The idea that the universe is a simulation proceeds as follows:

(1) Person notices that computer simulations are getting increasingly powerful. Maybe we will be able to simulate something like the universe one day which will have life in it.

(2) If simulating the universe is so easy and inevitable, what are the odds that we are at the top level?

The idea in the article would refute the inductive step.

Yes.

On a Von Neumann architecture computer, but maybe a quantum computer?

That's a good point.

One simulator would just "run the laws of our universe" (I don't care to make that precise, since presently it's a trivial statement, but hopefully it's clear that I mean to distinguish it from running a computer), but then that sort of trivializes the idea of "simulation".

Maybe it's possible for us to create a sub-universe of ours with a quantum computer such that we view the entities as a part of our universe, but the entities cannot be aware of us. (This is the insects at the surface of a pond idea, unaware of the dimension above or below.)

> The idea in the article would refute the inductive step.

No it doesn't. The article describes a proof that it is impossible for a computer to simulate this physical universe with perfect accuracy; but, that's not actually a problem for Nick Bostrom's simulation argument. For the simulation argument to work, you don't need to simulate the universe with perfect accuracy – just with sufficient accuracy that your simulated people can't distinguish it from a real one. And this proof isn't about "ability to simulate a universe to the point the simulated people can't tell that it is a simulation", it is about "ability to simulate a universe with perfect accuracy". So the proof isn't actually relevant to that argument at all.

Please explain how to simulate a universe which is indistinguishable from a simulation but which is not accurate according to the rules of the article.

Does the article propose anything empirically testable?

I mean, suppose we are actually in a computer simulation-what observations could we perform, which according to the rules of this article, would show that we were in one, and not the “real” world?

Addendum: from what I understand, the article’s proof relies on computational quantum gravity having a Gödel sentence. Now, quantum gravity is in practice, as far as we know, experimentally untestable-the distinctive phenomena it predicts only occur at scales far beyond our present technological ability to explore-and who can say if that will ever change. So, is it possible for a computer to simulate humanity as it currently exists, such that the simulated humans couldn’t detect they were simulated? I don’t know; but what I can confidently say, is this research has nothing useful to say about that question, because this is theoretical quantum gravity research, and I’m not aware of any good reason to believe quantum gravity has any relevance to answering that specific question. This research claims to show computers are incapable of simulating aspects of reality which are empirically unavailable to us; even if the research is right, it makes zero difference to the question of whether the actual empirical experiences we do have are simulated or not.

> just with sufficient accuracy

You need at least an idea about what the result will, roughly, be.

The article claims to prove no computer could accurately simulate quantum gravity. Suppose they are right, and as a result our simulators are forced to make quantum gravity experiments (if that were a thing) give “incorrect” answers, because the real ones are uncomputable. Would that be proof we live in a simulation? Or would it be taken as proof that quantum gravity (whether loop quantum gravity or M theory or whatever) had finally been empirically refuted?

That said, if they really wanted to give us the “correct” answer-why would they bother when we could never know that a wrong answer were wrong?-why couldn’t they just suspend the simulation, run the experiment themselves, then resume it simulating the result?

Not at all, the notion that the universe is an illusion or a dream is very old indeed and predates computers.

> (1) Person notices that computer simulations are getting increasingly powerful.

The problem is that you need good models to be able to simulate accurately. And when the manufacturers do not provide good datasheets to construct the model or if they don't provide good models, you're on your own. /s

At that point the whole idea becomes quite removed from what most people would think of when asked to consider if the universe is a simulation.

To clarify: without being able to simulate the universe from within the universe itself (i.e. needing to resort to some "outside" higher-fidelity universe), then the word "simulation" becomes meaningless.

We could just as easily refer to the whole thing (the inner "simulation" and the outer "simulation") as just being different "layers of abstraction" of the same universe, and drop the word "simulation" altogether. It would have the same ontology with less baggage.

According to the current mathematical model we use to define the universe, built from Einstein’s field equations, we’re not in a simulation.

The said model is significantly misaligned with human perception regarding the start and edges of spacetime, so it’s completely valid to point out that it’s just a model (and that we might be in a simulation).

the bible talks about Angels holding the universe so maybe the Angels are the computers? unscientific fiction is really powerful

If we follow your logic, then atoms or quarks could be considered computers simulating the universe.

The former isn't even a new proof:

https://arxiv.org/abs/0708.1362

https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthl...