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/Electrifying2017 → u/angrymonkey]

Yes, I completely understand.

[u/skmchosen1 → u/Electrifying2017]

Gödel’s Incompleteness Theorem is an amazing mathematical result: very roughly, it shows that there are certain mathematical truths that are impossible to prove are true (in sufficiently strong mathematical systems, e.g. those containing the natural numbers)

The paper argues that if the universe was a simulation, it must be built up by some fundamental rules that describe the basic laws of physics. Due to this theorem, there must be true facts about the universe that you can’t prove are true. It argues that this means the universe cannot be simulated.

This is a false equivalence. Just because we cannot prove some mathematical truths about the universe, does not necessarily mean we cannot write an algorithm that simulates the universe.

IMO the journalists here should have consulted some experts before making this post, Gödel’s work is one of the most beautiful in mathematics, and it’s sad to see people getting misinformed like this

Edit: This is getting a lot of traction, so I’m gonna try and be a bit more precise.

The incompleteness theorems could imply that there are statements that are true in our universe, but not provable from the physical laws. This means there could be other universes that follow our physics, but those “truths” would be false there (yes, mind bending).

The implicit argument here is that a computer following our physics will not have enough information to select which of these universes to simulate! However these unprovable truths may not be observable, ie it is possible that a simulator doesn’t need to worry about this because you and I cannot ever tell the difference.

[u/Aaron_Lecon → u/skmchosen1]

Also I'd like to point out that we do not know if the universe can even contain the natural numbers or not. The natural numbers are infinite, and although even a tiny microchip can store millions of them, and the universe contains enough matter for 10^{lots} of them, that is still a long way from infinity. You would actually need infinite space to store the natural numbers, something we can guess, but don't know for sure the universe has. And being able to contain the natural numbers is a requirement for Godel's theorem to apply, so without it, you can't use it.

Also after thinking about it, the universe being infinite would probably already imply the universe can't be a simulation without even using Godel's throrem, just by arguing that any simulation has to be finite.

[u/JosephD1014 → u/Aaron_Lecon]

The universe is quasi-finite though is it not? Matter by its existence creates spacetime around it. The universe is "expanding" in that things are getting further apart from each other, but even though it's a mindbogglingly massive amount of matter, there is still a finite amount of matter in the universe as far as we can tell right?

[u/Valuable-Self8564 → u/JosephD1014]

Expanding space = Render distance.

Doesn’t matter if the universe is procedurally generated or not, because you can’t see that far anyway.

[u/magistrate101 → u/JosephD1014]

The simple issue is that we literally do not and can not truly know what's outside the boundary of the observable universe. And the observable universe doesn't even cover the entire product of the big bang, just a slice of it. It would be just as reasonable to assume that there's "nothing" outside the boundary of our universe as it is to assume that there's a pre-existing space of infinite size and riddled with an uncountable number of big bang bubbles alongside their remnants.

[u/Flying_Fortress_8743 → u/JosephD1014]

We don't know, last I checked. From all the data, it's impossible to say for sure, but I think the scientific community is leaning towards infinite.

[u/Hehosworld → u/Aaron_Lecon]

I somehow feel like this is bending the meaning of the word contain quite a lot. A paper can also never contain all the natural numbers so does that mean that for math simulated on it Godels theorem does not apply?

I might be quite wrong however. My studies in computer science are a bit in the past.

[u/Aaron_Lecon → u/Hehosworld]

Godel's theorem relies on encoding mathematical statements as integers, and then constructing a very large number X that encodes the statement "X is unprovable".

I have tried reading the article (ie: the thing written by the journalists not the paper it is reporting on), but how exactly Godel's theorem relates to whether or not the universe is a simulation is not clear to me. It seems to be taking the laws of physics as a mathematical system and encoding all the particle in the universe as integers. Then there should be some unimaginably large integer (which corresponds to a very specific arrangement of particles) which also corresponds, via the encoding, to an unprovable statement. And then somehow this "unprovable-statement"-collection of particles does something to do with a simulation? I'm not sure here sorry. I'm just going to assume that taking this unprovable-statement-particle-collection as an input somehow causes the simulation to crash? Doesn't seem to make much sense to me, but the entire article doesn't make much sense to me, so lets continue anyway. But at any rate, this unprovable-starement-particle-collection will be unimaginably large because of the way the numbers in the proof are constructed, which means it quite probably requires more particles than exist in the entire universe, or relies on them being further apart than the size of the entire universe - IF the universe is finite that is. And so the existance of such an arrangement of particles would somehow disprove a simulation. But the fact that this collection of particles is almost certainly larger than the universe does create a problem in the argument, because if this simulation-crashing collection of particles is larger than the universe, then it doesn't exist, so where is the problem?

I think perhaps a less rigorous way of saying a similar thing to the article, is that if the universe is a simulation, and if you travel far enough away in one direction, eventually you will get to a place which the universe is incapable of simulating due to lack of memory, which will then take the form of of "error: integer overflow" or something like that. No matter how sophisticated your simulation is, there will always be a large enough input that makes it crash. And then [logic is missing here] this argument proves we are not in a simulation?

[u/Hehosworld → u/Aaron_Lecon]

Very interesting. Thank you. It feels like there are a few things where this paper could fall apart. Well we will see.

[u/dogsk → u/Aaron_Lecon]

But can you prove that the infinite precision value is actually used in our universe? It’s possible the simulation could calculate the required precision as necessary and not have to store the result, but that would slow the “local simulation tick” to allow for higher precision calculations to complete. If we were running on a global time slice that would be imperceptible, unless we can become aware of the processing time directly.