[aatd86]

Banach spaces looking like lightweight Euclidian spaces (in terms of constraints), and reality being experienced as data and applications, I'm going to try and say that:

Physics is a subset of Mathematics but which subset we don't exactly know.

In a sense, physics is the self-referential discovery of a subset of mathematics.

Makes sense since "existence" is impredicative.

[smj-edison]

Mathematics is perhaps a subset of logic? I'm not very familiar with this space, but I think it's pretty cool that so much of math can be represented with very simple rules building up, especially with things like the Lean proof language.

[lanstin]

I find infinite dimensional spaces even of zero curvature to be a bit creepy. Especially with a vector space structure, that just makes it worse.

[andrewflnr]

You're entirely missing the critical point of my comment, which is the initial conditions.

[aatd86]

I beg to differ. What are initial conditions if not some additional constraints?