Physics in Mind

Preface

The radio was on in the background when I became aware of some vaguely familiar chords. As I began to listen more intently, a few swells of harmony pushed a button somewhere: Bach, the chorale “Out of the Deep,” the faint final accords.

I hadn’t heard that piece in decades. But as a teenager I had sung it in the school choir. Hearing those notes, I remembered the music and words of the entire chorale, as well as the withering look of the conductor when I missed my cue … and yes, the face of that girl in the choir I had fancied.

A melody, a face, the sounds of rushing wind, the smell of honeysuckle, the touch of a hand long still—all this we can perceive with the mind’s eye. We see, we hear, we feel, we remember, we are aware.

But what precisely do we mean when we say, “We are aware of something”? What is this peculiar state, at once so utterly familiar and so bewilderingly mysterious, that we call consciousness? What is its mechanism?

I put it like that point blank, to show from the start the tenor of the way and hold implicitly forth the expectation that consciousness has a physics explanation. Such a prospect may be shocking to some. That our mind and perceptions, our joys and sorrows, our memories, our sense of self, or worse, the glittering jewel of human intellect, thought, could be reduced to physics terms, may be a blow to one’s self-esteem. But it is really no more so than anything evolutionary—Darwinian schemes always step on the peacock tail.

In any case, that prospect should no longer be as shocking as it might have been, say, 20 years ago. In the meantime, the neurosciences have advanced on a broad front, only to bolster reductionist aspirations. The advances have held up the mirror to the brain, its intricate web of a trillion neurons, letting us see in detail as never before the stream of information that nurses our perceptions and the information processing that precedes them.

I wrote this book in an attempt to make these advances accessible to a wide spectrum of readers. I center on the information processing that takes place at the sensory periphery of the brain and at the brain cortex and examine it in the light of information theory. I have been fortunate that in the past few years there has been a major breakthrough in an offspring of that theory, quantum computation; the most spectacular advances happened just as I penned the last three chapters. So I was able to view the sensory information processing in this new light, especially the parallel processing that is the hallmark of the cognitive brain. That processing is the antecedent of consciousness and is exquisitely sensitive and fast, offering a target to test one’s reductionist mettle.

I originally intended to limit my story to the brain’s sensory periphery, to the capture and transfer of information at sensory receptors, a field I had worked in early in my career. But as I went on with the story, my leading characters, a set of talented biological molecules, started to develop wills of their own and did things quite different from those I had planned for them. Well, I should have been forewarned. Those are molecules operating by the strange rules of quantum logic. And in no time they took over the brain’s ground floor, the quantum bottom, presenting a tableau in which the boundaries between biology and physics vanished into thin air. That was a sight I could not resist. So this became a book on the sensory brain outright.

The book is written for the general reader with an interest in science. No specialized knowledge of biology, physics, or information theory is assumed in advance. With the general reader in mind, I have dispensed with mathematical apparatus. The few equations I used are tucked away in a footnote and the appendix. But the reader who wishes to skip them will not lose the thread of the book; the concepts they embody are explained in plain language along the way.

I have taken the liberty to personify throughout the book the process of biological evolution. I hope the reader won’t mind. Such a personification comes naturally if one looks at things from the information angle. It simplifies the narrative of an evolutionary process that is rare, if not unique, in the physics universe, where the good throws of the dice needn’t be repeated over and over again—an evolutionary process that generates its own information repository to progressively reduce the element of chance.

It may be surprising that in a book on brain and mind there should appear more physicists than biologists. This merely reflects the fact that the mind is frontier territory. Indeed, it is not at all uncommon in biological history to find physical scientists at the leading edges. Even Darwin, contrary to popular belief, was originally not a biologist, or at least he didn’t think of himself as one when he set out on the voyage of the Beagle: “I a geologist have illdefined [sic] notion of land covered with ocean, former animals, slow force cracking surface . . . ,” he wrote in his notebook. Nor did things change very much in that regard a century later, when modern biology was well on its way and molecular genetics was still a territory of uncharted wonders. Then again physicists were among the pioneers. And an encore is happening these days as the mind is becoming the new frontier. Indeed, the brain-mind problem, a subject that for centuries had been lying uneasily at the border of science and philosophy, may be the natural meeting ground between biologists and physicists.

