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"human brains are turing complete" Are we sure we can really support that statement?

by mjfl 12y ago

cervice 12y ago
Would a not turing complete human brain be able to conceive turing completeness?
- JadeNB 12y ago
  That sounds like saying "Would a not-Turing complete markup language be able to record the definition of Turing completeness?" (If you argue that there's a difference between conceiving something and recording it, then I can soup up the markup language with a mild genetic algorithm equipped with a stop condition that'll let it generate the definition on its own.)
- actsasbuffoon 12y ago
  My brain can imagine what telepathy would be like, but that doesn't make it telepathic.
JadeNB 12y ago
> Are we sure we can really support that statement? I assume you mean "isn't it possible that the human brain would run out of memory?", but I think that it depends on what you mean by Turing complete. If I hand you the specification of a universal Turing machine, then you can certainly execute it, by hand, on a limitless supply of paper—making the paper your external memory. I think that this is a reasonable way of claiming that your brain is Turing complete. (Or perhaps you worry that one must include the rest of the body to achieve Turing completeness?)
Chinjut 12y ago
Well, augmented with a theoretical infinite memory device, and granted immortality (protection against senility, etc.), sure. Do you really doubt humans can carry out "Look up within this finite table what to do, based on the current state and current symbol at the cursor. Update the state and manipulate the cursor accordingly. Repeat."?
- kybernetikos 12y ago
  Humans are pretty bad at following instructions reliably and correctly, so maybe more like a turing machine with some probabilistic error rate.
  - TheLoneWolfling 12y ago
    We're assuming arbitrary amounts of time - in which case one can check calculations an arbitrary number of times. (Quick idea: recheck all calculations done so far at all computation steps that are powers of 2. So recheck everything after the first step, the second step, the fourth step, the eighth step, the sixteenth step, etc.)
murbard2 12y ago
People have already pointed out why. In addition, let me point out why it is also no more powerful than a Turing machine. If you accept physicalism, then thoughts arise as the result of electrical, mechanical, and chemical processes. As far as we know, those processes are governed by laws of physics which are all computable to arbitrary precision. Assuming that our thought processes are not infinitely sensitive to random perturbations, then the human brain can be simulated by a Turing machine. Thus, everything we know about nature indicates that the human brain is no more powerful than a Turing machine.
- TheLoneWolfling 12y ago
  > As far as we know, those processes are governed by laws of physics which are all computable to arbitrary precision. Look at, for example, electron shot noise for a counterexample. Given the state of a low-output lamp and a detector, one cannot compute the state of the detector after a period of time to arbitrary precision. We can say that the detector will have x% chance of triggering within the time period - but that is all. We cannot say definitely "the detector will trigger" or "the detector will not trigger", no matter how exactly we know the initial state of the system. And we already know that the human brain can be affected by similar processes (If nothing else, our eyes start registering at full night vision when <10 photons hit within 100ms, which is within the realm of shot noise.)
stegosaurus 12y ago
Other posters seem to be attacking this from the angle of providing examples of non-turing-complete systems which can describe or 'imagine' turing-complete systems. I would attack this by claiming that we have designed turing complete systems using no external input. That is to say - we can _produce_ a turing complete system, which implies we are a turing complete system given an IO port (limbs, for example). Fundamentally I could sit and perform calculations with pen and paper. I'm ignoring the unlimited criterion here, I assume colloquial usage. The only real way I could fathom otherwise is by deciding to isolate the brain and consider it as a single entity. But in that case a CPU isn't really turing-complete because it can't do anything on its' own.

"human brains are turing complete" Are we sure we can really support that statement?

by mjfl 12y ago

"human brains are turing complete" Are we sure we can really support that statement?

cervice 12y ago

Would a not turing complete human brain be able to conceive turing completeness?

JadeNB 12y ago
That sounds like saying "Would a not-Turing complete markup language be able to record the definition of Turing completeness?" (If you argue that there's a difference between conceiving something and recording it, then I can soup up the markup language with a mild genetic algorithm equipped with a stop condition that'll let it generate the definition on its own.)
actsasbuffoon 12y ago
My brain can imagine what telepathy would be like, but that doesn't make it telepathic.

JadeNB 12y ago

> Are we sure we can really support that statement? I assume you mean "isn't it possible that the human brain would run out of memory?", but I think that it depends on what you mean by Turing complete. If I hand you the specification of a universal Turing machine, then you can certainly execute it, by hand, on a limitless supply of paper—making the paper your external memory. I think that this is a reasonable way of claiming that your brain is Turing complete. (Or perhaps you worry that one must include the rest of the body to achieve Turing completeness?)

Chinjut 12y ago

Well, augmented with a theoretical infinite memory device, and granted immortality (protection against senility, etc.), sure. Do you really doubt humans can carry out "Look up within this finite table what to do, based on the current state and current symbol at the cursor. Update the state and manipulate the cursor accordingly. Repeat."?

kybernetikos 12y ago
Humans are pretty bad at following instructions reliably and correctly, so maybe more like a turing machine with some probabilistic error rate.
- TheLoneWolfling 12y ago
  We're assuming arbitrary amounts of time - in which case one can check calculations an arbitrary number of times. (Quick idea: recheck all calculations done so far at all computation steps that are powers of 2. So recheck everything after the first step, the second step, the fourth step, the eighth step, the sixteenth step, etc.)

murbard2 12y ago

People have already pointed out why. In addition, let me point out why it is also no more powerful than a Turing machine. If you accept physicalism, then thoughts arise as the result of electrical, mechanical, and chemical processes. As far as we know, those processes are governed by laws of physics which are all computable to arbitrary precision. Assuming that our thought processes are not infinitely sensitive to random perturbations, then the human brain can be simulated by a Turing machine. Thus, everything we know about nature indicates that the human brain is no more powerful than a Turing machine.

TheLoneWolfling 12y ago
> As far as we know, those processes are governed by laws of physics which are all computable to arbitrary precision. Look at, for example, electron shot noise for a counterexample. Given the state of a low-output lamp and a detector, one cannot compute the state of the detector after a period of time to arbitrary precision. We can say that the detector will have x% chance of triggering within the time period - but that is all. We cannot say definitely "the detector will trigger" or "the detector will not trigger", no matter how exactly we know the initial state of the system. And we already know that the human brain can be affected by similar processes (If nothing else, our eyes start registering at full night vision when <10 photons hit within 100ms, which is within the realm of shot noise.)

stegosaurus 12y ago

Other posters seem to be attacking this from the angle of providing examples of non-turing-complete systems which can describe or 'imagine' turing-complete systems. I would attack this by claiming that we have designed turing complete systems using no external input. That is to say - we can _produce_ a turing complete system, which implies we are a turing complete system given an IO port (limbs, for example). Fundamentally I could sit and perform calculations with pen and paper. I'm ignoring the unlimited criterion here, I assume colloquial usage. The only real way I could fathom otherwise is by deciding to isolate the brain and consider it as a single entity. But in that case a CPU isn't really turing-complete because it can't do anything on its' own.