Tag Archives: Penrose

Entangled Consciousness

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Entangled

Could the answer be quantum physics after all? Various people have suggested that the mystery of consciousness might turn out to be explicable in terms of quantum physics; most notably we have the theory championed ny Roger Penrose and Stuart Hameroff, which suggests that as-yet unknown quantum mechanics might be going on in the microtubules of neural cells. Atai Barkai has kindly shared with me his draft paper which sets out a different take on the matter.

Barkai’s target is subjective experience, or what he defines as the consciousness instance. We may be conscious of things in the world out there, but that kind of consciousness always involves an element of inference, explicit or not; the consciousness instance is free of those uncertainties, consisting only of the direct experience of which we can be certain. Some hardy sceptics would deny that there is anything in consciousness that we can be that sure of, but I think it is clear enough what distinction Barkai is making and that it is, as it were, first order experience he is aiming at.

The paper puts a complex case very carefully, but flinging caution to the winds I believe the gist goes like this. Typically, those who see a problem with qualia and subjective experience think it lies outside the account given by physics, which arguably therefore needs some extension. Barkai agrees that subjectivity is outside the classical account and that a more capacious concept of the universe is needed to accommodate it; but he thinks that quantum entanglement can already, properly read, provide what is needed.

It’s true that philosophical discussions generally either treat classical physics as being the whole subject or ignore any implications that might arise from the less intuitive aspects of quantum physics. Besides entanglement, Barkai discusses free will and its possible connection with the indeterminism of quantum physics. If there really is indeterminism in quantum physics; on this and other points I simply don’t have a clear enough grasp of the science to tackle the questions effectively (better informed comments would be welcome).

Entanglement, as I understand it, means that the states of two particles (or in principle, larger bodies) may be strongly connected in ways that do not depend on normal classical interaction and are not affected by distance. This means that information can in theory be transferred any distance, instantly and infallibly, which opens up the theoretical possibility of quantum computing, delivering the instant solution to computable problems of any finite size. Whether the brain might be doing this kind of thing is a question which Barkai leaves as an interesting speculation.

The main problem for me in the idea that entanglement explains subjectivity is understanding intuitively how that could be so. Entanglement seems to offer the possibility that there might be more information in our mental operations than classical physics could account for; that feels helpful, but does it explain the qualitative difference between mere dead data and the ‘something it is like’ of subjectivity? I don’t reject the idea, but I don’t think I fully grasp it either.

There is also a more practical objection. Quantum interactions are relevant at a microscopic level, but as we ascend to normal scales, it is generally assumed that wave forms collapse and we slip quickly back into a world where classical physics reigns. It is generally thought that neurons, let alone the whole brain, are just too big and hot for quantum interactions to have any relevance. This is why Penrose looks for new quantum mechanics in tiny microtubules rather than resting on what known quantum mechanics can provide.

As I say, I’m not really competent to assess these issues, but there is a neatness and a surprising novelty about Barkai’s take that suggests it merits further discussion.

Flatlanders

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Wrong again: just last week I was saying that Roger Penrose’s arguments seemed to have drifted off the radar a bit. Immediately, along comes this terrific post from Scott Aaronson about a discussion with Penrose.

In fact it’s not entirely about Penrose; Aaronson’s main aim was to present an interesting theory of his own as to why a computer can’t be conscious, which relies on non-copyability. He begins by suggesting that the onus is on those who think a computer can’t be conscious to show exactly why. He congratulates Penrose on doing this properly, in contrast to say, John Searle who merely offers hand-wavy stuff about unknown biological properties. I’m not really sure that Searle’s honest confession of ignorance isn’t better than Penrose’s implausible speculations about unknown quantum mechanics, but we’ll let that pass.

