[HN Gopher] Godel's theorem debunks the most important AI myth -...
___________________________________________________________________
Godel's theorem debunks the most important AI myth - Roger Penrose
[video]
Author : Lockal
Score : 40 points
Date : 2025-03-02 18:31 UTC (4 hours ago)
(HTM) web link (www.youtube.com)
(TXT) w3m dump (www.youtube.com)
| tmnvix wrote:
| Is anyone aware of some other place where Penrose discusses AI
| and consciousness? Unfortunately here, the interviewer seems well
| out of their depth and repeatedly interrupts with non sequiturs.
| dang wrote:
| It's painful, but listening to Penrose is worth it and (in the
| bits I watched) he somehow manages to politely stick to his
| thread despite the interruptions.
| codeulike wrote:
| The Emperors New Mind - Roger Penrose - published 1989
|
| Shadows Of The Mind - Roger Penrose - published 1994
|
| https://en.wikipedia.org/wiki/Penrose%E2%80%93Lucas_argument
| pfortuny wrote:
| The emperor's new mind is his work on this (not specifically on
| LLMs obviously).
| mitthrowaway2 wrote:
| For those of us without time to watch a video - what is the most
| important AI myth?
| exe34 wrote:
| that carbon chauvinism isn't real.
| qrios wrote:
| The question is answered in the full title:
|
| > "Godel's theorem debunks the most important AI myth. AI will
| not be conscious"
|
| Same statement from Penrose here with Lex Friedman:
| "Consciousness is Not a Computation" [1].
|
| [1] https://www.youtube.com/watch?v=hXgqik6HXc0
| drivebyhooting wrote:
| I feel like Penrose presupposes the human mind is non computable.
|
| Perhaps he and other true geniuses can understand things
| transcendently. Not so for me. My thoughts are serialized and
| obviously countable.
|
| And in any case: any kind of theorem or idea communicated to
| another mathematician needs to be serialized into language which
| would make it computable. So I'm not convinced I could be
| convinced without a computable proof.
|
| And finally just like computable numbers are dense in the reals,
| maybe computable thoughts are dense in transcendence.
| pfortuny wrote:
| I think (but may be wrong) that you are thinking
| metamathematics is a part of mathematics, which (to my
| knowledge) it is not.
| cwillu wrote:
| He explicitly believes that, yes.
| ForTheKidz wrote:
| This is accurate from his Emperor's New Mind. Penrose
| essentially takes for granted that human brains can reason
| about or produce results that are otherwise uncomputable. Of
| course, you can reduce all (historical) human reasoning to a
| computable heuristic as it is finite, but for some reason he
| just doesn't see this.
|
| His intent at the time was to open a physical explanation for
| free will by taking the recourse to quantum nano-tubules
| magnifying true randomness to the level of human cognition. As
| much as I'm also skeptical that this actually moves the needle
| on whether or not we have free will (...vs occasionally having
| access to statistically-certain nondeterminism? Ok...) the
| computable stuff was just in service of this end.
|
| I strongly suspect he just hasn't grasped how powerful
| heuristics are at overcoming general restrictions on
| computation. Either that or this is an ideological commitment.
|
| Kind of sad--penrose tilings hold a special place in my heart.
| drivebyhooting wrote:
| If stories are to be believed real geniuses can tap into
| God's mind. (See Ramanujan)
|
| If so then it really comes down to believing something not
| because you can prove it but because it is true.
|
| I'm just a mediocre mathematician with rigor mortis. So I
| won't be too hard on Penrose.
| tbrownaw wrote:
| > _His intent at the time was to open a physical explanation
| for free will by taking the recourse to quantum nano-tubules
| magnifying true randomness to the level of human cognition.
| As much as I 'm also skeptical that this actually moves the
| needle on whether or not we have free will (...vs
| occasionally having access to statistically-certain
| nondeterminism? Ok...) the computable stuff was just in
| service of this end._
|
| Free will is a useful abstraction. Just like life and
| continuity of self are.
