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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 unc

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 2y ago
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.
- Lerc 2y ago
  Those stories are not to be believed.
tbrownaw 2y ago
> 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 2y ago
  > 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.
  - tbrownaw 2y ago
    I suppose if you really wanted to you could view condensing useful abstractions out of a highly detailed system as a kind of language game, but I'm not convinced that that's useful in the context of investigating particular abstractions rather than investigating the nature of the process of making abstractions.
    - throwup238 2y ago
      I think the very concept of an abstraction is a language game, one that speaks to the old Platonic ideals of Greek philosophy - with all the good and bad that implies. This specific language game takes on a very concrete meaning to programmers that can be quantitatively analyzed by a compiler but epistemologically it’s just another abstract concept (I hate philosophical inception).
  - sunshowers 2y ago
    You could reasonably consider free will to be an abstraction or a language game, but it is closely linked to moral responsibility, prisons, punishment, etc, which are very much not language games. I don't think free will exists because I don't think supernatural phenomena exist, and there's certainly no natural explanation for free will (Penrose was correct about that). But I have a very non-nihilistic view on things [1]. [1] https://sunshowers.io/posts/there-is-no-free-will/ https://sunshowers.io/posts/there-is-no-free-will/
- bbor 2y ago
  Well said! In case anyone is curious how this is discussed in AI, this whole conversation is pretty well summed up by the idea of the "Frame Problem" https://plato.stanford.edu/entries/frame-problem/ https://plato.stanford.edu/entries/frame-problem/ Thus why intuitive algorithms change everything, even if they're useless on their own...
Animats 2y ago
> 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 2y ago
  > 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 2y ago
  > 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.
- gizajob 2y ago
  They’re better than your average human at producing jpegs. I think if you put any of your average humans in a closed room with nothing but canvases, paint, and a mirror, within a month or two they’d be producing pretty interesting paintings without having been fed an image of every single artwork humanity has ever made.

drivebyhooting 2y ago

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.

Lerc 2y ago
Those stories are not to be believed.

tbrownaw 2y ago

> 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 2y ago
> 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.
- tbrownaw 2y ago
  I suppose if you really wanted to you could view condensing useful abstractions out of a highly detailed system as a kind of language game, but I'm not convinced that that's useful in the context of investigating particular abstractions rather than investigating the nature of the process of making abstractions.
  - throwup238 2y ago
    I think the very concept of an abstraction is a language game, one that speaks to the old Platonic ideals of Greek philosophy - with all the good and bad that implies. This specific language game takes on a very concrete meaning to programmers that can be quantitatively analyzed by a compiler but epistemologically it’s just another abstract concept (I hate philosophical inception).
- sunshowers 2y ago
  You could reasonably consider free will to be an abstraction or a language game, but it is closely linked to moral responsibility, prisons, punishment, etc, which are very much not language games. I don't think free will exists because I don't think supernatural phenomena exist, and there's certainly no natural explanation for free will (Penrose was correct about that). But I have a very non-nihilistic view on things [1]. [1] https://sunshowers.io/posts/there-is-no-free-will/ https://sunshowers.io/posts/there-is-no-free-will/
bbor 2y ago
Well said! In case anyone is curious how this is discussed in AI, this whole conversation is pretty well summed up by the idea of the "Frame Problem" https://plato.stanford.edu/entries/frame-problem/ https://plato.stanford.edu/entries/frame-problem/ Thus why intuitive algorithms change everything, even if they're useless on their own...

Animats 2y ago

> 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 2y ago
> 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 2y ago
> 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.
gizajob 2y ago
They’re better than your average human at producing jpegs. I think if you put any of your average humans in a closed room with nothing but canvases, paint, and a mirror, within a month or two they’d be producing pretty interesting paintings without having been fed an image of every single artwork humanity has ever made.