Friday, October 24, 2008

Living in a simulation - part 2

Suppose you are living in a simulation and you wanted to discover the theory of everything. What would that theory be? Probably in your (simulated) mind it would be the set of laws that govern all physical phenomena in your (simulated) observable universe. You would also want to understand how your universe came about and where it will end up. Let's suppose that the programmer of your universe came up with a set of physical laws and let it run. As I discussed before, the programmer really can't be sure what will happen in his simulation but let's say he was inspired or lucky and hit upon something that led to a universe that produced an inhabitant that could ask about the theory of everything.

What then is the theory of everything? Well, one answer would be the set of physical laws that the programmer put in. Now suppose that the programmer didn't come up with any laws but just started off a cellular automaton (CA) with some rules and an initial condition. An example of a CA, which Steve Wolfram's book "A new kind of science" describes in great detail, is a one dimensional grid of "cells" that can be in one of two states. At each time step, each cell is updated according to what state it and its nearest neighbors are in. There are thus 2^8=256 possible rule sets, since each of the 8 configurations that 3 contiguous cells can have yields two possible updated states for the middle cell. Wolfram has ennumerated all of them in his book.

One of Wolfram's former employees, Matthew Cook, proved that rule 110 is a universal computer. Hence, all possible computations (simulations) can be obtained by running through all possible initial conditions. One of these initial conditions corresponds to the program with the same physical laws that the inspired programer came up with. However, in this case the physical laws will be an emergent phenomenon of the CA. What then is the theory of everything? Is it the the set of rules of the cellular automaton? Is it the combination of the rules and the initial condition? Is it still the set of emergent physical laws? In all likelihood, the elementary constituents of the emergent theory will be comprised of some number of cells. Below this scale, the emergent theory will no longer hold and at the very lowest level, there will be rule 110.

Finally, as has been pointed out previously, the inhabitants of a simulation can never know that they are in a simulation. Thus, there is really no way for us to know if we are living in a simulation. So what does that say about our theory of everything? Will it be an uber string theory or the CA rule and initial condition? Would we want to have a theory of everything that included a theory of the programmer and the programmer's world? This is why I've come to adopt the notion that a theory of everything is a theory of computation and that doesn't really tell us much about our universe.

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