MML usually (but not necessarily) restricts the reference machine to a non-universal form in the interest of computational feasibility.
Sure, but IIUC (I've just skimmed the paper), in order to make the comparison to Kolmogorov complexity, they consider arbitrary Turing machines as their hypotheses, which makes the analysis uncomputable.
How do you use Occam's Razor without an appeal a formal notion that grounds your intuition? What does your intuition rest on, if not information theory?
I think that's still an open problem. Solomonoff induction is certainly an attempt towards its formalization, but it doesn't yield anything that can be used for reasoning in practice. Saying "my hypothesis has smaller Kolmogorov complexity than yours" is meaningless unless you can make the argument formal.
MML and KC are conceptually and theoretically highly related concepts, MML is another stab at formalizing Occam's Razor in a more feasible manner, using the same approach as KC. No, they are not in fact identical, if that's what you meant (hence the different names ...)
Saying "my hypothesis has smaller Kolmogorov complexity than yours" is meaningless unless you can make the argument formal.
But saying "Based on Occam's Razor, my hypothesis is smaller than yours" isn't just as meaningless as long as your intuition stays sufficiently f...
r/HPMOR readers on heroic responsibility - not the OP, the comments. Holy snorkels this is good.