**[Roger Penrose:] **My main technical interest is in twistor theory — a radical approach to space and time — and, in particular, how to fit it in with Einstein's general relativity. There's a major problem there, in which some progress was made a few years ago, and I feel fairly excited about it. It's ultimately aimed at finding the appropriate union between general relativity and quantum theory.

When I was first seriously thinking of getting into physics, I was thinking more in terms of quantum theory and quantum electrodynamics than of relativity. I never got very far with quantum theory at that stage, but that was what I started off trying to do in physics. My Ph.D. work had been in pure mathematics. I suppose my most quoted paper from that period was on generalized inverses of matrices, which is a mathematical thing that physicists hardly ever mention. Then there were the nonperiodic tilings, which relate to quasi crystals, and therefore to solid-state physics to some degree. Then there's general relativity. What I suppose I'm best known for in that area are the singularity theorems that I worked on along with Stephen Hawking. I knew him when he was Dennis Sciama's graduate student; I've known him for a long time now. But the main things I've done in relativity apart from that have to do with spinors and with asymptotic structure of spacetimes, relating to gravitational radiation.

I believe that general relativity will modify the structure of quantum mechanics. Whereas people usually think that in order to unite quantum theory with gravity theory you should apply quantum mechanics, unmodified, to general relativity, I believe that the rules of quantum theory must themselves be modified in order for this union to be successful.

There's a connection between this area of physics and consciousness, in my opinion, but it's a bit roundabout; the arguments are negative. I argue that we shall need to find some noncomputational physical process if we're ever to explain the effects of consciousness. But I don't see it in any existing theory. It seems to me that the only place where noncomputability can possibly enter is in what is called "quantum measurement." But we need a new theory of quantum measurement. It must be a noncomputable new theory. There is scope for this, if the new theory involves changes in the very structure of quantum theory, of the kind that could arise when it's appropriately united with general relativity. But this is something for the distant future.

Why do I believe that consciousness involves noncomputable ingredients? The reason is Gödel's theorem. I sat in on a course when I was a research student at Cambridge, given by a logician who made the point about Gödel's theorem that the very way in which you show the formal unprovability of a certain proposition also exhibits the fact that it's true. I'd vaguely heard about Gödel's theorem — that you can produce statements that you can't prove using any system of rules you've laid down ahead of time. But what was now being made clear to me was that as long as you believe in the rules you're using in the first place, then you must also believe in the truth of this proposition whose truth lies beyond those rules. This makes it clear that mathematical understanding is something you can't formulate in terms of rules. That's the view which, much later, I strongly put forward in my book *The Emperor's New Mind*.

There are possible loopholes to this use of Gödel's theorem, which people can pick on, and they often do. Most of these counterarguments are misunderstandings. Dan Dennett makes genuine points, though, and these need a little more work to see why they still don't get around the Gödel argument. Dennett's case rests on the conten-tion that we use what are called "bottom-up" rather than "top-down" algorithms in our thinking — here, mathematical thinking.

A top-down algorithm is specific to the solution of some particular problem, and it provides a definite procedure that is known to solve that problem. A bottom-up algorithm is one that is not specific to any particular problem but is more loosely organized, so that it learns by experience and gradually improves, eventually giving a good solution to the problem at hand. Many people have the idea that bottom-up systems rather than top-down, programmed algorithmic systems are the way the brain works. I apply the Gödel argument to bottom-up systems too, in my most recent book,* Shadows of the Mind*. I make a strong case that bottom-up systems also won't get around the Gödel argument. Thus, I'm claiming, there's something in our conscious understanding that simply isn't computational; it's something different.

A lot of what the brain does you could do on a computer. I'm not saying that all the brain's action is completely different from what you do on a computer. I am claiming that the actions of consciousness are something different. I'm not saying that consciousness is beyond physics, either — although I'm saying that it's beyond the physics we know now.

The argument in my latest book is basically in two parts. The first part shows that conscious thinking, or conscious understanding, is something different from computation. I'm being as rigorous as I can about that. The second part is more exploratory and tries to find out what on earth is going on. That has two ingredients to it, basically.

My claim is that there has to be something in physics that we don't yet understand, which is very important, and which is of a noncomputational character. It's not specific to our brains; it's out there, in the physical world. But it usually plays a totally insignifi-cant role. It would have to be in the bridge between quantum and classical levels of behavior — that is, where quantum measurement comes in.

Modern physical theory is a bit strange, because one has two levels of activity. One is the quantum level, which refers to small-scale phenomena; small energy differences are what's relevant. The other level is the classical level, where you have large-scale phenomena, where the roles of classical physics — Newton, Maxwell, Einstein — operate. People tend to think that because quantum mechanics is a more modern theory than classical physics, it must be more accurate, and therefore it must explain classical physics if only you could see how. That doesn't seem to be true. You have two scales of phenomena, and you can't deduce the classical behavior from the quantum behavior any more than the other way around.

