> But this is not a given, of course; there can potentially be different ways to describe physical reality which are comparably successful, but which grow from entirely different foundations, are internally consistent, and otherwise work like our mathematics, but are not connected to it (yet).
Are you or anybody else aware of any other way to describe physical reality? Maybe some culture took a different path. That would be very interesting. It seems almost impossible to imagine one for me though.
Ted Chiang's short novel "Story of Your Life" [0], later turned into the movie "Arrival", describes an alien culture which uses variational calculus [1] as the normal way to describe physics, that is, their equations are mostly about finding functions with extrema of certain kind, not just derivatives (as are the normal PDUs we use in physics). The idea is that "our" equations mostly deal with the arrow of time and thus use terms like dx/dt extensively, while "their" equations are about the entire configuration of something in spacetime, not singling out the time dimension.
Are you or anybody else aware of any other way to describe physical reality? Maybe some culture took a different path. That would be very interesting. It seems almost impossible to imagine one for me though.