The essential components of a Turing Machine (for our purposes) are:
1) State information storage.
2) A means of recognizing part of that state and using it to modify the state to generate the next state.
3) A means to input and output some of that state.
That's it. The brain's neurons with their malleable interconnections map into that. The interesting part is in the details of next-state generation. Also remember that a TM can represent particular states using a form of fuzzy logic, where every representation is given a level of certainty.
Just how a particular function is implemented can vary widely. The exact same results for a function can be gotten from hard-wired logic gates, a program, neural-net hardware, neural-net program, etc. There's no need for a one-to-one fine-level mapping unless we're reverse-engineering parts of the brain, e.g., Blue Gene.
Well, I'm not asking for a one-to-one fine-level mapping, actually.
But, as you see it, which components of the brain -- be they actual physical structures or neural pathways or even coordinated actions or anything else, what have you -- do you think correspond to each of those components?
Or alternately, to use the list of components from a link roger gave earlier, which components of the brain correspond to the tape, head, table, state register, and (human) computer?
"Information" is not a metaphor here-- it's real. If I ask you to multiply two numbers, you receive information that includes those numbers and the command to multiply them. You can then return the number. I can ask a calculator to do the exact same multiplication and (hopefully!) get the same answer. Sure, I have to speak the calculator's language of buttons and display, but the critical information is the same.
I don't see the purpose of limiting the word "understand" to just humans, any more than we limit the word "memory". If a calculator gives me what I recognize as the right answer when I press its "multiply" key, then I say that the calculator fundamentally understands that keypress to mean "multiply". Any understanding that we may have beyond that doesn't take that away.
"Information" is always a metaphor, or at least an abstraction.
Yes, you can ask me to multiply two numbers, and I can give you an answer, and you can ask computer to do that and get an answer, but that's extremely high-level and symbolic. Only a human observer would be aware that any such thing had happened, even if a non-human observer could witness every physical action involved in both cases.
(Compare that to, say, a tree limb falling onto a rock.)
If we want to compare the brain and the computer, we have to compare what happens in the interim and see if we're getting these answers by similar means. (That is, we do if we want to establish whether these structures are entirely analogous or, rather, functionally analogous for a limited range of tasks.)
In the brain, sound waves are picked up and pattern-matched, and (here I'm afraid we have to deal with a black box) this pattern matching process leads to a physical response.
Is the computer actually going through a similar process if I enter the problem into an application and the patterns on a screen change as a result?
Here's why it matters:
If we say that the brain is not more powerful than a computer (TM), then we are saying (as I understand it) that this bodily organ cannot do anything a computer cannot do.
Therefore it is imperative that we do not assume from the beginning that brains and computers do the same kind of thing, and only that kind of thing. So we must be very careful that we're being entirely accurate and precise if we assert that they're both doing "information processing".
There are a few ways I can think of to ensure that the analogy holds.
First, we can show that brains and computers are, in their entirety, TMs. And we can do that by finding counterparts to the necessary components of TMs in the brain, with nothing left over.
Or, we could simply make a computer do everything the brain does. (This would be like comparing my full-size car to my functional model car.) And so far they've done a lot, but not all, so we're not there yet.
Or, we could show that what the brain does physically is entirely analogous to what a computer does. For instance, imagine we replace axons with wires or some such, and replace terminal buttons perhaps with nodes that release a tiny electrical charge when stimulated by the axon-wire, and replace dendrites with plates that send a charge down the next axon-wire when there's a sufficient charge in the synapse built up by the terminal nodes. Some setup like that.
So now we have a mechanical replica brain. Would that machine be doing what a computer does?