posts by Frank Wilczek




by Frank Wilczek

We usually think of the human brain as a single organ, but it is a complex assembly of modules that process different kinds of information in quite different ways. Somehow, we construct a rich world of objects out of the two-­dimensional images projected onto our retinas through two tiny irises effortlessly, and in real time. Human abilities here still far outstrip even the most powerful computers. Analytical processing of more abstract symbolic information, such as mathematical formulas or logical schemas (like family relationships, recipes or computer programs), occurs elsewhere. Visualization is the art of getting those two systems to speak a common language, so they can pool their strengths.  Family trees are a humble but eloquent example.

Historically, innovations in visualization have powered scientific advances. Take the memorable story of August Kekulé, the 19th-century German scientist and creative dreamer who was one of the great visionaries of theoretical chemistry.

In the 1850s, Kekulé developed the familiar chain-like representation of molecules using letters—indicating the constituent atoms—joined by lines representing “chemical bonds.” In 1865, he proposed the ring structure of benzene. That involved taking his abstract representation of molecules seriously, as a model of their geometry—a crucial step toward modern organic chemistry. By suggesting the possibility of new compounds and reactions, Kekulé’s visionary molecular hoops led almost immediately to important practical applications.

At a meeting of the German Chemical Society to celebrate the 25th anniversary of that discovery, Kekulé reminisced about the two crucial breakthroughs in his career. He associated both with unusual states of consciousness. The chaining of atoms, he said, occurred to him as he fell into a daydream while riding a horse-drawn London omnibus: “Lo, the atoms were gamboling before my eyes! I saw how, frequently, two smaller atoms united to form a pair…I saw how the larger combinations formed a chain, dragging the smaller ones after them but only at the ends of the chain.’’

As for the benzene ring, Kekulé recalled nodding off by a fire to find atoms again “gamboling before my eyes. This time, the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold confirmation: long rows, sometimes more closely fitted together, all twining and twisting in snake like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes.”

Kekulé’s snake-dream has become an iconic story of science, psychology and the sources of creativity. Carl Jung connected its power to the archetype of Ouroboros, the self-eating snake, which figures in metaphorical representations of rebirth and eternal return across several cultures.

Several other huge scientific breakthroughs were also breakthroughs in visualization. Descartes’s invention of analytic geometry, which translates between equations and geometric shapes, is a brilliant example. Through it, algebra bends, loops and generally comes to life while, conversely, shapes get boiled down to symbols that our minds can easily juggle.

Einstein’s 1905 special theory of relativity became more popular and far easier to use after Hermann Minkowski’s 1908 address “Space and Time,” in which Minkowski showed that the theory is best pictured by regarding time as a new, fourth dimension. In modern physics, Richard Feynman’s versatile visualizations of elementary processes—Feynman diagrams—are an essential mind-tool. They map the mathematics of space-time processes in quantum theory to simple, flexible wiring patterns. (They’ve changed my life more than once.) None of these breakthrough visualizations, unfortunately for Jung, involves snakes.

Today, at the frontiers of quantum theory, we routinely work in spaces and space-times of high dimension. Modern “big data” collections, depending on many variables, also define structure in high-dimensional spaces. They aren’t what our brain’s visual processors evolved to cope with. Yet in coping with vast and unfamiliar complexity, more than ever, we need to tap vision’s power—and to expand the intersection of art and science.


Dr. Wilczek, winner of the 2004 Nobel Prize in Physics, is a professor of physics at the Massachusetts Institute of Technology. His most recent book is “A Beautiful Question: Finding Nature’s Deep Design.”

This article appeared in The Wall Street Journal



Photo by Bruce Munro

by Frank Wilczek

Why is it so hard to accept, intuitively, that life and mind can emerge from matter? A big part of the answer, I think, is that we have little or no immediate experience of how physical systems represent information. Computers, we know, store and manipulate information in enormous patterns of 0s and 1s. But those patterns are based on arrangements of electrons, microscopically small and deeply hidden from the user interface.

Our brains store and manipulate information in patterns of electrical activation. Most neurobiologists accept that those patterns are the physical embodiment of mind—but they are encased in our skulls, buried in gelatinous brain tissue. We can’t scrutinize them or feel them directly.

One evening last month I had an extraordinary experience at the Desert Botanical Garden in Phoenix, where I viewed an installation called “Fields of Light” by Bruce Munro. The giant artwork used thousands of small spheres of light, strewed over several acres on the desert hills. I wandered among them. Their soft light pulsated, asynchronously, every few seconds, and modulated more slowly through a range of colors. As soon as some pattern became recognizable, a new, slightly different one began to replace it. The pace of that dynamic, comparable to the rhythm of heartbeats or of breathing, gave it an organic feel.

