I'm not familiar with Penrose, but he would be wrong if he meant that the incompleteness theorem can be defeated by biological brains. Only way to know whether a statement is true or not is through the application of formal logics. It's merely a belief if it is not proven. If he meant that human brains are capable of beliefs, well, electronic ones are capable of that too.
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Unutmaz post about AI model use for MECFS
- Thread starter Jaybee00
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Utsikt
Senior Member (Voting Rights)
LLMs are not good at maths.
LLMs would also have to be able to consistently translate between symbolic representations of logic (e.g. words) to the sub-symbolic values that neural networks consist of (nodes with values between 0 and 1). And understand and conserve the logical relationships between all of the entities. They are currently not very good at this.
Penrose's argument is not about humans being able to overcome completeness or consistency or that Turing machines are unable to handle arguments in ZF set theory, but rather that "proper AI" can't exist because human minds don't work algorithmically in the way computers do. You might say Turing machines lack "mathematical intuition" or that humans can work in between logical systems rather than being stuck to different systems or simply that there are a priori differences that can't be overcome. So you can still have an AI that is better than humans at basically everything, including mathematics, strategy, medical diagnosis, writing papers, summarising, writing poems, writing novels, composing music etc without it being "proper AI". Gödel's argument about a Gödel sentence existing and being true but unprovable relates to this in the way that if there is a formal system covering mathematical thoughts it would be consistent and thus the Gödel sentence ought to be true. He concludes that humans would be able to see that this sentence ought to be true, but that this process involves our mathematical thoughts and as such leads to a contradiction since this system doesn't contain the Gödel sentence. The conclusion is thus that a system that governs our mathematical thought cannot exist. But there are problems in relation to this argument relating to completeness that I have forgotten and never properly understood in the first place. But since Penrose is much smarter than me and has thought about these things with great care he will have thought about this as well. The argument is anyways not really the point, because Gödels theorems only apply to specific systems and I don't think anybody takes the argument very seriously. It's more there to illustrate something.
That isn't really related to LLM's who are of course capable of writing down the first incompleteness theorem and proving it of course. You don't need LLMs, neural networks, reinforcement learning or anything else for that, enough monkeys or a random symbol generator will do the job just fine. The general idea however seems to be that the mind is such a complex thing, that it is reasonable to assume that it is not computable. That's also my understanding of what the Chomskyans think who I think don't agree with the Penrose argument but still agree that the human mind works differently to a computer in a meaningful way. That is completely independent of whether you give your neural network a super complex topological structure, throw some probabilistic methods on it decided by the spin of a particle or what not else can be done. The argument is that there is a fundamental difference even before you start doing all of those things. Adding complexity doesn't overcome that.
I know there are some complicated theorems that state that for any neural network there are certain recursions that cannot be reached and my understanding is that whilst in practical terms the limitations for humans are much larger in theoretical terms there don't seem to be theorems for such limitations. You might say that humans are smart and lack computational power whilst computers are the opposite. Now you can argue that neural networks are not the end of it all as is it bounded in the complexity it can achieve. In practical terms, the limit of complexity the human mind is able to understand, I would think would be far smaller and some of Penrose most brilliant colleagues, such as Peter Scholze see a large need to verify their own work via things such as Lean, because the thought processes are already too complex to know whether their own proofs of their own ideas are correct. These things can be handled at ease by computers even if they have theoretical limits humans needn't have. There is no reason why the human mind has to be computable and there are no reasons to think that LLMs, NNs or else work in the same way just because they sometimes yield the same results.
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Jonathan Edwards
Senior Member (Voting Rights)
You should read Penrose's books. The argument is significantly more sophisticated than that but a bit abstruse. It rests largely on Penrose's own ability to prove a geometric theorem about infinite tiling must be valid despite the proof being uncomputable. I don't think there is any suggestion that the incompleteness theorem is defeated, rather that it is essential to the argument.
I am not sure that logic can show anything is true though - just logically valid, which is a far weaker requirement .
That is what I'm not convinced of, and I'm not aware of theorems that say so. That we don't know completely how the brain works does not mean that there are fundamental differences that cannot be breached. There already are claims of emergent behavior, and AI may eventually become organic or indeterministic, or at least appear to be, if that's what "proper AI" means. If plasticity is the issue, that can be emulated too.
Human mind ultimately deals with information, and information means computing. Sure, it computes differently from a Turing machine. But so does AI. That it is based on Turing machine does not mean it computes like Turing machine. That would be like saying the brain works like a cell because it is made up of cells.
Maybe the current crop of NNs indeed have limitations, I don't know. The question is though, whether there is anything fundamental that prevents the emulation of brain's intelligence on non-biological media. I'm not convinced of it, but I'm always ready to change my mind if somebody shows otherwise!
I'll have to. I haven't read a single book in the past 15 years, but I should get back to it now that I got my brain back.
True, a statement can be valid but not true. But axioms are considered a priori in abstract sense. The set would be much narrower if you accept only human experiences as the truth.
Mij
Senior Member (Voting Rights)
The chronic disease I mentioned below was chronic fatigue syndrome, or ME/CFS, a highly debilitating and heterogeneous disorder somewhat similar to Long Covid; thus, every patient presents slightly differently.
My friend performed mass-spec analysis of proteomic expression in this patient, which allowed Grok to identify an effective and very specific anti-inflammatory treatment. Also, my use of the word “cured” was overly strong-it’s unclear if the patient is completely cured yet-but the patient feels great for the first time after many years of suffering.
AI will have its greatest impact by personalizing treatments and diagnoses as in this example, which is truly the holy grail of medicine.
https://twitter.com/user/status/1902497336552833449
My friend performed mass-spec analysis of proteomic expression in this patient, which allowed Grok to identify an effective and very specific anti-inflammatory treatment. Also, my use of the word “cured” was overly strong-it’s unclear if the patient is completely cured yet-but the patient feels great for the first time after many years of suffering.
AI will have its greatest impact by personalizing treatments and diagnoses as in this example, which is truly the holy grail of medicine.
https://twitter.com/user/status/1902497336552833449
Mij
Senior Member (Voting Rights)
My close physician friend just messaged me-this is amazing: He had been following a patient with a chronic disease for many years, trying various treatments to no avail. He recently uploaded all the data to Grok, which suggested a specific treatment. Now, the patient seems cured!
https://twitter.com/user/status/1902381963111014819
https://twitter.com/user/status/1902381963111014819
Mij
Senior Member (Voting Rights)
I link I posted before that mentions that it was an ME/CFS patient. FWIW
Mij
Senior Member (Voting Rights)
I'm sorry but I was the one that confused you and should have posted it in sequence.
@Jonathan Edwards was negative-ish on anakinra
https://www.s4me.info/threads/germa...th-post-acute-covid-syndrome-precision.41474/
https://www.s4me.info/threads/germa...th-post-acute-covid-syndrome-precision.41474/
I can't see where it says the drug is Anakinra
From his post
“I was hesitant to share the treatment, but I received permission from my friend. The treatment was Anakinra, which inhibits a cytokine called IL-1 that is highly pro-inflammatory. However, this treatment could be highly specific to certain patients, as mentioned earlier, and may not work in many, since ME/CFS is a heterogeneous disease. It’s remarkable that Grok identified this treatment and that’s the whole point!”
“I was hesitant to share the treatment, but I received permission from my friend. The treatment was Anakinra, which inhibits a cytokine called IL-1 that is highly pro-inflammatory. However, this treatment could be highly specific to certain patients, as mentioned earlier, and may not work in many, since ME/CFS is a heterogeneous disease. It’s remarkable that Grok identified this treatment and that’s the whole point!”