Schmidhuber's paper explicitly assumes that only discrete universes exist, so that theories of computation can be applied. But this assumption may not be necessary. Consider a TM which implements an algorithm for numerically solving a fixed system of partial differential equations defining some continous universe. The TM would take as input a set of arbitrary-precision coordinates defining a region in this universe and a parameter specifying the precision of the output, and produce as output the content of that region to the specified precision.
Under the interpretation I proposed earlier, the regions of this continous universe would have physical existence as the output of the TM and therefore the universe as a whole would have physical existence. On a different note, I'm trying to learn enough quantum mechanics to figure out what a program for our universe might look like. Does anyone have suggestions for a good quantum mechanics text book?
