If you apply Ockham's razor in the form "prefer hypotheses with lower Kolmogorov complexity" together with Bayes' theorem, you get something that in a certain (

If you apply Ockham's razor in the form "prefer hypotheses with lower Kolmogorov complexity" together with Bayes' theorem, you get something that in a certain (rather artificial) sense is as effective a problem solver as anything mechanized can be. Unfortunately it's unimplementable in practice, because ... Coming across AIXI was what got me interested in algorithmic information theory. It is indeed useless in it's "pure" form, but there's a variation using Monte Carlo search that apparently does pretty well: http://arxiv.org/abs/0909.0801 http://arxiv.org/abs/0909.0801 (This is controversial, but it's my opinion and that of at least some other contributors here.) When assessing (e.g.) scientific hypotheses for "simplicity" or "parsimony", something like Kolmogorov complexity is the Right Way to understand (un)simplicity; failure to appreciate this is, e.g., what makes some people dislike the "many worlds" interpretation of quantum mechanics on the grounds of extravagance, or think that "God did it" is a useful explanation for otherwise-surprising features of the universe. Yes. In fact after reading the Less Wrong quantum physics sequence (http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ http://lesswrong.com/lw/r5/the_quantum_physics_sequence/), I find that "the wavefunction collapsed" and "God did it" are remarkably similar statements.