)|Property]]'' by [[w:Valerie Martin|Valerie Martin]] ===2004=== *''American Brutus: John Wilkes Booth and the Lincoln Conspiracies'' by [[w:Michael W. Kauffman|Michael W. Kauffman]] *''Arc of Justice: A Saga of Race, Civil Rights, and Murder in the Jazz Age'' by [[w:Kevin Boyle (historian)|Kevin Boyle]] *''[[w:Case Histories|Case Histories]]'' by [[w:Kate Atkinson|Kate Atkinson]] *''[[w:Happy Baby|Happy Baby]]'' by [[w:Stephen Elliott (author)|Stephen Elliott]] *''[[w:Jonathan Strange & Mr Norrell|Jonathan Strange & Mr Norrell]]'' by [[w:Susanna Clarke|Susanna Clarke]] *''[[w:The Line of Beauty|The Line of Beauty]]'' by [[w:Alan Hollinghurst|Alan Hollinghurst]] *''Nightingales: The Extraordinary Upbringing and Curious Life of Miss Florence Nightingale'' by [[w:Gillian Gill|Gillian Gill]] *''Skeletons on the Zahara: A True Story of Survival'' by [[w:Dean King|Dean King]] *''[[w:Snow (Pamuk novel)|Snow]]'' by [[w:Orhan Pamuk|Orhan Pamuk]] *''The Working Poor: Invisible in America'' by [[w:David K. Shipler|David K. Shipler]] ===2005=== Source:<ref>{{cite web |last1=Miller |first1=Laura |last2=Frey |first2=Hillary |title=The best books of 2005 |work=[[w:Salon (website)|Salon]] |date=December 19, 2005 |url=https://www.salon.com/2005/12/19/best_of_2/ |archive-url=https://web.archive.org/web/20111230083620/https://www.salon.com/2005/12/19/best_of_2/ |archive-date=2011-12-30 }}</ref> *''[[w:1491: New Revelations of the Americas Before Columbus|1491: New Revelations of the Americas Before Columbus]]'' by [[w:Charles C. Mann|Charles C. Mann]] *''The Assassins' Gate'' by [[w:George Packer|George Packer]] *''Dream Boogie: The Triumph of Sam Cooke'' by [[w:Peter Guralnick|Peter Guralnick]] *''[[w:Kafka on the Shore|Kafka on the Shore]]'' by [[w:Haruki Murakami|Haruki Murakami]] *''[[w:Magic for Beginners|Magic for Beginners]]'' by [[w:Kelly Link|Kelly Link]] *''[[w:Never Let Me Go (novel)|Never Let Me Go]]'' by [[w:Kazuo Ishiguro|Kazuo Ishiguro]] *''[[w:On Beauty|On Beauty]]'' by [[w:Zadie Smith|Zadie Smith]] *''Them: A Memoir of Parents'' by [[w:Francine du Plessix Gray|Francine du Plessix Gray]] *''[[w:Times Like These (novel)|Times Like These]]'' by [[w:Rachel Ingalls|Rachel Ingalls]] *''Tulia'' by [[w:Nate Blakeslee|Nate Blakeslee]] *''Veronica'' by [[w:Mary Gaitskill|Mary Gaitskill]] ===2006=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Authors' picks |work=[[w:Salon (website)|Salon]] |date=December 11, 2006 |url=https://www.salon.com/2006/12/11/authors_picks_2/ |archive-url=https://web.archive.org/web/20120430155625/https://www.salon.com/2006/12/11/authors_picks_2/ |archive-date=2012-04-30 }}</ref> *''[[w:The Amalgamation Polka|The Amalgamation Polka]]'' by [[w:Stephen Wright (writer)|Stephen Wright]] *''A Disorder Peculiar to the Country: A Novel'' by [[w:Ken Kalfus|Ken Kalfus]] *''The Family That Couldn't Sleep: A Medical Mystery'' by [[w:D.T. Max|D.T. Max]] *''[[w:Fun Home: A Family Tragicomic|Fun Home: A Family Tragicomic]]'' by [[w:Alison Bechdel|Alison Bechdel]] *''James Tiptree, Jr.: The Double Life of Alice B. Sheldon'' by [[w:Julie Phillips|Julie Phillips]] *''[[w:The Lost: A Search for Six of Six Million|The Lost: A Search for Six of Six Million]]'' by [[w:Daniel Mendelsohn|Daniel Mendelsohn]] *''[[w:The Omnivore's Dilemma: A Natural History of Four Meals|The Omnivore's Dilemma: A Natural History of Four Meals]]'' by [[w:Michael Pollan|Michael Pollan]] *''[[w:Special Topics in Calamity Physics|Special Topics in Calamity Physics]]'' by [[w:Marisha Pessl|Marisha Pessl]] *''Sweet and Low: A Family Story'' by [[w:Rich Cohen (author)|Rich Cohen]] *''[[w:Twilight of the Superheroes|Twilight of the Superheroes]]'' by [[w:Deborah Eisenberg|Deborah Eisenberg]] *''[[w:What Is the What|What Is the What]]'' by [[w:Dave Eggers|Dave Eggers]] *''[[w:Wizard of the Crow|Wizard of the Crow]]'' by [[w:Ngũgĩ wa Thiong'o|Ngũgĩ wa Thiong'o]] ===2007=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Salon Book Awards 2007 |work=[[w:Salon (website)|Salon]] |date=December 12, 2007 |url=https://www.salon.com/2007/12/12/best_books/ |archive-url=https://web.archive.org/web/20111112221324/https://www.salon.com/2007/12/12/best_books/ |archive-date=2011-11-12 }}</ref> *''[[w:The Brief Wondrous Life of Oscar Wao|The Brief Wondrous Life of Oscar Wao]]'' by [[w:Junot Díaz|Junot Díaz]] *''The Father of All Things: A Marine, His Son, and the Legacy of Vietnam'' by [[w:Tom Bissell|Tom Bissell]] *''Gertrude Bell: Queen of the Desert, Shaper of Nations'' by [[w:Georgina Howell|Georgina Howell]] *''[[w:Legacy of Ashes: The History of the CIA|Legacy of Ashes: The History of the CIA]]'' by [[w:Tim Weiner|Tim Weiner]] *''The Long Embrace: Raymond Chandler and the Woman He Loved'' by [[w:Judith Freeman (author)|Judith Freeman]] *''[[w:Sacred Games (novel)|Sacred Games]]'' by [[w:Vikram Chandra|Vikram Chandra]] *''[[w:Then We Came to the End|Then We Came to the End]]'' by [[w:Joshua Ferris|Joshua Ferris]] *''[[w:Tree of Smoke|Tree of Smoke]]'' by [[w:Denis Johnson|Denis Johnson]] *''[[w:The World Without Us|The World Without Us]]'' by [[w:Alan Weisman|Alan Weisman]] *''[[w:The Yiddish Policemen's Union|The Yiddish Policemen's Union]]'' by [[w:Michael Chabon|Michael Chabon]] ===2008=== *''[[w:2666 (novel)|2666]]'' by [[w:Roberto Bolaño|Roberto Bolaño]] *''Atmospheric Disturbances: A Novel'' by [[w:Rivka Galchen|Rivka Galchen]] *''Buying In: The Secret Dialogue Between What We Buy and Who We Are'' by [[w:Rob Walker (journalist)|Rob Walker]] *''The Likeness'' by [[w:Tana French|Tana French]] *''The Northern Clemency'' by [[w:Philip Hensher|Philip Hensher]] *''A Person of Interest: A Novel'' by [[w:Susan Choi|Susan Choi]] *''Pictures at a Revolution: Five Movies and the Birth of the New Hollywood'' by [[w:Mark Harris (American author)|Mark Harris]] *''The Suicide