What computer science has to say about the simulation hypothesis - Wolpert, David (Journal of physic, complexity, 2025)
The simulation hypothesis has recently excited renewed interest, especially in the physics and philosophy communities. However, the hypothesis speciﬁcally concerns computers that simulate physical universes, which means that to formally investigate it we need to couple computer science theory with physics. Here I couple those ﬁelds with the physical Church-Turing thesis. I then exploit that coupling to investigate some of the computer science theory aspects of the simulation hypothesis. In particular, I use Kleene’s second recursion theorem to prove that it is mathematically possible for us to be a simulation that is being run on a computer — by us. In such a self-simulation, there would be two identical instances of us; the question of which of those is “really us” is meaningless. I also show how Rice’s theorem provides some interesting impossibility results concerning simulation and self-simulation; brieﬂy describe the philosophical implications of fully homomorphic encryption for (self-)simulation; and brieﬂy investigate the graphical structure of universes simulating universes simulating universes . . ., among other issues. I end by describing some of the possible avenues for future research.