A brain is both, and more, and neither.
Either metaphor would be a gross oversimplification of what a brain is, what it does and how it works. That’s the point.
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We are having an ontological disagreement at some level. I say “A brain is a computer” and you say “A turing machine can’t produce acetylcholine.” Okay. To me though, the fact that our brains produce acetylcholine is entirely irrelevant to their “brainness”. If they produced some other neurotransmitter instead, it wouldn’t change a thing. The thing to me that is interesting about brains is that they possess intelligence.
I can see being interested in brains, as @Scientist suggests he is above, the same way a hydrophysicist might be interested in a river. But that won’t get at intelligence. You can point at all these things that are extraneous to intelligence like acetylcholine and I agree with you on that level, brains aren’t computers. They’re masses of organic matter. You can stick with the river metaphor if it makes you happy.
If on the other hand you’d like to abstract from there to “thing that does the thinking”, then I’d be interested in what is something that “the thing that does the thinking” does, that isn’t a calculation? What is a “thought” that isn’t a calculation?
If you prefer hydrology, cool; we just have different interests.
The fact that I specifically mentioned it as being not relevant or impressive in the previous sentence didn’t convey that things related to “controlling the body” wasn’t what I was asking for?
Seriously?
Yep, you got me. I spent ~60 hours a week for the past 2 decades studying the brain from every angle I could because I was hoping to find a cool metaphor for rivers. Sure
Not dismissive and condescending at all. Nope, not at all.
ETA: in case it needs saying (although no clue why it would), hydrology and river turbulence are both cool areas of study
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I’m not sure I understand your defensiveness here. Hydrologists studying a river are doing both important and practical as well as theoretically interesting work. Are you saying that comparing someone to them is insulting?
Look, zoology is cool and all…but ignoring the ways an elephant isn’t like a rope, which I am not interested in myself, how is an elephant not a rope?
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Very good. When I hear someone say, “A rope is a bad metaphor for an elephant”, I think “But an elephant is a rope.” Ha!
You, like most people, seem to be focusing on the brain as an informational processing unit. That’s understandable because we fancy our intelligence as the most important defining trait of our species.
What I’m saying is that the brain is also very much a physical biochemical organ that exists in balance with all the other organs and fluids and cells and nutrients in our bodies just like a liver or an adrenal gland (albeit more structurally and chemically complex).
So the idea that a human mind could exist entirely apart from the human body as some kind of code running on a calculating machine doesn’t have all that much more scientific basis than the idea of a soul existing apart from the body.
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I agree completely. The brain is much more complex and interesting than say a bladder. And should certainly be studied that way. If you say, “A computer is a bad metaphor for a brain” and it is analogous to “A septic tank is a bad metaphor for a bladder”, I agree.
It is only if you say, “Brains have something special about them that they can do something that in principle could never be modeled as a process on an abstract turing machine” that I say, “Well what is that thing then?”
You sure? Because nobody said anything about abstract Turing machines here until you brought them up, in response to an article on a book saying that a computer is a bad metaphor for a brain. I mean, the thread history is right here. 
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I’m sure. This is what I said:
Yep, that’s where you brought them up, like I literally just said you did…
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You mean that part where I agreed that “computers are a bad metaphor” and then went on to say that the specific interpretation where “computer” meant “Turing machine” was a different situation? Maybe “Fine” means “I disagree completely” in your dialect of English?
Look, I don’t want to do this fight, but I’m not going to be gaslighted. This is from the exact same post you quoted. Compare these statements and tell me if they don’t look at all contrary to you.
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If you say “A brain is a computer, the memory is the RAM and the left hemisphere is the graphics processor”, you are using a bad metaphor.
If you say, “The abstract properties of a brain that enable thought cannot be replicated on any device that is a morphism of an abstract turing machine”, you are not talking metaphorically.
If you say “A brain isn’t a computer” to mean “The abstract properties of a brain that enable thought cannot be replicated on any device that is a morphism of an abstract turing machine”, you are not talking metaphorically.
If you are speaking about the metaphor and say it is a bad metaphor, then I agree with you.
If you are speaking about the proposition “The abstract properties of a brain that enable thought cannot be replicated on any device that is a morphism of an abstract turing machine.” and you agree with that proposition, then I would like to know what those properties are that can’t be replicated.
The phrase “The computer is a brain” has a metaphorical interpretation and a non-metaphorical interpretation.
You ask me if I’m sure that I think these are two different things, and I say yes. Was I always sure? Yes. I indicated that I didn’t disagree with the “computer is bad metaphor” view with the word “Fine” and then brought up the fact that sometimes this is conflated with the non-metaphorical version of “The computer is a brain.” I claimed this here:
and you said:
I’m sure.
Why did I bring up the non-metaphorical interpretation of “The brain is a computer”? Because a lot of times people will make the argument that “The computer is a brain” is a bad metaphor and then claim it as evidence for “The abstract properties of a brain that enable thought cannot be replicated on any device that is a morphism of an abstract turing machine.” While I accept that “the computer is a brain” is a bad metaphor I do not accept that the abstract properties of a brain that enable thought cannot be replicated on any device that is a morphism of an abstract turing machine.
Another really terrible metaphor is the eye is a camera. But I digress…
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The OED defines computer as
A person who makes calculations or computations; a calculator, a reckoner; spec. a person employed to make calculations in an observatory, in surveying, etc.
So saying that a brain isn’t a computer makes little sense, unless one wishes to denigrate the contributions (and brains) of those who worked as computers-- mostly women.
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Yeah, which is why I said:
Why is this thread one long attempt to miss the entire point of the article, that electronic computers are a bad analogy for how our brain is set up, in favour of weird semantics to argue something else entirely? 
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THE OED also defines turing machines, but it isn’t tied in with the computer definition. Not sure I’d trust a lexicographer over a mathematician, but there is the notion that it’s a subset-- a specialization rather than a generalization. (which conflicts with Turing 1937, but what the hell)
A notional computing machine for performing simple reading, writing, and shifting operations in accordance with a prescribed set of rules, invoked in theories of computability and automata. It is represented as a scanner that has a number of internal states and moves left or right along a tape on which is a sequence of symbols. The symbol read and the state of the scanner determine (in accordance with the rules) what replacement symbol is written, what new state the scanner enters, and what move it makes along the tape before the cycle is repeated.
1937 Jrnl. Symbolic Logic 2 43 [Abstract of Turing’s paper.] Certain further restrictions are imposed on the character of the machine, but these are of such a nature as obviously to cause no loss of generality—in particular, a human calculator, provided with pencil and paper and explicit instructions, can be regarded as a kind of Turing machine.
1955 Sci. Amer. Apr. 62/1 To understand a Turing machine we need only know its table of commands.
1961 Proc. Symposium Appl. Math. 12 39 A Turing machine plus random elements is a reasonable model for the human brain.
1969 P. B. Jordain Condensed Computer Encycl. 550 No Turing machine has ever been physically constructed or realized in hardware as a device for its own sake, but general-purpose digital computers have been programmed to simulate Turing machines.
1984 Sci. Amer. May 70/1 Beginning with the intuitive idea that a method is an algorithm—a procedure that can be mechanically carried out without creative intervention—he [ sc. A. M. Turing] showed how the idea can be refined into a detailed model of the process of computation in which any algorithm is broken down into a sequence of simple, atomic steps. The resulting model of computation is the logical construct called a Turing machine.
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