|
| > _I strongly suspect he just hasn 't grasped how powerful
| heuristics are at overcoming general restrictions on
| computation._
|
| Allowing approximations or "I don't know" is what's helpful.
| The bpf verifier can work despite the halting problem being
| unsolvable, not because it makes guesses (uses heuristics)
| but because it's allowed to lump in "I don't know" with "no".
| throwup238 wrote:
| _> Free will is a useful abstraction. Just like life and
| continuity of self are._
|
| I think it's more useful to think of them as language games
| (in the Wittgenstein sense) than abstractions.
| Animats wrote:
| > Penrose essentially takes for granted that human brains can
| reason about or produce results that are otherwise
| uncomputable.
|
| That's Penrose's old criticism. We're past that. It's the
| wrong point now.
|
| Generative AI systems are quite creative. Better than the
| average human at art. LLMs don't have trouble blithering
| about advanced abstract concepts. It's concrete areas where
| these systems have trouble, such as arithmetic. Common sense
| is still tough. Hallucinations are a problem. Lying is a
| problem. None of those areas are limited by computability.
| It's grounding in the real world that's not working well.
|
| (A legit question to ask today is this: We now know how much
| compute it takes to get to the Turing test level of faking
| intelligence. How do biological brains, with such a slow
| clock rate, do it? That was part of the concept behind
| "nanotubules". Something in there must be running fast,
| right?)
| lowbloodsugar wrote:
| > It's concrete areas where these systems have trouble,
| such as arithmetic. Common sense is still tough.
| Hallucinations are a problem. Lying is a problem
|
| Gestures broadly at humanity
| Tuna-Fish wrote:
| > Something in there must be running fast, right?
|
| Nah. It just needs to be really wide. This is a very fuzzy
| comparison, but a human brain has ~100 trillion synaptic
| connections, which are the closest match we have to
| "parameters" in AI models. The largest such models
| currently have on the order of ~2 trillion parameters.
| (edit to add: and this is a low end estimate of the
| differences between them. There might be more stuff in
| neurons that effectively acts as parameters, and should be
| counted as such in a comparison.)
|
| So AI models are still at least two orders of magnitude off
| from humans in pure width. In contrast, they run much, much
| faster.
| sampo wrote:
| > I feel like Penrose presupposes the human mind is non
| computable.
|
| Yes. He has also written books about it.
|
| https://en.wikipedia.org/wiki/Roger_Penrose#Consciousness
| thrance wrote:
| What is "understanding transcendently"? Just because Penrose is
| an authority on some subjects in theoretical physics doesn't
| mean he is a universal genius and that his ideas on
| consciousness or AI hold any value.
|
| We gotta stop making infaillible super heroes/geniuses of
| people.
|
| In this particular case, Penrose is a convinced dualist and his
| theories are unscientific. There are very good reasons to not
| be a dualist, a minority view in philosophy, which I would
| encourage anyone to seek if they want to better understand
| Penrose's position and where it came from.
| saulpw wrote:
| > My thoughts are serialized and obviously countable.
|
| You might want to consider doing a bit of meditation...anyone
| who describes their thoughts as 'serialized' and 'obviously
| countable' has not much time actually looking at their
| thoughts.
| AlexCoventry wrote:
| I watched half of the video. He keeps appealing to the idea
| that Goedel applies to AI because AI doesn't understand what
| it's doing. But I seriously doubt that we humans really know
| what we're doing, either.
|
| IIRC, his Goedel argument against AI is that someone could
| construct a Goedel proposition for an intelligent machine which
| that machine could reason its way through to hit a
| contradiction. But, at least by default, humans don't base
| their epistemology on such reasoning, and I don't see why a
| conscious machine would either. It's not ideal, but frankly,
| when most humans hit a contradiction, they usually just ignore
| whichever side of the contradiction is most inconvenient for
| them.
| cowl wrote:
| > any kind of theorem or idea communicated to another
| mathematician needs to be serialized into language which would
| make it computable.
