> 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.
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?
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.
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.