Comment by Oleg on Complexity and Intelligence · 2008-11-04T01:59:45.000Z · LW · GW

Kolmogorov complexity of universe is more than just a description of its physical laws.

First of all, besides the physical laws, K should include the initial state of the universe. It may be large or even infinite. And it should be properly expressed in qubits.

Second, you'd need to pick the "present state", whatever that means, our of all possible future and past states. In a classical universe it may be only a 100bits or so, in a quantum multiverse, it's at least 1 bit per every branch.

Third, it is not at all obvious that the laws of universe are computable. Maybe it uses an oracle (the multiverse branching process can provide such an oracle) or maybe it uses real values in a non-trivial way. if this is true then we should either say that K is infinite, or use K relative to an oracle.

Fourth, K is defined only up to an additive constant, so it's not really correct to talk about The Kolmogorov Complexity. You can only talk about Kolmogorov complexity relative to a fixed Turing machine. For different turning machines the difference between the Ks will be roughly equal to the number of bits in a translator between their machine languages. In the extreme case when the reference Turing machine IS the universe then K(universe) is just 0.