There’s nothing to indicate the human brain can’t be implemented in a Turing machine too.
That is not true, this is a research branch from computer science and math, it is called Computability theory, it deals with the limits of expressiveness for different types of theoretical machines and expressions, and the most expressive of all is the Turing machine, and a Turing machine cannot do some stuff, the classic example is the Halting problem, a computer cannot definitely say if an algorithm ever stops (mathematica proven that it cannot do it), but a human can do so quite easily.
One may think that maybe a Turing Machine cannot do something but can simulate another machine that does, but that is also proven to be impossible, it cannot simulate something more expressive than itself.
I know computability theory, and I am very familiar with the halting problem. A human cannot solve it either. We made literal mathematical proof of it, and that proof is the halting problem.
The entire point of the halting problem is that if you assume that there is a black box that can answer whether a program halts, you then prove it can’t be the case by a proof of contradiction. You can replace the black box with a human brain and it works just as well, that’s the entire point of a black box.
That is not true, this is a research branch from computer science and math, it is called Computability theory, it deals with the limits of expressiveness for different types of theoretical machines and expressions, and the most expressive of all is the Turing machine, and a Turing machine cannot do some stuff, the classic example is the Halting problem, a computer cannot definitely say if an algorithm ever stops (mathematica proven that it cannot do it), but a human can do so quite easily.
One may think that maybe a Turing Machine cannot do something but can simulate another machine that does, but that is also proven to be impossible, it cannot simulate something more expressive than itself.
I know computability theory, and I am very familiar with the halting problem. A human cannot solve it either. We made literal mathematical proof of it, and that proof is the halting problem.
The entire point of the halting problem is that if you assume that there is a black box that can answer whether a program halts, you then prove it can’t be the case by a proof of contradiction. You can replace the black box with a human brain and it works just as well, that’s the entire point of a black box.
You’re misunderstanding the halting problem.
You are refuting something that wasn’t said. of course Turing machines cannot compute everything.