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I think -- roughly speaking -- Penrose argues that human capabilities such as transductive reasoning are clearly not computable, therefore falsifying the idea t

I think -- roughly speaking -- Penrose argues that human capabilities such as transductive reasoning are clearly not computable, therefore falsifying the idea that the mind reduces to an algorithm. He then goes on to propose how nonetheless what the mind does might be physically grounded, even if not in purely computational machinery.

rowanG077 2y ago
That doesn't make sense to me at all. If something is physically grounded and can be achieved then shouldn't it, by definition, be computable.
- usgroup 2y ago
  In your statement, I'm not sure by which definition physically grounded things are a sufficient condition for being computable, but I think Penrose depends on the Turing notion of computability and the hardness of the halting problem. We can of course move goal posts, redefine computability however we like, to get whatever conclusion we care for, but I think that Penrose effort is intellectually honest.
  - GoblinSlayer 2y ago
    Computing brain behavior is not the halting problem though. It's a computation of one algorithm.
    - usgroup 2y ago
      Yes, just like the algorithm that decides whether any given algorithm terminates could be "one algorithm" (if it was possible) :-)
      - GoblinSlayer 2y ago
        For that to be uncomputable brain must run the halting problem algorithm, which it doesn't, because the halting problem algorithm needs infinite memory. Being finite, brain has finite number of states, which all can be enumerated in finite time.
- lambdaone 2y ago
  I think the interesting question here is whether Penrose is claiming that the things of which the brain is capable (most notably the production of consciousness) are inherently non-computable by _any_ kind of artificial device, which is effectively a form of vitalism, or whether he is claiming that they _might_ be computable, but only with a quantum computer.
  - GoblinSlayer 2y ago
    Quantum computers are computable by classical computers. It's just a problem of exponential complexity.
  - baja_blast 2y ago
    Penrose argues just in terms of classical computers
- denton-scratch 2y ago
  > shouldn't it, by definition, be computable By which definition? Why does anything that is "physically grounded" and "achievable" be computable? Meanwhile, I don't know what "physically grounded" and "achievable" mean in this context.
- User23 2y ago
  No. Why should it be?
  - naasking 2y ago
    If it's physically grounded then it would be computable by some machine, just not necessarily a Turing machine. For instance, a hypercomputer can solve the Halting problem for Turing machines. We just have to be clear about the kind of machine on which a problem is computable.
    - User23 2y ago
      > If it's physically grounded then it would be computable by some machine, just not necessarily a Turing machine. What makes you think that? The overwhelming majority of functions aren’t computable. The evidence suggests, if anything, that the universe is uncomputable and at best some isolatable well-measured specific phenomena can have approximations computed to some arbitrary but inexact precision.
      - naasking 2y ago
        > What makes you think that? Because if it's physically grounded then you can build a physical analogue of it. > overwhelming majority of functions aren’t computable By Turing machines, not by any other type of machine. As I said, if hypercomputers exist then they can solve the Halting problem, which Turing machines cannot.
        lambdaone 2y ago
        Consider the set of functions that that map the reals onto other reals. Almost all of these functions are truly random, with no way of expressing them that does not require the storage of an infinite number of infinite strings. Not only is there no practical way of creating such a thing, most formulations of physics preclude any possibility of making one by placing finite limits of the amount of space or time accessible to us. (Not to mention that almost all reals are [Turing] uncomputable in their own right, but that's a more complex thing to demonstrate.)
mb64 2y ago
That wasn't the impression I got from Sabine's video. It's consciousness itself (the subjective experience) that isn't computable (AI will probably never be conscious).
- GoblinSlayer 2y ago
  Would you say that philosophical zombie is computable? AFAIK dualists agree that philosophical zombie is impossible in this universe, which means what is computable is a conscious being.
  - deleted 2y ago
    [deleted]

rowanG077 2y ago

That doesn't make sense to me at all. If something is physically grounded and can be achieved then shouldn't it, by definition, be computable.

usgroup 2y ago
In your statement, I'm not sure by which definition physically grounded things are a sufficient condition for being computable, but I think Penrose depends on the Turing notion of computability and the hardness of the halting problem. We can of course move goal posts, redefine computability however we like, to get whatever conclusion we care for, but I think that Penrose effort is intellectually honest.
- GoblinSlayer 2y ago
  Computing brain behavior is not the halting problem though. It's a computation of one algorithm.
  - usgroup 2y ago
    Yes, just like the algorithm that decides whether any given algorithm terminates could be "one algorithm" (if it was possible) :-)
    - GoblinSlayer 2y ago
      For that to be uncomputable brain must run the halting problem algorithm, which it doesn't, because the halting problem algorithm needs infinite memory. Being finite, brain has finite number of states, which all can be enumerated in finite time.
lambdaone 2y ago
I think the interesting question here is whether Penrose is claiming that the things of which the brain is capable (most notably the production of consciousness) are inherently non-computable by _any_ kind of artificial device, which is effectively a form of vitalism, or whether he is claiming that they _might_ be computable, but only with a quantum computer.
- GoblinSlayer 2y ago
  Quantum computers are computable by classical computers. It's just a problem of exponential complexity.
- baja_blast 2y ago
  Penrose argues just in terms of classical computers
denton-scratch 2y ago
> shouldn't it, by definition, be computable By which definition? Why does anything that is "physically grounded" and "achievable" be computable? Meanwhile, I don't know what "physically grounded" and "achievable" mean in this context.
User23 2y ago
No. Why should it be?
- naasking 2y ago
  If it's physically grounded then it would be computable by some machine, just not necessarily a Turing machine. For instance, a hypercomputer can solve the Halting problem for Turing machines. We just have to be clear about the kind of machine on which a problem is computable.
  - User23 2y ago
    > If it's physically grounded then it would be computable by some machine, just not necessarily a Turing machine. What makes you think that? The overwhelming majority of functions aren’t computable. The evidence suggests, if anything, that the universe is uncomputable and at best some isolatable well-measured specific phenomena can have approximations computed to some arbitrary but inexact precision.
    - naasking 2y ago
      > What makes you think that? Because if it's physically grounded then you can build a physical analogue of it. > overwhelming majority of functions aren’t computable By Turing machines, not by any other type of machine. As I said, if hypercomputers exist then they can solve the Halting problem, which Turing machines cannot.
      - lambdaone 2y ago
        Consider the set of functions that that map the reals onto other reals. Almost all of these functions are truly random, with no way of expressing them that does not require the storage of an infinite number of infinite strings. Not only is there no practical way of creating such a thing, most formulations of physics preclude any possibility of making one by placing finite limits of the amount of space or time accessible to us. (Not to mention that almost all reals are [Turing] uncomputable in their own right, but that's a more complex thing to demonstrate.)

mb64 2y ago

That wasn't the impression I got from Sabine's video. It's consciousness itself (the subjective experience) that isn't computable (AI will probably never be conscious).

GoblinSlayer 2y ago
Would you say that philosophical zombie is computable? AFAIK dualists agree that philosophical zombie is impossible in this universe, which means what is computable is a conscious being.
- deleted 2y ago
  [deleted]