Aaronson rests his own case not on subjectivity and qualia but on identity. He mentions several examples where the limitless copyability of a program seems at odds with the strong sense of a unique identity we have of ourselves – including Star Trek style teleportation and the fact that a program exists in some Platonic sense forever, whereas we only have one particular existence. He notes that at the moment one of the main differences between brain and computer is our ability to download, amend and/or re-run programs exactly; we can’t do that at all with the brain. He therefore looks for reasons why brain states might be uncopyable. The question is, how much detail do we need before making a ‘good enough’ copy? If it turns out that we have to go down to the quantum level we run into the ‘no-cloning’ theorem; the price of transferring the quantum state of your brain is the destruction of the original. Aaronson makes a good case for the resulting view of our probably uniqueness being an intuitively comfortable one, in tune with our intuitions about our own nature. It also offers incidentally a sort of reconciliation between the Everett many-worlds view and the Copenhagen interpretation of quantum physics: from a God’s eye point of view we can see the world as branching, while from the point of view of any conscious entity (did I just accidentally call God unconscious?) the relevant measurements are irreversible and unrealised branches can be ‘lopped off’. Aaronson, incidentally, reports amusingly that Penrose absolutely accepts that the Everett view follows from our current understanding of quantum physics; he just regards that as a reductio ad absurdum – ie, the Everett view is so absurd the link proves there must be something wrong with our current understanding of quantum physics.

What about Penrose? According to Aaronson he now prefers to rest his case on evolutionary factors and downplay his logical argument based on Godel. That’s a shame in my view. The argument goes something like this (if I garble it someone will perhaps offer a better version).

First we set up a formal system for ourselves. We can just use the letters of the alphabet, normal numbers, and normal symbols of formal logic, with all the usual rules about how they can be put together. Then we make a list consisting of all the valid statements that can be made in this system. By ‘valid’, we don’t mean they’re true, just that they comply with the rules about how we put characters together (eg, if we use an opening bracket, there must be a closing one in an appropriate place). The list of valid statements will go on forever, of course, but we can put them in alphabetical order and number them. The list obviously includes everything that can be said in the system.

Some of the statements, by pure chance, will be proofs of other statements in the list. Equally, somewhere in our list will be statements that tell us that the list includes no proof of statement x. Somewhere else will be another statement – let’s call this the ‘key statement’ – that says this about itself. Instead of x, the number of that very statement itself appears. So this one says, there is no proof in this system of this statement.

Is the key statement correct – is there no proof of the key statement in the system? Well, we could look through the list, but as we know it goes on indefinitely; so if there really is no proof there we’d simply be looking forever. So we need to take a different tack. Could the key statement be false? Well, if it is false, then what it says is wrong, and there is a proof somewhere in the list. But that can’t be, because if there’s a proof of the key statement anywhere,the key statement must be true! Assuming the key statement is false leads us unavoidably to the conclusion that it is true, in the light of what it actually says. We cannot have a contradiction, so the key statement must be true.

So by looking at what the key statement says, we can establish that it is true; but we also establish that there is no proof of it in the list. If there is no proof in the list, there is no possible proof in our system, because we know that the list contains everything that can be said within our system; there is therefore a true statement in our system that is not provable within it. We have something that cannot be proved in an arbitrary formal system, but which human reasoning can show to be true; ergo, human reasoning is not operating within any such formal system. All computers work in a formal system, so it follows that human reasoning is not computational.

As Aaronson says, this argument was discussed to the point of exhaustion when it first came out, which is probably why Penrose prefers other arguments now. Aaronson rejects it, pointing out that he himself has no magic ability to see “from the outside” whether a given formal system is consistent; why should an AI do any better – he suggests Turing made a similar argument. Penrose apparently responded that this misses the point, which is not about a mystical ability to perceive consistency but the human ability to transcend any given formal system and move up to an expanded one.

I’ll leave that for readers to resolve to their own satisfaction. Let’s go back to Aaronson’s suggestion that the burden of proof lies on those who argue for the non-computability of consciousness. What an odd idea that is!  How would that play  at the Patent Office?

“So this is your consciousness machine, Mr A? It looks like a computer. How does it work?”

“All I’ll tell you is that it is a computer. Then it’s up to you to prove to me that it doesn’t work – otherwise you have to give me rights over consciousness! Bwah ha ha!”

Still, I’ll go along with it. What have I got? To begin with I would timidly offer my own argument that consciousness is really a massive development of recognition, and that recognition itself cannot be algorithmic.

