Roger Penrose

Picture: PenroseBlandula Sir Roger Penrose is unique in offering something close to a proof in formal logic that minds are not merely computers. There is a kind of piquant appeal in an argument against the power of formal symbolic systems which is itself clothed largely in formal symbolic terms. Although it is this ‘mathematical’ argument, based on the famous proof by Gödel of the incompleteness of arithmetic, which has attracted the greatest attention, an important part of Penrose’s theory is provided by positive speculations about how consciousness might really work. He thinks that consciousness may depend on a new kind of quantum physics which we don’t, as yet, have a theory for, and suggests that the microtubules within brain cells might be the place where the crucial events take place. I think it must be admitted that his negative case against computationalism is much stronger than these positive theories.
Besides the direct arguments about consciousness, Penrose’s two books on the subject feature excellent and highly readable passages on fractals, tiling the plane, and many other topics. At times, it must be admitted, the relevance of some of these digressions is not obvious – I’m still not convinced that the Mandelbrot Set has anything to do with consciousness, for example – but they are all fascinating and remarkably lucid pieces in their own right. ‘The Emperor’s New Mind’ is particularly wide-ranging, and would be well worth reading even if you weren’t especially interested in consciousness, while a large part of ‘Shadows of the Mind’ is somewhat harder going, and focuses on a particular argument which purports to establish that “Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth”.

Bitbucket I like the books myself, mostly, but I don’t find them convincing. Of course, people find a lengthy formal argument intimidating, especially from someone of Penrose’s acknowledged eminence. But does anyone seriously think this kind of highly abstract reasoning can tell us anything real about how things actually work?

Blandula You don’t think maths tells us anything about the real world then? Well, let’s start with the Gödelian argument, anyway. Gödel proved the incompleteness of arithmetic, that is, that there are true statements in arithmetic which can never be proved arithmetically. Actually, the proof goes much wider than that. He provides a way of generating a statement, in any formal algebraic system, which we can see is true, but which cannot be proved within the system. Penrose’s point is that any mechanical, algorithmic, process is based on a formal system of some kind. So there will always be some truths that computers can’t prove – but which human beings can see are true! So human thought can’t be just the running of an algorithm.

Bitbucket These unprovable truths are completely uninteresting ones, of course: the sort of thing Gödel produces are arid self-referential statements of no wider relevance. But in any case, the doctrine that people can always see the truth of any such Gödel statement is a mere assertion. In the simple cases Penrose considers, of course human beings can see the truth of the statements, but there’s no proof that the same goes for more complex ones. If we actually defined the formal system which brains are running on, I believe we might well find that the Gödel statement for that system really was beyond the power of brains to grasp.

Blandula I don’t think that that could ever happen – it just doesn’t work like that. The complexity of the system in question isn’t really a factor. And in any case, brains are not ‘running on’ formal systems!

Bitbucket Oh, but they have to be! I’m not suggesting the ‘program’ for any given brain is simple, but I can see three ways we could in principle construct it.

  1. If we list all the sensory impressions and all the instructions to act that go into or out of a brain during a lifetime, we can treat them as inputs and outputs. Now there just must be some function, some algorithm, which produces exactly those outputs for those inputs. If nothing simpler is available (I’m sure it would be) there is always the algorithm which just lists the inputs to date and says ‘given these inputs, give this output’.
  2. If you don’t like that approach, I reckon the way neurons work is sufficiently clear for us to construct a complete neuronal model of a brain (in principle – I’m not saying it’s a practical proposition); and then that would clearly represent an implementation of a complex function for the person in question.
  3. As a last resort, we just model the whole brain in excruciating detail. It’s a physical object, and obeys the normal laws of physics, so we can construct a mechanical description of how it works.