|
| This is a fallacy. Just because you need to serialize a concept
| to communicate it doesnt mean the concept itself is computable.
| This is established and well proven:
|
| https://en.wikipedia.org/wiki/List_of_undecidable_problems
|
| The fact that we can come up with this kind of uncumputable
| problems is a big plus in supprt of Penrose's Idea that
| consciousnes is not computable and goes way beyond
| compatability.
| drivebyhooting wrote:
| Deciding an undecidable problem is well, undecidable. But
| describing it is clearly not. Otherwise we would not have
| been able to write about it.
| gizajob wrote:
| From where do those serialised thoughts arise?
| CityOfThrowaway wrote:
| He sets up a definition where "real intelligence" requires
| consciousness, then argues AI lacks consciousness, therefore AI
| lacks real intelligence. This is somewhat circular.
|
| The argument that consciousness can't be computable seems like a
| stretch as well.
| pfortuny wrote:
| I do not see the "circularity", it may lack foundation, but
| that is a different argument.
| zuhsetaqi wrote:
| Where's the circle?
| sampo wrote:
| Penrose believes that consciousness originates from quantum
| mechanics and the collapse of the wavefunction. Obviously you
| couldn't (effectively) simulate that with a classical computer.
| It's a very unconventional position, but it's not circular.
|
| https://en.wikipedia.org/wiki/The_Emperor%27s_New_Mind
|
| https://en.wikipedia.org/wiki/Shadows_of_the_Mind
| James_K wrote:
| Consciousness is not a result, it cannot be computed. It is a
| process, and we don't know how it interacts with computation.
| There are only two things I can really say about consciousness,
| and both are speculation: I think it isn't observable, and I
| think it is not a computation. For the first point, I can see
| no mechanism by which consciousness could affect the world so
| there is no way to observe it. For the second, imagine a man in
| a vast desert filled only with a grid of rocks that have two
| sides, a dark and light side and he has a small book which
| gives him instructions on how to flip these rocks. It seems
| unlikely that the rocks are sentient, yet certain
| configurations of rocks and books could produce the thought
| computation of the human mind. When does the sentience happen?
| If the man flips only a single rock according to those rules,
| would the computer be conscious? I doubt it. Does the
| consciousness exist between the flips of rock when he walks to
| the next stone? The idea that computation creates consciousness
| seems plainly untenable to me.
| prmph wrote:
| Indeed, I also think consciousness cannot be reduced to
| computation.
|
| Here is one more thing to consider. All consciousness we can
| currently observe is embodied; all humans have a body and
| identity. We can interact with separate people corresponding
| to separate consciousnesses.
|
| But if computation is producing consciousness, how is its
| identity determined? Is the identity of the consciousness
| based on the set of chips doing the computation? It is based
| on the algorithms used (i.e., running the same algorithm
| anywhere animates the same consciousness)?
|
| In your example, if we say that consciousness somehow arises
| from the computation the man performs itself, then a question
| arises: what exactly is conscious in this situation? And what
| are the boundaries of that consciousness? Is the set of rocks
| as a whole? Is it the computation they are performing itself?
| Does the consciousness has a demarcation in space and time?
|
| There are no satisfying answers to these questions if we
| assume mere computation can produce consciousness.
| aljarry wrote:
| LLMs (our current "AI") doesn't use logical or mathematical rules
| to reason, so I don't see how Godel's theorem would have any
| meaning there. They are not a rule-based program that would have
| to abide by non-computability - they are non-exact statistical
| machines. Penrose even mentions that he hasn't studied them, and
| doesn't exactly know how they work, so I don't think there's much
| substance here.
| pelario wrote:
| Despite the appearance, they do: despite the training, neurons,
| transformers and all, ultimately it is a program running in a
| turing machine.
| aljarry wrote:
| But it is only a program computing numbers. The code itself
| has nothing to do with the reasoning capabilities of the
| model.
