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.
The infinite tape doesn't have to be physically inside the brain. The tape is the universe itself, we read it through senses and write to it through actions.
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).
The universe is finite, so Turing machines are still more powerful. We know the universe is finite because it has a finite volume, and even if it were to expand infinitely, which is debatable, it still has finite extent in spacetime because of heat death.
The brain is not a finite state machine. If it is then it is clearly equivalent to a Turing machine. It seems like your position maybe is just based on there not being “infinite tape” or something but human intelligence is not anything like any computational model we have conceived, or at least no one has presented any such evidence.
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.
I mean you can quote those bounds all you like but this is not what a “finite state machine” is. You are using the words in a nominalistic way but for people in computing, we know very well what a finite state machine is and it encompasses things far greater than the “Bekenstein Bound”. It’s no problem to consider more states in an FSM than there are particles in the universe. Of course, this is silly because what you are describing as an FSM is not.
So you're saying that a set of finite states governed by a set of finite state transitions is not a finite state machine. Ok buddy.
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.
Your brain has a finite number of particles. The information content of your brain must be encoded in those particles. Thus, the brain's state space is 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.
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).