Comment by peri-cl
2 hours ago
> "I believe the inventor of Velcro got the idea from burrs?"
I think there's a provocative human-intelligence analog to be found there: "humans will never discover anything that doesn't already exist somewhere in nature. We can only recombine concepts we've seen—never invent truly new ones".
It's said that mathematics is "unreasonably effective" at describing the natural world. But what about the other way around? What if mathematics is unreasonably ineffective at escaping the convex-hull of concepts and patterns found in nature?
I'm working on a piece inspired in large part by William Thurston's "On proof and progress in mathematics"[1]. Should publish it next week.
Part of why math is effective is that its extraordinarily compressible. And you can take those ideas and apply them elsewhere (composition works well). The natural world has a lot of detail and is therefore hard to compress. That's why it's a good source of new ideas. Consider the relation between the McCulloch–Pitts neuron (MCP lol)[2], developed to model biological spiking neural networks, and an inspiration for modern artificial neural networks.
[1] https://arxiv.org/abs/math/9404236 [2] https://en.wikipedia.org/wiki/Artificial_neuron
> What if mathematics is unreasonably ineffective at escaping the convex-hull of concepts and patterns found in nature?
Interesting. My intuition here is quite the opposite, that math is vastly overpowered for physics. I don't think we invest a lot of work in figuring out math that isn't useful to describe the natural world.