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gedymin comments on An additional problem with Solomonoff induction - Less Wrong Discussion

2 Post author: gedymin 22 January 2014 11:34PM

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Comment author: gedymin 27 January 2014 10:52:42AM *  0 points [-]

Consider the measure:

 m(x) = 1, if x_i is the i-th bit of binary expansion of Chaitin's constant, and 0 otherwise

The measure is deterministic, but not computable. From SI point of view x is unpredictable (using the Universal prior). If we change the Universal prior of SI and base the prior on a Halting oracle instead of a universal Turing machine, m(x) becomes (hyper)computable. The question is - are there any conditions under which we should do this?

Comment author: Squark 27 January 2014 07:10:13PM 0 points [-]

You are right, in principle we can consider generalized SI for various hypercomputation models. In practice, SI is supposed to be a probability distribution over "testable hypotheses". Since testing a hypothesis involves some sort of computation, it doesn't seem to make sense to include uncomputable oracles. It would make sense for agents that are able to hypercompute themselves.

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