alright just for fun: AMA but only about math, will attempt to speed-explain stuff with as few symbols and equations as possible and see what happens
(esp happy to field questions about stuff that seems basic to you and that you feel like you should've gotten a long time ago!)
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yeah i don't really get it either. it maximizes entropy given fixed mean and variance and it shows up in the maxwell-boltzmann distribution and it even explains the asymptotics of a bunch of combinatorial sequences that don't come from the CLT. very mysterious to me still
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yeah but like... why should they be independent lol
(note that it's key that the degrees of freedom are orthogonal, it would be false otherwise)