Intuitively it seems clear to me that the recognition of linkages and underlying entities is what powers most of our thought processes. More formally, both of the main methods of reasoning rely on recognition; induction because it relies on recognising a real link (eg a causal link) between thing a and thing b; deduction because it reduces to the recognition of consistent truth values across certain formal transformations. But recognition itself cannot operate according to rules. In a program you just hand the computer the entities to be processed; in real world situations they have to be recognised. But if recognition used rules and rules relied on recognising the entities to which the rules applied, we’d be caught in a vicious circularity. It follows that this kind of recognition cannot be delivered by algorithms.

The more general case rests on, as it were, the non-universality of computation. It’s argued that computation can run any algorithm and deliver, to any required degree of accuracy, any set of physical states of affairs. The problem is that many significant kinds of states of affairs are not describable in purely physical or algorithmic terms. You cannot list the physical states of affairs that correspond to a project, a game, or a misunderstanding. You can fake it by generating only sets of states of affairs that are already known to correspond with examples of these things, but that approach misses the point. Consciousness absolutely depends on intentional states that can’t be properly specified except in intentional terms. That doesn’t contradict physics or even add to it the way new quantum mechanics might; it’s just that the important aspects of reality are not exhausted by physics or by computation.

The thing is, I think long exposure to programmable environments and interesting physical explanations for complex phenomena has turned us all increasingly into flatlanders who miss a dimension; who naturally suppose that one level of explanation is enough, or rather who naturally never even notice the possibility of other levels; but there are more things in heaven and earth than are dreamt of in that philosophy.

Perceptronium

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TegmarkEarlier this year Tononi’s Integrated Information Theory (IIT) gained a prestigious supporter in Max Tegmark, professor of Physics at MIT. The boost for the theory came not just from Tegmark’s prestige, however; there was also a suggestion that the IIT dovetailed neatly with some deep problems of physics, providing a neat possible solution and the kind of bridge between neuroscience, physics and consciousness that we could hardly have dared to hope for.

Tegmark’s paper presents the idea rather strangely, suggesting that consciousness might be another state of matter like the states of being a gas, a liquid, or solid.  That surely can’t be true in any simple literal sense because those particular states are normally considered to be mutually exclusive: becoming a gas means ceasing to be a liquid. If consciousness were another member of that exclusive set it would mean that becoming conscious involved ceasing to be solid (or liquid, or gas), which is strange indeed. Moreover Tegmark goes on to name the new state ‘perceptronium’ as if it were a new element. He clearly means something slightly different, although the misleading claim perhaps garners him sensational headlines which wouldn’t be available if he were merely saying that consciousness arose from certain kinds of subtle informational organisation, which is closer to what he really means.

A better analogy might be the many different forms carbon can take according to the arrangement of its atoms: graphite, diamond, charcoal, graphene, and so on; it can have quite different physical properties without ceasing to be carbon. Tegmark is drawing on the idea of computronium proposed by Toffoli and Margolus. Computronium is a hypothetical substance whose atoms are arranged in such a way that it consists of many tiny modules capable of performing computations.  There is, I think, a bit of a hierarchy going on here: we start by thinking about the ability of substances to contain information; the ability of a particular atomic matrix to encode binary information is a relatively rigorous and unproblematic idea in information theory. Computronium is a big step up from that: we’re no longer thinking about a material’s ability to encode binary digits, but the far more complex functional property of adequately instantiating a universal Turing machine. There are an awful lot of problems packed into that ‘adequately’.

The leap from information to computation is as nothing, however, compared to the leap apparently required to go from computronium to perceptronium. Perceptronium embodies the property of consciousness, which may not be computational at all and of which there is no agreed definition. To say that raises a few problems is rather an understatement.

Aha! But this is surely where the IIT comes in. If Tononi is right, then there is in fact a hard-edged definition of consciousness available: it’s simply integrated information, and we can even say that the quantity required is Phi. We can detect it and measure it and if we do, perceptronium becomes mathematically tractable and clearly defined. I suppose if we were curmudgeons we might say that this is actually a hit against the IIT: if it makes something as absurd as perceptronium a possibility, there must be something pretty wrong with it. We’re surely not that curmudgeonly, but there is something oddly non-dynamic here. We think of consciousness, surely, as a process, a  function: but it seems we might integrate quite a lot of information and simply have it sit there as perceptronium in crystalline stillness; the theory says it would be conscious, but it wouldn’t do anything.  We could get round that by embracing the possibility of static conscious states, like one frame out of the movie film of experience; but Tegmark, if I understand him right, adds another requirement for consciousness: autonomy, which requires both dynamics and independence; so there has to be active information processing, and it has to be isolated from outside influence, much the way we typically think of computation.

