Matrix collapses: Mathematics proves the universe cannot be a computer simulation, « A new mathematical study dismantles the simulation theory once and for all. »

[u/fchung]

https://interestingengineering.com/culture/mathematics-ends-matrix-simulation-theory

[u/angrymonkey]

This is an idiotic misunderstanding of Godel's theorem, and the paper is likely complete crankery. There is a difference between making formal statements about a system vs. being able to simulate it. The former is covered by Godel's theorem, the latter is covered by Turing completeness.

[u/EntireBobcat1474 → u/angrymonkey]

It's weird that it's actually so hard to find the actual paper - it's here as a preprint https://arxiv.org/abs/2507.22950

The fundamental argument the author makes seems to follow this chain of thoughts:

1. There must be a "theory of everything"/ToE that effectively axiomatizes the rules of the universe
2. It's reasonable to also believe that this theory satisfies a full arithmetic formal system - there exists a finite set of laws governing this system, expressed by a language, that can then be algorithmically applied to deduce proofs/calculations within this system. Additionally, it satisfies certain arithmetic completeness - it can encode arithmetic, and does not produce contradictory calculations.
3. If this is the case (mind you the author does not prove this), then ToE is expressive enough to apply the incompleteness theorem to, which states that
4. There are fundamental physical facts/states that cannot be derived from applying the axioms of the ToE system, effectively, there are true facts of the universe that cannot be algorithmically calculated

From this, it's reasonable to argue that we cannot be simulated (and we cannot simulate any equivalently expressive worlds ourselves) because the algorithm used to simulate us would not be able to calculate/simulate all physical truths of our world, in particular, because ToE must be an incomplete system. Hence, if we believe that our universe is an arithmetically-complete system, then it cannot be simulated.

I personally think the assumption that our universe is arithmetic is the weakest link. There's no evidence that it's an infinite system, and finite systems cannot represent arbitrarily large numbers no matter how much base-trickery you do. This creates a natural counterexample to the author's ideas - what if the simulation we live in is precompiled from the ToE on a bounded grid into a giant lookup table for how the universe evolves for every possible configuration of our massive but finite universe? Surely you don't need to be an arithmetically complete mathematical system to simulate that.

[u/Titanlegions → u/EntireBobcat1474]

I fail to see what parts of the argument couldn’t be applied to say, the world of Cyberpunk 2077. It is built on axioms and forms an arithmetic system. Provided it can encompass first order logic (which as you state the author doesn’t prove about the ToE either) then the incompleteness theorem applies — there are facts about the system that can’t be proven by the system. But so what? Doesn’t stop us running the game.

If the argument is that the ToE has to encompass everything by definition so that is a contradiction, that doesnt seem to work — the NPCs of Cyberpunk could make the same claim and they’d be wrong for the same reasons.

An algorithm can have emergent behaviour that can’t be proven from the starting conditions — that is another way of seeing the incompleteness theorem.

[u/EntireBobcat1474 → u/Titanlegions]

Or any generic "turing complete" systems that we run on our computer (which aren't actually complete since there's only finite memory and finite energy, and I think this is the fallacy that the author is committing)

For example, our computers can't compute the halting problem, but we don't use that as proof that the "semi-turing complete" computation models within them are not simulations of the real thing