Some years ago a group of students and colleagues of mine at Columbia University staged a mock biophysics symposium on my birthday. The “symposium” was an elaborate spoof on the vagaries of biophysics and the crowings of its practitioners. It was great fun, though much of it I have forgotten. But not the refrain of one of the ditties, and it has been haunting me ever since: “Biology is biology, and physics is physics, and never the twain shall meet.” If this book helps to sink that refrain into oblivion, that is the best I would ask for.

CHAPTER ONE

Our Sense of Time: Time’s Arrow

Our Awareness of Time

We begin our journey with an exploration of our sense of time. This sense is a prominent feature of consciousness, and I mean here not the sensing of periodicities and rhythms (the causes of which are reasonably well understood), but something more fundamental: the sensing of time itself, the passing of time. This we feel as something intensely real, as a constant streaming, as if there was an arrow inside us pointing from the past to the future.

This arrow is an integral part of our conscious experience, and more than that, a defining part of our inner selves. Yet for all its intimacy and universality, it has defied scientific explanation. Not that this is the only perverseness of consciousness, but I single it out because our sense of time appears to be the least ethereal and with some prodding, it might give ground. It has a measurable counterpart in physics, the quantity t. Indeed, that t occupies a high place in our descriptions of the physical universe—it enters into all equations dealing with events that evolve. However, we should be forewarned that that time and the one we sense may not be the same; t is a sort of housebroken variety of time, a variety that was tamed through mathematics. Nevertheless, it still has some wild qualities and, for something that has gone so thoroughly through the wringer of mathematics, it is surprisingly human.

This could hardly have been said before the revolution Einstein wrought. The t then was something that flowed uniformly and inexorably at the same universal rate, whether there was a human being there to observe it or not. It was, and I use Newton’s own words, an “absolute, true and mathematical time, [which] of itself, and from its own nature, flows equably without relation to anything external.” With a time like that, it didn’t matter who measured it, as long as a good clock was used. The theory of relativity put an end to this disemboweled, machinelike time. In contemporary physics each observer must take his or her own measure of it. Clocks, however good, do not necessarily mark the same time in the hands of different observers. Far from flowing equably, time varies, depending on the relative movement of the observer. This kind of notion is something one can warm to, though it may not have all the tints and hues of our inner time.

The Stream of Consciousness

But first, what is this thing we call time? St. Augustine, one of the early inquirers and among the most profound, captured the zeitgeist when he wrote at the turn of the fifth century in his Confessions, “If no one asks me, I know; but if someone wants me to explain it [time], I don’t know.” He might as well have said it today. We are still groping, and if we ponder the question in terms of current physics, we may well wonder why time should have a direction at all.

The roots of our sense of time are somehow interwoven with those of our conscious states. They can be traced to the transience of these states—their constant flitting, one state following another. Ordinarily those states are so many and follow each other so fast that one doesn’t see the forest for the trees. But that gets better if one fixes on a particular sequence—one streamlet in the stream. Try this, for example: have someone tap the tip of your index finger rhythmically with a pencil, spacing the taps half a second apart. You will feel a series of touch sensations that jointly convey a forward sense of time. The nerves in your finger send the tactile information in digital form to your brain; it takes somewhat under 50 milliseconds for that information to get to the cortex, and some 200–300 milliseconds for it to be processed at the various stations of the brain web and become a conscious state—enough time to give rise to an unslurred sequence of cognitive events. Now change the condition slightly and tag the sequence by making the second tap stronger than the first. You will feel the sensations in a distinct order, an outcome as revealing as it is plain: the conscious states are well ordered, and the order reflects that of the peripheral stimuli.

