Let's take the question of the human mind and whether it can be modeled by a non-quantum Turing machine out of the equation. Penrose's contention can be summed

Let's take the question of the human mind and whether it can be modeled by a non-quantum Turing machine out of the equation. Penrose's contention can be summed up without it. He basically thinks that gravity will be discovered to play a role in quantum wave function collapse. And that this role will render non-quantum Turing machines incapable of accurately modeling quantum gravity in some very serious way. Another way of saying it is that he believes when a real theory of quantum gravity is developed we'll find that non-quantum Turing machines will not be able to accurately model the physics of a black hole. Note that this says nothing whatsoever about the human mind or microtubes or formal systems, etc. This is about his subject of expertise: gravity, mathematical physics, and quantum gravity. He's one of the world's leading experts in these fields. And if he is right, he conjectures it will have strong implications for non-quantum Turing machines as a basis for Strong AI.