I know that. I was saying, given that people still prove things about Solomonoff induction's accuracy even though it's uncomputable, are there any results on how successful this type of prediction could be, relative to the standard set by Solomonoff induction? That is, how powerful can induction be if you have a mere NP oracle, compared to a halting oracle?
Many experts suspect that there is no polynomial-time solution to the so-called NP-complete problems, though no-one has yet been able to rigorously prove this and there remains the possibility that a polynomial-time algorithm will one day emerge. However unlikely this is, today I would like to invite LW to play a game I played with with some colleagues called what-would-you-do-with-a-polynomial-time-solution-to-3SAT? 3SAT is, of course, one of the most famous of the NP-complete problems and a solution to 3SAT would also constitute a solution to *all* the problems in NP. This includes lots of fun planning problems (e.g. travelling salesman) as well as the problem of performing exact inference in (general) Bayesian networks. What's the most fun you could have?