Earlier quoted context omitted.
Before CPUs existed, we would compare brains to steam engines. There was a very interesting article posted here on HN a while ago, explaining why humans always pattern match their understanding of the "mind" (or "soul") to whatever technology is fashionable in their time: steam engines, computers, etc. It also explained the pitfalls of doing so. I think there is at this time no indication human brains are in any way…
But steam engines and hydraulics and gear mechanisms are all Turing complete. There is nothing wrong with those models. You could build a brain out of any of them, unless the brain computes something that is not computable. If the brain does something that is not computable, that's a direct challenge to some of our most established science. It is possible, but I think very unlikely.
Could you? That's sort of begging the question. We do not know if something "Turing complete" can be used to build a brain like the human brain. That's precisely the point.
> If the brain does something that is not computable, that's a direct challenge to some of our most established science.
A challenge for computational neuroscience maybe. Otherwise I don't see the challenge for neither neuroscience nor computer science. If someone wants to make the claim you can build a human brain out of something Turin-machine-like, that's an extraordinary claim, not established science.