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.
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.