Before we start talking about philosophical implications, maybe we should reach a consensus about more basic questions.

What is the set of all possible universes? Max Tegmark says its the set of all mathematical structures, and Juergen Schmidhuber says its the set of all Turing machines, but neither gives much justification. I tend to agree with Schmidhuber, if only because Tegmark's definition does not seem to lead to an effective theory. For example, what does a uniform distribution on all mathematical structures mean? However it would be nice to have some stronger justifications for assuming that only computable universes exist. If we agree that all Turing machines exist, it's still not clear how they should be interpreted as physical universes. Schmidhuber suggests that the output of a Turing machine should be interpreted as the evolution of a universe. However this is problematic because it does not lead to an easy way to think about the complexities and probabilities of structures within a universe. For example, consider a simple Turing machine that enumerates the natural numbers. The output of this TM includes every possible configuration of every other universe. What is the probability that I'm living in this TM? I don't see a straightforward way to answer this question under Schmidhuber's interpretation. The problem is that even though this universe is very simple, it would take a lot of extra information to find anything in it, so the simplicity of the universe as a whole is deceptive. As an alternative, I suggest that each Turing machine should be thought of as taking the coodinates of a region of a universe as input and producing the content of that region as output. Here region should be broadly interpreted. It not only refers to volumes of space-time, but may also for example specify a branch of a quantum superposition. Let me clarify some terminology. When I say length of a region of a universe, I mean the length of the Turing machine plus the length of input specifying the extent of that region. When I say complexity of the content of region R, I mean the least length of all regions with the same content as R, which is just the content's Kolmogorov complexity. To compute the probability that I'm in a particular universe U, I would first find the universal prior probability PU(m) of my mind state. (I assume my mind state, which includes my memories and current perceptions, is the only information I have direct access to) Then I would find the region R in U that has my mind state as the content (for simplicity let's assume there is exactly one such region in U). Finally the probability that I'm in universe U is 2^-l(R)/P, where l(R) is the length of region R. The Baysian interpretation of the above procedure is that before taking into account my mind state, the prior probability that I'm any region R is 2^-l(R). After taking into account my mind state, I eliminate all regions that do not have my mind state as the content, so the posterior probability is 2^-l(R)/PU(m) if the content of R is m, and 0 if the content of R is not m.