[ianmcgowan]

That doesn't explain why math is so amazingly effective at describing reality - all the pure mathematical results seem to eventually end up being useful at describing some new aspect of the world (to the chagrin of the pure mathematician).

Maybe it's the other way around? Our minds work this way because that's the rules and we're just emergent from that reality. It's hard to argue that symmetry is not a mathematical ideal first, and a biological approximation to that ideal second.

[klik99]

Yeah I agree our minds evolved to think that way because it was useful, we succeeded because the way the brain works fits very nicely with how things operate at human scale. My point is that the scale matters, as we get further and further away from human scale, the maths get more esoteric and even start depending on probability. Compare the math for bodies in motion versus subatomic particles. There's no question math exists in nature, but given the potentially infinite scale both in time and scale of reality, of which we occupy a small sliver, it's not impossible that the tools we use to model reality all the way back to the big bang may not be fundamental to nature but an emergent property.

Biological symmetry in particular likely emerged as a way to half the data needed to encode life, needing less resources and therefore more likely to reproduce.

But anyway, for all purposes, I do agree. Math obviously exists in nature and it's our best tool at predicting things. I just find it interesting to think that math itself is an emergent property of some other thing. Otherwise, why does anything exist at all? If it was simply maths, then why did anything first pop into existence?