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passive_fist comments on Estimating the kolmogorov complexity of the known laws of physics? - Less Wrong
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It does make sense to talk of relative KC, actually, but it's not trivial to see why: http://en.wikipedia.org/wiki/Kolmogorov_complexity#Invariance_theorem
In particular, "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 chosen – such that
Yes, I'm aware of this. It's still true, I believe, that for any two finite strings s1 and s2 one can find description languages L1 and L2 (with complexity functions K1 and K2) such that
K1(s1) > K1(s2)
and
K2(s1) < K2(s2).
So there is no language-independent sense in which s1 is more complex than s2 (or vice versa). To make the claim more concrete, consider the fact that for any finite string, one could construct a Universal Turing Machine that outputs that string when given the input 0 (the string is essentially hard-coded into the structure of the machine). This corresponds to a description language in which that string has minimal K-complexity.
This is all compatible with the invariance theorem. As a simple illustration, let the constant c associated with L1 and L2 be 5, let K1(s1) be 10, K1(s2) be 9, K2(s1) be 6 and K2(s2) be 8. In this example, both the inequalities I've given above are true, and the invariance theorem isn't violated.