The claim that our universe is a computer simulation has been advanced in several forms, from Bostrom’s statistical “trilemma” to David Chalmers’ Reality+ or David Deutsch’s Fabric of Reality. These proposals assume that every physical truth is reducible to the output of a finite algorithm executed on a sufficiently powerful substrate.

Over the last decade, an increasing number of central problems in physics, in particular many motivated by quantum information theory, have been proven undecidable¹.

A Letter² published in the Journal of Holography Applications in Physics last June, argues that such algorithmic computation, and in fact a wholly algorithmic Theory of Everything is impossible:

Gödel’s incompleteness theorems, Tarski’s undefinability theorem, and Chaitin’s information-theoretic incompleteness establish intrinsic limits on any such algorithmic programme. Together, these results imply that a wholly algorithmic “Theory of Everything” is impossible: certain facets of reality will remain computationally undecidable and can be accessed only through non-algorithmic understanding. We formalize this by constructing a “Meta-Theory of Everything” grounded in non-algorithmic understanding, showing how it can account for undecidable phenomena and demonstrating that the breakdown of computational descriptions of nature does not entail a breakdown of science. Because any putative simulation of the universe would itself be algorithmic, this framework also implies that the universe cannot be a simulation.

Interestingly, the meta theory the authors propose explicitly contemplates an external truth predicate plus a non-effective inference mechanism. It is mathematically nice, but I’m afraid it is not too different to what our far distant ancestors called God.

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(1) Perales-Eceiza, Á., Cubitt, T., Gu, M., Pérez-García, D., & Wolf, M. M. (2025). Undecidability in Physics: A Review. Physics Reports, 1138, 1-29. https://doi.org/10.1016/j.physrep.2025.06.004

(2) Faizal, M., Krauss, L. M., Shabir, A., & Marino, F. (2025). Consequences of Undecidability in Physics on the Theory of Everything. Journal of Holography Applications in Physics, 5(2), 10-21. https://doi.org/10.22128/jhap.2025.1024.1118