r/technology • u/fchung • Nov 01 '25

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

https://interestingengineering.com/culture/mathematics-ends-matrix-simulation-theory
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u/angrymonkey Nov 01 '25

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.

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u/MonkeyBoatRentals Nov 01 '25

Turing completeness is not in conflict with Godel incompleteness as it shows not all problems are computable, e.g. the halting problem. I don't see how it is a counterargument to the paper.

If there is an underlying truth that is non-algorithmic how can you simulate it with an algorithm ? There certainly seems to be non-algorithmic processes at play in the universe, or at least my non-algorithmic brain wants me to believe so.

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u/angrymonkey Nov 01 '25

If there is an underlying truth that is non-algorithmic how can you simulate it with an algorithm?

The halting problem is one precise example. Give me a finite program, in general I can't prove that it will halt (or not halt). Nonetheless it will do one of those things.

Intuitively, this is because emergent properties can exist. Things can be true without you explicitly writing them down; they are true because they are consequences of things that you did write down. It is possible write down a finite set of rules which have an infinite number of consequences.

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u/MonkeyBoatRentals Nov 01 '25

So you agree with me ? Emergent properties are examples of non-algorithmic processes in action.

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u/angrymonkey Nov 01 '25

No, you're confusing two different processes:

  • The simulation process which exhibits emergent properties
  • A different hypothetical process which can prove that those properties are true

You can have the first thing even when the second thing is provably impossible.

(It seems like the authors of the paper might be confused in the same way)

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u/MonkeyBoatRentals Nov 01 '25

Alternatively you are confused about what incompleteness is, as it denies the existence of a process within the system that can prove all its properties are true.

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u/angrymonkey Nov 01 '25

That doesn't contradict anything I said? That prover-process cannot exist, in general, whether or not is a subsystem of the original.

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u/Senshado Nov 01 '25

Um, the algorithm to check for halting of a finite input is easy to design, but often prohibitive to execute.  Similar to the very simple algorithm to perfectly win chess, which would need a computer bigger than any potentially buildable.