We don't have a final quantum theory. We're a long way from that. What we have is a stopgap theory. And it's incomplete in ways that affect large-scale phenomena, not just things on the tiny scale of particles.

Current physics ideas will survive as limiting behavior, in the same sense that Newtonian mechanics survives relativity. Relativity modifies Newtonian mechanics, but it doesn't really supplant it. Newtonian mechanics is still there as a limit. In the same sense, quantum theory, as we now use it, and classical physics, which includes Einstein's general theory, are limits of some theory we don't yet have. My claim is that the theory we don't yet have will contain noncomputational ingredients. It must play its role when you magnify something from a quantum level to a classical level, which is what's involved in "measurement."

The way you treat this nowadays, in standard quantum theory, is to introduce randomness. Since randomness comes in, quantum theory is called a probabilistic theory. But randomness only comes in when you go from the quantum to the classical level. If you stay down at the quantum level, there's no randomness. It's only when you magnify something up, and you do what people call "make a measurement." This consists of taking a small-scale quantum effect and magnifying it out to a level where you can see it. It's only in that process of magnification that probabilities come in. What I'm claiming is that whatever it is that's really happening in that process of magnification is different from our present understanding of physics, and it is not just random. It is noncomputational; it's something essentially different.

This idea grew from the time when I was a graduate student, and I felt that there must be something noncomputational going on in our thought processes. I've always had a scientific attitude, so I believed that you have to understand our thinking processes in terms of science in some way. It doesn't have to be a science that we understand now. There doesn't seem to be any place for conscious phenomena in the science that we understand today. On the other hand, people nowadays often seem to believe that if you can't put something on a computer, it's not science.

I suppose this is because so much of science is done that way these days; you simulate physical activity computationally. People don't realize that something can be noncomputational and yet perfectly scientific, perfectly mathematically describable. The fact that I'm coming into all this from a mathematical background makes it easier for me to appreciate that there are things that aren't computational but are perfectly good mathematics.

When I say "noncomputational" I don't mean random. Nor do I mean incomprehensible. There are very clear-cut things that are noncomputational and are known in mathematics. The most famous example is Hilbert's tenth problem, which has to do with solving algebraic equations in integers. You're given a family of algebraic equations and you're asked, "Can you solve them in whole numbers? That is, do the equations have integer solutions?" That question — yes or no, for any particular example — is not one a computer could answer in any finite amount of time. There's a famous theorem, due to Yuri Matiyasevich, which proves that there's no computational way of answering this question in general. In particular cases, you might be able to give an answer by means of some algorithmic procedure. However, given any such algorithmic procedure, which you know doesn't give you wrong answers, you can always come up with an algebraic equation that will defeat that procedure but where you know that the equation actually has no integer solutions.

Whatever understandings are available to human beings, there are — in relation particularly to Hilbert's tenth problem — things that can't be encapsulated in computational form. You could imagine a toy universe that evolved in some way according to Hilbert's tenth problem. This evolution could be completely deterministic yet not computable. In this toy model, the future would be mathematically fixed; however, a computer could not tell you what this future is. I'm not saying that this is the way the laws of physics work at some level. But the example shows you that there's an issue. I'm sure the real universe is much more subtle than that.

The Emperor's New Mind served more than one purpose. Partly I was trying to get a scientific idea across, which was that noncomputability is a feature of our conscious thinking, and that this is a perfectly reasonable scientific point of view. But the other part of it was educational, in a sense. I was trying to explain what modern physics and modern mathematics is like.

Thus, I had two quite different motivations in writing the book. One was to put a philosophical point of view across, and the other was that I felt I wanted to explain scientific things. For quite a long time, I'd felt that I did want to write a book at a semipopular level to explain certain ideas that excited me — ideas that weren't particularly unconventional — about what science is like. I had it in the back of my mind that someday I would do such a thing.

It wasn't until I saw a BBC "Horizon" program, in which Marvin Minsky and various people were making some rather extreme and outrageous statements, that I was finally moved to write the book. I felt that there was a point of view which was essentially the one I believe in, but which I had never seen expressed anywhere and which needed to be put forward. I knew that this was what I should do. I would write this book explaining a lot of things in science, but this viewpoint would give it a focus. Also it had to be a book, because it's cross-disciplinary and not something you could express very well in any particular journal.

I suppose what I was doing in that book was philosophy, but somebody complained that I hardly referred to a single philosopher — which I think is true. That's because the questions that interest philosophers tend to be rather different from those that interest scientists; philosophers tend to get involved in their own internal arguments.