Any of these will do. The algorithms we come up with might well be huge and unwieldy, but they exist, which is all that matters. So we must be able to apply Gödel to people, too.
Blandula Nonsense! For a start, I don’t believe ‘inputs’ and ‘outputs’ to human beings can be defined in those terms – reality is not digital. But the whole notion of a person’s own algorithm is absurd! The point about computers is that their algorithms are defined by a programmer and kept in a recognised place, clearly distinguished from data, inputs, and hardware, so it’s easy to say what they are in advance. With a brain, there is nothing you can point to in advance as the ‘brain algorithm’. If you insist on interpreting the brain as running an algorithm, you just have to wait and see which bits of the brain and which bits of the rest of the person and their environment turn out to be relevant to their ‘outputs’ in what ways and then construct the algorithm to suit. We can never know what the total algorithm is until all the inputs and outputs have been dealt with. In short, it turns out not to be surprising that a person can’t see the truth of their own Gödel statement, because they have to dead before anyone can even decide what it is!

Bitbucket Alright, well look at it this way. We’re only talking about things that can’t be proved within a particular formal system. Humans can see the truth of these statements, and even prove them, because they go outside the formal system to do so. There’s no real reason why a computer can’t do the same. It may operate one algorithm to begin with, but it can learn and develop more comprehensive algorithms for itself as it goes. Why not?

BlandulaThat’s the whole point! Human beings can always find a new way of looking at something, but an algorithm can’t. You can’t have an algorithm which generates new algorithms for itself, because if it did, the new bits would by definition be part of the original algorithm.

Bitbucket I think it must be clear to anyone by now that you’re just playing with words. I still say that all this is simply too esoteric to have any bearing on what is essentially a practical computing problem. If I understand them correctly, both Dennett and your friend Searle agree with me (in their different ways). The algorithms in practical AI applications aren’t about mathematical proof, they’re about doing stuff.

Blandula I was puzzled by Dennett’s argument in ‘Darwin’s dangerous idea’ in particular. He’s quite dismissive about the whole thing, but what he seems to say is this. The narrow set of algorithms picked out by Penrose may not be able to provide an arithmetical proof, but what about all the others which Penrose has excluded from consideration? This is strange, because the ones excluded from consideration, according to Dennett, are: algorithms which don’t do anything at all; algorithms which aren’t interesting; algorithms which aren’t about arithmetic; algorithms which don’t produce proofs; and algorithms which aren’t consistent! Can we reasonably expect proofs from any of these? Maybe not, says Dennett, but some of them might play a good game of chess… This seems to miss the point to me.
What I fear is that this kind of reasoning leads to what I call the Roboteer’s argument (I’ve seen it put forward by people like Kevin Warwick and Rodney Brooks). The Roboteer says, OK, so computers will never work the way the human brain works. So what? That doesn’t mean they can’t be intelligent and it doesn’t mean they can’t be conscious. Planes don’t fly the way birds do, but we don’t say it isn’t proper flight because of that…

BitbucketPersonally, I don’t see anything wrong with that argument. What about this quantum malarkey? You’re not going to tell me you go along with that? There is absolutely no reason to think quantum physics has anything to do with this. It may be hard to understand, but it’s just as calculable and deterministic as any other kind of physics. All there really is to this is that both consciousness and quantum physics seem a bit spooky.

Blandula It isn’t conventional, established quantum physics we’re talking about. Having established that human thought goes beyond the algorithmic, Penrose needs to find a non-computable process which can account for it; but he doesn’t see anything in normal physics which fits the bill. He wants the explanation to be part of physics – you ought to sympathise with that – so it has to be in a new physical theory, and new quantum physics is the best candidate. Further strength is given to the case by the ideas Stuart Hameroff and he have come up with about how it might actually work, using the microtubules which are present in the structure of nerve cells.

Bitbucket They’re present in most other kinds of cell, too, if I understand correctly. Microtubules have perfectly ordinary jobs to do within cells which have nothing to do with thinking. We don’t understand the brain completely, but surely we know by now that neurons are the things that do the basic work.

Blandula It isn’t quite as clear as that. There has been a tendency, right since the famous McCulloch and Pitts paper of 1947, to see neurons as simple switches, but the more we know about them the less plausible that seems. Actually there is some highly complex chemistry involved. Personally, I would also say that the way neurons are organised looks very much like the sort of thing you might construct if you wanted to catch and amplify the effects of very small-scale events. One molecule – in the eye, one quantum, as Penrose points out – can make a neuron fire, and that can lead to a whole chain of other firings.

