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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:
“ 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. [1] “ 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?!
[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 don’t exist as physical objects, sure,
but geometry is less about material perfection than it’s about
relationships. Nature constantly approximates geometric regularities
because physics imposes them: energy minimization gives spheres,
space-filling gives hexagons, angular momentum gives spirals.
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.
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 “chunking” [0] — 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.
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