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| | | |.---.-..----.| |--..-----..----. | | |.-----..--.--.--..-----. | |
| | || _ || __|| < | -__|| _| | || -__|| | | ||__ --| | |
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| on Gopher (inofficial) | |
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| COMMENT PAGE FOR: | |
| How geometry is fundamental for chess | |
| sdenton4 wrote 20 hours 20 min ago: | |
| For 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. [1] (And if you care about | |
| measuring artificial intelligence, you should definitely care about | |
| what we've learned from trying to measure animal intelligence...) | |
| [1]: https://www.goodreads.com/book/show/30231743-are-we-smart-enou... | |
| layman51 wrote 20 hours 24 min ago: | |
| I 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 wrote 18 hours 57 min ago: | |
| Check out: [1] And the wiki page is a little limited but this subject | |
| can get complex but still very cool. | |
| [1]: https://en.wikipedia.org/wiki/Corresponding_squares | |
| senthil_rajasek wrote 20 hours 49 min ago: | |
| The 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 wrote 12 hours 52 min ago: | |
| I think the insight is that geometry on advanced level is fundamental | |
| for living creatures to create game of chess. | |
| fogleman wrote 20 hours 53 min ago: | |
| Kinda 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? | |
| NickC25 wrote 20 hours 58 min ago: | |
| I 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? | |
| TacticalCoder wrote 21 hours 37 min 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 ; ) | |
| jibal wrote 21 hours 52 min ago: | |
| Chess geometry is not the same as physical geometry. See, e.g., | |
| [1]: https://en.wikipedia.org/wiki/R%C3%A9ti_endgame_study | |
| KK7NIL wrote 19 hours 33 min ago: | |
| Indeed, it's not even the same between pieces! | |
| Kings have Chebysev geometry while Rooks have taxicab geometry: [1] | |
| It's left as an exercise for the reader to figure out the geometry of | |
| the remaining pieces. | |
| [1]: https://en.wikipedia.org/wiki/Taxicab_geometry#See_also | |
| daynthelife wrote 11 hours 52 min ago: | |
| Rooks don't have taxicab geometry. Their metric space is compact | |
| even on an infinite board. I think you're thinking of the wazir: | |
| [1]: https://en.wikipedia.org/wiki/Wazir_(chess) | |
| moi2388 wrote 5 days ago: | |
| â Humans are the only animals that we know that understand | |
| geometrical concepts. Things like lines and shapes (triangles, squares, | |
| circles etc.).â | |
| False. | |
| Crows for example understand geometry. Iâd wager there are plenty | |
| more. [1] â 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?â | |
| What makes you think lines and squares donât exist in nature? And | |
| what on earth does that have to do with how long life took to emerge?! | |
| [1]: https://www.science.org/doi/10.1126/sciadv.adt3718 | |
| lelanthran wrote 14 hours 45 min ago: | |
| >> 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? | |
| > And what on earth does that have to do with how long life took to | |
| emerge?! | |
| I think you misunderstood that part you quoted. He's not claiming | |
| that it had a causative effect on how long life took to develop, he's | |
| claiming that it took 4.5 billion years after life first appeared for | |
| those geometrical concepts to emerge. | |
| moi2388 wrote 12 hours 16 min ago: | |
| Ah, thanks. That makes sense. I still disagree that it took that | |
| long for these concepts to emerge. Perhaps words for these | |
| concepts. | |
| voxleone wrote 20 hours 9 min ago: | |
| Perfect lines and squares donât exist as physical objects, sure, | |
| but geometry is less about material perfection than itâs about | |
| relationships. Nature constantly approximates geometric regularities | |
| because physics imposes them: energy minimization gives spheres, | |
| space-filling gives hexagons, angular momentum gives spirals. | |
| Life didnât need 4.5 billion years to âinventâ geometry; | |
| geometry constrained life from the beginning. We only invented the | |
| formal language to describe it. | |
| andoando wrote 20 hours 38 min ago: | |
| Merely 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 wrote 11 hours 50 min ago: | |
| It 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. | |
| IAmBroom wrote 21 hours 21 min ago: | |
| It'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...) | |
| Tazerenix wrote 21 hours 46 min ago: | |
| [1] Here's Gromov, one of the greatest geometers of the last 50 | |
| years, discussing his viewpoint on this. | |
| [1]: https://youtu.be/EbzESiemPHs?si=4UNA7JGPt7OmfnOi&t=206 | |
| griffzhowl wrote 20 hours 46 min ago: | |
| He 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?" | |
| [1]: https://www.youtube.com/watch?v=aJAQVletzdY&list=PLx5f8Iel... | |
| plmpsu wrote 5 days ago: | |
| I 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. | |
| d4rkn0d3z wrote 5 days ago: | |
| Geometry is fundamental, period. | |
| nurettin wrote 5 days ago: | |
| If 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 wrote 22 hours 45 min ago: | |
| This is called âchunkingâ [0] â identifying grouped assortmen… | |
| of pieces as a single semantic unit - and has extensive research [1] | |
| behind it. | |
| [0] [1] | |
| [1]: https://www.chessprogramming.org/Chunking | |
| [2]: https://pmc.ncbi.nlm.nih.gov/articles/PMC4361603/ | |
| khelavastr wrote 5 days ago: | |
| Someone call Bernard Parharm lmao. | |
| <- back to front page |