Wolpert, David (2024) Implications of computer science theory for the simulation hypothesis. [Preprint]

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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.

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Item Type:	Preprint
Creators:	Creators Email ORCID Wolpert, David dhw@santafe.edu
Additional Information:	Simulation hypothesis, computer science theory, Kleene's second recursion theorem, Rice's theorem, Church-Turing thesis
Keywords:	Simulation hypothesis, computer science theory, Kleen's recursion theorem, Rice's theorem
Subjects:	Specific Sciences > Complex Systems Specific Sciences > Artificial Intelligence > Classical AI Specific Sciences > Physics > Classical Physics Specific Sciences > Computer Science Specific Sciences > Artificial Intelligence
Depositing User:	David Wolpert
Date Deposited:	18 Apr 2024 06:32
Last Modified:	18 Apr 2024 06:32
Item ID:	23278
Subjects:	Specific Sciences > Complex Systems Specific Sciences > Artificial Intelligence > Classical AI Specific Sciences > Physics > Classical Physics Specific Sciences > Computer Science Specific Sciences > Artificial Intelligence
Date:	8 April 2024
URI:	https://philsci-archive.pitt.edu/id/eprint/23278

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