The brain is a biological machine, it follows the laws of physics. There isn't any part of known physics that prevents us from simulating any number of atoms using a suitibly powerful computer.

A small aside, even simulating a small collection of quantum particles fully is enormously taxing with current computers and adding more particles increases complexity beyond just a linear increase. But this is a mathematical exercise.

Now, it's possible that the human brain depends on some law of physics that is not computable (possible to simulate on a computer), but given the level of study that had gone into neurons, along with the temperature of the brain vs the energy ranges we've examined with colliders, it seems super unlikely.

If it helps, Turing machines with n-dimensional tapes have been proven equivalent to the basic Turing machine.

The 'infinite tape' issue is a red herring that sometimes appears in discussions about these issues. Real computers (such as the one I am typing this on) are informally described as 'Turing equivalent' because they can implement a Universal Turing Machine up to the limitation imposed by their finite memory. An alternative way of looking at it is that their model of computation, augmented with unbounded memory, could implement or simulate a Universal Turing Machine.

This is not the equivocation that it may appear to be, as it establishes a sort of asymptotic boundary between what is possible and what is not (the more memory we have, the closer we can get to it.) It also means, for example, that we don't have to wonder if there is one computer instruction set or architecture that can perform computations that are impossible by another (again, up to having sufficient memory to complete it.)

The author of the claim you are questioning has not, so far, returned to explain what he means, but I think he is saying that the brain is Turing-equivalent in the informal sense given above: we can compute like a Turing machine, up to the available tape/memory (though with a very limited tape, if we are not writing things down...)

If that is so then I (one of the people here criticizing the article) must say that I don't think it is relevant. An alternative interpretation of the statement, that it says it has been shown that that there is a Turing machine equivalent to the human brain, would seem to depend on believing (as I happen to) that the brain's functioning is a matter of electro-biochemistry that could, in principle, be simulated by a computer, but no-one, so far, has given a demonstration, or even a convincing explanation, of how that works at a Turing-machine level of abstraction.

With regard to the quote you offer: I think it is a simple case of rhetorical overreach -- one might need to know the entire history of that brain to fully understand everything there is to know about its current state, but that does not mean that, absent that full history, the state is meaningless. In understanding what a person is thinking, what they remember (which is an aspect of their brain's state) is more important than what actually happened.

I’m a mathematician and tend to take things literally. I should not have mentioned the infinite tape part. What I should have said is that according to the article we don’t store memories in the way that a Turing machine does. There is no tape as such and there is no set of rules that the brains abides in terms of how to do the next step so to speak.

I gathered that the quote I referenced means that the state of a brain at time t is not sufficient to reconstruct memories or other meaningful information. The fundamental point of contention between you and others criticizing the article appears to be that you all believe that there is a storage mechanism in the brain in a similar (analogous?) fashion as a computer. I gather the author claims this is not so. Information is not stored in neurons in such a way that one “retrieves” it by accessing a storage location.

I don’t know enough about this stuff to intelligently comment on the veracity of it. I just know that someone far more knowledgeable than me and just about everyone else commenting says that our intuition about how this stuff works is wrong. That alone is worth causing me to reconsider my intuition on this stuff.

Speaking for myself (I don't necessarily agree with everything that has been said in opposition to this article), I think you are missing my point about memory.

The author is saying our brains do not function like our digital computers, something I think we do all agree on. It is not so clear how the author thinks our brains do work, but he apparently wants us to stop using computer metaphors when discussing their function.

He would have this prohibition extend to the notion that our brains store and retrieve information, which is absurd; one might as well argue that a computer is not a Turing-equivalent device because RAM is not a tape. The author says that scientists will never find copies of words or grammatical rules in the brain, and if, by copies, he means coded in something like UTF-8, then that is, of course, true, but beside the point: if his brain did not have some mechanism that supports the storage and retrieval of this information in some manner, how was he able to write the article in the first place? He claims you won't find copies of Beethoven's 5th. symphony in a brain, but I suspect that at least Beethoven himself, and many conductors of the piece, have had just that - and the soloists who play his piano concertos are not reading from a score, so where does that come from?

I think the author may have ended up making these absurd claims because he is trying to use the trivial brain-does-not-function-like-a-computer argument to prove something that is just an unargued-for intuition: he doesn't seem to think RAM (or perhaps any form of physical information store) could possibly be the foundation for something that works like human memory. He is apparently unaware of the extent that software such as neural networks (or even relational databases) have already extended the concept of information storage and retrieval beyond the simple model of randomly-addressable bytes (which does not, of course, make the point that human memory is like a computer's; what it does show is that the author's low-level comparisons are insufficient to make the larger point he is trying to squeeze out of them.)

My take on the article and in particular the quote that I referenced in my original post is that the author does not think memory is stored in the way that you and I think it is. The way I think of the brain working with regard to memory is analogous to how computers store information. I’m unable to model it in any other way. But then there’s the quote in the article that even if I had a snapshot of the brain at time t I would not be able to reconstruct something meaningful without knowing the history of that brain’s owner.

I don’t know enough to understand how that is possible or why someone knowledgeable about this stuff thinks this. I have basically the same conception of the brain and how it works as you do. But I’m confronted with the fact that a person far more knowledgeable than me thinks otherwise. It is that fact that causes me to persist in my view with caution. The author may be a crank. I don’t know.

This seems like a really fine distinction, but it's more of an unbounded tape rather than an infinite tape. The tape can only reach infinite length after infinite time.

True, but for a finite-tape machine, the possible outcomes include 'ran out of tape'. Also, for any finite-tape machine, there is a finite-tape machine that computes whether the first halts, runs out of tape, or runs forever.

> If true this seems to me (very much a non-expert) to give serious doubt to the notion that the brain is a computer.

Yeah. It also puts Quantum Mechanics into serious doubt...

So, I'll wait for better evidence than some random person on the internet thinking it feels right.

If I’m the random person you are referring to then you should not rely on evidence from me. My conclusion was based on what was written by the author of the article. I quoted from the article. You may want to rely on what the author says or on another expert. I did state that my opinion was a non expert one. The quote I made said that even if one had a snapshot of the current state of a person’s brain that would be meaningless without the full history of that brain’s owner. That’s a pretty damning fact if one wants to think of a brain as a computer.

I see from another comment that you disagree with the author. I’m guessing you aren’t an expert in this area either. Do you have more than visceral reasons to doubt the author’s conclusion? The author’s credentials seem to imply that he has thought about these issues far more that you or I. He presumably knows much more about how the brain works than you do. Why do you think your few minutes of thought on this article are enough to discount what he says and his conclusions? Isn’t that a bit arrogant?

Well, your comments are both much more reasonable and deserve much more confidence than the article. But no, not your comments, not the article, and not the quoted neurologist even assuming the article's author understood him correctly (what would be an exception) are enough.

That kind of claim requires a clear and reproducible effect, and confirmation of many people that they looked and found the it. That's the kind of claim that if I did an experiment and got the result myself, I wouldn't still trust it.

I understand your position better now. Thank you.

The quote I made certainly goes against my intuition. But I’ve not studied the issue and don’t know enough about it to trust my intuition. Apparently though there are people who have studied this at the level of an expert and they believe it. At the very least this indicates that possibly my intuition is wrong and that I shouldn’t be so ready to discount the article.