Metaphors connecting light to thought abound. We speak of “flashes of insight” and “bright ideas,” and cartoonists depict these as thought-balloon lightbulbs, emanations from the clever person’s head. Visual representations of communications networks or brains also often use flashes of light to indicate activity.

That night, for me, all those analogies and metaphors came together. In the ever-changing landscape of possibilities, I felt I’d gotten an inkling of what thought looks like. I had the uncanny sense that I was walking through my own mind, or at least a good model of it. I’ll never again think about brains, or myself, in quite the same way.

A great living physicist, Philip Anderson, famously asserted, “More is different.” When large numbers of units act together, fundamentally new structures and phenomena emerge. In one hierarchy, atoms combine to make semiconductor crystals, transistors and computing machines; along another trajectory, they combine to make biomolecules, nerve cells and brains. In these examples, it leaps out: Lots more is very different.

Mr. Munro’s light show embodied, in tangible form, the abstract mathematical concept of a “combinatorial explosion.” Let’s say one light can be either on or off. Then a system of two lights can be in four states: on-on, on-off, off-on, off-off. And a system of merely 30 lights, each of which might be on or off, supports over a billion possible states. When we have thousands of lights, each of which can exhibit a range of colors and brightness, and add the element of time, the explosion of potential far outstrips Carl Sagan’s “billions and billions.” It gives concrete, visceral meaning to the “lots” in “lots more.”

“Fields of Light” was intended as a work of art, not a scientific model. But its psychological power suggests the potential of a new form of visualization—visualization on a grand scale, involving dynamic, immersive environments, as a tool for teaching and understanding.

Using magnetic resonance imaging, positron emission tomography, fluorescent proteins and other technologies, neurobiologists have gathered a lot of objective information about flows of thought and emotion. There’s an opportunity here: Wouldn’t it be marvelous to bring all that information together and scale it up to produce an accurate, dynamic model of mind that is an enthralling, mind-expanding experience too?

In the famous Stargate sequence toward the end of “2001: A Space Odyssey,” astronaut Dave Bowman, approaching Jupiter, finds a strange monolith. When he touches its surface, he activates it. The monolith engulfs him in a swirling vortex of multicolored light, and his mind is altered. Dave Bowman’s expanded consciousness prepares him for further revelations, and at last a glorious rebirth. Maybe those monolith builders were on to something.

  • * * * * *

Dr. Wilczek, winner of the 2004 Nobel Prize in Physics, is a professor of physics at the Massachusetts Institute of Technology. His most recent book is “A Beautiful Question: Finding Nature’s Deep Design.”

This article appeared in The Wall Street Journal

by Frank Wilczek

The absence of an empirically identifiable meeting point between the non-physical mind and its physical extension has proven problematic …

— article on Mind-body Problem, Wikipedia

Philosophers love to invent thought experiments, imagining mad situations that shake up slumbering dogmas. One of their favorite targets is your everyday sense of identity. Are you sure that you are what you think you know that you are—a mind firmly attached to a specific, physical human body? Maybe you’re really a brain in a vat or a program running in some vast computer, mistaking a simulation for reality. Or maybe you’re actually your spouse, having a dream of role reversal. How would you know?

Those issues came to life for me last December, when I had an unforgettable experience of being in two places at once. So will you, very likely—soon, and then often. Routine out-of-body experience doesn’t require esoteric spiritual discipline, drugs or psychosis. It is a coming, practical technology.

My story: I had sent effusive, genuine regrets to the organizers of last year’s Nobel Week Dialogue in Sweden, a day-long, high-level science conference run by the Nobel Foundation’s media arm, saying I couldn’t attend due to scheduling conflicts. The dialogue’s theme was “The Future of Intelligence,” a long-term obsession of mine, and it looked to be a grand event.

The organizers in Gothenburg came back with “an interesting opportunity”: I could participate in a new way, without leaving my home in Cambridge, Mass., by using the BeamPro platform. From my desktop, I would control a large robot—roughly human-sized, though not humanoid. The robot would display live video and audio feeds, so people could see and hear me. It would also support typed messages. I too would be able to see and hear, using sensors attached to the robot and sharing its perspective. Naturally, I jumped at the chance.

My first voyages were tentative. I looked at the robot’s upper screen to decide where to go. Then I looked at the lower screen to check for obstacles, swiveled and slowly inched forward. Rinse, lather, repeat. At this stage, I was very aware that I was sitting at home, at a terminal in Cambridge, operating a machine in Gothenburg.

But after just a few minutes, I gained confidence. The process became fluid. Soon I navigated effortlessly and moved quickly. I could focus on the remote environment, taking in its sights and sounds. I was there.

