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.
In the post Complexity and Intelligence, Eliezer says that the Kolmogorov Complexity (length of shortest equivalent computer program) of the laws of physics is about 500 bits:
Where did this 500 come from?
I googled around for estimates on the Kolmogorov Complexity of the laws of physics, but didn't find anything. Certainly nothing as concrete as 500.
I asked about it on the physics stack exchange, but haven't received any answers as of yet.
I considered estimating it myself, but doing that well involves significant time investment. I'd need to learn the standard model well enough to write a computer program that simulated it (however inefficiently or intractably, it's the program length that matters not it's time or memory performance).
Based on my experience programming, I'm sure it wouldn't take a million bits. Probably less than ten thousand. The demo scene does some pretty amazing things with 4096 bits. But 500 sounds like a teeny tiny amount to mention off hand for fitting the constants, the forces, the particles, and the mathematical framework for doing things like differential equations. The fundamental constants alone are going to consume ~20-30 bits each.
Does anyone have a reference, or even a more worked-through example of an estimate?