That's of course true, but then most computers aren't that similar to a classic Turing machine either. The idea of Turing machines is that they can simulate anything else that we mean when we say "computation".

> Can a Turing machine simulate a brain - as in, create intelligence like the one our brains expose?

Yes, it can. I mean, if it can't, that means there's some notion of "computability" that a Turing machine doesn't capture - this would violate the "Church-Turing" thesis. Such a thing is possible, of course, since we have no proof that a Turing machine is the limit of what we mean by "computable" - but it would be a completely revolutionary fact in Computer Science, and one that is very unlikely, considering how many years people have been trying to come up with alternative models of "computation" that all turn out to be equivalent to Turing machines.

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The human brain isn't magic - it works according to the laws of physics like anything else. Either it is simulatable by a Turing machine, which would make the most sense, or it isn't, in which case we're missing something about how you can compute things, which would be surprising and amazing.

Because biological neurons are not computers? I think the argument is that our current theory of computation is not enough to explain the human mind, not that human minds are magickal and special compared to other computational devices. We just happen to understand one category of computational device that does not include human minds.

I think if we look hard enough we can find examples of computational systems that exist in nature and that are not Turing machines. For examples, a weighted chain forming a catenary can instantly calculate the shape of a load-bearing arch, without going through any states: it suffices to set up the computational system (the weighted chain) and the result of the computation (the shape of the arch) is immediately known.

Meaning, "there are more things in heaven and earth that are dreamt of" in our computer science. Our mind is probably the biggest fucking mystery in all of existence and it is a little ridiculous to think we can understand it, and simulate it, with our primitive science and technology.

Short of building such a machine I can’t see how you’d produce evidence of that, let alone “concrete” evidence.

Regardless, we don’t know of any measurable physical process that the brain could be using that is not computable. If we found one (in the brain or elsewhere), we’d use it to construct devices that exceeded the capacity of Turing machines, and then use those to simulate human brains.

You'll see in my comment and your quote that I don't say the brain can't compute. I agree, the brain can compute. But that doesn't mean it is a computer, because computing is an ability. People can do many other things aside from computing, none of which rely on computation, for instance they can imagine, which is the ability to think new thoughts. Computers can't imagine because all they do is compute: that's their programming. No amount of programming can produce imagination. Computation and imagination are categorically distinct as different intellectual powers and abilities.

You are conflating an ability with ontology. We know what a brain is. It's a collection of fatty material with neurons that do not explicitly fire exactly like a computer. Key word there is like. Church-Turing built a model of computational logic off of intuitions about the brain and formal mathematical logic. That's it's not provable doesn't prove your point; it removes any distinction between it being right or wrong: because it is a model (lets make something like the brain).

That an industry was built on computation doesn't prove anything. We know computation is an ability. For instance it's also something we can do with abacuses. We could have built an enormous industry on building elaborate abacuses. We built computers do be extremely fast at computation. We didn't build computers to be brains.

You'll notice, if you read the review, that the author of the review repeatedly cites cognitive neuroscientists, even evangelists of the singularity, philosophers, psychologists, and zoologists, who have published at length on this topic and repeatedly critcise and disrupt the simple idea that the brain is a computer or an algorithm or even a machine. An entire branch of philosophy developed off of Ludwig Wittgenstein to counter the computational model of consciousness. Numerous books in the Philosophy of Mind argue that the assumption that the brain is a computer is not just unsupported, it is logically nonsensical.

I think, rather, it reveals the fundamental lack of clarity of the contrary position.

> e.g., the brain is computer because everything is a computer, including the nearest rock, since it's also a physics-governed system.

Right. But no one is questioning the ability to build a computer that simulates the behavior of a rock; or most other physics-governed systems. The AI-is-impossible position boils down to the argument that the mind is not like all other physics governed systems, though it tends to waffle and hedge and bob and weave around that point rather than coming right out with it. Pointing to Turing equivalence and the apparent computability of natural phenomena forces the AI-is-impossible-because-the-mind-is-not-the-kind-of-thing-a-computer-can-simulate argument to come straight out and either (1) reject the universal computability of physical systems, or (2) reject the mind as a physical system.

It still, of course, leaves plenty of room for the proposition that AI is possible but really quite hard.

Again, please point to any research you know of indicating that the universe itself is fully Turing-computable.

The brain can compute. That's extraordinary. I say one type of thing does that, computers. You say no, two things, computers and then also brains. But when pressed to explain what is a brain if not a computer you'll just sputter (probably at length) without offering any substance.

In a sense that's the wrong way up to explain it. Church-Turing intuitively defines computation (the things computers can do) in terms of what our brains can do, so the match is not a coincidence but it also isn't there for the reason you probably expect. Because it's an intuition Church-Turing isn't provable, but you may notice that we subsequently built an _entire world-changing industry_ upon it in a lifetime.

You pointed to a review, others have written entire books, always they can be summarised as simply arguments from incredulity. "What? Nonsense, the brain can't be a computer, I simply won't believe that". It's unfortunate that we have woken such people from their daydreaming, I have no doubt that if similarly aroused they'd give the mathematicians what for too, "What? Nonsense, how can there be numbers which aren't ratios of whole numbers, I simply won't believe it".