Bitbucket At the end of the day, the problem is that quantum physics just doesn’t help. It doesn’t give us any explanatory resources we couldn’t get from normal physics.

Blandula That’s too sweeping. There are actually several reasons, in my view, to think that quantum physics might be relevant to consciousness (although these are not Penrose’s reasons). One is that the way two different states of affairs can apparently be held in suspense resembles the way two different courses of action can be suspended in the mind during the act of choice. A related point is the possibility that exploiting this kind of suspension could give us spectacularly fast computing, which might explain some of the remarkable properties of the brain. Another is the special role of observation – becoming conscious of things – in causing the collapse of the wavefunction. A third is that quantum physics puts some limits on how precisely we can specify the details of the world, which seems to militate against the kind of argument you were making earlier, about modelling the brain in total detail. I know all of these are open to strong objections: the real reason, as I’ve already said, is just that quantum physics is the most likely place to find the kind of new science which Penrose thinks is needed.

Bitbucket I don’t see it. It seems to me inevitable that any new physics that may come along is going to be amenable to simulation on a computer – if it wasn’t, it hardly seems possible it could be clear enough to be a reasonable theory.

Blandula In other words, your mind is closed to any possibility except computationalism. Consciousness seems to me to be such an important phenomenon that I simply cannot believe it is something just ‘accidentally’ conjured up by a complicated computation…


  1. 1. David says:

    I like the discussion, but the commentary on quantum mechanics is rife with error. QM is the foundation of the understanding all modern physics, excepting general relativity. At the most fundamental level it is entirely stochastic, but decoherence often ensures this property is diminished on the macro scale.

  2. 2. Peter says:

    Thanks, David: the remarks above may well be a bit garbled on that subject – ‘entirely stochastic’ though -is that right?

  3. 3. Sci says:

    Apparently Penrose got this idea from JR Lucas, who in turn based his argument from a remark from Godel on the difference between minds and machines implied by incompleteness.

    Lucas wrote a book about this that I’ve not read entitled Freedom of the Will, though I did find two good papers that at least give better understanding though still not sure I fully understand:

    1) The Godelian Argument –

    2) Minds, Machines and Gödel –

    Lucas has a long list of arguments and counterarguments on his site (second link).

  4. 4. Sci says:

    It seems Orch-OR was right about quantum vibrations in the microtubules?:

    Still not clear to me how this evokes or creates consciousness though? I guess it is a kind of panpsychism, where you need a brain to draw out the potential of consciousness at the QM level?

  5. 5. Peter says:

    No, I don’t really get the relevance of the quantum stuff; but a point scored for Penrose and Hameroff, possibly.

  6. 6. Sci says:

    If this pans out it’ll be an interesting question whether any other model for consciousness has had any similar successes in predicting something that was, in the past, so controversial.

    I feel like 10 years ago the idea of quantum biology was a non-starter, yet Orch-OR has been around for awhile AFAIK. 1994 was the publication year for Shadow of the Mind.

  7. 7. Emergent C says:

    Peter, the quantum stuff, for me, does two things:

    (1) The ‘intellectual’ argument – algorithmic computation offers nothing like the power of qubit computation. The tilings and quasicrystals are possible only with the collapse of superimposed states – quantum computations. So this form of computation exists in nature, we might be a product of it rather than just Turing machines.

    (2) The ’emotional’ part. This warms me, then worries me, because I find it so comforting. Are any of us really above the seduction of believing what we want to believe? If consciousness is a function of quantum technology, then it is delocalised in space, and probably time too (Bell’s Theorem). What we see is a fraction of what our consciousness is. It does not have to fit within our experience of the birth-life-death existential and anomic void.

    There is the possibility of a decoherence of the information of our consciousness into a more permanent fabric of a bigger reality when we die. Our consciousness probably really exists more fundamentally at this level in whatever form (the granular, uneven, deepest background fabric of the universe that Penrose hints appears uneven – therefore containing information (physical laws, raw information of the data-set of reality) in this irregularity.

