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: www.InfiniteChess.org
Support me and its development on my Patreon, and get your name in the credits of my videos: / naviary
Join the Infinite Chess Discord server: / discord
Access the spreadsheet board editor: docs.google.com/spreadsheets/...
\/ 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: math.colgate.edu/~integers/og2...
Omega*2 by Noam. D. Elkies: mathoverflow.net/a/63841/514442
Omega^4 by C. D. A. Evans, Joel Hamkins, and Norman Lewis Perlmutter: math.colgate.edu/~integers/rg4...
Omega_1 Proof by Matthew Bolan: mathoverflow.net/questions/63...
Subscribe to his channel! / @matthewbolan8154
Some clips are from Joel Hamkins presentation, “The theory of infinite games, including infinite chess”, watch it here! • TMWYF: The theory of i...
See more presentations on The Infinite Games Workshop: / @infinitegamesworkshop...
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: • Detective Music For In...
Looking For Clues by David Robson: • Suspenseful Detective ...
Witness Testimony by David Robson: • Mysterious Detective B...
Viking by Aakash Gandhi: • Viking - Aakash Gandhi
Mario Bava Sleeps In a Little Later Than He Expected To by Chris Zabriskie: • Mario Bava Sleeps In a...
This is licensed under a Creative Commons Attribution 4.0 license. creativecommons.org/licenses/...
Source: chriszabriskie.com/vendaface/
Artist: chriszabriskie.com/
Anime Song 2 by Montage of Chips: • Anime Song 2
Music: True Detective by Soundridemusic
Link to Video: • Suspense Detective, Cr...
White Hats by Wayne Jones: • White Hats - Wayne Jones
Artemis by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
Video: • 'Artemis' [Inspiration...
Needle In A Haystack by David Robson: • Investigation Crime Sc...
Signal to Noise by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
Video: • 'Signal to Noise' [Cin...
Weirder Stuff by Geographer: • Weirder Stuff - Geogra...
Many of these songs are provided by FesliyanStudios! Make a donation to also gain access to their music :) 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".
Негізгі бет Ойындар The Search for the Longest Infinite Chess Game
Пікірлер: 1,5 М.