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.
> 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.
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.
You can use things without understanding them. See people asking chatgpt to do sth for them.
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...)
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?!