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


  1. 1. Tom Clark says:

    Thanks Peter. This paper is so wild and wooly that it occurred to me it might be another Sokals’s Hoax type ploy, something put over on the editor to show how even the physics community can be taken in by quantum babble-speak. Except, of course, that it’s by Tegmark and the references seem solid. So in this case the babble is in the eye of the beholder.

  2. 2. Arnold Trehub says:

    An interesting side note about microgravity: The retinoid theory of consciousness explains the moon illusion as a natural result of the anisotropy of retinoid space where UP and DOWN are determined by the systematic effect of gravity on the vestibular system. The theory predicts that in the environment of micro-gravity the moon illusion will be experienced as an irregular/chancy phenomenon. I asked several astronauts about their observations of the moon while in space and this prediction was confirmed.

  3. 3. Sci says:

    As I recall Tegmark believes all reality is really just an infinite set of platonic mathematical structures. It seems (perhaps erroneously) to me his confusion of abstractions with actualities in metaphysics has carried over to his misunderstanding of the Hard Problem. I think Searle’s major critique(1) of IIT still applies here (and possibly to Graziano’s Master of Puppets weirdness):

    “So on their view every proton and neutron is conscious. But the integrated information in all of these is just as observer-relative as was the information in the photodiode. There is no intrinsic absolute information in protons and neutrons, nor in my personal computer, nor in my smart phone. The information is all in the eye of the beholder…

    …But the deepest objection is that the theory is unmotivated. Suppose they could give a definition of integrated and differentiated information that was not observer-relative, that would enable us to tell, from the brute physics of a system, whether it had such information and what information exactly it had. Why should such systems thereby have qualitative, unified subjectivity? In addition to bearing information as so defined, why should there be something it feels like to be a photodiode, a photon, a neutron, a smart phone, embedded processor, personal computer, “the air we breathe, the soil we tread on,” or any of their other wonderful examples? As it stands the theory does not seem to be a serious scientific proposal.”

    Flipping through the paper I don’t see Tegmark fully addressing this criticism. Admittedly his physics equations are beyond my knowledge of the subject but I can’t help but feel the answer to Searle’s criticism should be philosophical rather than mathematical. Even the development of treatments/technology based on IIT as a measurable quality wouldn’t really answer *why* integrated information produces consciousness.

    (1)Can a Photodiode Be Conscious?


  4. 4. Peter says:

    …wild and wooly…

    On his own site (charmingly retro, but who am I to talk?) Tegmark remarks that for every ten serious papers he allows himself a wacky one…

  5. 5. TonyK says:

    “But I must surely be misunderstanding.” I don’t think so! It seems to me too that Tegmark has misunderstood Penrose’s argument completely. Penrose is talking about the gravitational fields generated by objects smaller than dust particles, and how wave function collapse might occur when the difference between the gravitational fields of alternative quantum states of such an object becomes large enough (in some sense).

    By the way, Einstein’s Equivalence Principle can be interpreted as saying that the force of gravity is literally absent — to first order, anyway — in free fall. So I would say there are no aspersions to be cast on Tegmark’s physicist credentials there.

  6. 6. ihtio says:

    I have to remarks with respect to IIT:

    First: information is in the eye of the beholder. What is the meaning or the difference between 0000 and 0001? There is none, if we don’t have anything to interpret the data (actual physical strings). In other words: in general, between those two strings of bits there is no difference that makes a difference, simply because there is no one or nothing who/what would differentiate between the two.

    This computationalism may be all cool and “into the future”, but why exactly information IS consciousness and digestion is not?

  7. 7. ask says:

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    this article is in fact a good post, keep it up.

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