Which section of the 850 page book contains a clear explanation of this? On initial review they seem to talk about hypotheses, for hundreds of pages, without trying to define them or explain what sorts of things do and do not qualify or how Solomonoff hypotheses do and do not match the common sense meaning of a hypothesis.
I’d rather frame this as good news. The good news is that if you want to learn about Solomonoff induction, the entire first half-and-a-bit of the book is a really excellent resource. It’s like if someone directed you to a mountain of pennies. Yes, you aren’t going to be able to take this mountain of pennies home anytime soon, and that might feel awkward, but it’s not like you’d be materially better off if the mountain was smaller.
If you just want the one-sentence answer, it’s as above—“X or Y” is not a Turing machine. If you want to be able to look the whole edifice over on your own, though, it really will take 200+ pages of work (it took me about 3 months of reading on the train) - starting with prefix-free codes and Kolmogorov complexity, and moving on to sequence prediction and basic Solomonoff induction and the proofs of its nice properties. Then you can get more applied stuff like thinking about how to encode what you actually want to ask in terms of Solomonoff induction, minimum message length prediction and other bounds that hold even if you’re not a hypercomputer, and the universal prior and the proofs that it retains the nice properties of basic Solomonoff induction.
Which section of the 850 page book contains a clear explanation of this? On initial review they seem to talk about hypotheses, for hundreds of pages, without trying to define them or explain what sorts of things do and do not qualify or how Solomonoff hypotheses do and do not match the common sense meaning of a hypothesis.
I’d rather frame this as good news. The good news is that if you want to learn about Solomonoff induction, the entire first half-and-a-bit of the book is a really excellent resource. It’s like if someone directed you to a mountain of pennies. Yes, you aren’t going to be able to take this mountain of pennies home anytime soon, and that might feel awkward, but it’s not like you’d be materially better off if the mountain was smaller.
If you just want the one-sentence answer, it’s as above—“X or Y” is not a Turing machine. If you want to be able to look the whole edifice over on your own, though, it really will take 200+ pages of work (it took me about 3 months of reading on the train) - starting with prefix-free codes and Kolmogorov complexity, and moving on to sequence prediction and basic Solomonoff induction and the proofs of its nice properties. Then you can get more applied stuff like thinking about how to encode what you actually want to ask in terms of Solomonoff induction, minimum message length prediction and other bounds that hold even if you’re not a hypercomputer, and the universal prior and the proofs that it retains the nice properties of basic Solomonoff induction.