| whilenot-dev wrote:
| > LLMs (our current "AI") doesn't use logical or mathematical
| rules to reason.
|
| I'm not sure I can follow... what exactly is decoding/encoding
| if not using logical and mathematical rules?
| aljarry wrote:
| Good point, I meant the reasoning is not encoded like a
| logical or mathematical rules. All the neural networks and
| related parts rely on e.g. matrix multiplication which works
| by mathematical rules, but the models won't answer your
| questions based on pre-recorded logical statements, like
| "apple is red".
| kadoban wrote:
| Pick a model, a seed, a temperature and fix some floating-point
| annoyances and the output is a deterministic algorithm from the
| input.
| layble wrote:
| Maybe consciousness is just what lives in the floating-point
| annoyances
| aljarry wrote:
| That's true with any neural network or ML model. Pick a few
| points, use the same algorithm with the same hyperparameters
| and random seed, and you'll end up with the same result.
| Determinism doesn't mean that the "logic" or "reason" is an
| effect of the algorithm doing the computations.
| northern-lights wrote:
| If it is running on a computer/Turing machine, then it is
| effectively a rule-based program. There might be multiple steps
| and layers of abstraction until you get to the rules/axioms,
| but they exist. The fact they are a statistical machine,
| intuitively proves this, because - statistical, it needs to
| apply the rules of statistics, and machine - it needs to apply
| the rules of a computing machine.
| moefh wrote:
| This argument by Penrose using Godel's theorem has been discussed
| (or, depending on who you ask, refuted) before in various places,
| it's very old. The first time I've seen it was in Hofstadter's
| "Godel, Escher, Bach", but a more accessible version is this
| lecture[1] by Scott Aaronson. There's also an interview with
| Aaronson with Lex Friedman where he talks about it some more[2].
|
| Basically, Penrose's argument hinges on Godel's theorem showing
| that a computer is unable to "see" that something is true without
| being able to prove it (something he claims humans are able to
| do).
|
| To see how the argument makes no sense, one only has to note that
| even if you believe humans can "see" truth, it's undeniable that
| sometimes humans can also "see" things that are not true (i.e.,
| sometimes people truly believe they're right when they're wrong).
|
| In the end, stripping away all talk about consciousness and other
| stuff we "know" makes humans different from machines, and confine
| the discussion entirely over what Godel's theorem can say about
| this stuff, humans are no different from machines, and we're left
| with very little of substance: both humans and computers can say
| things that are true but unprovable (humans can "see" unprovable
| truths, and LLMs can hallucinate), and both also sometimes say
| things that are wrong (humans are sometimes wrong, and LLMs
| hallucinate).
|
| By the way "LLMs hallucinate" is a modern take on this: you just
| need a computer running a program that answers something that is
| not computable (to make interesting, think of a program that
| randomly responds "halts" or "doesn't halt" when asked whether
| some given Turing machine halts).
|
| (ETA: if you don't find my argument convincing, just read
| Aaronson's notes, they're much better).
|
| [1] https://www.scottaaronson.com/democritus/lec10.5.html
|
| [2] https://youtu.be/nAMjv0NAESM?si=Hr5kwa7M4JuAdobI&t=2553
| derriz wrote:
| I think you're being overly dismissive of the argument.
| Admittedly my recollection is hazy but here goes:
|
| Computers are symbol manipulating machines and moreover are
| restricted to a finite set of symbols (states) and a finite set
| of rules for their transformation (programs).
|
| When we attempt to formalize even a relatively basic branch of
| human thinking, simple whole-number arithmetic, as a system of
| finite symbols and rules, then Goedel's theorem kicks in. Such
| a system can never be complete - i.e. there will always be
| holes or gaps where true statements about whole-number
| arithmetic cannot be reached using our symbols and rules, no
| matter how we design the system.
|
| We can of course plug any holes we find by adding more rules
| but full coverage will always evade us.
