# Abstract

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 properly investigate it we need to couple computer science theory with physics. Here I
do this by exploiting the physical Church-Turing thesis. This allows me to introduce a preliminary
investigation of some of the computer science theoretic aspects of the simulation hypothesis.
In particular, building on Kleene's second recursion
theorem, I prove that it is mathematically possible for us to be in a simulation that is being run on a computer \textit{by us}.
In such a case, 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; 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 that this preliminary investigation reveals.