The really exciting part, however,  is the potential linkage with deep cosmological problems – in particular the quantum factorisation problem. This is way beyond my understanding, and the pages of equations Tegmark offers are no help, but the gist appears to be that  quantum mechanics offers us a range of possible universes.  If we want to get ‘physics from scratch’, all we have to work with is, in Tegmark’s words,

two Hermitian matrices, the density matrix p encoding the state of our world and the Hamiltonian H determining its time-evolution…

Please don’t ask me to explain; the point is that the three things don’t pin down a single universe; there are an infinite number of acceptable solutions to the equations. If we want to know why we’ve got the universe we have – and in particular why we’ve got classical physics, more or less, and a world with an object hierarchy – we need something more. Very briefly, I take Tegmark’s suggestion to be that consciousness, with its property of autonomy, tends naturally to pick out versions of the universe in which there are similarly integrated and independent entities – in other words the kind of object-hierarchical world we do in fact see around us. To put it another way and rather baldly, the universe looks like this because it’s the only kind of universe which is compatible with the existence of conscious entities capable of perceiving it.

That’s some pretty neat footwork, although frankly I have to let Tegmark take the steering wheel through the physics and in at least one place I felt a little nervous about his driving. It’s not a key point, but consider this passage:

Indeed, Penrose and others have speculated that gravity is crucial for a proper understanding of quantum mechanics even on small scales relevant to brains and laboratory experiments, and that it causes non-unitary wavefunction collapse. Yet the Occam’s razor approach is clearly the commonly held view that neither relativistic, gravitational nor non-unitary effects are central to understanding consciousness or how conscious observers perceive their immediate surroundings: astronauts appear to still perceive themselves in a semi-classical 3D space even when they are effectively in a zero-gravity environment, seemingly independently of relativistic effects, Planck-scale spacetime fluctuations, black hole evaporation, cosmic expansion of astronomically distant regions, etc

Yeah… no. It’s not really possible that a professor of physics at MIT thinks that astronauts float around their capsules because the force of gravity is literally absent, is it? That kind of  ‘zero g’ is just an effect of being in orbit. Penrose definitely wasn’t talking about the gravitational effects of the Earth, by the way; he explicitly suggests an imaginary location at the centre of the Earth so that they can be ruled out. But I must surely be misunderstanding.

So far as consciousness is concerned, the appeal of Tegmark’s views will naturally be tied to whether one finds the IIT attractive, though they surely add a bit of weight to that idea. So far as quantum factorisation is concerned, I think he could have his result without the IIT if he wanted: although the IIT makes it particularly neat, it’s more the concept of autonomy he relies on, and that would very likely still be available even if our view of consciousness were ultimately somewhat different. The linkage with cosmological metaphysics is certainly appealing, essentially a sensible version of the Anthropic Principle which Stephen Hawking for one has been prepared to invoke in a much less attractive form

Quanta and Qualia

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sorates and branestawmQuentin Ruyant has written a thoughtful piece about quantum mechanics and philosophy of mind: in a nutshell he argues both that quantum theory may be relevant to the explanation of consciousness and that consciousness may be relevant to the interpretation of quantum theory.

Is quantum theory relevant to consciousness? Well. of course some people have said so, notably Sir Roger Penrose and Stuart Hameroff.  I think Ruyant is right, though, that the majority of philosophers and probably the majority of physicists dismiss the idea that quantum theory might be needed to explain consciousness. People often suggest that the combination of the two only appeals because both are hard to explain: ‘here’s one mystery and here’s another: maybe one explains the other’. Besides, people say, the brain is far too big and hot and messy for anything other than classical physics to be required

In making the case for the relevance of quantum theory, Ruyant relies on the Hard Problem.  His position is that the Hard Problem is not biological but a matter of physics, whereas the Easy Problem, to do with all the scientifically tractable aspects of consciousness, can be dealt with by biology or psychology.

