I would like someone who understands Solomonoff Induction/the univeral prior/algorithmic probability theory to explain how the conclusions drawn in this post affect those drawn in this one. As I understand it, cousin_it's post shows that the probability assigned by the univeral prior is not related to K-complexity; this basically negates the points Eliezer makes in Occam's Razor and in this post. I'm pretty stupid with respect to mathematics, however, so I would like someone to clarify this for me.
Solomonoff's universal prior assigns a probability to every individual Turing machine. Usually the interesting statements or hypotheses about which machine we are dealing with are more like "the 10th output bit is 1" than "the machine has the number 643653". The first statement describes an infinite number of different machines, and its probability is the sum of the probabilities of those Turing machines that produce 1 as their 10th output bit (as the probabilities of mutually exclusive hypotheses can be summed). This probability is not...
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