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I just recently read the journal article (below) about the Orchestrated Objective Reduction theory put forth by Roger Penrose and Stuart Hammeroff.

According to this theory, the phenomenon of 'understanding' is the result of a non-computable process, e.g. standard silicon-chip computers cannot 'understand' like humans can because they cannot compute non-computable elements. The idea that human beings have the ability to 'understand' suggests that we are able to compute and take advantage of the results of these non-computable processes, and Penrose & Hammeroff seem to believe that quantum mechanics is behind this.

Ultimately, I don't understand how quantum mechanics can allow for the computation of these non-computable elements.

Penrose & Hammeroff: http://www.sciencedirect.com/science/article/pii/S1571064513001188

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    $\begingroup$ Nobody understands what "consciousness" is, at the moment, so pretty much anything Penrose et al. can say about these things is questionable. In general, I have a feeling, that Penrose has lost it, lately. He tries to play in areas which he really doesn't understand, with predictable results. Quantum computers have been shown to be able to compute exactly the same things as classical computers. You, by the way, are a purely classical computer. Your decoherence time is far, far below the switching time of your neurons. The proposed "quantum" aspect of neural nets is perfectly classical, BTW. $\endgroup$ – CuriousOne Jul 7 '16 at 18:54
  • $\begingroup$ @CuriousOne what do you mean by 'switching time'? Are there other theories out there that you know of that challenge Penrose et al.? I would be very interested to read them. $\endgroup$ – Emil_Longshore Jul 7 '16 at 18:56
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    $\begingroup$ Nobody can even define what consciousness is, in science, so even Penrose can't write an article about it. The claims are simply overstating what science knows about these things. You don't need a theory to call bs. Lack of definitions is sufficient. Again, what these guys are proposing isn't even proper quantum mechanics. They claim that neural nets simulate a rather trivial aspect of quantum mechanics, which may or may not be true, but to connect that to a mostly philosophical and humanist term that has no technical definition within science is "far out". $\endgroup$ – CuriousOne Jul 7 '16 at 19:00
  • $\begingroup$ @CuriousOne Actually, Penrose's argument doesn't mention 'consciousness'. $\endgroup$ – lemon Jul 7 '16 at 19:14
  • $\begingroup$ @lemon: The link goes to "Consciousness in the universe: A review of the ‘Orch OR’ theory".... so they don't mean "consciousness" even though it's the first word of their title??? What are you saying here? $\endgroup$ – CuriousOne Jul 7 '16 at 19:21
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Can quantum computers compute non-computable elements?

No.

Why?

Quantum computers can be simulated by classical computers. If quantum computers could compute uncomputable things, so could classical computers. But if a classical computer can compute it, it's computable. Not uncomputable.

(The simulation is very slow, but 'computable' doesn't require 'tractable'.)

But Penrose and Orchestrated Reduction...

Orchestrated reduction is not quantum computation. It is a hypothetical process above and beyond what a quantum computer could do. It's also extremely controversial, both philosophically and scientifically. It's not widely accepted.

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  • $\begingroup$ Where did you find this information? I thought a classical computer can only approximate a quantum computer... $\endgroup$ – Emil_Longshore Jul 8 '16 at 14:57
  • $\begingroup$ @ncamarda I'm not sure why you would think that's a problem. Quantum computers are already inherently noisy, so even the real thing is based on approximations and error bounds vs the ideal case. We have constructions to make the approximations arbitrarily accurate. $\endgroup$ – Craig Gidney Jul 8 '16 at 16:52
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Ultimately, I don't understand how quantum mechanics can allow for the computation of these non-computable elements.

Neither does Penrose. He doesn't actually explain how quantum mechanics gives rise to non-computation. What he does claim though, in his books The Emperor's New Mind and Shadows of the Mind, is that quantum mechanics (specifically the measurement problem, i.e. wave-function collapse) leaves room for non-computation.

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  • $\begingroup$ He may not have claimed these things in the past, now he does, according to the link in the original question. Let's be honest here... Penrose has lost it a couple decades ago. Having said that, nonsense like this sells beautifully. $\endgroup$ – CuriousOne Jul 7 '16 at 19:22
  • $\begingroup$ @CuriousOne I can't see anything especially new in that article - his theory still depends on quantum gravity providing the magic ingredient... $\endgroup$ – lemon Jul 7 '16 at 19:53
  • $\begingroup$ You can ask in the psychology SE if people tend to go back to normal once they are flying... :-) $\endgroup$ – CuriousOne Jul 7 '16 at 20:41
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Penrose has been debunked by many philosophers of the mind. His argument amounts to: we do not understand consciousness, we do not understand quantum mechanics, thus both must be related.

Additional issues, 1) It has been shown that you cannot use quantum mechanics, or quantum logic to solve non-computable problems. The only advantage of a quantum computer is speed as compared to a classical one. 2) Very few of the people who study the mind or artificial intelligence believes that humans can solve uncomputable problems, but quite the opposite.

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  • $\begingroup$ Penrose is not suggesting that quantum computation is responsible (see ch 7 of SOTM), he instead refers even deeper to the wave-function collapse itself. $\endgroup$ – lemon Jul 7 '16 at 19:50
  • $\begingroup$ @lemon I agree with that, it is just that to me, there is a small step from collapse/consciousness/hyper computations originating in the brain's microtubules due to some unclear property of QM, to the conclusion that you can build a quantum computer that does the same. $\endgroup$ – Wolphram jonny Jul 7 '16 at 20:10
  • $\begingroup$ The big step for the proposed paper would be to actually measure any of that, which they haven't done. It's pseudo-scientific confabulation. Why any journal would even publish that is not clear to me. If I were the editor, I would send the paper back to the authors and suggest they find a different publisher. $\endgroup$ – CuriousOne Jul 7 '16 at 21:48
  • $\begingroup$ What do these philosophers of the mind propose instead then? What is the leading theory? $\endgroup$ – Emil_Longshore Jul 8 '16 at 15:02

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