Implications of computer science theory for the simulation hypothesis
<|reference_start|>Implications of computer science theory for the simulation hypothesis: 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.<|reference_end|>
@article{wolpert2024implications,
    title={Implications of computer science theory for the simulation hypothesis},
    author={David H. Wolpert},
    journal={arXiv preprint arXiv:2404.16050},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.16050},
    primaryClass={cs.LO physics.hist-ph}
}