First, remember that Kolmogorov complexity is only well-defined up to a constant, which is determined by your model of computation. [...]
Right, if you do something like (say) take away the addition instruction then the shortest program might get longer because it has to emulate addition using subtraction and negation (or use a totally different approach, or include a translation pass that expands the additions into negate+subtract or include a universal turing machine that runs the original machine or... yeah).
Second, the article addresses why you can have the paradoxical situation of the Universe being low-complexity while specific things in the Universe are of high complexity.
In this case I care about the complexity of the laws that govern the change in state (positions of atoms or values of the wave functions) with respect to time. I will not make you pay for the presumably absurd amount of data required for the initial state of >10^(82) atoms. That would make talking about the complexity of the laws laughably negligible. I realize that this is, in a sense, an arbitrary distinction but... that's the question I want to know the answer to.
According to string theory (which is a Universal theory in the sense that it is Turing-complete) the landscape of possible Universes is 2^500 or so, which leads to 500 bits of information. Perhaps this is where Eliezer got the figure from (though I admit that I don't exactly know where he got it from either).
Interesting guess at where the number could have come from. I just assumed he tallied up various aspects of the standard model somehow and got an answer between 450 and 510.
The standard model is over here, see page 36: http://arxiv.org/pdf/hep-th/0610241v1.pdf
I will not make you pay for the presumably absurd amount of data required for the initial state of >10^(82) atoms.
You don't have any atoms in the initial state - nor anything that can reasonably be called matter. My (very ignorant) guess is that we won't even know what it takes to specify the initial state before we have a unified GR+QFT theory.
...According to string theory (which is a Universal theory in the sense that it is Turing-complete) the landscape of pos
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?