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Math is informed by physics, but not constrained by it. Very loosely speaking, pi can take a different values on non-euclidean planes. This ends up becoming re
by NegativeK 2y ago
Math is informed by physics, but not constrained by it.
Very loosely speaking, pi can take a different values on non-euclidean planes. This ends up becoming relevant on the surface of the earth or, say, the saddle of a horse. I'm not sure if the motivation was from looking at curved surfaces, but it just as easily could've come from the rejection of Euclid's parallel postulate and seeing what results. Similarly, I think imaginary numbers were motivated by the math well before they found applications in reality.
There are also plenty of other mathematical constructions that are informed by reality (since that's what our brains are constrained to,) but I'm pretty sure are far from actually describing reality. Transfinite cardinals/ordinals, fast growing hierarchies, Turing degrees, Goldbach's conjecture, how the hypervolume of a hypersphere eventually decreases as dimension increases...
You can even reject the standard axioms and construct math that can not be compatible with reality. Or argue that the standard axioms permit too much wiggle room to create concepts that have no relation to reality. (But maybe you shouldn't; that sounds like philosophy.)