by wat10000 | 2025-07-19 19:04:30+00:00
> and given that the brain is an existence-proof that a sufficiently compact UTM is possible

This is where it goes wrong. You’ve got the implication backwards. The existence of a program and a physical computer that can run it to produce a certain behavior is proof that such behavior can be done with a physical system. (After all, that computer and program are themselves a physical system.) But the existence of a physical system does not imply that there can be an actual physical computer that can run a program that replicates the behavior. If the laws of physics are computable (as they seem to be) then the existence of a system implies that there exists some Turing machine that can replicate the behavior, but this is “exists” in the mathematical sense, it’s very different from saying such a Turing machine could be constructed in this universe.

Forget about intelligence for a moment. Consider a glass of water. Can the behavior of a glass of water be predicted by a physical computer? That depends on what you consider to be “behavior.” The basic heat exchange can be reasonably approximated with a small program that would trivially run on a two-cent microcontroller. The motion of the fluid could be reasonably simulated with, say, 100-micron accuracy, on a computer you could buy today. 1-micron accuracy might be infeasible with current technology but is likely physically possible.

What if I want absolute fidelity? Thermodynamics and fluid mechanics are shortcuts that give you bulk behaviors. I want a full quantum mechanical simulation of every single fundamental particle in the glass, no shortcuts. This can definitely be computed with a Turing machine, and I’m confident that there’s no way it can come anywhere close to being computed on any actual physical manifestation of a Turing machine, given that the state of the art for such simulations is a handful of particles and the complexity is exponential in the number of particles.

And yet there obviously exists a physical system that can do this: the glass of water itself.

Things that are true or at least very likely: the brain exists, physics is probably computable, there exists (in the mathematical sense) a Turing machine that can emulate the brain.

Very much unproven and, as far as I can tell, no particular reason to believe they’re true: the brain can be emulated with a physical Turing-like computer, this computer is something humans could conceivably build at some point, the brain can be emulated with a neural network trained with gradient descent on a large corpus of token sequences, the brain can be emulated with such a network running on a computer humans could conceivably build. Talking about the computability of the human brain does nothing to demonstrate any of these.

I think non-biological machines with human-equivalent intelligence are likely to be physically possible. I think there’s a good chance that it will require specialized hardware that can’t be practically done with a standard “execute this sequence of simple instructions” computer. And if it can be done with a standard computer, I think there’s a very good chance that it can’t be done with LLMs.