5 ms·

> This past March, when I called Penrose in Oxford, he explained that his interest in consciousness goes back to his discovery of Gödel’s incompleteness theorem

by dvt 10y ago

> This past March, when I called Penrose in Oxford, he explained that his interest in consciousness goes back to his discovery of Gödel’s incompleteness theorem while he was a graduate student at Cambridge. Gödel’s theorem, you may recall, shows that certain claims in mathematics are true but cannot be proven. “This, to me, was an absolutely stunning revelation,” he said. “It told me that whatever is going on in our understanding is not computational.” This is a very strange conclusion to make. Maybe someone can elucidate. Godel's theorems apply to tightly-controlled formal systems. And they do not, in fact, apply to particularly weak systems (e.g. sentential logic). Why would Penrose think that Godel has anything to do with consciousness? All it seems to have done is prove that, in some systems, there are known unknowables (specifically, that the consistency of sufficiently-complex systems cannot be proved). If anything, it should lead us to take a train of thought similar to Chalmers': consciousness is unknowable (maybe kind of like God), but even that's a stretch. Because, like I mentioned above, Godel's theorems are about formal systems. Not only is the real world not a formal system, but (at least on the quantum level), it's also non-deterministic. Now, there are probabilistic logics out there that follow Godel's findings, but there's a lot of work that needs to be done to bring that in the real world.

HONEST_ANNIE 10y ago
Indeed. There is nothing to indicate that human brains have done anything that can't be achieved with polynomial time heuristic search algorithm. Most people who have read the "Emperors New Mind" have been surprised that Penrose don't' seem to realize that. He has very strong intuition about consciousness and cognition but he can't explain it to others.
- goatlover 10y ago
  There are at least two things correlated with brains that we have no algorithm for: 1. Consciousness (subjective experience, qualia) 2. Intentionality (the aboutness of mental content) What would a conscious algorithm even look like?
  - mannykannot 10y ago
    That should not be taken for proof that they could not arise from algorithms - if so, then by a corresponding argument, all unproven conjectures would be false.
    - sgt101 10y ago
      Agreed, but conversely it's not sufficient to demand that because they might they will - Godel gave the room for that. We many end up with formalisations and mechanisms for these things, but we also may not.
      - dvt 10y ago
        This thread is a bit removed from my original point, but, again, Godel's theorems really have nothing to do with reality. They have to do with very specific formal systems (and not even all formal systems, at that). I just don't really understand why invoking him is even relevant.
        Koshkin 10y ago
        Unfortunately, the only reliable way to understand reality has been through the use of such formal system.
        qubex 10y ago
        Penrose's point, at least as I understand it, is that insofar human intuition can lead us to see the 'truth' of not-provable-within-the-formal-constraints-of-the-system statements, we are doing something 'informal', aka non-computable, and that insofar if our brains were merely "computers made of meat" we would be unable to transcend the formalism, then we must have some non-computable process going on inside our brains somewhere.
        blackflame7000 10y ago
        Excellent summary. An example of this is human's ability to process statements like "This sentence is false"
- sgt101 10y ago
  >polynomial time heuristic search algorithm. Like create culture, write the works of Shakespeare or create a workable theory of the mind of others? Or fall in love, teach a child to play cricket or understand (and act on) an Opera? Also why should I care a heckin' heck about a heuristic time polynomial search? I'll work out complexity when I have bounds on correctness... not before. The argument that those that find something beyond formalism must formalise it in order to be regarded as serious is not a serious argument!
  - aeorgnoieang 10y ago
    > The argument that those that find something beyond formalism must formalise it in order to be regarded as serious is not a serious argument! Eh; waving your hands around and claiming, without much evidence, that of course there's "something beyond formalism" isn't a "serious argument" either. It seems like you, being presented with The Mystery of Consciousness, and having the option to either explain, worship, or ignore it, are opting to worship it. Hence: > > polynomial time heuristic search algorithm. > > Like create culture, write the works of Shakespeare or create a workable theory of the mind of others? Or fall in love, teach a child to play cricket or understand (and act on) an Opera?
