- 5
- 2 420 103
Naviary
Приєднався 24 сер 2022
Infinite Chess creator
Channel created: Aug 24, 2022
Channel created: Aug 24, 2022
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: www.InfiniteChess.org
Support me and its development on my Patreon, and get your name in the credits of my videos: www.patreon.com/Naviary
Join the Infinite Chess Discord server: discord.gg/NFWFGZeNh5
Access the spreadsheet board editor: 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: math.colgate.edu/~integers/og2/og2.pdf
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/rg4.pdf
Omega_1 Proof by Matthew Bolan: mathoverflow.net/questions/63423/checkmate-in-omega-moves/440147#440147
Subscribe to his channel! ua-cam.com/channels/B4XuRBJZBOpnoJSWekMohw.html
Some clips are from Joel Hamkins presentation, “The theory of infinite games, including infinite chess”, watch it here! ua-cam.com/video/1_bVL1FG2gI/v-deo.html
See more presentations on The Infinite Games Workshop: ua-cam.com/channels/ZP2ve0DNfwAq8HrjBANc0Q.html
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: ua-cam.com/video/r13MWpaUnVQ/v-deo.html
Looking For Clues by David Robson: ua-cam.com/video/YCi6znptiH8/v-deo.html
Witness Testimony by David Robson: ua-cam.com/video/C5US0Ycu7QU/v-deo.html
Viking by Aakash Gandhi: ua-cam.com/video/XkIhUzHehXY/v-deo.html
Mario Bava Sleeps In a Little Later Than He Expected To by Chris Zabriskie: ua-cam.com/video/YV2x_FUpasQ/v-deo.html
This is licensed under a Creative Commons Attribution 4.0 license. creativecommons.org/licenses/by/4.0/
Source: chriszabriskie.com/vendaface/
Artist: chriszabriskie.com/
Anime Song 2 by Montage of Chips: ua-cam.com/video/iNSuzDPbpno/v-deo.htmlsi=lzoqtrDKQ9LXOou3
Music: True Detective by Soundridemusic
Link to Video: ua-cam.com/video/iCI-yY8QZIs/v-deo.html
White Hats by Wayne Jones: ua-cam.com/video/VcZmSNhxC4o/v-deo.html
Artemis by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
Video: ua-cam.com/video/vqb0XsZ04Og/v-deo.html
Needle In A Haystack by David Robson: ua-cam.com/video/xJiD6LvjFag/v-deo.html
Signal to Noise by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
Video: ua-cam.com/video/x43OJXk8idI/v-deo.html
Weirder Stuff by Geographer: ua-cam.com/video/PeWgLUs40Pw/v-deo.html
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".
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: www.patreon.com/Naviary
Join the Infinite Chess Discord server: discord.gg/NFWFGZeNh5
Access the spreadsheet board editor: 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: math.colgate.edu/~integers/og2/og2.pdf
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/rg4.pdf
Omega_1 Proof by Matthew Bolan: mathoverflow.net/questions/63423/checkmate-in-omega-moves/440147#440147
Subscribe to his channel! ua-cam.com/channels/B4XuRBJZBOpnoJSWekMohw.html
Some clips are from Joel Hamkins presentation, “The theory of infinite games, including infinite chess”, watch it here! ua-cam.com/video/1_bVL1FG2gI/v-deo.html
See more presentations on The Infinite Games Workshop: ua-cam.com/channels/ZP2ve0DNfwAq8HrjBANc0Q.html
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: ua-cam.com/video/r13MWpaUnVQ/v-deo.html
Looking For Clues by David Robson: ua-cam.com/video/YCi6znptiH8/v-deo.html
Witness Testimony by David Robson: ua-cam.com/video/C5US0Ycu7QU/v-deo.html
Viking by Aakash Gandhi: ua-cam.com/video/XkIhUzHehXY/v-deo.html
Mario Bava Sleeps In a Little Later Than He Expected To by Chris Zabriskie: ua-cam.com/video/YV2x_FUpasQ/v-deo.html
This is licensed under a Creative Commons Attribution 4.0 license. creativecommons.org/licenses/by/4.0/
Source: chriszabriskie.com/vendaface/
Artist: chriszabriskie.com/
Anime Song 2 by Montage of Chips: ua-cam.com/video/iNSuzDPbpno/v-deo.htmlsi=lzoqtrDKQ9LXOou3
Music: True Detective by Soundridemusic
Link to Video: ua-cam.com/video/iCI-yY8QZIs/v-deo.html
White Hats by Wayne Jones: ua-cam.com/video/VcZmSNhxC4o/v-deo.html
Artemis by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
Video: ua-cam.com/video/vqb0XsZ04Og/v-deo.html
Needle In A Haystack by David Robson: ua-cam.com/video/xJiD6LvjFag/v-deo.html
Signal to Noise by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
Video: ua-cam.com/video/x43OJXk8idI/v-deo.html
Weirder Stuff by Geographer: ua-cam.com/video/PeWgLUs40Pw/v-deo.html
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".
Переглядів: 471 752
Відео
Mate-in-Omega, The Great Phenomenon of Infinite Chess
Переглядів 570 тис.9 місяців тому
What does it mean for a chess position to be Mate-in-Omega? Let's find out! Support me and the development of Infinite Chess on Patreon! www.patreon.com/Naviary Watch my previous video, "I Made Chess, but It's Infinite"! ua-cam.com/video/rav29N0-h2c/v-deo.html Play Infinite Chess at: www.InfiniteChess.org Join the official Infinite Chess Discord! discord.gg/NFWFGZeNh5 The positional examples of...