When I argue that the action of the conscious brain is noncomputational, I'm not talking about quantum computers. Quantum computers are perfectly well-defined concepts, which don't involve any change in physics; they don't even perform noncomputational actions. Just by themselves, they don't explain what's going on in the conscious actions of the brain. Dan Dennett thinks of a quantum computer as a skyhook, his term for a miracle. However, it's a perfectly sensible thing. Nevertheless, I don't think it can explain the way the brain works. That's another misunderstanding of my views. But there could be some element of quantum computation in brain action. Perhaps I could say something about that.

One of the essential features of the quantum level of activity is that you have to consider the coexistence of various different alternative events. This is fundamental to quantum mechanics. If X can happen, and if Y can happen, then any combination of X and Y, weighted with complex coefficients, can also occur. According to quantum mechanics, a particle can have states in which it occupies several positions at once. When you treat a system according to quantum mechanics, you have to allow for these so-called superpositions of alternatives.

The idea of a quantum computer, as it's been put forward by David Deutsch, Richard Feynman, and various other people, is that the computations are the things that are superposed. Rather than your computer doing one computation, it does a lot of them all at once. This may be, under certain circumstances, very efficient. The problem comes at the end, when you have to get one piece of information out of the superposition of all those different computations. It's extremely difficult to have a system that does this usefully.

It's pretty radical to say that the brain works this way. My present view is that the brain isn't exactly a quantum computer. Quantum actions are important in the way the brain works, but the brain's noncomputational actions occur at the bridge from the quantum to the classical level, and that bridge is beyond our present understanding of quantum mechanics.

The most promising place by far to look for this quantum- classical borderline action is in recent work on microtubules by Stuart Hameroff and his colleagues at the University of Arizona. Eukaryotic cells have something called a cytoskeleton, and parts of the cytoskeleton consist of these microtubules. In particular, microtubules inhabit neurons in the brain. They also control one celled animals, such as parameciums and amoebas, which don't have any neurons. These animals can swim around and do very complicated things. They apparently learn by experience, but they're not controlled by nervous systems; they're controlled by another kind of structure, which is probably the cytoskeleton and its system of microtubules.

Microtubules are long little tubes, a few nanometers in diameter. In the case of the microtubules lying within neurons, they very likely extend a good deal of the length of the axons and the dendrites. You find them from one end of the axons and dendrites to the other. They seem to be responsible for controlling the strengths of the connections between different neurons. Although at any one moment the activity of neurons could resemble that of a computer, this computer would be subject to continual change in the way it's "wired up," under the control of a deeper level of structure. This deeper level is very probably the system of microtubules within neurons.

Their action has a lot to do with the transport of neurotransmitter chemicals along axons, and the growth of dendrites. The neurotransmitter molecules are transported along the microtubules, and these molecules are critical for the behavior of the synapses. The strength of the synapse can be changed by the action of the microtubules. What interests me about the microtubules is that they're tubes, and according to Hameroff and his colleagues there's a computational action going along on the tubes themselves, on the outside.

A protein substance called tubulin forms interpenetrating spiral arrangements constituting the tubes. Each tubulin molecule can have two states of electric polarization. As with an electronic computer, we can label these states with a 1 and a 0. These produce various patterns along the microtubules, and they can go along the tubes in some form of computational action. I find this idea very intriguing.

By itself, a microtubule would just be a computer, but at a deeper level than neurons. You still have computational action, but it's far beyond what people are considering now. There are enormously more of these tubulins than there are neurons. What also interests me is that within the microtubules you have a plausible place for a quantum-oscillation activity that's isolated from the outside. The problem with trying to use quantum mechanics in the action of the brain is that if it were a matter of quantum nerve signals, these nerve signals would disturb the rest of the material in the brain, to the extent that the quantum coherence would get lost very quickly. You couldn't even attempt to build a quantum computer out of ordinary nerve signals, because they're just too big and in an environment that's too disorganized. Ordinary nerve signals have to be treated classically. But if you go down to the level of the microtubules, then there's an extremely good chance that you can get quantum- level activity inside them.

For my picture, I need this quantum-level activity in the microtubules; the activity has to be a large scale thing that goes not just from one microtubule to the next but from one nerve cell to the next, across large areas of the brain. We need some kind of coherent activity of a quantum nature which is weakly coupled to the computational activity that Hameroff argues is taking place along the microtubules.

There are various avenues of attack. One is directly on the physics, on quantum theory, and there are certain experiments that people are beginning to perform, and various schemes for a modification of quantum mechanics. I don't think the experiments are sensitive enough yet to test many of these specific ideas. One could imagine experiments that might test these things, but they'd be very hard to perform.

On the biological side, one would have to think of good experiments to perform on microtubules, to see whether there's any chance that they do support any of these large-scale quantum coherent effects. When I say "quantum coherent effects," I mean things a bit like superconductivity or superfluidity, where you have quantum systems on a large scale.

Excerpted from *The Third Culture: Beyond the Scientific Revolution* by John Brockman (Simon & Schuster, 1995). Copyright © 1995 by John Brockman. All rights reserved.