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pengvado comments on Open thread for January 1-7, 2014 - Less Wrong
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Sorry if stupid question. Let's assume that the universe (mathematical multiverse?) gives us observations sampled from some simplicity-based distribution, like the universal distribution in UDASSA. Can that explain the initial low entropy of our universe (fewer bits to specify), and also the fact that we're not in a tiny ordered bubble surrounded by chaos?
ETA: I see Rolf Nelson made the same point in 2007. This just makes me more puzzled why Eliezer insists on using causality, given that the causal arrow of time comes from initial low entropy of the universe in the first place, so mathematical simplicity seems to be the more fundamental thing.
A low entropy microstate takes fewer bits to specify once you're given the macrostate to which it belongs, since low entropy macrostates are instantiated by fewer microstates than high entropy ones. But I don't see why that should be the relevant way to determine simplicity. The extra bits are just being smuggled into the macrostate description. If you're trying to simply specify the microstate without any prior information about the macrostate, then it seems to me that any microstate -- low or high entropy -- should take the same number of bits to specify, no?
If you can encode microstate s in n bits, that implies that you have a prior that assigns P(s)=2^-n. The set of all possible microstates is countably infinite. There is no such thing as a uniform distribution over a countably infinite set. Therefore, even the ignorance prior can't assign equal length bitstrings to all microstates.