The same can be said for the states underlying our auditory and visual experiences. A series of notes played on the piano is heard in the sequence the notes were played, and a series of pictures flashed on a TV screen is seen in the same serial sequence. There are limits to the speed with which our nervous system can handle and resolve individual events, but within these limits, our conscious states always occur in an unjumbled sequence.*

This also holds true for multiple sensory input. We see the finger movements of a pianist in the same sequence as the notes she produces, or we hear the taps of the tap dancer in step with his movements. Not even an illusion—such as hearing an extra note when there was none or seeing a phantom dance step—will jumble the picture. The bogus information is merely inserted into the sequence. And when memory comes into play, the imagined information reels off with the true information.

I bring up the matter of bogus images because it bears on the conscious states originating from within our brain in the absence of an immediate sensory input. Such intrinsic states seem to occur in orderly sequence, too—at least those in logical reasoning do. It is not by chance that we speak of a “train” of thought. Moreover, when we try to transmit this sort of information to somebody else, we tend to do so step by step, in a concatenated series. Indeed, all our language communications—be they in English, Chinese, mathematical symbols, clicks, or grunts—are based on systematic, ordered information sequences.

Thus a good part of our consciousness seems to be based on an orderly streaming of information states—a stream broken only during our sleeping hours, and sometimes not even then. It is probably this constant streaming that gives us a sense of the flow of time.

Inner Time versus Physics Time

So much for the flow. But what of its direction? Why the asymmetry of time, the never-deviating progression from past to future? Offhand, there seems to be no intrinsic reason why that flow should always have the direction it has. Indeed, from the point of view of physics, it might as well go the other way round.

Take Newtonian physics, for example. There the time t describing the evolution of a system has no preferred direction—it flows forward, as in our stream of consciousness, but it can also flow backward. The laws governing clockwork going in reverse are the same as those of clockwork going the usual way—the variable merely becomes –t. Time in Newtonian physics is inherently symmetrical, and no consideration of boundary condition has any significant bearing on this pervasive property.

The same may be said for all of physics. All the successful equations—from Hamilton’s to Maxwell’s to Einstein’s to Schrödinger’s—can be used as well in one time direction as in the other. In Einstein’s relativity, time doesn’t even flow. It is interwoven with space into one fabric, space-time. This fabric is a coordinate system, something static, so time flows here no more than space does. And if we artificially reverse the way things normally unfold, say by running a film of planets and stars backward, their movement still would conform to Einstein’s laws.

Such symmetry also holds for quantum physics, the physics of small-scale things (10^-14 cm and less). Although the theories here made a clean sweep of many traditional physics concepts, including some aspects of the notion of time, they held fast to the past in regard to the symmetry of time. They took over Newton’s notion of an absolute and universal time, and just as a Newtonian system evolving in time traces a trajectory in space, a quantum system traces it in an infinite-dimensional state space. Thus in the micro-domain, the time dimension is not a mere Einsteinian coordinate, but rather something that flows, and it does so with no asymmetries.* As in the macro-domain, there is no fundamental distinction between past and future—the future merely repeats the past.

All this is a far cry from the way we perceive time in our conscious experience, and it makes one wonder why we feel time as something always progressing in one direction. Well, perhaps the Queen had it right when she explained to Alice the run of things in Wonderland:

The Way the Cookie Crumbles

Yet we have every reason to believe that the distinction between past and future, the time asymmetry, reflects reality—well, at least the reality of the universe we live in. I shall go into this in more detail; this point is too important for just a lick and a promise. But before beginning the argument itself, I want to briefly explain what sort of argument it is and what terrain it covers. The case is based on the laws ruling the world of molecules, the world out of which we have evolved. We will make an excursion into that world and search for natural time asymmetries—all the while, to be fair, keeping our intuitive notion of time at arm’s length. With something like time, we cannot rely on intuition—time is too familiar, and the familiar is wont to make us blind or numb to the intrinsic reality.

Indeed, temporal asymmetry is so deeply ingrained in the ways one thinks about the world that it is very difficult to cut oneself loose from presuppositions. So we will keep intuition at a respectful distance and look for mathematically demonstrable time asymmetries in the world of molecules. Once we spot some, we will stake out their boundaries and set them over and against those of Evolution. And as we then reconnoiter the common ground, we will reap where we have sown: a time that is as pigheadedly directional as our inner time.

