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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 w

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 9y 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 9y 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 9y 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 9y 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 9y ago
        Unfortunately, the only reliable way to understand reality has been through the use of such formal system.
      - qubex 9y 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 9y ago
        Excellent summary. An example of this is human's ability to process statements like "This sentence is false"
sgt101 9y 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 9y 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 9y ago
    Am I wrong that incompleteness demonstrates that there are systems that cannot be completely described in formal terms?
    - Elrac 9y 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 9y ago
Humans can find good routes on TSPs in linear time. Our best algorithms can only do this in quadratic time or worse.
cscurmudgeon 9y 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.

goatlover 9y 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 9y 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 9y 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 9y 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 9y ago
      Unfortunately, the only reliable way to understand reality has been through the use of such formal system.
    - qubex 9y 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 9y ago
        Excellent summary. An example of this is human's ability to process statements like "This sentence is false"

sgt101 9y 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 9y 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 9y ago
  Am I wrong that incompleteness demonstrates that there are systems that cannot be completely described in formal terms?
  - Elrac 9y 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 9y ago

Humans can find good routes on TSPs in linear time. Our best algorithms can only do this in quadratic time or worse.

cscurmudgeon 9y 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.