I mean, there's nothing physically stopping us from simulating a brain, right? It's a finite object with a finite amount of physical ingredients, and therefore with a finite amount of computing power we can simulate what it does. To me personally, that's a computational process. Maybe that's an overly broad definition of computation, but I think these debates tend to be about whether there is something fundamentally different about "life" (by which I assume you include consciousness). But maybe that's not what you're saying.

> He points out that "if we are to suppose that the brain is a digital computer, we are still faced with the question 'And who is the user?'"

What does that question even mean? I think it seems deep because we humans have a tendency to ascribe some sort of supernatural aura to our lived experience. Life is something incredible but that (at least to my knowledge) is not uncomputable...

> There is no computational process that will produce the sensations of colour or sound or touch.

Got one: the brain!

> At best you will have some representation that requires having actually experienced those sensations to understand it.

Why does a computer not "experience" something?

This is not true.

I wish I could respond with something more interesting, but that's all there is to it. You are just saying something that is incorrect. Our brains are information-theoretically and complexity-theoretically entirely reasonable.

That is definitely false. "In computability theory, a system of data-manipulation rules... is said to be Turing-complete... if it can be used to simulate any Turing machine." [0] A Turing machine has infinite memory; the human brain does not.

[0] https://en.wikipedia.org/wiki/Turing_completeness

Correct me if I'm wrong, but wouldn't a system that computes a non-recursive function be some sort of box where, given the same inputs, you invariably obtain the same outputs; however there is no way of finding any mathematical or algorithmic expression that could, in any finite amount of time, predict the same result? To find yourself in that situation, you need a physical process that is intrinsically non-computable; being unable to compute the sum of computable processes is not enough.

Then why do you think it's a hypercomputer? These are all classical physical effects. What math problems do you think the human brain can solve that a Turing machine with sufficient time can't?

Our brains are fallible, and so only approximately equivalent to Turing machines; and even ignoring that can only compute every computable thing given both infinite error-free storage capacity (which they don't have internally or externally) and sufficient time to execute the necessary steps of the computation.

Realistically, there are computable functions which no human brain will be ever be capable of computing.

Whether being able to compute a thing is sufficient, necessary, or tangential to understanding it is also a question.

This is just my thinking: a turing machine, or equivalently a digital circuit, doesn't want anything. It's an artificial construct, effectively a simulation, that can exist as an abstract mathematical idea.

If there is a real world where real stuff happens, real things have their own goals - generally increasing entropy or minimizing energy. Although it seems like we should just be able to capture this mathematically, in doing so, we remove the actual desire... this sounds a bit nutty maybe, but what else is the difference between reality and simulation? An abstract calculation, anything equivalent to a Turing machine has no skin in the game. Something happened in the universe does - and this could include conciousness, as a property of matter, which for example could be effectively sum of the compulsions of the composing matter to minimize their energy (you can look this up, there are theories about conciousness that posit it's a property of matter).

If there is no difference between reality and a simulation, I'm wrong, we can all be represented on a universal computer, and so as abstract math, and in some sense existence is meaningless it just follows from math. My experience doesn't support this, but presumably I would have evolved a blind spot if my existence actually was meaningless.

TLDR, I think there is some undiscovered difference between reality and simulation, that I would guess relates to desire / conciousness, that means we can't simulate conciousness or real intelligence

I'm a scientist, I know the above doesn't withstand any scrutiny, I'm just trying to share my speculation because you asked

I agree with your main point, however I don't find this a compelling argument. Regardless of what our brains are constructed for, with pen and paper and a set of rules we can roughly approximate a turing machine. Everything we as humanity know about computation suggests that at minimum this is equivalent to any computation possible using all known physical properties & interactions with some amount of overhead (even quantum can be simulated classically).

Thus, while it's possible there is an unknown kind of interaction that we cannot understand or simulate classically, the fact that our brain is more or less designed around survival and reproduction is irrelevant; change or optimize our DNA and the new super-human will still be at best roughly equivalent to a turing machine in terms of computation.

If what the brain is doing is computational, then it's not doing anything more powerful than a Turing Machine could do. There would be some Turing Machine design that could do the same processing.

In what way can this be proven?

It's very tempting in an era of tech-centered growth to think of computers as the solution to everything, but we are barely even beginning to understand the brain. We know computers fairly well and can talk about them, but how can we make such a claim when we don't know the other thing we're talking about?

In fact, the brain created the computer, didn't it? Therefore, from that standpoint it is arguable that the brain is a superset of the computer. It's not something I really believe in (because my opinion is that you can't really equate things that are of entirely different units, one of which being unknown), but just a "devil's advocate".

Must?

It's one thing to observe that the brain appears to do computation, and to have as a working hypothesis that everything the brain does is a form of computation.

It's something else to say that it must be true, when, for the moment, the brain also appears to do things that we have no idea how to make computers do, that we have significant difficulty getting computers to even pretend to do.

Could you? That's sort of begging the question. We do not know if something "Turing complete" can be used to build a brain like the human brain. That's precisely the point.

> If the brain does something that is not computable, that's a direct challenge to some of our most established science.

A challenge for computational neuroscience maybe. Otherwise I don't see the challenge for neither neuroscience nor computer science. If someone wants to make the claim you can build a human brain out of something Turin-machine-like, that's an extraordinary claim, not established science.