Index: Putting My Father's Death in Order'' by [[w:Joan Wickersham|Joan Wickersham]] *''The Suspicions of Mr. Whicher: A Shocking Murder and the Undoing of a Great Victorian Detective'' by [[w:Kate Summerscale|Kate Summerscale]] ===2009=== Source:<ref>{{cite web |last=Miller |first=Laura |title=Best of 2009 |work=[[w:Salon (website)|Salon]] |date=December 8, 2009 |url=http://www.salon.com/topic/best_of_2009/page/2/ |archive-url=https://web.archive.org/web/20120601152805/http://www.salon.com/topic/best_of_2009/page/2/ |archive-date=2012-06-01 }}</ref> *''[[w:The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science|The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science]]'' by [[w:Richard Holmes (biographer)|Richard Holmes]] *''Await Your Reply'' by [[w:Dan Chaon|Dan Chaon]] *''[[w:The Children's Book|The Children's Book]]'' by [[w:A. S. Byatt|A. S. Byatt]] *''[[w:Chronic City|Chronic City]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''[[w:Columbine (book)|Columbine]]'' by [[w:Dave Cullen|Dave Cullen]] *''[[w:The Little Stranger|The Little Stranger]]'' by [[w:Sarah Waters|Sarah Waters]] *''Love in Infant Monkeys: Stories'' by [[w:Lydia Millet|Lydia Millet]] *''A New Literary History of America (Harvard University Press Reference Library)'' by [[w:Greil Marcus|Greil Marcus]] *''Somewhere Towards the End: A Memoir'' by [[w:Diana Athill|Diana Athill]] *''Tall Man: The Death of Doomadgee'' by [[w:Chloe Hooper|Chloe Hooper]] ===2010=== Source:<ref name="salon-nonfiction-2010">{{cite web |last=Miller |first=Laura |date=December 7, 2010 |title=The best nonfiction books of 2010 |url=http://www.salon.com/books/laura_miller/2010/12/07/best_books_nonfiction |website=[[w:Salon (website)|Salon]]}}</ref><ref name="salon-fiction-2010">{{cite web |last=Miller |first=Laura |date=December 6, 2010 |title=The best fiction of 2010 |url=http://www.salon.com/books/laura_miller/2010/12/06/best_books_fiction |website=[[w:Salon (website)|Salon]]}}</ref> *''The Possessed: Adventures With Russian Books and the People Who Read Them'' by [[w:Elif Batuman|Elif Batuman]] *''[[w:The Big Short|The Big Short]]'' by [[w:Michael Lewis (author)|Michael Lewis]] (tied with John Lanchester) *''I.O.U.: Why Everyone Owes Everyone and No One Can Pay'' by [[w:John Lanchester|John Lanchester]] (tied with Michael Lewis) *''Let the Swords Encircle Me: Iran – a Journey Behind the Headlines'' by [[w:Scott Peterson (writer)|Scott Peterson]] *''[[w:The Immortal Life of Henrietta Lacks|The Immortal Life of Henrietta Lacks]]'' by [[w:Rebecca Skloot|Rebecca Skloot]] *''[[w:The Warmth of Other Suns|The Warmth of Other Suns]]'' by [[w:Isabel Wilkerson|Isabel Wilkerson]] *''[[w:Room (novel)|Room]]'' by [[w:Emma Donoghue|Emma Donoghue]] *''[[w:A Visit From the Goon Squad|A Visit From the Goon Squad]]'' by [[w:Jennifer Egan|Jennifer Egan]] *''[[w:Freedom (novel)|Freedom]]'' by [[w:Jonathan Franzen|Jonathan Franzen]] *''[[w:Faithful Place|Faithful Place]]'' by [[w:Tana French|Tana French]] *''[[w:Super Sad True Love Story|Super Sad True Love Story]]'' by [[w:Gary Shteyngart|Gary Shteyngart]] ===2011=== Source:<ref name="salon-fiction-2011">{{cite web |last=Miller |first=Laura |date=December 7, 2011 |title=The best fiction of 2011 |url=http://entertainment.salon.com/2011/12/07/the_best_fiction_of_2011/ |website=[[w:Salon (website)|Salon]]}}</ref><ref name="salon-nonfiction-2011">{{cite web |last=Miller |first=Laura |date=December 8, 2011 |title=The best nonfiction of 2011 |url=http://www.salon.com/2011/12/08/the_best_nonfiction_of_2011/ |website=[[w:Salon (website)|Salon]]}}</ref> *''[[w:The Marriage Plot|The Marriage Plot]]'' by [[w:Jeffrey Eugenides|Jeffrey Eugenides]] *''[[w:Pym (novel)|Pym]]'' by [[w:Mat Johnson|Mat Johnson]] *''[[w:State of Wonder|State of Wonder]]'' by [[w:Ann Patchett|Ann Patchett]] *''[[w:The Tragedy of Arthur|The Tragedy of Arthur]]'' by [[w:Arthur Phillips|Arthur Phillips]] *''[[w:The Pale King|The Pale King]]'' by [[w:David Foster Wallace|David Foster Wallace]] *''Townie: A Memoir'' by [[w:Andre Dubus III|Andre Dubus III]] *''Love and Capital: Karl and Jenny Marx and the Birth of a Revolution'' by [[w:Mary Gabriel (author)|Mary Gabriel]] *''[[w:The Information: A History, a Theory, a Flood|The Information: A History, a Theory, a Flood]]'' by [[w:James Gleick|James Gleick]] *''Catherine the Great: The Portrait of a Woman'' by [[w:Robert K. Massie|Robert K. Massie]] *''[[w:Lost in Shangri-La|Lost in Shangri-La]]'' by [[w:Mitchell Zuckoff|Mitchell Zuckoff]] ===2012=== New award established as "What To Read Awards" with books chosen by a system of points from an array of other journalists top-10 lists.<ref>{{cite web |last1=Miller |first1=Laura |title=What to Read Awards: Laura Miller |work=[[w:Salon (website)|Salon]] |date=December 23, 2012 |url=https://www.salon.com/2012/12/23/what_to_read_awards_laura_miller/ |archive-url=https://web.archive.org/web/20121223162820/https://www.salon.com/2012/12/23/what_to_read_awards_laura_miller/ |archive-date=2012-12-23 }}</ref><ref name="daley2012">{{cite web |url=http://www.salon.com/2012/12/23/the_what_to_read_awards_top_10_books_of_2012/ |title=The What To Read Awards: Top 10 Books of 2012 |website=[[w:Salon (website)|Salon]] |last=Daley |first=David |date=December 23, 2012 |access-date=December 24, 2012}}</ref> See also Laura Miller's top-10 picks.