Blaise: Now just apply that rule to the infinity of possible computer programs that assign probabilities to the observed data, update their posterior probabilities based on the probability they've assigned to the evidence so far, sum over all of them to get your next prediction, and we're done\. And yes, that requires a hypercomputer that can solve the halting problem, but we're talking ideals here\.
Looks like there is a typo with the fraction. sense 1…n . 1?
Comments
Eliezer Yudkowsky
I was trying to say "append 1 to previous sequence". I guess it needs explanation.
Nate Soares
I tweaked this to make it a bit clearer while also cleaning up the latex (I think it's standard to use mathrm on multi-letter variable names, to disambiguate them from the multiplication of many single variables, etc. etc.), but I still think that parts of the equation (such as InterpretProb) need types and explanations. (I think you also want to explain how it handles non-halting programs, which requires renormalization in the Solomonoff induction case, unless you want to talk about the semimeasure instead.)