|
| The argument is that computers are subject to this same
| limitation. I.e. no matter how we attempt to formalize human
| thinking using a computer - i.e. as a system of symbols and
| rules, there will be truths that the computer can simply never
| reach.
| moefh wrote:
| > Computers are symbol manipulating machines and moreover are
| restricted to a finite set of symbols (states) and a finite
| set of rules for their transformation (programs).
|
| > [...] there will be truths that the computer can simply
| never reach.
|
| It's true that if you give a computer a list of consistent
| axioms and restrict it to only output what their logic rules
| can produce, then there will be truths it will never write --
| that's what Godel's Incompleteness Theorem proves.
|
| But those are not the only kinds of programs you can run on a
| computer. Computers can (and routinely do!) output
| falsehoods. And they can be inconsistent -- and so Godel's
| Theorem doesn't apply to them.
|
| Note that nobody is saying that it's definitely the case that
| computers and humans have the same capabilities -- it MIGHT
| STILL be the case that humans can "see" truths that computers
| will never be able to. But this argument involving Godel's
| theorem simply doesn't work to show that.
| gmuslera wrote:
| I've read from Hoftadter "I am a strange loop" that should go
| around those ideas too. The point of how you define
| consciousness (he does it in a more or less computable way, a
| sort of self-referential loop), so it may be within the reach
| of what we are doing with AIs.
|
| But in any case, it is about definitions, not having very
| strict ones for consciousness, intelligence and so on, and
| human perception and subjectivity (the Turing Test is not so
| much about "real" consciousness but if an observer can decide
| if is talking with a computer or a human).
| pwdisswordfishz wrote:
| Any theory which purports to show that Roger Penrose is able to
| "see" the truth of the consistency of mathematics has got to
| explain Edward Nelson being able to "see" just the opposite.
| thrance wrote:
| Penrose is a dualist, he believes the mind is detached from the
| material world.
|
| He has been desperately seeking proof of quantum phenomenons in
| the brain, so he may have something to point to when asked how
| this mind, supposedly external to the physical realm, can pilot
| our bodies.
|
| I am not a dualist, and I don't think what Penrose has to say
| about AI or consciousness holds much value.
| estebarb wrote:
| I'm not sure about it makes sense to apply Godel's theorem to AI.
| Personally, I prefer to think about it in terms of basic
| computability theory:
|
| We think, that is a fact.
|
| Therefore, there is a function capable of transforming
| information into "thinked information", or what we usually call
| reasoning. We know that function exists, because we ourselves are
| an example of such function.
|
| Now, the question is: can we create a smaller function capable of
| performing the same feat?
|
| If we assume that that function is computable in the Turing sense
| then, kinda yes, there are an infinite number of turing machines
| that given enough time will be able to produce the expected
| results. Basically we need to find something between our own
| brain and the Kolmogorov complexity limit. That lower bound is
| not computable, but given that my cats understands when we are
| discussing to take them to the vet then... maybe we don't really
| need a full sized human brain for language understanding.
|
| We can run Turing machines ourselves, so we are at least Turing
| equivalent machines.
|
| Now, the question is: are we at most just Turing machines or
| something else? If we are something else, then our own CoT won't
| be computable, no matter how much scale we throw at it. But if we
| are then it is just matter of time until we can replicate
| ourselves.
| thrance wrote:
| Penrose is a dualist, he does not believe that function can be
| computed in our physical universe. He believes the mind comes
| from another realm and "pilots" us through quantum phenomenons
| in the brain.
| falcor84 wrote:
| Interesting. Does that fit with the simulation hypothesis?
| That the world's physics are simulated on one computer, but
| us characters are simulated on different machines, with some
| latency involved?
| mcgee21 wrote:
| Its all pop pseudoscience. Things exist. Anything that
| exists has an identity. Physics exists and other things
| (simulations, computing, etc.) that exist are subject to
| those physics. To say that it happens the other way around
| is poor logic and/or lacks falsifiability.
