I want to say something like: “The bigger N is, the bigger a computer needs to be in order to implement that prior; and given that your brain is the size that it is, it can’t possibly be setting N=3↑↑↑↑↑3.”
Now, this isn’t strictly correct, since the Solomonoff prior is uncomputable regardless of the computer’s size, etc. - but is there some kernel of truth there? Like, is there a way of approximating the Solomonoff prior efficiently, which becomes less efficient the larger N gets?
There are practical anti-occam calculations. Start uniform over all bitstrings. And every time you find a short program that produces a bitstring, turn the probability of that bitstring down.
I want to say something like: “The bigger N is, the bigger a computer needs to be in order to implement that prior; and given that your brain is the size that it is, it can’t possibly be setting N=3↑↑↑↑↑3.”
Now, this isn’t strictly correct, since the Solomonoff prior is uncomputable regardless of the computer’s size, etc. - but is there some kernel of truth there? Like, is there a way of approximating the Solomonoff prior efficiently, which becomes less efficient the larger N gets?
There are practical anti-occam calculations. Start uniform over all bitstrings. And every time you find a short program that produces a bitstring, turn the probability of that bitstring down.