alt Hacker News“ 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?!
Replies
>> 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.
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.
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.
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...)
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.