| bbor wrote:
| Which is--to use the latest philosophy lingo--dumb. To be
| fair to Penrose, the "Godel's theory about formal systems
| proves that souls exist" is an extremely common take; anyone
| following LLM discussions has likely seen it rediscovered at
| least once or twice.
|
| To pull from the relevant part of Hofstadter's incredible _I
| am a Strange Loop_ (a book also happens to more rigorously
| invoke Godel for cognitive science): And this
| is our central quandary. Either we believe in a nonmaterial
| soul that lives outside the laws of physics, which amounts to
| a nonscientific belief in magic, or we reject that idea, in
| which case the eternally beckoning question "What could ever
| make a mere physical pattern be me?" After all, a
| phrase like "physical system" or "physical substrate" brings
| to mind for most people... an intricate structure consisting
| of vast numbers of interlocked wheels, gears, rods, tubes,
| balls, pendula, and so forth, even if they are tiny,
| invisible, perfectly silent, and possibly even probabilistic.
| Such an array of interacting inanimate stuff seems to most
| people as unconscious and devoid of inner light as a flush
| toilet, an automobile transmission, a fancy Swiss watch
| (mechanical or electronic), a cog railway, an ocean liner, or
| an oil refinery. Such a system is not just probably
| unconscious, it is *necessarily* so, as they see it. This is
| the kind of single-level intuition so skillfully exploited by
| John Searle in his attempts to convince people that computers
| could never be conscious, no matter what abstract patterns
| might reside in them, and could never mean anything at all by
| whatever long chains of lexical items they might string
| together.
|
| Highly recommend it for anyone who liked _Godel, Escher,
| Bach_ , but wants more explicit scientific theses! He
| basically wrote it to clarify the more artsy/rhetorical
| points made in the former book.
| jfengel wrote:
| It feels really weird to say that Roger Penrose is being
| dumb.
|
| It's accurate. But it feels really weird.
|
| It's not uncommon for great scientists to be totally out of
| their depth even in nearby fields, and not realize it. But
| this isn't the hard part of either computability or
| philosophy of mind.
| northern-lights wrote:
| > there is a function capable of transforming information into
| "thinked information", or what we usually call reasoning. We
| know that function exists, because we ourselves are an example
| of such function.
|
| We mistakenly assume, they are true because perhaps we want
| them to be true. But we have no proof that either of these are
| true.
| bwoj wrote:
| It is a big mistake to think that most computability theory
| applies to AI, including Godel's Theorem. People start off
| wrong by talking about AI "algorithms." The term applies more
| correctly to concepts like gradient descent. But the inferences
| of the resulting neural nets is not an algorithm. It is not a
| defined sequence of operations that produces a defined result.
| It is better described as a heuristic, a procedure that
| approximates a correct result but provides no mathematical
| guarantees.
|
| Other aspects of ANN that show that Godel doesn't apply is that
| they are not formal systems. Formal system is a collection of
| defined operations. The building blocks of ANN could perhaps be
| built into a formal system. Petri nets have been demonstrated
| to be computationally equivalent to Turing machines. But this
| is really an indictment on the implementation. It's the same as
| using your PC, implementing a formal system like its
| instruction set to run a heuristic computation. Formal system
| can implement informal systems.
|
| I don't think you have to look at humans very hard to see that
| humans don't implement any kind of formal system and are not
| equivalent to Turing machines.
| btilly wrote:
| With sufficient compute capacity, a complete physical
| simulation of a human should be possible. This means that, even
| though we are fallible, there is nothing that we do which can't
| be simulated on a Turing machine.
| chromanoid wrote:
| May still only yield a philosophical zombie. You can simulate
| gravity but never move something with its simulation.
| skywhopper wrote:
| Not every fact is computable. We are not Turing machines.
| cowl wrote:
| he starts with "consciousnes is not computable". You can not
| just ignore it as a central argument withouth explaining why
| your preference to think on it as basic computability theory
| makes more sence than his.
