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Oscar_Cunningham comments on Crisis of Faith - Less Wrong
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The minimum description length formulation doesn't allow for that at all. You are not allowed to pick whatever language you want, you have to pick the optimal code. If in the most concise code possible, state 'a' has a smaller code than state 'b', then 'a' must be more probable than 'b', since the most concise codes possible assign the smallest codes to the most probable states.
So if you wanna know what state a system is in, and you have the ideal (or close to ideal) code for the states in that system, the probability of that state will be strongly inversely correlated with the length of the code for that state.
Aren't you circularly basing your code on your probabilities but then taking your priors from the code?
Yep, but that's all the proof shows: the more concise your code, the stronger the inverse correlation between the probability of a state and the code length of that state.