The authors make a classic mistake: the brain is not comparable to a Turing Machine, it is a finite state machine. There’s no infinite tape in a brain.
Brain is not the Turing Machine, but it's the controller part of it, which we often treat as the same thing.
We have multiple controllers (brains) operating on a shared tape (universe).
Yes it is, all finite volumes contain finite information. This is a consequence of physics called the Bekenstein Bound. This means the brain can be fully captured by a finite state machine. It has a very large state space, but it's still finite.
A finite set of configurations is enumerable, and can be mapped to any other finite set of same or larger size, like a computer's memory, with no loss of information.
Therefore, any state your brain can enter can similarly be created within a computer, in principle.
Not necessarily: https://en.wikipedia.org/wiki/Orchestrated_objective_reducti...
The only questionable thing is whether quantum effects are essential in brain activity.
Of course it's disputable. There are at least two well known deterministic interpretations of quantum mechanics that are indistinguishable from orthodox QM, Many Worlds and Bohmian mechanics.
And so can a finite state machine with the same state space as your brain. Size of state space is not a difference of kind but of degree.
Furthermore, the proof I laid out is a corollary of simple physics. If you want a more rigorous version, look up the Bekenstein Bound, which proves conclusively that any finite volume can only contain finite information. Your body is a finite volume, therefore it contains finite information, therefore it can be captured by a finite state machine.
Edit: I just realized I also replied to you above, so I'll take up the thread there.
Don't confuse expressiveness and state space. Even if there are more faithful encodings that better preserve other properties, what I said is strictly true and it's important for people to understand that human cognition is not as powerful as some think: a finite state space means a human can be fully captured by a finite state machine.