We did not have this mathematical framework before the age of Turing, Church, Russel, et al.
This doesn't mean that brains are very similar to CPUs, they are not, just like they were not similar to mechanical machines before.
Yet we do now have a way of studying the similarities they have.
What does matter is whether CPUs are theoretically able to achieve all the things that a brain can do (and even more) And indeed CPUs as turing complete, programmable machine are a strict superset of what brains can do. The gap between what task and at which accuracy a brain achieve vs a CPU is decreasing each year as you can contemplate on the paperswithcode.com leaderboards. The difficulty is in software, hardware through clusterisation has arguably order of magnitude more compute than a brain has.
There are four big missing pieces to match human brain performance:
1) Matching its pattern recognition abilities I believe that current statistical learning techniques of SOTA neural networks actually outperform humans on learning continuous data. But humans outperforms by far current software at zero/few shot learning on sparse/discrete data (where gradient descent is not applicable) I believe humans have this performance edge because of 2), 3) and 4):
2) humans can encode and decode meaning with great accuracy in a high level, descriptive complete declarative language called natural languages. They are in many ways far superior to current GQL/datalog/SQL DB languages at encoding and retrieving meaning (that is an isomorphic description of a denoted thing). The field of semantic parsing (+ question answering from the parsed knowledge) is the key to general language understanding and crucially lack funding. Once machines will be able to understand language and retrieve all the knowledge of say Wikipedia, they will be able to transcend human performance on many intelligence/erudition tasks.
3) humans seems to be able to do meaningful runtime code generation.
That is you can develop on demand new solutions to new problems: such as https://www.kaggle.com/c/abstraction-and-reasoning-challenge The field of specification and implementation generation is too underfunded.
4) is the observation that 3) is probably a necessary key for unlocking 2) and that both 2) and 3) are needed to achieve this communication/feedback loop between high level semantic reasoning and statistical operations.
As we can see, humanity overfocus funding on 1) despite being the most solved of all others necessary foundation's to achieve AGI and hence, as a side effect, empirically prove that CPUs superset brains
Turing completeness implies infinite recursion, which the brain obviously can't do.
There is a subtle difference between unbounded recursion, which a Turing machine is taken to be capable of, and the actual ability to achieve infinite recursion. In no application of a Turing machine, either as an actual physical device or as a hypothetical one in a logical argument, is it ever required to perform infinite recursion, which would just be one way of not halting.
For all practical and theoretical purposes, what matters is that the machine being considered does not exhaust its ability to recurse while performing the computations being considered. Consequently, the standard practice, of saying that computers and certain other devices are Turing-equivalent, with the usually-implicit caveat of being so up to the limit of their recursive ability, is both reasonable and useful.
You're right, and thanks for the more strict definition.
Regardless, the 'recursion limit' of the human brain is really low. (Say, seven things at once or thereabout; not going to links proofs but it's a non-controversial statement.)
Certainly not enough to implement any sort of computing machine. Human brains are notoriously bad at arithmetic and state machines.
But also, the claim lacks evidence: We’ve never seen a human being yet whose program didn’t eventually halt.
That doesn’t mean the hardware isn’t capable of running a program that never halts, just that we haven’t found such a program yet.
Indeed if you consider human mindware as a whole, given that when humans reproduce they create new copies of the mind running in new bits of hardware... maybe Human minds are infinitely recursive after all?
However this is forbidden by Bekensteins bound, so unless modern physics is horribly broken it’s ruled out at least in any sense visible to us even in principle.
However, for anything operating at human temperatures we can reasonably assume that any effective behavior can be simulated by discrete operations, as any nuances of fundamental analogousness would be drowned by thermal noise and the amount of precision that any behavior can require is rather low, much lower than e.g. any standard floating point number in a discrete CPU.
I was thinking more about what's going on in the brain. We have all the regions mapped to specific functions with higher and lower level parts. The low level parts seem to be like hard-wired stimulus-response mechanisms. Are the higher level systems the same at a meta level or is there a type of program running on the hardware of the brain?
Anyway, that wasn't really what I was asking about. Is there any separation between the biological hardware of the brain and the instructions of software?
It is not proven in any way. Turing's postulate is just a postulate, it is not even a theorem, just a conjecture. And AFAIK it cannot be proven, actually.
This is a fundamental assertion that I do not believe you can make.
The brain cannot simulate a turing machine. It does not have infinite memory, which is a requirement for a turing machine. It can, however, stimulate a linearly bounded automata.
It is also not implicitly obvious that a turing machine can simulate a brain. The primary difficulty that I do not yet see a way around is the fact that a turing machine, which has as its control unit a finite State machine, is bound by the finiteness of those states (finiteness of representation, not of number). The brain has no such constraint. It is analog, and therefore infinite in State representation.
