The argument isn't "something like, or a little better, than current CPUs can perform everything a brain can," but something more like "a turing machine can perform everything a brain can or more." This is more an ontological exercise, not an empirical one. If you reduce everything to a "black box" model with inputs and outputs, then sure, the mathematical abstractions of theoretical brains and theoretical CPUs have a congruence. Most objections to this seem to resolve around qualia being something not modelable in machines, but I'm skeptical of that claim.

Can an "arbitrarily advanced computer do everything a brain can do?" Empirically, right now, current machines can't but we are talking about "future machines, via line-of-sight extrapolation". Not fundamental leaps in tech, but incremental ones. It seems plausible, but it seems we expand the depths of the complexity of the requirements nearly as fast as we advance current capabilities. I don't know, but I'd put my money on the technology catch up.

Being skeptical of the claim that a certain qualia is not modelable in machine is just as valid as being skeptical of the exact opposite. This is exactly why I asked if there was anything beyond what the original poster said. Without it, a post based on the exact opposite assumption could have been written and considered just as valid.

Fair criticism, I didn't tackle that head-on. The following doesn't actually make a cogent argument either, but I'll elaborate that my intuition is that qualia (conceived as something nearly tangible) are more like "the soul" or "spirits" and that, as such, thinking they exist in the brain or a turing-machine is nonsense. To the extent they are more like some combination of memory and emotional-stimuli, then they just represent a particularly interesting set of internal states, but are still something that can be mathematically modeled.

> In what way can this be proven?

Proven? Nothing in science is ever proven.

But on half a millenium we have failed to find anything that can't be simulated by math, and Turing completeness means a computer can simulate anything that can be simulated by math. We also can simulate all the smallest components of a brain.

At this point the claim that math can not simulate it is highly extraordinary.

> Turing completeness means a computer can simulate anything that can be simulated by math

Technically, it is not proven that Turing machines can compute all computable functions, so there is some purely theoretical possibility that the brain could be able to compute functions that a Turing machine can't.

Personally I find that extremely unlikely, and agree that it would be extremely surprising. But it wouldn't invalidate anything we have proven so far.

It would imply that our brains are using currently-unknown physics, since all current theories are computable.

We have not been able to simulate any aspect of subjective, conscious experience using a mathematical model, and personally I think we have no good reason to believe we ever will. The qualitative, by definition, cannot be quantified.