did you know there’s really big holes in mathematics? i do and it’s always bugged me. https://troynikov.io/alien-mathematics/

dynamics should be something we understand really well by now but we just kinda don’t? nobody has figured out the deal with turbulence, n-body gravitational dynamics, or even our simple friend the double pendulum (wheee look at him go)

these are problems so classically difficult that the thesis advisors of almost every dominant 20th century mathematician assigned them to work on one of these problems, mostly turbulence

this is one of the very many holes in the simulation hypothesis and if you believe the brain is a nonlinear dynamical system (and you should because it is) it’s also an enormous problem if you want your brain to be in a computer (why?)

one of the things that keeps me up at night is whether or not human logic (which is at the foundation of all mathematics and therefore all physics) is parochial or universal, and which parts are which

the only real attempt i’ve encountered in constructing a consistent ‘alien’ logical system is of course intuitionistic mathematics which throws away the law of excluded middle then tries to rebuild math on top of it. surprisingly, it works.

https://en.wikipedia.org/wiki/Intuitionistic_logic

the problem with intuitionistic logic as an ‘alien’ system though is it immediately results in everything provable also being computable (via BHK and curry-howard) so it’s actually _worse_ if you’re trying to escape computability

jury’s still out on whether quantum computing has any chance of doing better than classical turing machines when it comes to dynamics

this is what i’m gonna work on when i ‘retire’

thanks also to @glowcoil for many conversations forcing me to refine and make these ideas more exact

the double pendulum is to me, proof that whatever it is the universe is doing when physical states change, it’s not (classical?) computing