I just got around to reading Schmidhuber's new paper, and noticed there is
something strange about the Speed Prior S. With all of the candidate
priors we have seen so far, the probability of a random (incompressible)
string of length n is about 2^-n. But with the Speed Prior S, the
probability is about 2^-2n (unless I misunderstood something?). I think it
might make sense to have a prior that favors strings that are fast to
compute, but it certainly doesn't make sense that it also makes random
strings much more unlikely than they have to be. And BTW, I think this is
the reason that S predicts the universe is run by a pseudo-random number
generator rather than a true random number generator. The other priors do
not seem to make this prediction.

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