“ 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

“ 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?!

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.

Chess geometry is not the same as physical geometry. See, e.g., https://en.wikipedia.org/wiki/R%C3%A9ti_endgame_study

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.

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.

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 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.

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.

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?

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?

> 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 ; )

Geometry is fundamental, period.

Someone call Bernard Parharm lmao.