If our reality consists of mathematical programs and the multiverse theory holds, then the theory of everything is a simple incrementing binary counter. Every possible binary string is ran on a Turing machine in a different universe.
The halting problem (endless loops) is sidestepped by being contained to a single universe. Also, apparently our universe got lucky as we get to live in an ordered universe, and not dissolve into nothingness due to a bug in our universe's binary code.
Of course, like "normal" mathematics, "reality" mathematics should also be incomplete. Furthermore, there is no way to know everything of the universe one is a part of, as this requires at least 1 bit more than there are available bits in the universe. But this still allows for the possibility of the universe itself being an inference machine.
Edit: Then again, I believe that mathematics is a mental construct, mathematics does not exist without brains, or if it really exists external to human minds, it exists in all possible forms: Humans do not discover maths as a whole, they cast a local net of subjective observation over it, and keep the things that make sense to our brains and are consistent within the current framework. Again, this does not preclude the possibility that our mathematical reality exists inside the mind of a giant supercomputer.
The halting problem (endless loops) is sidestepped by being contained to a single universe. Also, apparently our universe got lucky as we get to live in an ordered universe, and not dissolve into nothingness due to a bug in our universe's binary code.
Of course, like "normal" mathematics, "reality" mathematics should also be incomplete. Furthermore, there is no way to know everything of the universe one is a part of, as this requires at least 1 bit more than there are available bits in the universe. But this still allows for the possibility of the universe itself being an inference machine.
Edit: Then again, I believe that mathematics is a mental construct, mathematics does not exist without brains, or if it really exists external to human minds, it exists in all possible forms: Humans do not discover maths as a whole, they cast a local net of subjective observation over it, and keep the things that make sense to our brains and are consistent within the current framework. Again, this does not preclude the possibility that our mathematical reality exists inside the mind of a giant supercomputer.