Perceptronium

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

The Consciousness Meter

Picture: meter. It has been reported in various places recently that Giulio Tononi is developing a consciousness meter.  I think this all stems from a New York Times article by the excellent Carl Zimmer where, to be tediously accurate, Tononi said “The theory has to be developed a bit more before I worry about what’s the best consciousness meter you could develop.”   Wired discussed the ethical implications of such a meter, suggesting it could be problematic for those who espouse euthanasia but reject abortion.

I think a casual reader could be forgiven for dismissing this talk of a consciousness meter. Over the last few years there have been regular reports of scientific mind-reading: usually what it amounts to is that the subject has been asked to think of x while undergoing a scan; then having recorded the characteristic pattern of activity the researchers have been able to spot from scans with passable accuracy the cases where the subject is thinking of x rather than y or z.  In all cases the ability to spot thoughts about x are confined to a single individual on a single occasion, with no suggestion that the researchers could identify thoughts of x in anyone else, or even in the same individual a day later. This is still a notable achievement; it resembles (can’t remember who originally said this) working out what’s going on in town by observing the pattern of lights from an orbiting spaceship; but it falls a long way short of mind-reading.

But in Tononi’s case we’re dealing with something far more sophisticated.  We discussed a few months ago Tononi’s Integrated Information Theory (IIT), which holds that consciousness is a graduated phenomenon which corresponds to Phi: the quantity of information integrated. If true, the theory would provide a reasonable basis for assessing levels of consciousness, and might indeed conceivably lead to something that could be called a consciousness meter; although it seems likely that measuring the level of integration of information would provide a good rule-of-thumb measure of consciousness even if in fact that wasn’t what constituted consciousness. There are some reasons to be doubtful about Tononi’s theory: wouldn’t contemplating a very complex object lead to a lot of integration of information? Would that mean you were more conscious? Is someone gazing at the ceiling of the Sistine Chapel necessarily more conscious than someone in a whitewashed cell?

Tononi has in fact gone much further than this: in a paper with David Balduzzi he suggested the notion of qualia space. The idea here is that unique patterns of neuronal activation define unique subjective experiences.  There is some sophisticated maths going on here to define qualia space, far beyond my clear comprehension; yet I feel confident that it’s all misguided.  In the first place, qualia are not patterns of neuronal activation; the word was defined precisely to identify those aspects of experience which are over and above simple physics;  the defining text of Mary the colour scientist is meant to tell us that whatever qualia are, they are not information. You may want to reject that view; you may want to say that in the end qualia are just aspects of neuron firing; but you can’t have that conclusion as an assumption. To take it as such is like writing an alchemical text which begins: “OK, so this lead is gold; now here are some really neat ways to shape it up into ingots”.

And alas, that’s not all. The idea of qualia space, if I’ve understood it correctly, rests on the idea that subjective experience can be reduced to combinations of activation along a number of different axes.  We know that colour can be reduced to the combination of three independent values (though experienced colour is of course a large can of worms which I will not open here) ; maybe experience as a whole just needs more scales of value.  Well, probably not.  Many people have tried to reduce the scope of human thought to an orderly categorisation: encyclopediae;  Dewey’s decimal index; and the international customs tariff to name but three; and it never works without capacious ‘other’ categories.  I mean, read Borges, dude:

I have registered the arbitrarities of Wilkins, of the unknown (or false) Chinese encyclopaedia writer and of the Bibliographic Institute of Brussels; it is clear that there is no classification of the Universe not being arbitrary and full of conjectures. The reason for this is very simple: we do not know what thing the universe is. “The world – David Hume writes – is perhaps the rudimentary sketch of a childish god, who left it half done, ashamed by his deficient work; it is created by a subordinate god, at whom the superior gods laugh; it is the confused production of a decrepit and retiring divinity, who has already died” (‘Dialogues Concerning Natural Religion’, V. 1779). We are allowed to go further; we can suspect that there is no universe in the organic, unifying sense of this ambitious term. If there is a universe, its aim is not conjectured yet; we have not yet conjectured the words, the definitions, the etymologies, the synonyms, from the secret dictionary of God.

The metaphor of ‘x-space’ is only useful where you can guarantee that the interesting features of x are exhausted and exemplified by linear relationships; and that’s not the case with experience.  Think of a large digital TV screen: we can easily define a space of all possible pictures by simply mapping out all possible values of each pixel. Does that exhaust television? Does it even tell us anything useful about the relationship of one picture to another? Does the set of frames from Coronation Street describe an intelligible trajectory through screen space? I may be missing the point, but it seems to me it’s not that simple.

Phi

Picture: Phi. I was wondering recently what we could do with all the new computing power which is becoming available.  One answer might be calculating phi, effectively a measure of consciousness, which was very kindly drawn to my attention by Christof Koch. Phi is actually a time- and state-dependent measure of integrated information developed by Giulio Tononi in support of the Integrated Information Theory (IIT) of consciousness which he and Koch have championed.  Some readable expositions of the theory are here and here with the manifesto here and a formal paper presenting phi here. Koch says the theory is the most exciting conceptual development he’s seen in “the inchoate science of consciousness”, and I can certainly see why.

The basic premise of the theory is simply that consciousness is constituted by integrated information. It stems from the phenomenological observations that there are vast numbers of possible conscious states, and that each of them appears to unify or integrate a very large number of items of information. What really lifts the theory above the level of most others in this area is the detailed mathematical under-pinning, which means phi is not a vague concept but a clear and possibly even a practically useful indicator.

One implication of the theory is that consciousness lies on a continuum: rather than being an on-or-off matter, it comes in degrees. The idea that lower levels of consciousness may occur when we are half-awake, or in dogs or other animals, is plausible and appealing. Perhaps a little less intuitive is the implication that there must be in theory be higher states of consciousness than any existing human being could ever have attained. I don’t think this means states of greater intelligence or enlightenment, necessarily; it’s more  a matter of being more awake than awake, an idea which (naturally enough, I suppose) is difficult to get one’s head around, but has a tantalising appeal.

Equally, the theory implies that some minimal level of consciousness goes a long way down to systems with only a small quantity of integrated information. As Koch points out, this looks like a variety of panpsychism or panexperientialism, though I think the most natural interpretation is that real consciousness probably does not extend all that far beyond observably animate entities.

One congenial aspect of the theory for me is that it puts causal relations at the centre of things: while a system with complex causal interactions may generate a high value of phi, a ‘replay’ of its surface dynamics would not. This seems to capture in a clearer form the hand-waving intuitive point I was making recently in discussion of Mark Muhlestein’s ideas.  Unfortunately calculation of Phi for the human brain remains beyond reach at the moment due to the unmanageable levels of complexity involved;  this is disappointing, but in a way it’s only what you would expect. Nevertheless, there is, unusually in this field, some hope of empirical corroboration.

I think I’m convinced that phi measures something interesting and highly relevant to consciousness; perhaps it remains to be finally established that what it measures is consciousness itself, rather than some closely associated phenomenon, some necessary but not sufficient condition. Your view about this, pending further evidence, may be determined by how far you think phenomenal experience can be identified with information. Is consciousness in the end what information – integrated information – just feels like from the inside? Could this be the final answer to the insoluble question of qualia? The idea doesn’t strike me with the ‘aha!’ feeling of the blinding insight, but (and this is pretty good going in this field) it doesn’t seem obviously wrong either.  It seems the right kind of answer, the kind that could be correct.

Could it?