Thanks for clarifying the provability issue. I think I understand and agree with you.

On Tue, Nov 13, 2001 at 12:05:22PM +0100, Juergen Schmidhuber wrote: > What about exploitation? Once you suspect you found the PRG you can use > it > to predict the future. Unfortunately the prediction will take enormous > time to stabilize, and you never can be sure it's finished. > So it's not very practical. By exploiting the fact that we're in an oracle universe I didn't mean using TMs to predict the oracle outputs. That is certainly impractical. There are a couple of things you could do though. One is to use some oracle outputs to predict other oracle outputs when the relationship between them is computable. The other, much more important, is to quickly solve arbitrarily hard computational problem using the oracles. > I prefer the additional resource assumptions reflected > by the Speed Prior. They make the oracle universes very unlikely, and > yield computable predictions. Why do you prefer the Speed Prior? Under the Speed Prior, oracle universes are not just very unlikely, they have probability 0, right? Suppose one day we actually find an oracle for the halting problem, or even just find out that there is more computing power in our universe than is needed to explain our intelligence. Would you then (1) give up the Speed Prior and adopt a more dominant prior, or (2) would you say that you've encountered an extremely unlikely event (i.e. more likely you're hallucinating)? If you answer (1) then why not adopt the more dominant prior now?