A few early arrivers—a group of students visiting from Malaysia—entered the discussion area. I strolled up and introduced myself. The conversation began awkwardly. Usually, body language conveys lots of basic information, such as whom we’re addressing and whether a message has been understood. At first, I had to attend consciously to a checklist: I’d turn toward the person I wanted to address, somehow make eye contact (doing a little jig, if necessary, to get their attention) and type out, “Am I loud enough?” But in sustained conversation, the strangeness of the situation quickly faded, and we got to a meeting of minds. Several of us went for a stroll together, followed by an orgy of selfies.

Then, in an adjoining auditorium, the session proper began. I was scheduled to make a surprise appearance. It was dark backstage and (as is the way of these things) chaotic. On cue, I entered through a long narrow runway, demarcated by dozens of dazzling lights, moving at a good clip for dramatic effect. I had the uncanny but exhilarating feeling that I was living inside a videogame. I made it onstage, and the audience got a glimpse of the future of robotics, communication, and reality.

I have seen the future, and it almost works. With more powerful sensors and actuators, out-of-body experiences will become even more compelling. It is easy to imagine brilliantly attractive possibilities: immersive tourism to anywhere, anytime, without needing to leave home. Fragile human bodies are ill-suited to deep-space environments, but human minds will experience them richly.

We’ll need to rethink how we answer the question “Where am I?”—and then, inevitably, “What am I?”

Dr. Frank  Wilczek, winner of the 2004 Nobel Prize in Physics, is a professor of physics at the Massachusetts Institute of Technology. His most recent book is “A Beautiful Question: Finding Nature’s Deep Design.”

This article appeared in The Wall Street Journal

In the year to come, plausibly, but almost certainly within the next few years, physicists will detect tremors in space-time—or, to use the scientific term, gravitational waves. Through gravitational waves we will be able, for the first time, to monitor some of the most violent, dramatic events the universe has to offer.

My prediction is inspired by an extraordinary instrument, the Laser Interferometer Gravitational-Wave Observatory, or LIGO, which is operated by Caltech and MIT. LIGO is designed to detect extremely tiny changes in the distances between a few pairs of mirrors. The numbers are mind-boggling. The mirrors are four kilometers apart, and the distances between them are expected to change by less than one thousandth of the diameter of a proton. All kinds of things can jiggle mirrors, but gravitational waves produce a unique pattern of changes, so their signal can emerge from the noise.

It is poetic that this first observation of gravitational waves will coincide with the centenary of Einstein’s prediction that they exist. They’re a logical consequence of his general theory of relativity. According to general relativity, space and time aren’t rigid structures but form a kind of elastic medium—an ubiquitous cosmic Jell-O.  Massive bodies cause stress in space-time, and the distortion they produce affects the motion of other bodies. This is how general relativity accounts for gravity.

But Einstein carried his reasoning a major step further. As massive bodies move, space-time tries to dance to their tune. But the cosmic Jell-O has inertia, so it can’t follow rapid motions perfectly. Some of its distortions break free, take on a life of their own and spread at the speed of light. This is the origin of gravitational waves.

Space-time Jell-O is far stiffer than steel, so it takes enormous forces to produce significant tremors. (Memo to wormhole and time-­travel fans: Bending space-­time is hard.) Even with LIGO, we can only hope to observe gravitational waves produced by extremely massive bodies in extremely rapid motion.   These waves signal spectacular events, like the death throes of binary systems involving white dwarfs, neutron stars or black holes.

LIGO eventually should be able to detect pulses that emerge from such catastrophes anywhere within our local group of galaxies. No doubt we’ll discover, once again, that the universe is a strange place.

Dr. Frank Wilczek, winner of the 2004 Nobel Prize in Physics, is a professor of physics at the Massachusetts Institute of Technology. His most recent book is “A Beautiful Question: Finding Nature’s Deep Design.”

This essay originally appeared in The Wall Street Journal

ABeautifulQuestion_3d (1)

Writing a book is an unnatural act of communication.   

Speaking to a person, or even to an audience, is an interaction.   Very different styles are suited to an expert, a curious layperson, or a student on assignment or to a one-on-one, a salon, or a lecture theater.   When we do those things we get feedback – including lots of nonverbal feedback – in real time; and we tailor our message accordingly.   Often the most important feedback comes from the look of the audience.  We see whether we are engaging their interest, making them laugh, or putting them to sleep.

Writers, on the other hand, do their basic work in solitude.   An author directs his or her message to … ummmm — well, the answer to that question is a crucial decision, which shapes the process of creation.   In my new book, A Beautiful Question, I came to answer that question in an interesting and unusual way, as I’ll now explain. 

