The Search for the Longest Infinite Chess Game

We explore extremely long Infinite Chess games, starting with Mate in Omega, and progressively climbing to higher and higher transfinite ordinals! Play Infinite Chess at: https://www.InfiniteChess.org Support me and its development on my Patreon, and get your name in the credits of my videos: https://www.patreon.com/Naviary Join the Infinite Chess Discord server: https://discord.gg/NFWFGZeNh5 Access the spreadsheet board editor: https://docs.google.com/spreadsheets/d/1Eo1SIo2esUijZ3LQzGy8QLKTOVh77DdDQuqEBILec9I/edit?usp=sharing \/ Credits for the positions shown, along with links to learn more about them! \/ Omega, Omega^2, Omega^3 by Joel Hamkins and C. D. A. Evans: http://math.colgate.edu/~integers/og2/og2.pdf Omega*2 by Noam. D. Elkies: https://mathoverflow.net/a/63841/514442 Omega^4 by C. D. A. Evans, Joel Hamkins, and Norman Lewis Perlmutter: http://math.colgate.edu/~integers/rg4/rg4.pdf Omega_1 Proof by Matthew Bolan: https://mathoverflow.net/questions/63423/checkmate-in-omega-moves/440147#440147 Subscribe to his channel! https://www.youtube.com/channel/UCB4XuRBJZBOpnoJSWekMohw Some clips are from Joel Hamkins presentation, “The theory of infinite games, including infinite chess”, watch it here! https://www.youtube.com/watch?v=1_bVL1FG2gI See more presentations on The Infinite Games Workshop: https://www.youtube.com/channel/UCZP2ve0DNfwAq8HrjBANc0Q Note for the chapter “Climbing the Ordinal Tower”: I often mention “this to the power of this infinitely…”, or “infinite epsilons above this…”. When I word things like this, what I really mean is to take the limit, or supremum, as we approach doing that operation infinitely. I have chosen this wording to make things more intuitive to the viewer and those who may have zero ordinal arithmetic knowledge. This chapter is not meant to be a detailed explanation of ordinal arithmetic. 🎶 Music used (in order) 🎶 Background Check by David Robson: https://www.youtube.com/watch?v=r13MWpaUnVQ Looking For Clues by David Robson: https://www.youtube.com/watch?v=YCi6znptiH8 Witness Testimony by David Robson: https://www.youtube.com/watch?v=C5US0Ycu7QU Viking by Aakash Gandhi: https://www.youtube.com/watch?v=XkIhUzHehXY Mario Bava Sleeps In a Little Later Than He Expected To by Chris Zabriskie: https://www.youtube.com/watch?v=YV2x_FUpasQ This is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/ Source: http://chriszabriskie.com/vendaface/ Artist: http://chriszabriskie.com/ Anime Song 2 by Montage of Chips: https://youtu.be/iNSuzDPbpno?si=lzoqtrDKQ9LXOou3 Music: True Detective by Soundridemusic Link to Video: https://www.youtube.com/watch?v=iCI-yY8QZIs&t=0s White Hats by Wayne Jones: https://www.youtube.com/watch?v=VcZmSNhxC4o Artemis by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au Video: https://www.youtube.com/watch?v=vqb0XsZ04Og Needle In A Haystack by David Robson: https://www.youtube.com/watch?v=xJiD6LvjFag Signal to Noise by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au Video: https://www.youtube.com/watch?v=x43OJXk8idI Weirder Stuff by Geographer: https://www.youtube.com/watch?v=PeWgLUs40Pw Many of these songs are provided by FesliyanStudios! Make a donation to also gain access to their music :) https://www.fesliyanstudios.com/policy Chapters: 0:00 Introduction 1:18 The Game Tree 3:21 Omega 5:17 Why Ordinals? 8:04 Omega+1 8:58 Omega*2 10:41 Omega^2 12:27 Omega^3 14:48 Omega^4 20:20 Matthew’s Proof 24:09 Climbing the Ordinal Tower 26:53 Conclusion Other stock footage is from Pixabay.com If I missed, or incorrectly gave credit, please don’t hesitate to contact me using my email! Located in the "About" section of my channel, click "View email address".