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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2) relative entropy comes from sanov's theorem:
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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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