Here’s an article arguing that Solomonoff induction is compatible with belief in a personal God, as long as one accepts that God is computable (that is, there is an Turing machine that computes everything God does and thinks). You might agree or disagree quite strongly, but it’s probably worth checking out, at least as a thought experiment.
I think I’m missing something here, but if the Universal Dovetailer implies the existence of this universe (among great amounts of junk), I don’t understand the need to switch to a more sophisticated “god” algorithm. Shouldn’t Occam’s Razor tell us that the UD is more likely?
The information needed to describe our particular laws of physics < info needed to describe the concept of “habitable universe” in general < info needed to describe human-like mind.
The biggest slip is the equivocation of the word intelligence. The Kolmogorov complexity of AIXI-tl is quite small, so intelligence’s in that sense of the word are likely to exist in the universal prior.
Humanlike minds have not only the clear mark of evolution, but the mark of stone age tribal interactions across their psyche. An arbitrary mind will be bizarre and alien. Wondering if such a mind might be benevolent is hugely privileging the hypothesis. The most likely way to make a humanlike mind is the process that created humans. So in most of the universes with humanoid deities, those deities evolved. This becomes the simulation hypothesis.
The best hypothesis is still the laws of quantum physics or whatever.
If we assume that Mathematical universe hypothesis is true, as EY and Tegrmark did, and all possible math structures actually exist, it means that any possible AIs also exist. More over, for any AI there is another AI (and not one) which is simulating the first AI and its world.
Thus we are simulated by infinitely large AI, which could be interpreted as a proof that “God exists”. However, the practical meaning of it could be only some update of the simulation hypothesis.