|
> rather, it's that we saw those relationships and went looking for the minimum set of rules from which they could all be derived. There are (of course) other choices we could have made, which are useful in different cases, such as talking about geometry on a sphere instead of geometry on a flat piece of paper. OK, this makes sense now! > It gave a corpus of different approaches, linked up the intuitive notions with formalisms, and led to several generalizations applied to different contexts. And I guess this gives you multiple points from which to verify new ideas. > If you need an analogy to what this would be like in a different field, we discovered (modern) formalism around the same time that biology discovered evolution, and formal (mechanical) computation around the same time they discovered DNA This kinda reminds me of the Bohr atomic model from 1925: it went through many iterations since, a lot of which were kind of true but not quite. They discovered that, oops, the electron orbits are elliptical, not circular. And the more weird and odd particles and effects we discover, the more accurate the model gets, but the original wasn't that bad at modelling reality. Or the Newtonian physics vs modern stuff. Newtonian physics was 90% there, but not quite enough to explain things happening in extreme circumstances that are difficult to observe. > you might want to check out Category Theory or Homotopy Type Theory. Both are very applicable to programming or science, if either is your field! Category Theory is definitely on my list of things to learn. HTT seems quite new fangled, I remember seeing that the book made a big fuss on HN recently. I'll have to read more into it to see if it's worth it for me to delve deeper into. I'd love to hear more about book recommendations! I'm a software engineer and I've had a CS education, so I've had a decent chunk of college-level math (including linalg, diffeqs...), automata theory, etc. So, some exposure to post-1700s math, some formal paper-reading, etc. You can find my e-mail in my HN profile if you like. Thanks again. Good talk! |