  The simulation hypothesis has recently excited renewed interest, especially
in the physics and philosophy communities. However, the hypothesis specifically
concerns \textit{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 of 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.
