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CronoDAS comments on From the "weird math questions" department... - Less Wrong
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Follow-up: Would AIXI (the ideal implementation of Solomonoff induction) do significantly worse at predicting the next digit of Chaitin's constant than a computable algorithm that "knows" that it's trying to predict the next digit of a specific uncomputable sequence with defined properties?
Also, for the lulz, I'd like to run AIXItl on "A Million Random Digits" and see if it really is algorithmically random.
No matter what input sequence you have and what algorithm you use to predict it, as you process more and more digits, your accumulated log score will stay lower than Solomonoff induction's log score plus a constant (the constant is allowed to depend on the input sequence and your algorithm).