Actually, turning aside from the main thread of Ruyant’s argument, there are some reasons to suggest that quantum physics is relevant to the Easy Problem. Penrose’s case, in fact, seems to suggest just that: in his view consciousness is demonstrably non-computable and some kind of novel quantum mechanics is his favoured candidate to fill the gap. Penrose’s examples, things like solving mathematical problems, look like ‘Easy’ Problem matters to me.

Although I don’t think anyone (including me) advocates the idea, it also seems possible to argue that the ‘spooky action at a distance’ associated with quantum entanglement might conceivably have something to tell us about intentionality and its remarkable power to address things that are remote and not directly connected with us.

Anyway, Ruyant is mainly concerned with the Hard Problem, and his argument is that metaphysics and physics are closely related. Topics like the essential nature of physical things straddle the borderline between the two subjects, and it is not at all implausible therefore that the deep physics of quantum mechanics might shed light on the deep metaphysics of phenomenal experience. It seems to me a weakish line of argument, possibly tinged with a bit of prejudice: some physicists are inclined to feel that while their subject deals with the great fundamentals, biology deals only with the chance details of life; sort of a more intellectual kind of butterfly collecting.  That kind of thinking is not really well founded, and it seems particularly odd to think that biology is irrelevant when considering a phenomenon that, so far as we know, appears only in animals and is definitely linked very strongly with the operation of the brain. John Searle for one argues that ‘Hard Problem’ consciousness arises from natural biological properties of brain tissue. We don’t yet know what those properties are, but in his view it’s absurd to think that the job of nerves could equally well be performed by beer cans and string. Ruth Millikan, somewhat differently, has argued that consciousness is purely biological in nature, arising from and defined by evolutionary needs.

I think the truth is that it’s difficult to get anywhere at this meta-theoretical level:  we don’t really decide what kind of theory is most likely to be right and then concentrate on that area; we decide what the true theory most likely is and then root for the kind of theory it happens to be. That, to a great extent, is why quantum theories are not very popular: no-one has come up with a particular one that is cogent and appealing.  It seems to me that Ruyant likes the idea of physics-based theories because he favours panpsychism, or panphenomenalism, and so is inclined to think that the essential nature of matter is likely to be the right place to look for a theory.

To be honest, though, I doubt whether any kind of science can touch the Hard Problem.  It’s about entities that have no causal properties and are ineffable: how could empirical science ever deal with that? It might well be that a scientist will eventually give us the answer, but if so it won’t be by doing science, because neither classical nor quantum physics can really touch the inexpressible.

Actually, though there is a long shot.  If Colin McGinn is partly on the right track, it may be that consciousness seems mysterious to us simply because we’re not looking at it the right way: our minds won’t conceptualise it correctly. Now the same could be true of quantum theory. We struggle with the interpretation of quantum mechanics, but what if we could reorient our brains so that it simply seemed natural, and we groped instead for an acceptable ‘interpretation’ of spooky classical physics? If we could make such a transformation in our mental orientation, then perhaps consciousness would make sense too? It’s possible, but we’re back to banging two mysteries together in the hope that some spark will be generated.

Ruyant’s general case, that metaphysicians should be informed by our best physics is hard to argue with. At the moment few philosophers really engage with the physics and few physicists really grasp the philosophy. Why do philosophers avoid quantum physics? Partly, no doubt, just because it’s difficult, and relies on mathematics which few philosophers can handle. Partly also, I think there’s an unspoken fear that in learning about quantum physics your intuitions will be trained into accepting a particular weltanschauung that might not be helpful. Connected with that is the fear that quantum physics isn’t really finished or definitive. Where would I be if I came up with a metaphysical system that perfectly supported quantum theory and then a few years later it turns out that I should have been thinking in terms of string theory? Metaphysicians cross their fingers and hope they can deal with the key issues at a level of generality that means they won’t be rudely contradicted by an unexpected advance in physics a few years later.

I suppose what we really need is someone who can come up with a really good specific theory that shows the value of metaphysics informed by physics, but few people are qualified to produce one. I must say that Ruyant seems to be an exception, with an excellent grasp of the theories on both sides of the divide. Perhaps he has a theory of consciousness in his back pocket…?