Richard wrote: "The probability of a model of reality is 2-K where K is the complexity of the model". And this in the context of talk of objective reality. This seems to me to suggest that Richard himself has a rather odd model of reality. Two questions that may indicate what's bothering me:

  1. Complexity as measured how? Of course it doesn't matter if all you care about is probability-up-to-a-bounded-factor, but if you're making claims about actual, objective, probabilities – not merely about what would constitute a reasonable starting point for Bayesian inference with a large amount of data – then I really don't think it will do to leave it undecided.

  2. On what grounds do you believe this, as a statement about reality? Do you, for instance, have some reason to think that underlying our universe is a vast computational substrate executing random programs, with our universe being the operation of a randomly chosen one of those programs?

(Perhaps your answer to #1 is that it doesn't matter: that, when it's all of reality that we're modelling, smallish finite changes of program that don't change the viability of the resulting universe for intelligent life can only take the form of modest tweaking of (say) fundamental constants or something, so that all our inferences come out almost exactly the same regardless of exactly how we measure complexity. Well, maybe, but I'd like to see some details.)

Gareth McCaughan

changed October 25, 2007