    - sgt101 10y ago
      Am I wrong that incompleteness demonstrates that there are systems that cannot be completely described in formal terms?
      - Elrac 10y ago
        I'm no expert, but yes, I think you're wrong about that. This explanation https://www.scientificamerican.com/article/what-is-godels-theorem/ https://www.scientificamerican.com/article/what-is-godels-th..., a little closer to layperson level, uses integer arithmetic as a simple example. Peano's axioms completely describe integer arithmetic - easy peasy! What Gödel says is that there are, nevertheless, statements about results in this system that cannot be proved true (or false). The problem appears to be not describing the system but proving every possible conjecture about it.
- yters 10y ago
  Humans can find good routes on TSPs in linear time. Our best algorithms can only do this in quadratic time or worse.
- cscurmudgeon 10y ago
  > but he can't explain it to others. Umm because it is open an open problem? This is like saying the problem of dark matter is not a scientific problem because we don't know everything about it.
mannykannot 10y ago
The full argument can be found in "The Emperor's New Mind". According to Scot Aaronson, however, Penrose is no longer defending it. http://www.scottaaronson.com/blog/?p=2756 http://www.scottaaronson.com/blog/?p=2756
posterboy 10y ago
> > Gödel’s theorem, you may recall, shows that certain claims in mathematics are true but cannot be proven This is not correct to begin with. Incompleteness in this setting means that a formal system is either unprovable or indeed inconsistent (ie. wrong). A "known unknown" is just an oxymoron. > that the consistency of sufficiently-complex systems cannot be proved that sounds more like it. EDIT: I have to read up on it again and again ... the consistency of sufficiently-complex systems cannot be proved within that system.
- dvt 10y ago
  > that sounds more like it. EDIT: I have to read up on it again and again ... the consistency of sufficiently-complex systems cannot be proved within that system. Nope. Godel's Incompleteness Theorems (GIT) are metalogical[1]. They leak to any (sufficiently-complex) formal system. You can't logic them away by going up a level of abstraction. Let's say you have a (sufficiently-complex) system A which is susceptible to GIT. You can describe A in terms of a meta-system B. By definition, B will also be susceptible to GIT. You can describe B in terms of C, and so on, but every meta-system that follows will still be susceptible to GIT. [1] http://www.mbph.de/Logic/Para/Metalogic.pdf http://www.mbph.de/Logic/Para/Metalogic.pdf
plainOldText 10y ago
Is the real world truly non-deterministic? See: http://people.idsia.ch/~juergen/randomness.html http://people.idsia.ch/~juergen/randomness.html
mixedbit 10y ago
> Maybe someone can elucidate. Godel's theorems apply to tightly-controlled formal systems Turing machine is a tightly-controlled formal system. Either the brain is a Turing machine, which means it can be accurately simulated on our computers and it is a subject of the limitations of the Godel theorem, or it is not a Turing machine, which Penrose argues for, in which case it can't be accurately simulated on Turing machines.
- dvt 10y ago
  As a trained philosopher and logician, I completely understand how a Turing machine relates to Godel's Theorems, but I think you're passing the buck here. You can make all kinds of claims: - Either the brain is a V12 engine or it's not - Either the brain is a perfect circle or it's not - Either the brain is X or it's not All these statements are trivially true, but it's not like I look at a V12 engine thinking "hmm, I wonder if it's conscious" (some pan-psychists do but that's still weird to me). Similarly, looking at the property of a formal system and jumping to consciousness makes (to me) little sense. Besides, my knock-down argument goes something like this: I can concede that our brains are machines, but suppose I believe they are Presburger counting machines, where Godel's incompleteness does not apply. What then? There is no insight in that claim. I just think Turing machines and Godel are used as a bait and switch. Because, really, any theory of consciousness will not have anything to do with either.
  - mixedbit 10y ago
    In the context of the Penrose hypothesis, the question if the brain is a Turing machine is key, because if it is, the hypothesis is false.
    - qubex 10y ago
      The point posed by Penrose isn't (quite) whether the human brain is a Universal Turing Machine or not: it clearly is, in the sense that we can sit down with pencil and paper and emulate a Turing Machine of our choosing (infinite storage excepted, of course). Penrose's statement is that we are a superset of Turing Machines that can both emulate any Turing Machine and do non-computable things, too.