|
| What's more, whatever you like to call the transoforming of
| information into thinked information by definition can not be a
| (mathematical) function, because it would require all people to
| process the same information in the same way and this is
| plainly false
| irickt wrote:
| Daniel Dennett thoroughly debunks Penrose' argument in Chapter 15
| of Darwin's Dangerous Idea. Quoting reviewers of a Penrose paper
| ... "quite fallacious," "wrong," "lethal flaw" and "inexplicable
| mistake," "invalid," "deeply flawed." "The Al community [of 1995]
| was, not surprisingly, united in its dismissal of Penrose's
| argument."
| lowbloodsugar wrote:
| If an elderly but distinguished scientist says that something is
| possible, he is almost certainly right; but if he says that it is
| impossible, he is very probably wrong.
|
| - Arthur C Clarke
| James_K wrote:
| > The interviewer is barely treading water in the ocean of
| Penrose's thought. He mistakes his spasmodic thrashing for
| swimming.
|
| The comments below this video are utterly insane. Roger Penrose
| seems to have a fanatical cult attached to him.
| whatshisface wrote:
| If anyone thinks the human mind is computable, tell me the
| location of even one particle.
| PeterWhittaker wrote:
| OK, try this for size, bearing in mind that it is a heuristic
| argument.
|
| No one can "know", with certainty, the location of any
| particle. Or, to be slightly more accurate, the more we know of
| its location, the less we know of its movement. This is
| essentially Heisenberg/QM 101.
|
| But we see the results of "computation" all around us, all the
| time: Any time a chemical or physical reaction settles to an
| observable result, whether observed by one of us, that is, a
| human, or another physical entity, like a tree, a squirrel, a
| star, etc. This is essentially a combination of Rovelli's
| Relational QM and the viewing of QM through an information
| centric lens.
|
| In other words, we can and do have solid reality at a macro
| level without ever having detailed knowledge (whatever that
| might mean) at a micro/nano/femto level.
|
| Having said that, I read your comment as implying that "the
| human mind" (in quotes because that is not a well defined
| concept, at least not herein; if we can agree on an operational
| definition, we may be able to go quite far) is somehow
| disconnected from physical reality, that is, that you are
| suggesting a dualist position, in which we have physics and
| physical chemistry and everything we get from them, e.g.,
| genetics, neurophysiology, etc., all based ultimately on QM,
| and we have "consciousness" or "the mind" as somehow being
| outside/above all of that.
|
| I have no problem with that suggestion. I don't buy it, and am
| mostly a reductionist at heart, so to speak, but I have no
| problem with it.
|
| What I'd like to see in support of that position would be
| repeatable, testable statements as to how this "outside/above"
| "thing" somehow interacts with the physical substrate of our
| biological lives.
|
| Preferably without reference to the numinous, the ephemeral, or
| the magical.
|
| Honestly, I really would like to see this. It would represent
| one of the greatest advances in knowledge in human history.
| like_any_other wrote:
| I think all the debunkings of Penrose's argument are rather
| overcomplicated, when there is a much simpler flaw:
|
| Which operation can computers (including quantum computers) not
| perform, that human neurons can? If there is no such operation,
| then a human-brain-equivalent computer can be built.
| overu589 wrote:
| I complement Penrose for his indifference to haters and harsh
| skeptics.
|
| Our minds and consciousness do not fundamentally use linear logic
| to arrive at their conclusions, they use constructive and
| destructive interference. Linear logic is simulated upon this
| more primitive (and arguably superior) cognition.
|
| It is true that any outcome of any process may be modeled in
| serialized terms or computational postulations, this is different
| than the interference feedback loop used by intelligent human
| consciousness.
|
| Constructive and destructive interference is different and
| ultimately superior to linear logic on many levels. Despite this,
| the scalability of artificial systems may very well easily
| surpass human capabilities on any given task. There may be an
| arguable energy efficiency angle.
|
| Constructive/destructive interference builds holographic
| renderings which work sufficiently when lacking information. A
| linear logic system would simulate the missing detail from
| learned patterns.