In my opinion, this is more akin to the P versus NP problem, and that we know what needs to be equivalent in order to say that P equals NP, but no one has proved it or disproved it yet. That's how I feel about the statement about Turing machines and the brain. I do not believe we can be dogmatic on that aspect yet either way. We may have opinions, just as we may have opinions about P vs NP, but we must also be careful about stating what is provable and what is opinion, and that is all I'm trying to do.
Of course, I am willing and very interested to gain more insight in this area, so discussion is welcome!
In practice we call modern computers turing-complete even though they don't have infinite memory. The brain can simulate such a machine.
> The brain has no such constraint. It is analog, and therefore infinite in State representation.
If this mattered, then it would mean analog computers are more powerful than digital computers and therefore the Church-Turing thesis is wrong
The reason that it's difficult to apply in regards to the brain is that we don't exactly know how the brain is computing... or if it "computes" at all! To my knowledge, we don't have a model of computation for consciousness, emotion, free will, Etc.
Perhaps these are better classified as emergent Behavior rather than computation, but if that is the case I still don't know of a model explaining what computations or rules give rise to the emergent Behavior.
Perhaps the problem is in our definition of computation and what it means to compute.
We do know that the cardinality of the set of possible computational problems is larger than the cardinality of the set of all possible Turing machines. This is provable by simple diagonalization proofs.
The question, then, is whether or not the computations of the brain fall Within the set of Turing recognizable languages (computational problems). To my knowledge, this has not been shown.
A Turing machine can run a simulation based on such physical laws to any desired level of precision (which is enough, because as mentioned in TFA, processes in the brain aren't individually very precise). This is true because of the nature of these laws, which are mostly just asking you to integrate differential equations. If you accept this, then it should follow that a Turing machine can in fact simulate a brain: just run a physics sim on a brain's initial state.
(I do realize that this is far outside the realm of what's doable today, but it seems to provide a solid justification for why it's conceptually possible).
It is possible that the brain's imprecision (I would argue that "inconsistency" might be a better word) is a requirement of it's computational ability. Again, we haven't defined how the brain computes, nor do we have a model for explaining its computation, encoding or representation of knowledge, or emergent behavior. We have observed phenomena related to some of these things, but we are far from understanding it. It may be that the computational processes are dependent on the surrounding environment. We know that the biological processes are influenceable by the physical world, but we do not know much about how these external forces affect, limit, or are required for, the process of brain computation.
The quantum world may play a part in consciousness (or no, we don't know). Non-determinism may play a part. It is possible that, in order to simulate a brain, one would have to simulate the entire universe around it in order to predict the behavior... meaning that it may well require a universe to perform the simulation.
Which brings us to a related theory of whether or not we are living in a simulation, but I digress... :)
Is it possible that brain is in fact a quantum computer? I can imagine that under all those neural networks there is a small part where, trapped in some complex protein structure, some qbits exist and are crucial to most advanced brain functions, such as consciousness.
It's an interesting thing to ponder.
Quantum computing is still just another computational model, and it's main Advantage is that it involves non determinism. But non determinism, in and of itself, can be modeled by deterministic computer.
I think the biggest problem is that we don't understand what computation is taking place in the brain, or even if it is "computation" according to our current definition of the word. I think that this issue is the biggest problem in reconciling whether or not it is possible to accurately model the human brain.
Well, we know certain approximations of those laws. Purely theoretically, it is possible that the exact laws at some level of detail that we have not yet been able to observe involve functions that are not computable by a Turing machine, and then it is theoretically possible that the brain itself is computing functions which are not computable by a Turing machine (this would of course assume that the Church-Turing thesis is actually wrong).
As long as the Church-Turing thesis is not proven, we can't say with absolute certainty that the physical world can be simulated to any level of detail by a Turing machine.
Furthermore, even if the Church-Turing thesis was proven, is it possible that the physical world involves transformations that are not even computable at all (even if they can be approximated by computable functions)?
Just to be clear, I do not believe these things. But it is fun to think about the limits of our knowledge.
What part of the experiment in the paper released did you feel like was inadequate?
> The brain has no such constraint. It is analog, and therefore infinite in State
Not necessarily infinite. A lot of people believe that nothing in the world is truly infinite (just very large/small). Infinite quantities in mathematics are just approximations that simplify calculations.
This is a common misconception.
I'm sure you are aware that analog signals can be approximated by digital values -- a 10 bit ADC will read a channel to one part in 1024, etc.
You might say that even a 64 bit representation is a poor approximation of a real life signal, which is a real number with infinite precision... But it isn't.
