It is literally possible to reduce the theory of Turing machines to real analytic ODEs.
Okay, that sounds interesting (reference?), but what about the rest of my comment?
Here is Pour-El and Richards. Here is a more recent reference that makes my claim more explicitly. Both are gated.
What about the rest of my comment?
I'm not sure what to say. You've accused me of "confusing levels," but I'm exactly disputing the idea that sets are at a lower level than real numbers. Maybe I know how to address this:
...But likewise, the standard reduction to set theory does not illuminate differential equations
...and nor does the reduction of biology to physics "illuminate" human behavior. That just isn't the po
Did computer programming make you a clearer, more precise thinker? How about mathematics? If so, what kind? Set theory? Probability theory?
Microeconomics? Poker? English? Civil Engineering? Underwater Basket Weaving? (For adding... depth.)
Anything I missed?
Context: I have a palette of courses to dab onto my university schedule, and I don't know which ones to chose. This much is for certain: I want to come out of university as a problem solving beast. If there are fields of inquiry whose methods easily transfer to other fields, it is those fields that I want to learn in, at least initially.
Rip apart, Less Wrong!