    Emotionally, quantum consciousness opens many doors to a secular soul; a persistence of self probably before and after our window of subjective consciousness now.

    The urgency of his argument that consciousness is not just hosted by recursive technology, feels like it might be motivated by fear of death to me. If consciousness is lifted to a QM property, we might just be immortal. This is not to say there’s an intellectual problem here, just that we should beware of emotional clouds.

  8. 8. Shaikh Raisuddin says:


    For all about consciousness please see my post

  9. 9. Nattering Nabob says:

    “I have solved puzzle of consciousness.
    Consciousness is simple and easy…”
    –Shaikh Raisuddin


    This better be good. If not, improvise.

  10. 10. Sci says:

    @Emergent C: “The urgency of his argument that consciousness is not just hosted by recursive technology, feels like it might be motivated by fear of death to me. If consciousness is lifted to a QM property, we might just be immortal. This is not to say there’s an intellectual problem here, just that we should beware of emotional clouds.”

    AFAIK Penrose – despite his acceptance of Popper’s 3 worlds of Math/Matter/Mind – rejects the any kind of soul. Someone asked him about this at the end of a talk he gave at Google IIRC. Hammeroff has speculated on the possibility of post-mortem survival but has specifically noted Penrose is not on board.

    Lucas, who initially came up with the non-computability argument, also thinks when we die that’s the end. In fact, as I recall Lucas is a materialist akin to Searle.

  11. 11. Emergent C says:

    Thanks Sci.

    I heard Hammeroff (youtube video – an easy search) mooting quantum decoherence from quantum consciousness during death. As there is progressive loss of wave phase, there was the inference that this information passed, from our brains, to the environment – therefore persisted in some form.

    He mentions too, the observed runs of mesolimbic gamma synchronicity just before death, which, at face-value, do sound surprising in a moribund brain.

    I’m interested in death; in particular our response to its impending visit. What is a ‘normal’ response to this information that our (right) frontal cortex allows us fully to anticipate? Yalom believes, as I do, that fear is much more broadly evoked by this future than we care to talk about. There’s much to say historically, culturally (including religion) here, but my point is that we must be aware of this fear, during a quest to understand consciousness.

    Huge topic; so interesting, but too little time (no metaphor here!).

  12. 12. Sci says:

    @Emergenct C: But it seems everyone has fears and desires underwriting their goals. Materialists want the mental to explicable in the way matter is, atheists don’t want God while theists do, and so on.

    Best thing to do is let science rather than philosophy decide, something I personally suspect is at least several decades away though the timetable seems like it’ll depends on if/how evolution has exploited quantum level phenomenon. (I can’t recall if photosynthesis utilizing quantum phenomenon is fully accepted.)

  13. 13. Sci says:

    Relating to quantum biology (AFAICTell) rather than directly with consciousness but perhaps a prelude of things to come? ->

    Sound-like bubbles whizzing around in DNA are essential to life

    “The terahertz sound-like bubbles we have seen alter our fundamental understanding of biochemical reactions. There were earlier suggestions for a role of delocalized quantum phenomena in light harvesting, magneto reception, and olfaction. The new results now imply a much more general role for sound-like delocalized phenomena in biomolecular processes.”

  14. 14. Sci says:

    On the quantum biology side, there might be a quale for photon detection:

    ‘The techniques used in the study also open up ways of testing how quantum properties—such as the ability of photons to be in two places at the same time—affect biology, he adds.

    “The most amazing thing is that it’s not like seeing light. It’s almost a feeling, at the threshold of imagination,”’

  15. 15. Sci says:

    More hope for Penrose & Hammeroff with unending coherence:

    Forever quantum: physicists demonstrate everlasting quantum coherence.

  16. 16. Sci says:

    Can Quantum Physics Explain Consciousness?

    “A new approach to a once-farfetched theory is making it plausible that the brain functions like a quantum computer.”

Leave a Reply