The brain operates at about 300 Kelvin, and so there's a noise floor to all analog signals of about that times Boltzmann's constant, or 10^-20 J. If a neuron impedance is 1 ohm, and at a bandwidth of just 10 kHz, the thermal noise is about 1 nV. For a membrane potential of 100 mV, that's a maximum possible noise to signal ratio of one part in 100 million, which is 26 bits.
Now the brain could depend on the signal below the noise floor, but if so those would be extremely fragile operations, and you could get the same thing on a computer by padding your numbers with random data.
I think there is at this time no indication human brains are in any way similar to CPUs. It might be interesting to consider the question, of course.
The point is, I think, people from the steam engine era had similar reasons why the mind/soul was exactly like a steam engine. I won't try to reproduce them here, but I'm sure there were convincing arguments at the time. Who has the awareness to claim, before the current fashionable technology becomes unfashionable, that maybe no, the brain is not a close match for an information processing machine? ;)
If the brain does something that is not computable, that's a direct challenge to some of our most established science. It is possible, but I think very unlikely.
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.
If a brain cannot be produced in a turing machine, it must perform some non-computable activity. That would mean physics cannot be accurately simulated in a computer, which I believe would be earth-shaking in that world. That brains can be reproduced in a simulation is a default assumption, that something composed of molecules can produce outcomes that cannot be computed is an extraordinary claim, for which, I believe, there is no evidence.
The first of your big missing pieces starts from the best that we have been able to achieve with computers so far, and while its completion might be a big step in computing, it would not necessarily be a big step in understanding the human brain - after all, quite primitive animals have impressive abilities in this regard. Using the best computing has done as the yardstick for quantifying the human brain's ability is the wrong way round.
The remaining missing pieces are vague, with no clear indication that they fit into the brain-as-CPU model. For example, while it is true that "[human languages] are in many ways far superior to current GQL/datalog/SQL DB languages at encoding and retrieving meaning (that is an isomorphic description of a denoted thing)", this vastly understates the capabilities of language. Once again, you are using current technology as the yardstick, with no basis for assuming that it is of the right scale.
Overall, you seem to be assuming that the rest of the puzzle is almost within reach. That is certainly a logical possibility, but not one with a great deal of objective evidence in support. FWIW, my opinion on the matter is that we probably don't even know, in any well-defined way, all the questions to be answered.
Even if we grant the premise that a suitably-programmed computer (not just a CPU) could have capabilities that are a superset of those of a human brain, that would not necessarily justify saying one is very like the other - that would be like saying a dynamo is a solar cell because they both produce electric current.
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".
Proven? Nothing in science is ever proven.
But on half a millenium we have failed to find anything that can't be simulated by math, and Turing completeness means a computer can simulate anything that can be simulated by math. We also can simulate all the smallest components of a brain.
At this point the claim that math can not simulate it is highly extraordinary.
Technically, it is not proven that Turing machines can compute all computable functions, so there is some purely theoretical possibility that the brain could be able to compute functions that a Turing machine can't.
Personally I find that extremely unlikely, and agree that it would be extremely surprising. But it wouldn't invalidate anything we have proven so far.
Can an "arbitrarily advanced computer do everything a brain can do?" Empirically, right now, current machines can't but we are talking about "future machines, via line-of-sight extrapolation". Not fundamental leaps in tech, but incremental ones. It seems plausible, but it seems we expand the depths of the complexity of the requirements nearly as fast as we advance current capabilities. I don't know, but I'd put my money on the technology catch up.
As others already replied, that’s a statement that isn’t universally accepted to be true.
As an example, there’s consciousness. People disagree about whether it exists, whether it’s (fully) ‘in’ the brain, and on whether computers could in theory be conscious.
There are people who answer those questions with yes, yes, and no, and, since we don’t even have a good idea about what consciousness is, one cannot reliably argue that they are wrong (also not that they are right, of course)
Edsger Dijkstra, EWD898, 1984
I am ignorant in this area. But I keep reading how brains are nothing like computers the more we learn. Your statement seems to suggest otherwise and id love to read about it. Can you drop something where I can start exploring about how the brain has become more evident that it's merely a kind of computer? Thanks!
1. There is nothing going on in the brain that would require simulation to infinite accuracy. Not even a chaotic system would have this property, because they take a finite time to "blow up" an initial uncertainty, and the smaller the initial uncertainty the longer they take to blow up. For this proposition to be violated there would have to be an undiscovered fininite-time nondeterministic blowup, which is unlikely, but I've heard rumblings that we haven't proven that it can't happen in Navier-Stokes. So maybe it can happen in the brain.
2. There is nothing going on in the brain that depends on nuclear physics or anything more "powerful" than quantum electrodynamics.
I have not seen any evidence that 1 or 2 aren't true for the brain, so that puts something behind saying it's "merely a computer."