How Geometry Is Fundamental for Chess
Key topics
The fascinating link between geometry and chess sparked a lively discussion, with commenters chiming in on the role of spatial awareness in the game. Some pointed out that top players like Hikaru Nakamura frequently visualize geometric shapes on the board, while others highlighted the concept of "chunking" - identifying groups of pieces as a single unit - as a key aspect of chess strategy. The conversation took an interesting turn when one commenter disputed the claim that humans are the only animals that understand geometric concepts, citing examples of crows and other animals demonstrating spatial awareness. As the debate unfolded, it became clear that the intersection of geometry and cognition is a rich and complex topic that extends far beyond the chessboard.
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- 01Story posted
Dec 11, 2025 at 5:23 PM EST
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Dec 18, 2025 at 3:11 AM EST
16 days ago
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[0] https://www.chessprogramming.org/Chunking
[1] https://pmc.ncbi.nlm.nih.gov/articles/PMC4361603/
False.
Crows for example understand geometry. I’d wager there are plenty more.
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?!
Here's Gromov, one of the greatest geometers of the last 50 years, discussing his viewpoint on this.
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=PLx5f8IelFR...
I'd go even further and postulate that all intelligence is an understanding of geometry.
> 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.
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...)
This probably goes back to the classic debate between rationalism and empiricism. Do we have squares as a priori knowledge, or do we generalize from examples? But then how do we make abstract deductions about things? Do these deductions skew a certain way?
Clearly, deductive logic exists, yet also clearly, empiric observations exist. How do you properly marry the two?
https://intellectualmathematics.com/blog/rationalism-2-0-kan...
Life didn’t need 4.5 billion years to “invent” geometry; geometry constrained life from the beginning. We only invented the formal language to describe it.
Kings have Chebysev geometry while Rooks have taxicab geometry: 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.
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.
And the wiki page is a little limited but this subject can get complex but still very cool.
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...)
I've beaten over 2500 ELO in Crazyhouse on Lichess (2518 to be exact). Currently rated around 1900.
Am I missing something?
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.
> 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?