wow model theorists are wild
projecteuclid.org/euclid.ndjfl/1
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i'm still lowkey working slowly in the background on a long-term project to understand what the hell entropy is and "the logarithm of the cardinality of a nonstandard finite set" is actually kinda relevant to that i think
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Can you drop any nuggets of your progress?
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i don't have very clean formulations of anything yet or i'd just write them down but for starters,
1) there's no such thing as entropy, only relative entropy (KL divergence); entropy as normally understood is relative entropy wrt the uniform distribution (on a finite set)
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wait so entropy is a statistical phenomenon and not strictly a 'natural property' of the world? (e.g. planck constants)
So it seems entropy would occur in a fairly simple mathematical facsimile of reality
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yeah, entropy is a statistical phenomenon, it's entirely about the macroscopic world being made up of very very large numbers of microscopic bits
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and i'm still learning about the mathematics of very large numbers of microscopic bits but the basic idea is that in that regime things have a "generic" ("high-entropy") behavior and everything else is exponentially unlikely relative to that (e.g. heat flowing from cold to hot)
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most of this should be basically standard statistical mechanics in some sense, certainly not claiming to have any new ideas here, but hopefully i can at least try to write things down in a language that makes sense to me and other mathematically inclined people
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well, i haven't done anything but watch some mathy youtube's since finishing calculus and i think i'm getting the gist of what you're saying!
so you're doing a really good job communicating 😄
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