<ref>{{cite web |url=http://www.salon.com/2012/12/22/laura_millers_best_books_of_2012/ |title=Laura Miller’s best books of 2012 |website=[[w:Salon (website)|Salon]] |last=Miller |first=Laura |date=December 22, 2012 |access-date=December 24, 2012}}</ref> #[[w:Katherine Boo|Katherine Boo]], ''[[w:Behind the Beautiful Forevers|Behind the Beautiful Forevers]]'' #[[w:Hilary Mantel|Hilary Mantel]], ''[[w:Bring Up the Bodies|Bring Up the Bodies]]'' #[[w:Ben Fountain|Ben Fountain]], ''Billy Lynn’s Long Halftime Walk'' #[[w:Zadie Smith|Zadie Smith]], ''NW'', and [[w:Andrew Solomon|Andrew Solomon]], ''Far From the Tree'' (co-winners) #[[w:Sheila Heti|Sheila Heti]], ''How Should a Person Be'' #[[w:Gillian Flynn|Gillian Flynn]], ''Gone Girl'' #[[w:Lauren Groff|Lauren Groff]], ''Arcadia'' #[[w:Jess Walter|Jess Walter]], ''Beautiful Ruins'' #[[w:Sarah Manguso|Sarah Manguso]], ''The Guardians'' ==Notes== {{Reflist}} ==Wikiversity status== {{Complete}} [[Category:Literature]] 5pzmxgkka4w2ggvm61tymhp7w62iit0 2844848 2844847 2026-11-08T03:50:33Z GreenC 268373 /* 2004 */ 2844848 wikitext text/x-wiki The '''Salon Book Awards''' were an annual [[w:literary award|literary feature]] issued by the online magazine [[w:Salon (website)|Salon.com]] from 1996 to 2011, recognizing the year's fiction and nonfiction. The awards were established in December 1996 by Salon's literary editors [[w:Laura Miller (writer)|Laura Miller]] and [[w:Dwight Garner (critic)|Dwight Garner]] during the early days of the web. It was a period when the site was helping to establish a new industry of professional cultural criticism that was published digitally on the web. Rather than a formal juried prize with a physical ceremony or endowment, the award served as the publication's year-end "Best Of" list. The editors' methodology for selecting the winning books was highly personal. In the inaugural 1996 announcement, Miller and Garner emphasized that they deliberately excluded books written by personal friends to avoid the appearance of nepotism, and favored unified novels and narratives over short-story or essay collections. The overarching criteria were: :"..the books we'd wholeheartedly recommend to our friends, books we'd clear our social calendar to finish, books we returned to eagerly even when we could barely focus our eyes on a page. They remind us of why we fell in love with reading and why we keep at it in a world that's simultaneously cluttered with mediocre books and increasingly indifferent to the written word."<ref name="1996 award">{{cite web |last1=Miller |first1=Laura |last2=Garner |first2=Dwight |title=Books of the Year |url=https://www.salon.com/1996/12/09/awards961209/ |archive-url=https://web.archive.org/web/20190722223228/https://www.salon.com/1996/12/09/awards961209/ |archive-date=2019-07-22 |date=December 9, 1996 |website=[[w:Salon (website)|Salon]]}}</ref> Following the 2011 awards, the original format was retired. In 2012, a new accolade was established called the '''What To Read Awards''', named after Salon's ongoing "What to Read" column. Although Laura Miller continued to publish a separate "Best Books of the Year" top-10 list, the new awards crowdsourced the selections by polling the broader literary community. The editors tabulated the What To Read Awards as follows: :"we surveyed our favorite book critics, both print and online, from high-profile publications to the hottest literary blogs. We asked for their top-10 books of 2012, and then tabulated the winners by assigning 10 points for a No. 1 selection, 9 for No. 2, all the way to 1 point for No. 10."<ref name="daley2012"/> ==Winners of Salon Book Awards== The following is a list of the winners of the Salon Book Awards for each year. ===1996=== Source:<ref name="1996 award" /> *''[[w:Angela's Ashes|Angela's Ashes]]'' by [[w:Frank McCourt|Frank McCourt]] *''[[w:The Family Markowitz|The Family Markowitz]]'' by [[w:Allegra Goodman|Allegra Goodman]] *''The Giant's House: A Romance'' by [[w:Elizabeth McCracken|Elizabeth McCracken]] *''[[w:Infinite Jest|Infinite Jest]]'' by [[w:David Foster Wallace|David Foster Wallace]] *''The Living and the Dead: Robert McNamara and Five Lives of a Lost War'' by [[w:Paul Hendrickson|Paul Hendrickson]] *''[[w:The Moor's Last Sigh|The Moor's Last Sigh]]'' by [[w:Salman Rushdie|Salman Rushdie]] *''[[w:My Dark Places (book)|My Dark Places]]'' by [[w:James Ellroy|James Ellroy]] *''Reader's Block'' by [[w:David Markson|David Markson]] *''The Shadow Man'' by [[w:Mary Gordon (writer)|Mary Gordon]] *''The Temple Bombing'' by [[w:Melissa Fay Greene|Melissa Fay Greene]] ===1997=== Source:<ref>{{cite web |last1=Miller |first1=Laura |last2=Garner |first2=Dwight |title=The second annual Salon Book Awards |work=[[w:Salon (website)|Salon]] |date=January 5, 1998 |url=https://www.salon.com/1998/01/05/the_second_annual_salon_book_awards/ |archive-url=https://web.archive.org/web/20171010021903/https://www.salon.com/1998/01/05/the_second_annual_salon_book_awards/ |archive-date=2017-10-10 }}</ref> *''[[w:Alias Grace|Alias Grace]]'' by [[w:Margaret Atwood|Margaret Atwood]] *''Because They Wanted to: Stories'' by [[w:Mary Gaitskill|Mary Gaitskill]] *''Close to the Machine: Technophilia and Its Discontents'' by [[w:Ellen Ullman|Ellen Ullman]] *''[[w:Cold Mountain (novel)|Cold Mountain]]'' by [[w:Charles Frazier|Charles Frazier]] *''Echoes of a Native Land: Two Centuries of a Russian Village'' by [[w:Serge Schmemann|Serge Schmemann]] *''How Proust Can Change Your Life'' by [[w:Alain de Botton|Alain de Botton]] *''[[w:Into Thin Air|Into Thin Air: A Personal Account of the Mt. Everest Disaster]]'' by [[w:Jon Krakauer|Jon Krakauer]] *''[[w:Mason & Dixon|Mason & Dixon]]'' by [[w:Thomas Pynchon|Thomas Pynchon]] *''[[w:The Reader|The Reader]]'' by [[w:Bernhard Schlink|Bernhard Schlink]] *''[[w:The Spirit Catches You and You Fall Down|The Spirit Catches You and You Fall Down]]'' by [[w:Anne Fadiman|Anne Fadiman]] ===1998=== *''At Home with the Marquis de Sade: A Life'' by [[w:Francine du Plessix Gray|Francine du Plessix Gray]] *''[[w:A Beautiful Mind (book)|A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash]]'' by [[w:Sylvia Nasar|Sylvia Nasar]] *''[[w:Birds of America (stories)|Birds of America]]'' by [[w:Lorrie Moore|Lorrie Moore]] *''[[w:Blindness (novel)|Blindness]]'' by [[w:José Saramago|José Saramago]] *''A Slant of Sun: One Child's Courage'' by [[w:Beth Kephart|Beth Kephart]] *''[[w:Starting Out in the Evening|Starting Out in the Evening]]'' by [[w:Brian Morton (American author)|Brian Morton]] *''[[w:The Surgeon of Crowthorne|The Surgeon of Crowthorne]]'' by [[w:Simon Winchester|Simon Winchester]] *''Thirst'' by [[w:Ken Kalfus|Ken Kalfus]] *''The Voyage of the Narwhal'' by [[w:Andrea Barrett|Andrea Barrett]] *''[[w:We Wish to Inform You That Tomorrow We Will be Killed With Our Families|We Wish to Inform You That Tomorrow We Will be Killed With Our Families: Stories from Rwanda]]'' by [[w:Philip Gourevitch|Philip Gourevitch]] ===1999=== *''[[w:Black Hawk Down: A Story of Modern War|Black Hawk Down: A Story of Modern War]]'' by [[w:Mark Bowden|Mark Bowden]] *''Careless Love: The Unmaking of Elvis Presley'' by [[w:Peter Guralnick|Peter Guralnick]] *''[[w:Cryptonomicon|Cryptonomicon]]'' by [[w:Neal Stephenson|Neal Stephenson]] *''Lost on Earth: Nomads of the New World'' by [[w:Mark Fritz|Mark Fritz]] *''[[w:Motherless Brooklyn|Motherless Brooklyn]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''Original Bliss'' by [[w:A. L. Kennedy|A. L. Kennedy]] *''[[w:Plainsong (novel)|Plainsong]]'' by [[w:Kent Haruf|Kent Haruf]] *''[[w:A Prayer for the Dying|A Prayer for the Dying]]'' by [[w:Stewart O'Nan|Stewart O'Nan]] *''Secrets of the Flesh: A Life of Colette (Ballantine Reader's Circle)'' by [[w:Judith Thurman|Judith Thurman]] *''Show Me a Hero: A Tale of Murder, Suicide, Race, and Redemption'' by [[w:Lisa Belkin|Lisa Belkin]] ===2000=== Source:<ref>{{cite web |last1=Russo |first1=Mario |last2=Miller |first2=Laura |title=Salon Book Awards |work=Salon |date=December 18, 2000 |url=https://www.salon.com/2000/12/18/bookawards/ |archive-url=https://web.archive.org/web/20160212125119/https://www.salon.com/2000/12/18/bookawards/ |archive-date=2016-02-12 }}</ref> *''[[w:Richard_Slotkin#Abe:_A_Novel_of_the_Young_Lincoln|Abe: A Novel of the Young Lincoln]]'' by [[w:Richard Slotkin|Richard Slotkin]] *''An American Story'' by [[w:Debra Dickerson|Debra Dickerson]] *''[[w:Being Dead|Being Dead]]'' by [[w:Jim Crace|Jim Crace]] *''The Blood Runs Like a River Through My Dreams'' by [[w:Nasdijj|Nasdijj]] *''Boxer Rebellion: The Dramatic Story of China's War on Foreigners that Shook the World in the Summer of 1900'' by [[w:Diana Preston|Diana Preston]] *''Lying Awake'' by [[w:Mark Salzman|Mark Salzman]] *''The Name of the World: A Novel'' by [[w:Denis Johnson|Denis Johnson]] *''Pontius Pilate : The Biography of an Invented Man'' by [[w:Ann Wroe|Ann Wroe]] *''The Social Lives of Dogs'' by [[w:Elizabeth Marshall Thomas|Elizabeth Marshall Thomas]] *''[[w:White Teeth|White Teeth]]'' by [[w:Zadie Smith|Zadie Smith]] ===2001=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Our favorite books |work=[[w:Salon (website)|Salon]] |date=January 9, 2002 |url=https://www.salon.com/2002/01/09/bestbooks_2/ |archive-url=https://web.archive.org/web/20120712170827/https://www.salon.com/2002/01/09/bestbooks_2/ |archive-date=2012-07-12 }}</ref> *''[[w:Austerlitz (novel)|Austerlitz]]'' by [[w:W. G. Sebald|W. G. Sebald]] *''[[w:Bel Canto (novel)|Bel Canto]]'' by [[w:Ann Patchett|Ann Patchett]] *''Borrowed Finery: A Memoir'' by [[w:Paula Fox|Paula Fox]] *''[[w:The Corrections|The Corrections]]'' by [[w:Jonathan Franzen|Jonathan Franzen]] *''[[w:John Adams (book)|John Adams]]'' by [[w:David McCullough|David McCullough]] *''[[w:John Henry Days|John Henry Days]]'' by [[w:Colson Whitehead|Colson Whitehead]] *''[[w:Seabiscuit: An American Legend|Seabiscuit: An American Legend]]'' by [[w:Laura Hillenbrand|Laura Hillenbrand]] *''Stranger Things Happen: Stories'' by [[w:Kelly Link|Kelly Link]] *''Strip City: A Stripper's Farewell Journey Across America'' by [[w:Lily Burana|Lily Burana]] *''[[w:Wittgenstein's Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers|Wittgenstein's Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers]]'' by [[w:David Edmonds (philosopher)|David Edmonds]] ===2002=== No awards were given for the year of 2002. ===2003=== *''American Woman: A Novel'' by [[w:Susan Choi|Susan Choi]] *''[[w:Any Human Heart|Any Human Heart]]'' by [[w:William Boyd (writer)|William Boyd]] *''Brick Lane'' by [[w:Monica Ali|Monica Ali]] *''The Bug'' by [[w:Ellen Ullman|Ellen Ullman]] *''[[w:The Curious Incident of the Dog in the Night-Time|The Curious Incident of the Dog in the Night-Time]]'' by [[w:Mark Haddon|Mark Haddon]] *''[[w:Drop City|Drop City]]'' by [[w:T. C. Boyle|T. C. Boyle]] *''[[w:The Fortress of Solitude|The Fortress of Solitude]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''I Should Be Extremely Happy in Your Company: A Novel of Lewis and Clark'' by [[w:Brian Hall (author)|Brian Hall]] *''[[w:Old School (novel)|Old School]]'' by [[w:Tobias Wolff|Tobias Wolff]] *''[[w:Property (novel)|Property]]'' by [[w:Valerie Martin|Valerie Martin]] ===2004=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Top ten |work=[[w:Salon (website)|Salon]] |date=December 7, 2004 |url=https://www.salon.com/2004/12/07/top_ten/ |archive-url=https://web.archive.org/web/20120530134925/https://www.salon.com/2004/12/07/top_ten/ |archive-date=2012-05-30 }}</ref> *''American Brutus: John Wilkes Booth and the Lincoln Conspiracies'' by [[w:Michael W. Kauffman|Michael W. Kauffman]] *''Arc of Justice: A Saga of Race, Civil Rights, and Murder in the Jazz Age'' by [[w:Kevin Boyle (historian)|Kevin Boyle]] *''[[w:Case Histories|Case Histories]]'' by [[w:Kate Atkinson|Kate Atkinson]] *''[[w:Happy Baby|Happy Baby]]'' by [[w:Stephen Elliott (author)|Stephen Elliott]] *''[[w:Jonathan Strange & Mr Norrell|Jonathan Strange & Mr Norrell]]'' by [[w:Susanna Clarke|Susanna Clarke]] *''[[w:The Line of Beauty|The Line of Beauty]]'' by [[w:Alan Hollinghurst|Alan Hollinghurst]] *''Nightingales: The Extraordinary Upbringing and Curious Life of Miss Florence Nightingale'' by [[w:Gillian Gill|Gillian Gill]] *''Skeletons on the Zahara: A True Story of Survival'' by [[w:Dean King|Dean King]] *''[[w:Snow (Pamuk novel)|Snow]]'' by [[w:Orhan Pamuk|Orhan Pamuk]] *''The Working Poor: Invisible in America'' by [[w:David K. Shipler|David K. Shipler]] ===2005=== Source:<ref>{{cite web |last1=Miller |first1=Laura |last2=Frey |first2=Hillary |title=The best books of 2005 |work=[[w:Salon (website)|Salon]] |date=December 19, 2005 |url=https://www.salon.com/2005/12/19/best_of_2/ |archive-url=https://web.archive.org/web/20111230083620/https://www.salon.com/2005/12/19/best_of_2/ |archive-date=2011-12-30 }}</ref> *''[[w:1491: New Revelations of the Americas Before Columbus|1491: New Revelations of the Americas Before Columbus]]'' by [[w:Charles C. Mann|Charles C. Mann]] *''The Assassins' Gate'' by [[w:George Packer|George Packer]] *''Dream Boogie: The Triumph of Sam Cooke'' by [[w:Peter Guralnick|Peter Guralnick]] *''[[w:Kafka on the Shore|Kafka on the Shore]]'' by [[w:Haruki Murakami|Haruki Murakami]] *''[[w:Magic for Beginners|Magic for Beginners]]'' by [[w:Kelly Link|Kelly Link]] *''[[w:Never Let Me Go (novel)|Never Let Me Go]]'' by [[w:Kazuo Ishiguro|Kazuo Ishiguro]] *''[[w:On Beauty|On Beauty]]'' by [[w:Zadie Smith|Zadie Smith]] *''Them: A Memoir of Parents'' by [[w:Francine du Plessix Gray|Francine du Plessix Gray]] *''[[w:Times Like These (novel)|Times Like These]]'' by [[w:Rachel Ingalls|Rachel Ingalls]] *''Tulia'' by [[w:Nate Blakeslee|Nate Blakeslee]] *''Veronica'' by [[w:Mary Gaitskill|Mary Gaitskill]] ===2006=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Authors' picks |work=[[w:Salon (website)|Salon]] |date=December 11, 2006 |url=https://www.salon.com/2006/12/11/authors_picks_2/ |archive-url=https://web.archive.org/web/20120430155625/https://www.salon.com/2006/12/11/authors_picks_2/ |archive-date=2012-04-30 }}</ref> *''[[w:The Amalgamation Polka|The Amalgamation Polka]]'' by [[w:Stephen Wright (writer)|Stephen Wright]] *''A Disorder Peculiar to the Country: A Novel'' by [[w:Ken Kalfus|Ken Kalfus]] *''The Family That Couldn't Sleep: A Medical Mystery'' by [[w:D.T. Max|D.T. Max]] *''[[w:Fun Home: A Family Tragicomic|Fun Home: A Family Tragicomic]]'' by [[w:Alison Bechdel|Alison Bechdel]] *''James Tiptree, Jr.: The Double Life of Alice B. Sheldon'' by [[w:Julie Phillips|Julie Phillips]] *''[[w:The Lost: A Search for Six of Six Million|The Lost: A Search for Six of Six Million]]'' by [[w:Daniel Mendelsohn|Daniel Mendelsohn]] *''[[w:The Omnivore's Dilemma: A Natural History of Four Meals|The Omnivore's Dilemma: A Natural History of Four Meals]]'' by [[w:Michael Pollan|Michael Pollan]] *''[[w:Special Topics in Calamity Physics|Special Topics in Calamity Physics]]'' by [[w:Marisha Pessl|Marisha Pessl]] *''Sweet and Low: A Family Story'' by [[w:Rich Cohen (author)|Rich Cohen]] *''[[w:Twilight of the Superheroes|Twilight of the Superheroes]]'' by [[w:Deborah Eisenberg|Deborah Eisenberg]] *''[[w:What Is the What|What Is the What]]'' by [[w:Dave Eggers|Dave Eggers]] *''[[w:Wizard of the Crow|Wizard of the Crow]]'' by [[w:Ngũgĩ wa Thiong'o|Ngũgĩ wa Thiong'o]] ===2007=== Source:<ref>{{cite web |last1=Miller |first1=Laura |title=Salon Book Awards 2007 |work=[[w:Salon (website)|Salon]] |date=December 12, 2007 |url=https://www.salon.com/2007/12/12/best_books/ |archive-url=https://web.archive.org/web/20111112221324/https://www.salon.com/2007/12/12/best_books/ |archive-date=2011-11-12 }}</ref> *''[[w:The Brief Wondrous Life of Oscar Wao|The Brief Wondrous Life of Oscar Wao]]'' by [[w:Junot Díaz|Junot Díaz]] *''The Father of All Things: A Marine, His Son, and the Legacy of Vietnam'' by [[w:Tom Bissell|Tom Bissell]] *''Gertrude Bell: Queen of the Desert, Shaper of Nations'' by [[w:Georgina Howell|Georgina Howell]] *''[[w:Legacy of Ashes: The History of the CIA|Legacy of Ashes: The History of the CIA]]'' by [[w:Tim Weiner|Tim Weiner]] *''The Long Embrace: Raymond Chandler and the Woman He Loved'' by [[w:Judith Freeman (author)|Judith Freeman]] *''[[w:Sacred Games (novel)|Sacred Games]]'' by [[w:Vikram Chandra|Vikram Chandra]] *''[[w:Then We Came to the End|Then We Came to the End]]'' by [[w:Joshua Ferris|Joshua Ferris]] *''[[w:Tree of Smoke|Tree of Smoke]]'' by [[w:Denis Johnson|Denis Johnson]] *''[[w:The World Without Us|The World Without Us]]'' by [[w:Alan Weisman|Alan Weisman]] *''[[w:The Yiddish Policemen's Union|The Yiddish Policemen's Union]]'' by [[w:Michael Chabon|Michael Chabon]] ===2008=== *''[[w:2666 (novel)|2666]]'' by [[w:Roberto Bolaño|Roberto Bolaño]] *''Atmospheric Disturbances: A Novel'' by [[w:Rivka Galchen|Rivka Galchen]] *''Buying In: The Secret Dialogue Between What We Buy and Who We Are'' by [[w:Rob Walker (journalist)|Rob Walker]] *''The Likeness'' by [[w:Tana French|Tana French]] *''The Northern Clemency'' by [[w:Philip Hensher|Philip Hensher]] *''A Person of Interest: A Novel'' by [[w:Susan Choi|Susan Choi]] *''Pictures at a Revolution: Five Movies and the Birth of the New Hollywood'' by [[w:Mark Harris (American author)|Mark Harris]] *''The Suicide Index: Putting My Father's Death in Order'' by [[w:Joan Wickersham|Joan Wickersham]] *''The Suspicions of Mr. Whicher: A Shocking Murder and the Undoing of a Great Victorian Detective'' by [[w:Kate Summerscale|Kate Summerscale]] ===2009=== Source:<ref>{{cite web |last=Miller |first=Laura |title=Best of 2009 |work=[[w:Salon (website)|Salon]] |date=December 8, 2009 |url=http://www.salon.com/topic/best_of_2009/page/2/ |archive-url=https://web.archive.org/web/20120601152805/http://www.salon.com/topic/best_of_2009/page/2/ |archive-date=2012-06-01 }}</ref> *''[[w:The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science|The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science]]'' by [[w:Richard Holmes (biographer)|Richard Holmes]] *''Await Your Reply'' by [[w:Dan Chaon|Dan Chaon]] *''[[w:The Children's Book|The Children's Book]]'' by [[w:A. S. Byatt|A. S. Byatt]] *''[[w:Chronic City|Chronic City]]'' by [[w:Jonathan Lethem|Jonathan Lethem]] *''[[w:Columbine (book)|Columbine]]'' by [[w:Dave Cullen|Dave Cullen]] *''[[w:The Little Stranger|The Little Stranger]]'' by [[w:Sarah Waters|Sarah Waters]] *''Love in Infant Monkeys: Stories'' by [[w:Lydia Millet|Lydia Millet]] *''A New Literary History of America (Harvard University Press Reference Library)'' by [[w:Greil Marcus|Greil Marcus]] *''Somewhere Towards the End: A Memoir'' by [[w:Diana Athill|Diana Athill]] *''Tall Man: The Death of Doomadgee'' by [[w:Chloe Hooper|Chloe Hooper]] ===2010=== Source:<ref name="salon-nonfiction-2010">{{cite web |last=Miller |first=Laura |date=December 7, 2010 |title=The best nonfiction books of 2010 |url=http://www.salon.com/books/laura_miller/2010/12/07/best_books_nonfiction |website=[[w:Salon (website)|Salon]]}}</ref><ref name="salon-fiction-2010">{{cite web |last=Miller |first=Laura |date=December 6, 2010 |title=The best fiction of 2010 |url=http://www.salon.com/books/laura_miller/2010/12/06/best_books_fiction |website=[[w:Salon (website)|Salon]]}}</ref> *''The Possessed: Adventures With Russian Books and the People Who Read Them'' by [[w:Elif Batuman|Elif Batuman]] *''[[w:The Big Short|The Big Short]]'' by [[w:Michael Lewis (author)|Michael Lewis]] (tied with John Lanchester) *''I.O.U.: Why Everyone Owes Everyone and No One Can Pay'' by [[w:John Lanchester|John Lanchester]] (tied with Michael Lewis) *''Let the Swords Encircle Me: Iran – a Journey Behind the Headlines'' by [[w:Scott Peterson (writer)|Scott Peterson]] *''[[w:The Immortal Life of Henrietta Lacks|The Immortal Life of Henrietta Lacks]]'' by [[w:Rebecca Skloot|Rebecca Skloot]] *''[[w:The Warmth of Other Suns|The Warmth of Other Suns]]'' by [[w:Isabel Wilkerson|Isabel Wilkerson]] *''[[w:Room (novel)|Room]]'' by [[w:Emma Donoghue|Emma Donoghue]] *''[[w:A Visit From the Goon Squad|A Visit From the Goon Squad]]'' by [[w:Jennifer Egan|Jennifer Egan]] *''[[w:Freedom (novel)|Freedom]]'' by [[w:Jonathan Franzen|Jonathan Franzen]] *''[[w:Faithful Place|Faithful Place]]'' by [[w:Tana French|Tana French]] *''[[w:Super Sad True Love Story|Super Sad True Love Story]]'' by [[w:Gary Shteyngart|Gary Shteyngart]] ===2011=== Source:<ref name="salon-fiction-2011">{{cite web |last=Miller |first=Laura |date=December 7, 2011 |title=The best fiction of 2011 |url=http://entertainment.salon.com/2011/12/07/the_best_fiction_of_2011/ |website=[[w:Salon (website)|Salon]]}}</ref><ref name="salon-nonfiction-2011">{{cite web |last=Miller |first=Laura |date=December 8, 2011 |title=The best nonfiction of 2011 |url=http://www.salon.com/2011/12/08/the_best_nonfiction_of_2011/ |website=[[w:Salon (website)|Salon]]}}</ref> *''[[w:The Marriage Plot|The Marriage Plot]]'' by [[w:Jeffrey Eugenides|Jeffrey Eugenides]] *''[[w:Pym (novel)|Pym]]'' by [[w:Mat Johnson|Mat Johnson]] *''[[w:State of Wonder|State of Wonder]]'' by [[w:Ann Patchett|Ann Patchett]] *''[[w:The Tragedy of Arthur|The Tragedy of Arthur]]'' by [[w:Arthur Phillips|Arthur Phillips]] *''[[w:The Pale King|The Pale King]]'' by [[w:David Foster Wallace|David Foster Wallace]] *''Townie: A Memoir'' by [[w:Andre Dubus III|Andre Dubus III]] *''Love and Capital: Karl and Jenny Marx and the Birth of a Revolution'' by [[w:Mary Gabriel (author)|Mary Gabriel]] *''[[w:The Information: A History, a Theory, a Flood|The Information: A History, a Theory, a Flood]]'' by [[w:James Gleick|James Gleick]] *''Catherine the Great: The Portrait of a Woman'' by [[w:Robert K. Massie|Robert K. Massie]] *''[[w:Lost in Shangri-La|Lost in Shangri-La]]'' by [[w:Mitchell Zuckoff|Mitchell Zuckoff]] ===2012=== New award established as "What To Read Awards" with books chosen by a system of points from an array of other journalists top-10 lists.<ref>{{cite web |last1=Miller |first1=Laura |title=What to Read Awards: Laura Miller |work=[[w:Salon (website)|Salon]] |date=December 23, 2012 |url=https://www.salon.com/2012/12/23/what_to_read_awards_laura_miller/ |archive-url=https://web.archive.org/web/20121223162820/https://www.salon.com/2012/12/23/what_to_read_awards_laura_miller/ |archive-date=2012-12-23 }}</ref><ref name="daley2012">{{cite web |url=http://www.salon.com/2012/12/23/the_what_to_read_awards_top_10_books_of_2012/ |title=The What To Read Awards: Top 10 Books of 2012 |website=[[w:Salon (website)|Salon]] |last=Daley |first=David |date=December 23, 2012 |access-date=December 24, 2012}}</ref> See also Laura Miller's top-10 picks.<ref>{{cite web |url=http://www.salon.com/2012/12/22/laura_millers_best_books_of_2012/ |title=Laura Miller’s best books of 2012 |website=[[w:Salon (website)|Salon]] |last=Miller |first=Laura |date=December 22, 2012 |access-date=December 24, 2012}}</ref> #[[w:Katherine Boo|Katherine Boo]], ''[[w:Behind the Beautiful Forevers|Behind the Beautiful Forevers]]'' #[[w:Hilary Mantel|Hilary Mantel]], ''[[w:Bring Up the Bodies|Bring Up the Bodies]]'' #[[w:Ben Fountain|Ben Fountain]], ''Billy Lynn’s Long Halftime Walk'' #[[w:Zadie Smith|Zadie Smith]], ''NW'', and [[w:Andrew Solomon|Andrew Solomon]], ''Far From the Tree'' (co-winners) #[[w:Sheila Heti|Sheila Heti]], ''How Should a Person Be'' #[[w:Gillian Flynn|Gillian Flynn]], ''Gone Girl'' #[[w:Lauren Groff|Lauren Groff]], ''Arcadia'' #[[w:Jess Walter|Jess Walter]], ''Beautiful Ruins'' #[[w:Sarah Manguso|Sarah Manguso]], ''The Guardians'' ==Notes== {{Reflist}} ==Wikiversity status== {{Complete}} [[Category:Literature]] bf4p1vl9xr0wrexmggk262nyhirpx67 1 332866 2844842 2026-11-08T00:18:39Z Jtneill 10242 Book chapter feedback 2844842 wikitext text/x-wiki <!