by dvt 10y ago

HONEST_ANNIE 10y ago

Indeed. There is nothing to indicate that human brains have done anything that can't be achieved with polynomial time heuristic search algorithm. Most people who have read the "Emperors New Mind" have been surprised that Penrose don't' seem to realize that. He has very strong intuition about consciousness and cognition but he can't explain it to others.

goatlover 10y ago
There are at least two things correlated with brains that we have no algorithm for: 1. Consciousness (subjective experience, qualia) 2. Intentionality (the aboutness of mental content) What would a conscious algorithm even look like?
- mannykannot 10y ago
  That should not be taken for proof that they could not arise from algorithms - if so, then by a corresponding argument, all unproven conjectures would be false.
  - sgt101 10y ago
    Agreed, but conversely it's not sufficient to demand that because they might they will - Godel gave the room for that. We many end up with formalisations and mechanisms for these things, but we also may not.
    - dvt 10y ago
      This thread is a bit removed from my original point, but, again, Godel's theorems really have nothing to do with reality. They have to do with very specific formal systems (and not even all formal systems, at that). I just don't really understand why invoking him is even relevant.
      - Koshkin 10y ago
        Unfortunately, the only reliable way to understand reality has been through the use of such formal system.
      - qubex 10y ago
        Penrose's point, at least as I understand it, is that insofar human intuition can lead us to see the 'truth' of not-provable-within-the-formal-constraints-of-the-system statements, we are doing something 'informal', aka non-computable, and that insofar if our brains were merely "computers made of meat" we would be unable to transcend the formalism, then we must have some non-computable process going on inside our brains somewhere.
        blackflame7000 10y ago
        Excellent summary. An example of this is human's ability to process statements like "This sentence is false"
sgt101 10y ago
>polynomial time heuristic search algorithm. Like create culture, write the works of Shakespeare or create a workable theory of the mind of others? Or fall in love, teach a child to play cricket or understand (and act on) an Opera? Also why should I care a heckin' heck about a heuristic time polynomial search? I'll work out complexity when I have bounds on correctness... not before. The argument that those that find something beyond formalism must formalise it in order to be regarded as serious is not a serious argument!
- aeorgnoieang 10y ago
  > The argument that those that find something beyond formalism must formalise it in order to be regarded as serious is not a serious argument! Eh; waving your hands around and claiming, without much evidence, that of course there's "something beyond formalism" isn't a "serious argument" either. It seems like you, being presented with The Mystery of Consciousness, and having the option to either explain, worship, or ignore it, are opting to worship it. Hence: > > polynomial time heuristic search algorithm. > > Like create culture, write the works of Shakespeare or create a workable theory of the mind of others? Or fall in love, teach a child to play cricket or understand (and act on) an Opera?
  - sgt101 10y ago
    Am I wrong that incompleteness demonstrates that there are systems that cannot be completely described in formal terms?
    - Elrac 10y ago
      I'm no expert, but yes, I think you're wrong about that. This explanation https://www.scientificamerican.com/article/what-is-godels-theorem/ https://www.scientificamerican.com/article/what-is-godels-th..., a little closer to layperson level, uses integer arithmetic as a simple example. Peano's axioms completely describe integer arithmetic - easy peasy! What Gödel says is that there are, nevertheless, statements about results in this system that cannot be proved true (or false). The problem appears to be not describing the system but proving every possible conjecture about it.
yters 10y ago
Humans can find good routes on TSPs in linear time. Our best algorithms can only do this in quadratic time or worse.
cscurmudgeon 10y ago
> but he can't explain it to others. Umm because it is open an open problem? This is like saying the problem of dark matter is not a scientific problem because we don't know everything about it.

mannykannot 10y ago

The full argument can be found in "The Emperor's New Mind". According to Scot Aaronson, however, Penrose is no longer defending it. http://www.scottaaronson.com/blog/?p=2756 http://www.scottaaronson.com/blog/?p=2756

posterboy 10y ago

> > Gödel’s theorem, you may recall, shows that certain claims in mathematics are true but cannot be proven This is not correct to begin with. Incompleteness in this setting means that a formal system is either unprovable or indeed inconsistent (ie. wrong). A "known unknown" is just an oxymoron. > that the consistency of sufficiently-complex systems cannot be proved that sounds more like it. EDIT: I have to read up on it again and again ... the consistency of sufficiently-complex systems cannot be proved within that system.

dvt 10y ago
> that sounds more like it. EDIT: I have to read up on it again and again ... the consistency of sufficiently-complex systems cannot be proved within that system. Nope. Godel's Incompleteness Theorems (GIT) are metalogical[1]. They leak to any (sufficiently-complex) formal system. You can't logic them away by going up a level of abstraction. Let's say you have a (sufficiently-complex) system A which is susceptible to GIT. You can describe A in terms of a meta-system B. By definition, B will also be susceptible to GIT. You can describe B in terms of C, and so on, but every meta-system that follows will still be susceptible to GIT. [1] http://www.mbph.de/Logic/Para/Metalogic.pdf http://www.mbph.de/Logic/Para/Metalogic.pdf

plainOldText 10y ago

Is the real world truly non-deterministic? See: http://people.idsia.ch/~juergen/randomness.html http://people.idsia.ch/~juergen/randomness.html

mixedbit 10y ago

> Maybe someone can elucidate. Godel's theorems apply to tightly-controlled formal systems Turing machine is a tightly-controlled formal system. Either the brain is a Turing machine, which means it can be accurately simulated on our computers and it is a subject of the limitations of the Godel theorem, or it is not a Turing machine, which Penrose argues for, in which case it can't be accurately simulated on Turing machines.

dvt 10y ago
As a trained philosopher and logician, I completely understand how a Turing machine relates to Godel's Theorems, but I think you're passing the buck here. You can make all kinds of claims: - Either the brain is a V12 engine or it's not - Either the brain is a perfect circle or it's not - Either the brain is X or it's not All these statements are trivially true, but it's not like I look at a V12 engine thinking "hmm, I wonder if it's conscious" (some pan-psychists do but that's still weird to me). Similarly, looking at the property of a formal system and jumping to consciousness makes (to me) little sense. Besides, my knock-down argument goes something like this: I can concede that our brains are machines, but suppose I believe they are Presburger counting machines, where Godel's incompleteness does not apply. What then? There is no insight in that claim. I just think Turing machines and Godel are used as a bait and switch. Because, really, any theory of consciousness will not have anything to do with either.
- mixedbit 10y ago
  In the context of the Penrose hypothesis, the question if the brain is a Turing machine is key, because if it is, the hypothesis is false.
  - qubex 10y ago
    The point posed by Penrose isn't (quite) whether the human brain is a Universal Turing Machine or not: it clearly is, in the sense that we can sit down with pencil and paper and emulate a Turing Machine of our choosing (infinite storage excepted, of course). Penrose's statement is that we are a superset of Turing Machines that can both emulate any Turing Machine and do non-computable things, too.