|
| Constructive/destructive interference does not require intensive
| computation
|
| An additive / reduction strategy may change the terms of a
| dilemma to support a compromised (or alternatively superior)
| "human" outcome which a logic system simply could not "get" until
| after training.
|
| There is more, though these are a worthy start.
|
| And consciousness is the inflection (feedback reverberation if
| you like) upon the potential of existential being (some animate
| matter in one's brain). The existential Universe (some part of
| matter bound in the neuron, those micro-tubes perhaps) is
| perturbed by your neural firings. The quantum domain is an echo
| chamber. Your perspectives are not arranged states, they are
| potentials interfering.
|
| Also, "you all" get intelligence and "will" wrong. I'll pick that
| fight on another day.
| Chance-Device wrote:
| I swear this was on the front page 2 minutes ago and now it's
| halfway down page 2.
|
| Anyway, I'm not really sure where Penrose is going with this. As
| a summary, incompleteness theorem is basically a mathematical
| reformulation of the paradox of the liar - let's state this here
| for simplicity as "This statement is a lie" which is a bit easier
| than talking about " All Cretans are liars", which is the way I
| first heard it.
|
| So what's the truth value of "This statement is a lie"? It
| doesn't have one. If it's false, then it's true. But if it's
| true, then it must be false. The reason for this paradox is that
| it's a self-referential statement: it refers to its own truth
| value in the construction of its own truth value, so it never
| actually gets constructed in the first place.
|
| You can formulate the same sort of idea mathematically using
| sets, which is what Godel did.
|
| Now, the thing about this is that as far as I am aware (and I'm
| open to be corrected on this) this never actually happens in
| reality in any physical system. It seems to be an artefact of
| symbolic representation. We can construct a series of symbols
| that reference themselves in this way, but not an actual system.
| This is much the same way as I can write "5 + 5 = 11" but it
| doesn't actually mean anything physically.
|
| The closest thing we might get to would be something that
| oscillates between two states.
|
| We also ourselves, don't have a good answer to this problem as
| phrased. What is the truth value of "This statement is a lie"? I
| have to say "I don't know" or "there isn't one" which is a bit
| like cheating. Am I incapable of consciousness as a result? And
| if I am indeed conscious instead because I _can_ make such a
| statement instead of simply "True" or "False", well I'm sure that
| an AI can be made to do likewise.
|
| So I really don't think this has anything to do with
| intelligence, or consciousness, or any limits on AI.
| dang wrote:
| > I swear this was on the front page 2 minutes ago and now it's
| halfway down page 2.
|
| It set off the flamewar detector. I've turned that off now.
| Chance-Device wrote:
| Thanks!
| funktour wrote:
| (for the record, I think the Penrose take on Godel and
| consciousness is mostly silly and or confused)
|
| I think your understanding of the incompleteness theorem is a
| little, well, incomplete. The _proof_ of the theorem does
| involve, essentially, figuring out how to write down "this
| statement is not provable" and using liar-paradox-type-
| reasoning to show that it is neither provable nor disprovable.
|
| But the incompleteness theorem itself is not the liar paradox.
| Rather, it shows that any (consistent) system rich enough to
| express arithmetic cannot prove or disprove all statements.
| There are things in the gaps. Godel's proof gives one example
| ("this statement is not provable") but there are others of very
| different flavors. The standard one is consistency (e.g. Peano
| arithemtic alone cannot prove the consistency of Peano
| arithmetic, you need more, like much stronger induction; ZFC
| cannot prove the consistency of ZFC, you need more, like a
| large cardinal).
|
| And this very much _does_ come up for real systems, in the
| following way. If we could prove or disprove each statement in
| PA, then we could also solve the halting problem! For the same
| reason there 's no general way to tell whether each statement
| of PA has a proof, there's no general way to tell whether each
| program will halt on a given input.
___________________________________________________________________
(page generated 2025-03-02 23:00 UTC)