An aesthetic (with a hint of rigor, but only a hint) one is: if one is enumerating (and running) Turing machines (using a correspondence between them and the naturals), then ones with a short code (i.e. small description number) will be reached first.
(This argument is working on the premise that a Turing machine could, in theory, simulate a universe such as ours (if not exactly, then at least approximate it, arbitrarily accurately)).
And so, if one then has some situation where the enumeration has some chance of being stopped after each machine, then those with shorter codes have a greater likelihood than those with longer codes. (Or some other situation, like (for instance) the enumeration is occurring in a universe with finite lifespan)
This paper by Russell Standish expresses a similar notion.
Given that the Solomonoff prior is the main reason for arguing in favor of the Mathematical Universe Hypothesis, it is potentially circular to then use the MUH to justify Occam’s Razor.
An aesthetic (with a hint of rigor, but only a hint) one is: if one is enumerating (and running) Turing machines (using a correspondence between them and the naturals), then ones with a short code (i.e. small description number) will be reached first.
(This argument is working on the premise that a Turing machine could, in theory, simulate a universe such as ours (if not exactly, then at least approximate it, arbitrarily accurately)).
And so, if one then has some situation where the enumeration has some chance of being stopped after each machine, then those with shorter codes have a greater likelihood than those with longer codes. (Or some other situation, like (for instance) the enumeration is occurring in a universe with finite lifespan)
This paper by Russell Standish expresses a similar notion.
Given that the Solomonoff prior is the main reason for arguing in favor of the Mathematical Universe Hypothesis, it is potentially circular to then use the MUH to justify Occam’s Razor.