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Qiaochu_Yuan comments on Open thread, July 29-August 4, 2013 - Less Wrong
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Hypotheses in this description are probabilistic Turing machines. These can be cashed out to programs in a probabilistic programming language.
I think it's going too far to call this a "problem with Solomonoff induction." Solomonoff induction makes no claims; it's just a tool that you can use or not. Solomonoff induction as a mathematical construct should be cleanly separated from the claim that AIXI is the "best intelligence," which is wrong for several reasons.
Can probabilistic Turing machines be considered a generalization of deterministic Turing machines, so that DTMs can be described in terms of PTMs?
Editing in reply to your edit: I thought Solomonoff Induction was made for a purpose. Quoting from Legg's paper:
I'm just pointing out what I see as a limitation in the domain of problems classical Solomonoff Induction can successfully model.
Yes.
I don't think anyone claims that this limitation doesn't exist (and anyone who claims this is wrong). But if your concern is with actual coins in the real world, I suppose the hope is that AIXI would eventually learn enough about physics to just correctly predict the outcome of coin flips.
The steelman is to replaces coin flips with radioactive decay and then go through with the argument.
Yes.