It is. This happens to some people who discover undecidability is a thing. Then they get carried away and try to generalize to other areas. Branches of this line of thinking include the concept that intelligence must be analog with infinite precision, (this is the same line of thinking as the argument against digital audio) or intelligence must be "quantum". (Penrose).
The formal answer to the halting problem is that deterministic systems with finite memory must repeat a previous state or halt. Undecidability requires unbounded memory. Finite memory systems may have so many states and be so complex that decidability is computationally infeasible. But that's not impossibility. I used to get this objection when I was working on proof of correctness systems. We now know that some programs are hard to decide, but many useful ones are not.
If your program is anywhere near undecidable, it's probably broken. Microsoft's position with their Static Driver Verifier was that if 45 minutes of symbolic execution hadn't found a way out, you failed driver verification. This is one of those problems, like linear programming, where part of the problem space is really hard in a computational sense, but most of it isn't.
(I sometimes wonder if Penrose was on to something with his idea that the brain uses quantum effects in microtubules.[1] Penrose is a first-rate physicist. His philosophy is not as good. It's become clear that we can do artificial intelligence with acres of transistors and gigawatts of power, but the efficiency is terrible. We need either a more efficient algorithm or better hardware elements. LLM training now is like a Newcomen steam engine, where something the size of a house had the power output of a modern motorcycle engine.)
[1] https://en.wikipedia.org/wiki/Orchestrated_objective_reducti...
The computer scientist says “The halting problem cannot be solved, I have proven it” and the software engineer goes “30 second timeout, if the answer’s not ready by then we don’t need it”
Maybe. That's if you assume that the universe is a conventional computer. Far from settled and the alternative isn't necessarily just "God does it" - it might be that the universe is a "computer-plus", with some processes that produce results not computable by Turing means. It would be strange, but so is quantum mechanics, so...
Well great. Then where are you? You are precisely nowhere. You haven’t disproved the results in the system and you haven’t proved anything else.
If the universe indeed uses real values, it's possible that it's more powerful than Turing machines.
However, this doesn't mean that TMs can't operate on such numbers. You can compute the fact that pi + pi = 2 * pi even if you can't enumerate all of pi's decimals.
> However, this doesn't mean that TMs can't operate on such numbers.
Well, it kinda does. For example, you can't compute the sum of two arbitrary real values in a finite number of steps.
That being said, it's possible that the universe actually is not "running" on real numbers. This would also mean that our physics built on top of calculus is just an approximation.
This has always fascinated me. You can't really construct a meaningful amount of calculus without having real-valued variables. The intermediate value theorem depends on it, and it's one of the foundational parts.
I tried to construct something like "bounded error rational calculus", by trying to use rational ranges instead of real values and then constraining the range size. I was able to recover _some_ calculus, but I really have not studied it in enough details.
For example, let's take two arbitrary real numbers, call them x and y. They're almost certainly irrational uncomputable numbers, of course. Now, what is their sum? It's x + y, of course - I can tell you that without doing an infinity of computational work. Now, is this a useful representation? It very much depends on the use you have for it. For two unrelated uncomputable numbers, their sum is almost certainly uncomputable anyway, so there's not going to be any meaningful representation of it either. However, we can still derive useful properties about it, and use it in physical simulations as we need. For example, if both x and y are positive, I can tell you that x+y is greater than either of them, so I can also tell you that the electromagnetic force between two particles that are at distance x+y will be weaker than the force between two particles at distances of just x or just y.
So, what would it mean for the universe to "compute the exact value" of these two, or of their sum? What can physics do, assuming that some aspects are indeed continuous, that a simulation running on a TM actually can't?