-- Official book chapter feedback --> {{MEBF/2026 |1= <!-- Overall comments... --> # This is an insufficient chapter # The chapter title and sub-title were incorrect (fixed) # Why were the title and sub-title changed without consultation? {{sad}} # By not completing the topic development exercise, no initial feedback was provided about the plan; consequently, the key problem with the full chapter is that it does not tackle the topic (it changed the assigned title and sub-title) which makes it almost impossible for the chapter to be sufficient # The main area(s) for potential improvement: #* tackle the originally assigned topic rather than going on your tangent #* use the best psychological theory about the topic #* provide more detailed review of the best psychological research about the topic #* improve the quality of written expression #* integrate more strongly with other chapters by using embedded links to related topics #* more substantial engagement in social contribution <!-- Overall - Edit summaries --> # The edit history is quite brief, showing limited development # Use more specific [[Motivation and emotion/Wikiversity/Edit summary|edit summaries]] to clearly communicate the changes made in each edit <!-- Overall – Citations --> # Insufficient use of academic, peer-reviewed citations to support claims <!-- Overall – Copy edits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FTime_perception_in_mood_disorders&diff=2844841&oldid=2839807 these copy edits] |2= <!-- Overview – Comments... --> # Insufficient <!-- Overview – Scenario --> <!-- Overview – Scenario - Description --> # Reasonably good scenario or case study # The scenario could be more compelling if it illustrated both the lengthening and shortening of time perceptions # Why does the scenario show time slowing down for anxiety, when the evidence seems to suggest that the opposite occurs? <!-- Overview – Scenario - Figure --> # Figure 1 is relevant to the scenario <!-- Overview – Explains problem --> # Explains the psychological problem or phenomenon reasonably in a basic way # Anxiety is not a mood disorder # Bipolar depression is a mood disorder and can involved sped up time perception during manic phases <!-- Overview – Focus questions --> # The focus questions are insufficient ## How do anxiety and depression influence the subjective experience of time? (anxiety is not a mood disorder) ## Which psychological theories explain these changes? (vague) ## What does peer-reviewed research reveal, and why do findings sometimes disagree? (embed/integrate research throughout, rather than as a standalone question) # The focus questions could be improved by: ## being presented in a feature box to help guide the reader (fixed) |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # Insufficient use of relevant psychological theory about this topic # Reduce focus on anxiety; increase focus on mood disorders <!-- Theory – Builds on --> # Doesn't build on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms <!-- Theory – Depth --> # Promising depth is provided about time perception; however, this theory is not sufficiently applied to mood disorders; it gets side-tracked into anxiety and away from mood disorders other than depression <!-- Theory – Tables/Figures/Lists --> # Basic use of tables, figures, and/or lists to convey key theoretical information <!-- Theory – Citations --> # In many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic. <!-- Theory – Examples --> # Basic use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Insufficient review of relevant research # Some emphasis on systematic reviews and/or meta-analyses; more emphasis would be ideal # More detail about key studies would be ideal # In many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic. <!-- Research – Critical thinking --> # Basic [[w:Critical thinking|critical thinking]] about relevant research is evident # [[w:Critical thinking|Critical thinking]] about research could be further evidenced by: ## focusing on research about TP and MDs ## describing the methodology (e.g., sample, country, measures) in important studies ## considering the strength of relationships |5= <!-- Integration comments... --> # Basic integration between the most relevant theory(ies) and the best research # Insufficient integration with related [[Motivation and emotion/Book|chapters]] |6= <!-- Conclusion comments... --> # Promising but insufficient as a cohesive summary of the best psychological theory and research about the topic # Highlight the importance of the problem or phenomenon of interest <!-- Conclusion – Key points --> # Key points are summarised in a basic way <!-- Conclusion – Focus questions --> # Address the focus questions <!-- Conclusion – Take-home messages --> # Add practical, take-home message(s) <!-- Conclusion – Word count --> # Not counted for marking purposes due to the chapter being over the maximum word count |7= <!-- Style comments... --> <!-- Style – Written expression --> # Written expression ## The quality of written expression is basic <!-- Style – Paragraphs --> ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. <!-- Style – Layout --> # Layout ## The structure is overly complicated; simplify and integrate ## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings ## Integrate research throughout rather than having it as a stand-alone section(s) <!-- Style – Grammar --> # Grammar and spelling are excellent ## Use past tense when describing research studies, although implications of findings could be in the present tense <!-- Style – APA style --> # APA style ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY] (also known as the Oxford comma) ## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)] <!