Let’s begin with the molecular sphere. A search for asymmetries there won’t take long. Two immediately stand out: the cosmological arrow and the thermodynamics arrow. The first was put on the map by astronomers toward the second half of the twentieth century, following the discovery that the galaxies are rushing apart with a speed approaching that of light (the distance between any pair of typical galaxies doubles every 10 billion years). The cosmological arrow points in the direction of that expansion—that is, away from the initial state, the Big Bang—and this is the direction it has taken ever since. Whether it will continue to do so forever is a matter of interesting uncertainty. This depends on the total mass in the universe, an unknown. If there is enough mass, the expansion should come to a halt (as the mass exerts its mutual gravitational pull) and be superseded by contraction ending in collapse, the so-called Big Crunch. According to data currently on hand, the universe contains only about 30 percent of the mass needed to halt expansion. As I write these lines, the results of observations of distant supernovas are coming in, suggesting that the universe’s expansion may actually be speeding up, rather than slowing down. Thus the odds currently favor a picture of a perennially expanding universe.* But the jury is still out, and there is still much to be learned about the energy that is latent in empty space.

The second arrow, the thermodynamics one, points in the direction that the events in the molecular sphere normally unfold. Things there have not just an ordering in time, but also a direction: from high to low order. And this trend prevails in the entire coarse-grained universe—the macro-domain of physics. We are no strangers to this trend: cookies crumble, but don’t reassemble; eggs scramble in the frying pan, but don’t jump back into their shells; chinaware shatters, waves fizzle, trees fall to dust … and all the king’s horses and all the king’s men couldn’t put them together again.

The plight of the Humpty Dumpties of this world is independent of the universe’s expansion; in a contracting universe, the thermodynamics arrow would still point the way it does (it would do so even at the enormous spacetime warpage of black holes). The arrow represents a seemingly ineluctable trend and encompasses the entire sphere of molecules. The systems there constitute worlds by themselves, which can harbor immense numbers of units—a drop of seawater contains some 10¹⁹ molecules of sodium salt. Those molecules dance perennially to the thermals and tend to be scattered randomly about in what is called their equilibrium state. However, before they reach that higgledy-piggledy state, they show a penchant to deploy themselves in an orderly manner, forming aggregates—loose molecular associations, tightly bonded compounds, and so on—the sort of molecular states chemists use for their concoctions.

All those states are rather short lived. How much order a molecular system can embed depends on how much information there was to start with and how much gets pumped in afresh. But information is something difficult to keep captive. It gives one the slip, as it were, and eventually will wriggle out of the strongest molecular bond; not even diamonds, which are all bonds, last forever. There is in truth no shackle, chain, or wall that could stop information from ultimately escaping—the thickest wall on Earth won’t stop the transfer of heat or shield off the gravitational force. So in the long run, a molecular system left to its own devices becomes disordered.

That goes for complex systems, too, including us. The laboratory of bioevolution used the same sort of molecular aggregates for its concoctions as the chemists do. Our own organism holds immense amounts of information, and its systems are complex and tangled; but made of molecules as they are, their eventual decay to disorder is inevitable. We, and the other living beings, manage to stay that fate for a while by pumping in fresh information, and we do so ceaselessly and in enormous quantities to stay alive. Alas, time’s arrow points its pitiless course day in, day out, and nobody can pump enough to keep the horseman with the scythe away forever.

How to Predict the Future from the Past

So much for the directionality of time and the distinction between past and future. As for the present, I intentionally left it out. Time flies continuously from being past to being future, and in such a continuum there is no room for a present. However, I do not wish to belittle what many hold so dear. I leave the present, and not without a little envy, to someone like the writer Luis Borges, who knew how to celebrate it so brilliantly. In quite a few of his tales the present holds center stage, and who could resist their spell when they bring a world to life, where the wish of things is to continue being what they are—the stone wishes to be stone, the tiger, tiger … and Borges, Borges.

Well, for us scientists, that “being” is but a “becoming,” though we are perhaps the poorer for it.

