A paper this week in the Journal of Holography Applications in Physics left me scratching my head.
To get why it's so puzzling -- and why not only I (an admitted layperson), but some actual physicists, are inclined to doubt its rather earth-shattering conclusion -- a little background first.
A few months ago I wrote here at Skeptophilia about Kurt Gödel's Incompleteness Theorem. This astonishing piece of work, published in 1931, dashed the hopes of people like David Hilbert that it could be proved that a purely algorithmic system like mathematics was both complete (all true statements that can be expressed within it are provable) and consistent (all provable statements that can be expressed within it are true). Gödel proved, beyond any doubt, that mathematics cannot be both; if it is consistent, it is incomplete (some true statements are unprovable); if it is complete, it is inconsistent (some provable statements are untrue).
It was a devastating result. We think of math as being cut-and-dried, a system where there's no fuzzy ambiguity. Turns out there's a built-in flaw (although some might object to my calling it that); and not just mathematics, but any sufficiently powerful algorithmic system you could invent, would fall to the same death blow.
The other piece of background is also something I've dealt with here before; the possibility that we might live in a simulation. The claim has been seriously considered by people like Nick Bostrom (of the University of Oxford) and David Kipping (of Columbia University); they looked at the questions of (1) if we were in a simulation, how we could tell, and (2) if simulation is possible, what our chances are of inhabiting the real, original universe (turns out, a fairly persuasive argument concludes that it's near zero). Of course, that doesn't settle the truth of the major premises; (1) are we in a simulation? and (2) are simulations possible?, respectively. And as anyone who's taken a course in logic knows, if the first part of a syllogism is false, you can conclude any damnfool thing you want from it. (More accurately, if the major premise is false, the conclusion could be true or false, and there's no way to tell for sure.)
Okay. So what this week's paper did is to look at the possibility of our being in a simulation, from a Gödelian perspective. And their conclusion was that if the universe is a simulation, then it is by definition an algorithmic system, because anything that is runnable on a computer (even a super-powerful one) would have to be, at its basis, a set of algorithms. Therefore, by Gödel's Theorem, there would have to be true statements that are unreachable from within the system, meaning there is more to the universe than can be reached from inside the simulation. Conclusion: we can't be in a simulation, because it would be inherently incomplete.
My first thought on reading this was that I must be misinterpreting them, because the conclusion seemed like an enormous overreach. But here is a quote from one of the authors, Mir Faizal of the University of British Columbia - Okanagan:
Drawing on mathematical theorems related to incompleteness and indefinability, we demonstrate that a fully consistent and complete description of reality cannot be achieved through computation alone. It requires non-algorithmic understanding, which by definition is beyond algorithmic computation and therefore cannot be simulated. Hence, this universe cannot be a simulation.
And another, by study co-author Lawrence Krauss, of Australian National University:
The fundamental laws of physics cannot be contained within space and time, because they generate them. It has long been hoped, however, that a truly fundamental theory of everything could eventually describe all physical phenomena through computations grounded in these laws. Yet we have demonstrated that this is not possible. A complete and consistent description of reality requires something deeper -- a form of understanding known as non-algorithmic understanding.
So I don't think I'm misunderstanding their logic -- although I will certainly defer to wiser heads if there are any physicists in the studio audience.
The problem for me is that it is yet to be shown that the universe is non-algorithmic. I'll buy that if it is algorithmic, there will be truths we can't reach by mathematical logic; so if this were a simulation, there'd be parts of it we couldn't get at. But... so what? I have no problem imagining a sufficiently complex simulation that gave such a convincing appearance of reality that any unreachable truths would be remote enough we might not have found them.
I think Faizal et al. may have too high an opinion of the capacity of the human brain for elucidating the workings of the universe.
Turns out I'm not the only one who has issues with this paper. Physicist Sabine Hossenfelder did a brilliant take-down of the Faizal et al. study, and in fact gave it a nine out of ten on her infamous Bullshit Meter. She said:
Unfortunately, [the paper] assumes its major premise. We have never measured any quantity that is provably uncomputable. To assume we can do this is logically equivalent to assuming we don't live in a simulation. To see what I mean, let me turn their argument around. Maybe the fact that we have never measured any quantity we can't also compute is proof that we are part of an algorithm that simulates the universe...
We don't know any counterexamples. The cases which I've mentioned that have been discussed in the literature always take some limit to infinity. For example, they might use infinitely many atoms. Or a lattice with an infinitely small spacing... In these mathematical idealizations, yes, there are quantities that provably can't be computed in a finite time. But we don't know any real-world examples. Not a single one. Isn't that weird? It's like we actually can't measure anything that an algorithm could not also compute. So maybe... we are algorithms.
In conclusion, the headlines I've seen, along the lines of, "Physicists Prove We're Not In A Simulation," strike me as a bit premature. We haven't escaped from Bostrom and Kipping's matryoshka universe quite that easily. Me, I'm going to stay in the "I don't know" column. The Simulation Hypothesis certainly hasn't been proven, but despite Faizal et al., I don't think it's going to be easy to disprove, either.
So I guess we haven't settled whether the insane *gestures around vaguely at everything* we've been dealing with is real, or is (as I've suggested before) the result of stoned aliens twiddling the knobs just to fuck with us. I'm honestly not sure which would be worse, frankly.
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