-- Style – Figures --> ## Figures ### Figures should be uploaded to [[c:|Wikimedia Commons]], not Wikiversity as discussed in tutorials ### Very welly well captioned <!-- Style – Figures - Citations --> ### Refer to each Figure at least once within the main text (e.g., "(see Figure 1)") <!-- Style – Tables --> ## Table(s) ### Very well captioned <!-- Style – Tables - Citations --> ### Refer to each Table at least once within the main text (e.g., see Table 1) <!-- Style – Citations --> # In many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags) ## Use ampersand (&) inside [[w:Bracket#Parentheses|parentheses]] and "and" outside parentheses <!-- Style – References --> ## The list of References is quite brief ## References use excellent APA style <!-- Feedback responsiveness ---> ## No evidence of responsiveness to feedback on talk page |8= <!-- Learning features comments... --> # Insufficient use of learning features <!-- Learning features – Wikipedia embedded links --> # Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. <!-- Learning features – Wikiversity embedded links --> # Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. <!-- Learning features – Figures, tables, feature boxes, scenarios --> # Basic use of figure(s) # Good use of table(s) # No use of feature boxes other than the opening scenario # Basic use of scenarios, case studies, or examples <!-- Learning features – Quizzes --> # Basic use of quiz(zes) and/or reflection question(s) # Make the quiz questions more interactive by using the [[Help:Quiz|quiz]] feature # The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end # The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]]) <!-- Learning features – See also --> # Insufficient use of the [[{{PAGENAME}}#See also|See also]] section # Also link to related book chapters <!-- Learning features – External links --> # No use of the [[{{PAGENAME}}#External links|External links]] section |9= <!-- Social contribution comments... --> # No logged contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:18, 8 November 2026 (UTC) ifjbdfkyy3ri8wwz4cv9tyt042t9ude 2 332867 2844859 2026-11-08T09:21:26Z Dick Bos 24466 test 2844859 wikitext text/x-wiki first try in working with LaTeX, especially for building formulas: see: [[:w:en:Luigi Pasinetti#A mathematical formulation of the Ricardian system]]) Here the Template:Equation is used (which numbers equations) As far as I can see that is not recommended. {{Equation|1=Y = f(N) \,|2=1.1|3=center}}<br /> {{Equation|f(0) \geq 0 |1.1a|center}}<br /> {{Equation|f'(0) > \mu \,|1.1a|center}}<br /> {{Equation|f''(N) < 0 \,|1.1a|center}} There is a different way to number equations. See: [[:w:en:Help:Displaying_a_formula#Equation numbering]]: {{NumBlk|:|<math>Y = f(N)</math>|{{EquationRef|1.1}}}} {{NumBlk|:|<math>f(0) \geq 0</math>|{{EquationRef|1.1a}}}} {{NumBlk|:|<math>f'(0) > \mu</math>|{{EquationRef|1.1a}}}} {{NumBlk|:|<math>f''(N) < 0</math>|{{EquationRef|1.1a}}}} and check if it is not a bit strange to give three different equations the same name..... See if this works to make a link to equation ({{EquationNote|1.1}}), ({{EquationNote|1.1a}}) Apart from the fact that it does not look nice to see the ref nrs bold, it works. Check Pasinetti source! sfvshv1qe7dvsr1juwxjlzcrf2mlimz 2844860 2844859 2026-11-08T09:22:59Z Dick Bos 24466 not in Wikiv 2844860 wikitext text/x-wiki first try in working with LaTeX, especially for building formulas: see: [[:w:en:Luigi Pasinetti#A mathematical formulation of the Ricardian system]]) Here the Template:Equation is used (which numbers equations) As far as I can see that is not recommended (and apparently it does not work in Wikiversity). {{Equation|1=Y = f(N) \,|2=1.1|3=center}}<br /> {{Equation|f(0) \geq 0 |1.1a|center}}<br /> {{Equation|f'(0) > \mu \,|1.1a|center}}<br /> {{Equation|f''(N) < 0 \,|1.1a|center}} There is a different way to number equations. See: [[:w:en:Help:Displaying_a_formula#Equation numbering]]: {{NumBlk|:|<math>Y = f(N)</math>|{{EquationRef|1.1}}}} {{NumBlk|:|<math>f(0) \geq 0</math>|{{EquationRef|1.1a}}}} {{NumBlk|:|<math>f'(0) > \mu</math>|{{EquationRef|1.1a}}}} {{NumBlk|:|<math>f''(N) < 0</math>|{{EquationRef|1.1a}}}} and check if it is not a bit strange to give three different equations the same name..... See if this works to make a link to equation ({{EquationNote|1.1}}), ({{EquationNote|1.1a}}) Apart from the fact that it does not look nice to see the ref nrs bold, it works. Check Pasinetti source! dpoumbytym28g2piinap9n082dweivg 2844861 2844860 2026-11-08T09:42:29Z Dick Bos 24466 help 2844861 wikitext text/x-wiki first try in working with LaTeX, especially for building formulas: * Excellent (practical) introduction: [[:w:en:Help:Displaying a formula]] * Completely different example: [[:w:en:Luigi Pasinetti#A mathematical formulation of the Ricardian system]]) Here the Template:Equation is used (which numbers equations) As far as I can see that is not recommended (and apparently it does not work in Wikiversity). {{Equation|1=Y = f(N) \,|2=1.1|3=center}}<br /> {{Equation|f(0) \geq 0 |1.1a|center}}<br /> {{Equation|f'(0) > \mu \,|1.1a|center}}<br /> {{Equation|f''(N) < 0 \,|1.1a|center}} But I can use it! There is a different way to number equations. See: [[:w:en:Help:Displaying_a_formula#Equation numbering]]: {{NumBlk|:|<math>Y = f(N)</math>|{{EquationRef|1.1}}}} {{NumBlk|:|<math>f(0) \geq 0</math>|{{EquationRef|1.1a}}}} {{NumBlk|:|<math>f'(0) > \mu</math>|{{EquationRef|1.1a}}}} {{NumBlk|:|<math>f''(N) < 0</math>|{{EquationRef|1.1a}}}} and check if it is not a bit strange to give three different equations the same name..... See if this works to make a link to equation ({{EquationNote|1.1}}), ({{EquationNote|1.1a}}) Apart from the fact that it does not look nice to see the ref nrs bold, it works. Check Pasinetti source! 5eqxtz0ayx2gqslm3g84lgwecdz6sak