I Made Chess, but It's Infinite
Переглядів 1,4 млн11 місяців тому
What if chess held no borders? What if it was infinite? Play now at: www.InfiniteChess.org Patreon: www.patreon.com/Naviary More devlogs: www.chess.com/forum/view/chess-variants/infinite-chess-app-devlogs-and-more 0:00 Introduction 1:48 Infinite Chess 2:57 Why? 4:57 How to play 8:09 Credits Mate-in-ω positions: arxiv.org/pdf/1302.4377.pdf Mate-in-ω^4: www.semanticscholar.org/paper/A-Position-in...
A infinite mate actually can be made in no 50 move rule and infinite chess.
“Hah, you didn’t see the bishop on zzzd353035!
We might actually resign from life ⚰️ before we decide to resign the game 😂!!
well how about breaking the fundamental rules of the reality and find mate in √-44
could you construct a position where both black and white could checkmate eachother (a.k.a neither have a forced checkmate) but it is impossible to stalemate? so that there is no branch in the game tree where black or white is in stalemate.
It's not actually the 50 move rule, it's a draw if one of the players claim a draw, it's a forced draw after 75 moves
if ω^4 is not stupidly long itself for you then if every anoucment would be 100 the game would lasts 100 000 000 ( 100 million ) moves
Bishop is a menace in this chess board
I'll bet I would do all the moves and blunder away the checkmate at the end
This video made me cry while watching this at 12am
"What?! How is this not checkmate?" That one bishop on Z781: 👻
how long is that bishop cannon 😭😭
Somehow you managed to fit ordinal collapsing functions into a chess video.
7:35 But if the rook moves then the king will keep moving forever
Hold on what is white doing in the intro 1. e3 e6 - okay, already dumb. 2. e4 - somewhere, GothamChess fell out of a chair
“You know what, let’s call it a draw”
2:05 Is there any proof why is the bound of n for mate-in-n always finite for finite chess?
I took acid before watching this video
I before I heard the name of the omega one, I thought it was Absolute Infinity
The same symbol is used for both, but they are different concepts.
Wait, if we can construct the 3 index+, Can't we use e's to make it bigger
4:21 just move the rook to the left or right.
Wait, at 4:01 you can take the right pawn with a rook.
"The most realistic positions"
"A bigger infinity": Let's say we have infinity A and infinity B; iA and iB. Where iB is the bigger infiity. I would say: it is the same as dividing by zero. It is not possible. Because you can't count to iA and you can't count to iB; both possibilities are zero. Let's say ZeroA for counting to iA, and ZeroB for counting to iB. To see the difference in size, you have to divide ZeroB by ZeroA. But as ZeroA is 0, you are dividing by zero. Therefore "A bigger infinity" is the same as dividing by zero: it is simply not possible. You can't have a "bigger infinity".
That Mate in omega position isnt just moving the rook TREE(3) spaces far, all i need to do is to move the middle rook away :D
I hate when my opponent plays Qd(10^301)
im sorry to tell u navary but u are wrong in the first example u gave after black moves the rook up)lets say white king is on e2 pawn d2 pawn g3 qd2 rf4 and for black ke5 and rooks e6 c6 g6 ) white has Qd7 and mates with re5 and c4
What is this video about?
You have infinite board now Is it possible to add other board games like go to this? Especially because the rules of Go are very simple I must experience infinite go before death And I will probably never see it Because no one is as crazy as you to want to make something like that (take this as a compliment)
I could see this being adapted for infinite go one day!
If it was 3d infinite chess we could reach w_1
Wouldn't the first position without those black rooks be mate in Ω?
Thanks for the video! This video is very interesting
I was playing a chess game for 10 MINUTES AND YOU SCREWED UP MY BOARD NOW YOU GOTTA PUT IT ALL BACK
imagine pawn sisyphus trying to reach the end to become queen...
2:33 Bro was exiled💀
Sore loser tech geek gets tired of losing in classical chess, so creates boundary-less chess (i.e. NOT CHESS.)
obvious ragebait
White on the air checkmate move: Oh shit, I didn’t line it up-
Now you need to create real chess, where there are no squares so you _can_ get mate in Ω.
Look its diagonaliztion
Would 3d chess influence it at all. Probably not since the infinite levels of 2d space wouldnt make Omega.
Imagine blundering mate in Church-Kleene Ordinal
Now make infinite go
Meanwhile hikaru seeing mate in omega one
Ok but what about Ω-1?
Infinite pieces maybe just maybe destroys the value of the pieces Is there a special method or arrangement for pieces to fix this possible problem?
. CK How to mate in ω 1 Step 1: Get a rook Step 2: Mate with rook
ε ζ η φ Γ Ψ Ω
How do you promote??
Watch the first infinite chess video
75% of the video: actual chess stuff The last 25% at the end: Super complicated math lesson about ordinals brought to you by Naviary
I have serious doubt a chess engine can ever be created for infinite chess, as there would simply be too much legal moves for the engine to even reach a depth of 1. Sure, you could create a move distance limit, but i still think it would be extremely hard. And the engine would likely be extremely slow.
And it would likely be unable to see mates as long as shown in this video.
An idea is to only look search squares that are diagonal/orthogonal instersection squares between any 2 pieces. Nonetheless it will be very challenging, no computer will probably beat humans at Infinite Chess for a very long time. And for detecting mate in omega there would have to be some sort of pattern recognition, but it's impossible to detect all kinds of mate in omegas.
@@Naviary yeah, an infinite chess computer would probably take years or even decades of development to even stand a chance against humans