Universe can't be a simulation?

r/badmathematics have already looked at it.

"Being very generous, I think their attempt is to invoke this result of Chaitin to basically say "if the universe was a simulation, then there would be a formal system that described how the universe worked. By Chaitin, there's some 'complexity bound' for which statements beyond this bound are undecidable. But, these statements have physical meaning so we could theoretically construct the statement's analog in our universe, and then the simulation would have to be able to decide these undecidable statements."

What they don't explain is:

• why we should think that we're guaranteed to be able to construct such physical analogs of these statements,
• why they think that whatever universe that is simulating ours must have the same axioms as ours (e.g. Godel only applies to proving statements within the formal system under considerations),
• why they can rule out that the hypothetical simulating computer wouldn't be able to just throw some random value out when it encounters an undecidable statement (i.e. how do we know that physics is actually consistent without examining all events everywhere in the universe?),
• ...or a bunch of other necessary assumptions that they're making and not really talking much about.

They also get into some more bad mathematics (maybe bad philosophy?) by appealing to Penrose-Lucas to claim that "human cognition surpasses formal computation," but I don't think this is anywhere near a universally accepted stance."

The paper is mostly in the "not even wrong territory" so it's hard to offer a concrete refutation, but their arguments apply equally to Conway's Game of Life, a Turing-Complete cellular automata for which Gödel undecidable questions may be asked yet which is easily simulated on a computer.

I'm probably not competent to look at the details, but their paper sets off my BS detector by its reference to Godel's incompleteness theorem and its notion of "non-algorithmic understanding". These are both reminiscent of the Lucas-Penrose idea that consciousness requires uncomputability and that humans have some sort of magical ability to determine the truth-values of Godel sentences. I think the conventional view, sometimes known as the Church-Turing thesis, is that the universe is in fact computable.