A Beautiful Question evolved from something fundamentally different, namely a public lecture.  The original lecture was titled “Quantum Beauty,” and it was delivered at Darwin College, Cambridge University. It was not a title, or a subject, that I chose. They assigned me that title when inviting me to give the lecture.  I very nearly turned the invitation down out of hand, because the subject seemed so peculiar and esoteric.  But Cambridge is a special place.  Because of its glorious history – Newton! Maxwell! Rutherford! Dirac! Hawking! Darwin! Crick and Watson! – Cambridge is, to me, holy ground.  It is also very beautiful.  And I like challenges, as long as I feel I’ve got a fighting chance.  So I didn’t turn the invitation down.  Instead I asked what the audience would be like, and promised to consider it. 

The audience, I was told, would be a mixture of young and old, town and gown, laypeople and scientists (and it was).   In that sense it would a diverse audience.  But in another sense it was a special audience – namely, the kind of people who would voluntarily spend an evening at Darwin College to listen to a lecture on “Quantum Beauty”.    With that concept in mind, I began to think how I might try to rise to the challenge.   

To my surprise, I found the subject and the project resonating in my brain.  Two happy ideas transformed, to my mind, “Quantum Beauty” from a bizarre challenge into an attractive opportunity.  First, I decided to sneak up on the “Quantum” aspect.  It would appear as the climax of a narrative starting from prescientific ideas and leading through classical physics, with Beauty as the connecting thread.   Second, I would show the Beauty that science reveals at the heart of nature, not just tell about it.   I discovered new ways to visualize concepts, and brought in lots of images, to let an eloquent, elegant world speak for itself. 

With those two guiding principles providing a framework, and with a “clear enough” picture of the audience before me, the lecture seemed to prepare itself, and it went well.    Afterward, Darwin College decided to collect written versions of several lectures in the “Beauty” series into a book, and to include my write-up of “Quantum Beauty” as one of the chapters.   I was able to do that very efficiently, because the performance had been recorded, and 3Play Media made an excellent written transcript.  I just had to polish the language up a bit and insert the images, and the thing was ready to go.   (I’d never worked this way before, but I highly recommend it!)   I had to battle to keep the images, and to sacrifice their color, but since I’d arranged things so that the piece didn’t make sense without them, and I refused to re-write on a massive scale, victory was inevitable.   

After finishing a project I usually have a satisfying feeling of completion, or at least of exhaustion.  I move on to a new, fresh project, and I don’t look back.  But in this case, that didn’t happen: Quite the contrary.   New questions and ideas kept boiling up from the old ferment.   I kept accumulating material, and it became clear to me that I should use it to write a book.

Why was this time different?   The open-ended nature of the subject – that is, the beauty we discover at the heart of Nature – was a necessary condition for its continuing fascination, but not a sufficient explanation.   (There are lots of open-ended subjects!)   Certainly my immersion in imagery forms a big part of the answer.   I’d considered many images that in the end I couldn’t fit into the lecture, and some of them were unforgettable.   Humans are visual creatures.  A big fraction of our brains specialize in image processing, and they can enthrall the rest.    But I also found that specific ideas and images I had used kept rising into my consciousness, unbidden, and growing: Einstein’s proof of the Pythagorean theorem, the Platonic solids, Newton’s Mountain, the atomic Music of the Spheres, the dimensions of color, and others.   

Something deep was working in me.   It took me a while to figure out what that was.  When I did it came as a profound, delightful surprise.  I’d entered a real-life time machine. 

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I had returned to the charmed circle of visions and hopes that originally inspired me, as a child and an adolescent, to take up my career in science.  Those recurrent images and ideas were my roots, exposed.  In researching the history of Beauty in the physical world, I’d gone back to the sources of my own intellectual life.    I was living the experience T. S. Eliot famously described:

And the end of all our exploring

Will be to arrive where we started

And know the place for the first time.

And so, as I settled into writing A Beautiful Question, I knew my audience.   It was myself, as a child and an adolescent.   That person was full of questions.  He wanted to know how the world worked.  He hoped that such knowledge would bring power to his life, and meaning to his existence.    There are many things I’d like to tell him, and to show him.   Above all, this: The world does embody mind-stretching beauty; we can understand it; and coming to understand it is a joyful journey.    Whether he would find my answers fully satisfying is doubtful, but I feel sure he would enjoy them, as he planned to do better.  And he’d love the images.

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Professor Frank Wilczek is considered one of the world’s most eminent theoretical physicists. He is known, among other things, for the discovery of asymptotic freedom, the development of quantum chromodynamics, the invention of axions, and the discovery and exploitation of new forms of quantum statistics (anyons). When only 21 years old and a graduate student at Princeton University, in work with David Gross he defined the properties of color gluons, which hold atomic nuclei together.

Professor Wilczek in 2004 he received the Nobel Prize in Physics, and in 2005 the King Faisal Prize. He is a member of the National Academy of Sciences, the Netherlands Academy of Sciences, and the American Academy of Arts and Sciences, and is a Trustee of the University of Chicago. He contributes regularly to Physics Today and to Nature, explaining topics at the frontiers of physics to wider scientific audiences.

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