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Patrick comments on Open Problems Related to Solomonoff Induction - Less Wrong
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I take your point re: length vs speed. The theorem that I think justifies calling Kolmogorov Complexity objective is this:
"If K1 and K2 are the complexity functions relative to description languages L1 and L2, then there is a constant c (which depends only on the languages L1 and L2) such that |K1(s) - K2(s)| <= c for all strings s."
(To see why this is true, note that you can write a compiler for L2 in L1 and vice versa)
I don't see why code modelling symmetric laws should be longer than code modelling asymmetric laws (I'd expect the reverse; more symmetries means more ways to compress.) Nor why 3 spatial dimensions (or 10 if you ask string theorists) is the minimum number of spatial dimensions compatible with intelligent life.
The whole point of Solomonoff induction is that the priors of a theory are not arbitrary. They are determined by the complexity of the theory, then you use Bayes rule on all theories to do induction.
A kilobit of improbability requires only a kilobit of data to offset it, which isn't very crackpot at all. Proving minimum length is impossible, but proving an upper bound on length is very easy, and that proves a lower bound on probability.