5 ms·
How geometry is fundamental for chess
- khelavastr 10mo agoSomeone call Bernard Parharm lmao.
- nurettin 10mo agoIf you watch any Hikaru Nakamura content, you will see him draw "classic right angle triangle"s with three pieces, "classic wooden shield"s (a cross showing the scope of a centralized bishop), so he definitely uses some kind of geometry while playing. Not sure if he just recognizes the shapes as they appear or tries to make them appear, would be nice if he came here to answer.
- chatmasta 10mo agoThis is called “chunking” [0] — identifying grouped assortments of pieces as a single semantic unit - and has extensive research [1] behind it. [0] https://www.chessprogramming.org/Chunking https://www.chessprogramming.org/Chunking [1] https://pmc.ncbi.nlm.nih.gov/articles/PMC4361603/ https://pmc.ncbi.nlm.nih.gov/articles/PMC4361603/
- d4rkn0d3z 10mo agoGeometry is fundamental, period.
- plmpsu 10mo agoI found this article very interesting. I would've also appreciated a discussion of how intuition of geometry might apply to chess playing abilities and how it might not be sufficient for playing chess well. As a side note, I appreciated the small typos as a further signal that this was written by a human.
- moi2388 10mo ago“ Humans are the only animals that we know that understand geometrical concepts. Things like lines and shapes (triangles, squares, circles etc.).” False. Crows for example understand geometry. I’d wager there are plenty more. https://www.science.org/doi/10.1126/sciadv.adt3718 https://www.science.org/doi/10.1126/sciadv.adt3718 “ These geometrical concepts do not exist in nature. There are no lines and squares. If it's obvious then why did it take 4.5 billion years since the development of life to emerge?” What makes you think lines and squares don’t exist in nature? And what on earth does that have to do with how long life took to emerge?!
- Tazerenix 10mo agohttps://youtu.be/EbzESiemPHs?si=4UNA7JGPt7OmfnOi&t=206 https://youtu.be/EbzESiemPHs?si=4UNA7JGPt7OmfnOi&t=206 Here's Gromov, one of the greatest geometers of the last 50 years, discussing his viewpoint on this.
- griffzhowl 10mo agoHe always has these brilliant ond original perspectives on even the simplest concepts. He also has this series of talks beginning with the question "What is probability, what is randomness?" https://www.youtube.com/watch?v=aJAQVletzdY&list=PLx5f8IelFRgGo3HGaMOGNAnAHIAr1yu5W https://www.youtube.com/watch?v=aJAQVletzdY&list=PLx5f8IelFR...
- IAmBroom 10mo agoIt's the usual "until we prove animals do _X_ we can safely assert only humans do _X_" trope of biology. As we learn that animals do things like have homosexual relationships, giggle when tickled, and understand basic rules of economics... biologists are learning to phrase it as "until we prove animals do _X_ we cannot be sure if animals do _X_", which is much safer. (Also, there are trillions of lines in nature - WTF? Squares are somewhat rarer, except on the ground in wombat territory...)
- deleted 10mo ago[deleted]
- andoando 10mo agoMerely being able to differentiate a door from a wall, as dog does, takes an understanding of geometry. I'd go even further and postulate that all intelligence is an understanding of geometry.
- ajuc 10mo agoIt doesn't. It takes an application of geometry. It does not require understanding. You can use things without understanding them. See people asking chatgpt to do sth for them.
- jibal 10mo agoChess geometry is not the same as physical geometry. See, e.g., https://en.wikipedia.org/wiki/R%C3%A9ti_endgame_study https://en.wikipedia.org/wiki/R%C3%A9ti_endgame_study
- KK7NIL 10mo agoIndeed, it's not even the same between pieces! Kings have Chebysev geometry while Rooks have taxicab geometry: https://en.wikipedia.org/wiki/Taxicab_geometry#See_also https://en.wikipedia.org/wiki/Taxicab_geometry#See_also It's left as an exercise for the reader to figure out the geometry of the remaining pieces.
- daynthelife 10mo agoRooks don't have taxicab geometry. Their metric space is compact even on an infinite board. I think you're thinking of the wazir: https://en.wikipedia.org/wiki/Wazir_(chess) https://en.wikipedia.org/wiki/Wazir_(chess)
- jibal 10mo agohttps://en.wikipedia.org/wiki/Chebyshev_distance https://en.wikipedia.org/wiki/Chebyshev_distance for kings, but on a clear board the rook distance between any two squares is 1 or 2, whereas with Taxicab it could be as much as 14.
- TacticalCoder 10mo ago> Chimpanzees, instead of seeing 6 and 7, they feel 6ish-7ish. I see what the author did there. I've got a kid so "what the sigma" and "six seven" are a thing. Type "six seven" in Google search and you should get the screen wobbling ; )
- NickC25 10mo agoI was never particularly good at geometry. I've beaten over 2500 ELO in Crazyhouse on Lichess (2518 to be exact). Currently rated around 1900. Am I missing something?
- fogleman 10mo agoKinda disappointing article. Not much substance regarding the link between geometry and chess, as suggested by the title. > Shapes are hypothesized to be formed by a programming language in the brain. And what does this even mean? What does it mean for there to be a "programming language" in the brain?
- senthil_rajasek 10mo agoThe title is "How geometry is fundamental for chess." but 60% of this article is about how animals don't have a sense for numbers or bad at geometry. Only a couple brief mentions about how chess piece moves are lines and transforms of lines. Other than that the author never establishes the title. I was actually looking for some insight about chess and did not get any.
- ozim 10mo agoI think the insight is that geometry on advanced level is fundamental for living creatures to create game of chess.
- layman51 10mo agoI thought this article was going to be about how chess at its core is a game about intersecting lines or crosses (+ or x). Also, there are really interesting ideas that could be explored around why a rook on a bare board always controls the same number of squares no matter where it is placed, but for other pieces like the bishop or the knight, they control more squares the closer they are to the center of the board.
- zippyman55 10mo agoCheck out: https://en.wikipedia.org/wiki/Corresponding_squares https://en.wikipedia.org/wiki/Corresponding_squares And the wiki page is a little limited but this subject can get complex but still very cool.
- sdenton4 10mo agoFor anyone actually interested in the question of measuring animal intelligence, I recommend the book 'Are we smart enough to know how smart animals are?' by frans de waal. https://www.goodreads.com/book/show/30231743-are-we-smart-enough-to-know-how-smart-animals-are https://www.goodreads.com/book/show/30231743-are-we-smart-en... (And if you care about measuring artificial intelligence, you should definitely care about what we've learned from trying to measure animal intelligence...)
- alisonkisk 10mo agoSubmitted blog post is from Lichess user (rated ~2150 on Lichess), not Lichess organization itself.