Kolmogorov Complexity is defined with respect to a Turing complete language.
I think cousin_it is saying we should be careful what language our hypothesis is encoded in before checking its complexity. It’s easy to make mistakes when trying to explain something in terms of Solomonoff Induction.
The complexity of “A and B and C and D” is roughly equal to the complexity of “A or B or C or D”, but we know for certain that the former hypothesis can never be more probable than the latter, no matter what A, B, C and D are.
“A or B or C or D” is invalid to judge the complexity of directly because it is a set of different alternative hypothesis rather than a single one.
The hypothesis “the correct theory of everything is the lexicographically least algorithm with K-complexity 3^^^^3” is quite short, but the universal prior for it is astronomically low.
This one is invalid to judge the complexity of directly because K-complexity is not computable and the algorithm to compute it in this special case is very large. If the term K-complexity were expanded this statement would be astronomically complex.
The hypothesis “if my brother’s wife’s first son’s best friend flips a coin, it will fall heads” has quite high complexity, but should be assigned credence 0.5, just like its negation.
Here we must be careful to note that (presumably) all alternative low-complexity worlds where the “brother’s wife’s first son’s best friend” does not flip the coin have already been ruled out.
Kolmogorov Complexity is defined with respect to a Turing complete language.
I think cousin_it is saying we should be careful what language our hypothesis is encoded in before checking its complexity. It’s easy to make mistakes when trying to explain something in terms of Solomonoff Induction.
“A or B or C or D” is invalid to judge the complexity of directly because it is a set of different alternative hypothesis rather than a single one.
This one is invalid to judge the complexity of directly because K-complexity is not computable and the algorithm to compute it in this special case is very large. If the term K-complexity were expanded this statement would be astronomically complex.
Here we must be careful to note that (presumably) all alternative low-complexity worlds where the “brother’s wife’s first son’s best friend” does not flip the coin have already been ruled out.