Implications of computer science theory for the simulation hypothesis
🤖 AI Summary
This paper formally analyzes the “simulation hypothesis” from a theoretical computer science perspective, addressing the core question: whether the universe—including human intelligence—can be computationally simulated, particularly whether “self-simulation” (i.e., running an exact simulation of ourselves) is possible. Methodologically, it employs Kleene’s Second Recursion Theorem to rigorously establish the mathematical feasibility and logical consistency of self-simulation for the first time; leverages Rice’s Theorem to demonstrate the undecidability of simulation existence; and integrates the physical Church–Turing thesis with fully homomorphic encryption theory to characterize the concealability and observational indistinguishability of self-simulation. Key contributions include: (i) establishing the computability-theoretic foundations of self-simulation; (ii) constructing a graph-structured model of simulation hierarchies; and (iii) systematically characterizing fundamental limits on the observability, identifiability, and verifiability of simulations.
Application Category
📝 Abstract
The simulation hypothesis has recently excited renewed interest, especially in the physics and philosophy communities. However, the hypothesis specifically concerns extit{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.
Problem
Research questions and friction points this paper is trying to address.
Investigating the simulation hypothesis using computer science theory
Coupling computer science with physics via Church-Turing thesis
Proving possibility and impossibility results for simulation scenarios
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses physical Church-Turing thesis coupling
Applies Kleene's second recursion theorem
Employs Rice's theorem for impossibility proofs
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