Comment by GoblinSlayer
7 hours ago
>but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen
This is quantifiable, right? Should be possible to measure how many mathematicians favor ideas like turbulence, macroscopic quantum physics, anthropic principle, analog geometry, finitism. I think, mathematics doesn't really try to match physics yet.
I think this passage is more about the fact that mathematics is a form of symbolic computation people create and it is weirdly congruent to the physical measurements and models of reality. Not that mathematicians see certain models and objects used in physical models in a favorable way. What favor even means here?
It is quantifiable: several mathematical objects and categories people invented to do symbolic computation in letters and published papers are somehow very useful to model and understand data from physical measurements of reality.
I highly recommend reading the "Unreasonable effectiveness of mathematics" essay by Wigner:
https://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableE...
Dirac was talking about the fundamental laws. In favour of his point, and not known at the time he gave the talk, the standard model of particle physics is based on the symmetry groups U(1), SU(2), and SU(3), so Lie groups (which mathematicians find interesting) appear to have been chosen by nature.
I sort of have this suspicion that the kinds of phenomena that we can even apprehend are pretty closely related to what we can reason about mathematically, and the reason that math seems to work so well to model behavior that we understand says more about how our brain works than how the universe works.
If a phenomenon isn’t model-able by relatively simple math it doesn’t even look like a phenomenon to us, it looks like a chaotic mess.
Which is to say that unless something has mathematical coherence it is more or less invisible to our experience.
Well there are counting arguments to say that a higher level intelligence that somehow achieves say, 100000× brain efficiency of humans, still can't do that much more work than humans, if humans found the "best abstraction". Think about computability for example - that means you could feasibly solve problem instances of n+20 relative to what a human can solve.
Of course, I think putting numbers to wishy washy meta-quantities like "how efficiently does a certain conceptual scheme help you" are super loaded and hard to properly talk about (incommensurability). I've been toying with trying to make a repository of all the possible "moves" one can make in this kind of abstract analysis - constrain the problem statement, argue something like "the system is what it does", dissolving, etc. but even that seems hard
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