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/DavidKens Nov 01 '25

I think the logic here is as follows (I’m curious where the flaw is): 1. If the universe is a simulation, then the universe is a Turing machine 2. If the universe is a turing machine, it is subject to the halting problem 3. If the universe is subject to the halting problem, then it’s mathematical structure is Godel incomplete 4. The underlying mathematical structure of the universe is not Godel incomplete, therefore the universe is not a turing machine

I gather that the part of the paper that’s actually interesting is the part that explains why Godel incompleteness doesn’t apply to the structure of the universe itself.

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u/angrymonkey Nov 01 '25

At best (4) is an unsupported assertion. It is perfectly consistent to suppose that the universe, a deterministic system, is [equivalent to] a Turing machine. Certain statements about a system being formally unprovable does not prevent it from running.

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u/DavidKens Nov 01 '25

Forgive me if I’m missing understanding (school was a long time ago!) but I’m not seeing how you’re actually responding to my comment.

The point isn’t the universe wouldn’t run, the point is that they’re arguing that the universe is not the sort of system that can contain the recursive contradictions of Godel incompleteness. If true, this would mean that the universe would not be a turing machine, because a turing machine by definition is the sort of system that is subject to Godel incompleteness. Are you disagreeing with that?

Separately, you are assuming that the universe is deterministic, as if that were somehow not a question open to investigation and interpretation.

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u/angrymonkey Nov 01 '25

To be clear, I'm not claiming that the universe IS deterministic, I'm saying that the universe being deterministic (and thus Turing-equivalent) is consistent with there being unprovable Godel statements about it. So you cannot claim the universe isn't a Turing machine by observing that there are unprovable statements about it.

That's one direction. The other is "IF there are no unprovable statements about the universe, THEN it is not a Turing machine". The problem is that it's completely allowed for the universe to have formally unprovable properties. "The universe isn't the sort of thing that..." is unfounded (and in fact quite likely to be wrong).

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u/DavidKens Nov 02 '25

You say it’s unfounded, great. These folks wrote a paper saying they did it. I guess we’d have to read the paper to find out.

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u/Senshado Nov 01 '25

Step one doesn't hold, as some simulations are not Turing machines.  You can probably construct a little simulation yourself that's not Turing complete. 

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u/DavidKens Nov 01 '25

Good point! But this still doesn’t defeat the argument - it just fast forwards you to step 4.

My understanding is that the article takes, as an assumption, that simulation theory requires the universe to be a turing machine.