But to get back to the directionality of time, its proximate cause lies in the world of molecules, the world out of which life has evolved. There, fickle chance holds court, and systems are tossed together by the throw of the dice. Molecular systems—their component states, the molecular aggregates—are statistical in makeup and are therefore not too dependable. However, this doesn’t mean that these states are totally unpredictable. They are not as predictable as those of the stars and planets in the celestial sphere, or those of the rise and fall of tides, or the fall of apples—not with the same degree of certainty. The movements of large objects are governed by Newton’s laws, and his F = ma predicts such events completely. That formula says that if the force F acting on a given mass m is known, its acceleration a is completely predictable. So, if the position and velocity of a thing can be measured at a given time (t), all we have to do is apply the rules of calculus to compute its position for a subsequent time, t + dt. Each of the locations then is completely determined by the ones before—they are specified for all times.

Such determinacy is something satisfying—it betokens regularity and order, which appeal to the human mind. Our mind abhors disorder and is perennially searching for regularities, even though such things may be scarce outside the inner I. That is an old yen, as old as human history. Folktales and traditions abound with personifications equating order with good and light: in Greek mythology the primordial world was one of disorder and darkness; the Bible speaks of formless darkness until “there was light!”; and the heroes in the Nibelungen Ring never seem to tire of battling the forces of darkness and of seeking the light. Well, when in years to come science will be lore, those heroes may still be at it, though their leitmotiv will have mellowed to something like “The light is in the regularities, in Nature’s laws” (and be sung a merciful decibel lower).

Our brain somehow seems to be wired for such regularities—aeons of evolution have seen to that. All this development was given momentum by one basic need: to know and understand what happens around us. From there, it was but another step to wanting to know what will happen before it actually happens, and Newton’s laws filled that desire more fully than anything before then. Indeed, his F = ma is better than any crystal ball. It not only predicts the location of moving things, as we saw previously, but when coupled to another of his formulas, a law governing the force whereby two things at a distance attract each other, it can predict all sorts of events, like the paths of planets or comets, the wobble of the moon, the trajectory of a missile, the mass of the earth, the gaps in Saturn’s rings, or the fall of a stone. When Newton presented the formulas to the Royal Society of London in 1686, he could say with justifiable pride: “I now demonstrate the frame of the System of the World.”

It would eventually turn out that this frame bounded only a part of the world. But that’s beside the point. What matters is that within those bounds, the formulas’ predictions were infallible and still are—within those bounds, the future is completely determined by the past.

Now, as we descend to the molecular realm, some of that infallibility is gone. Here we encounter shades of determinacy, degrees of certainty, depending on the amount of information on hand. It is not possible to describe the individual motions of every single molecule, let alone predict them. The complexity is enormous. Say you try to describe the behavior of just a few molecules out of the zillions in a gas or a liquid. Those within that small group may follow straight paths for a short period, then bounce off each other in ways you may be able to predict from their previous paths. But just as you begin to discern a pattern, a molecule from another group zips along and crashes the party, breaking the pattern. And before you can blink an eye, along comes another molecule, and another, and another. . . . The complexities with so many moving pieces are overwhelming.

Nevertheless, if enough information is on hand, one can still pin down the states of a system with reasonable accuracy. Given some information about the significant variables in the molecular throw of dice, like position and speed, temperature and pressure, or chemical constitution and reaction rate, Newton’s formula still works its magic. One has to bring in statistics to cope with the vast numbers of molecular pieces. But this is not too difficult—that sort of statistical mechanics in the gross is rather routine nowadays. Unavoidably, one loses some definition here—that’s in the nature of the statistical beast. But one brings home the bacon: the probability of the system’s states, or to be precise, the probability amplitude (which is simply the square of a measured quantity or the sum of such squares, when the event can occur in more than one way). And when that probability is high enough, it still can claim the dignity of being nature’s law.

Thus, despite the turmoil and hazard of the die, we can still discern the regularities and predict events in the molecular world—the blurredness vanishes in the focus of the mathematics, as it were. There is a deficit of information in the molecular sphere, but that deficit is often small enough, so that the future is determined by the past in terms of statistical probabilities.

Why the Cookie Crumbles