An Ocean of Instance, An Ocean of Law

by Jessica Reed

-appeared originally in Isotope: A Journal of Literary Science and Nature Writing

(click here for pdf)

An Ocean of Instance, an Ocean of Law

Jessica Reed

Physics is an easy discipline to love. I was very young when my informal relationship with physics began, when my father engaged me in discussions about cosmology, surrounded me with books that surveyed the landscape of twentieth century physics, and uncovered in me a hunger to know more about the origins of our expanding universe. One summer, recovering from a surgery that forced me to stay inside, I used those books to plunge into the concepts and objects of modern physics. Unable to leave the room physically, I nonetheless managed to visit the unseen physical world, which I found to be as striking as it was inviting. I read about Heisenberg’s Uncertainty Principle and Schrödinger’s Cat, about cosmic rays, black holes and white dwarfs, warped space-time, wormholes, length contracting and time dilating. I read about particles whose fundamental importance elevated as their size shrunk, with delightful family names like bosons and fermions, and offspring dubbed photons, gluons, leptons, whose neutrinos came in flavors, and quarks, strange and charmed. Every encounter with a new concept was thrilling; the territory became more exotic and alien with each step. The kick wasn’t just how odd it all was, but that it was real. I had to know the world in its true form, stripped of perceptual trickery. So began my informal immersion into physics.

I was also privileged to have a formal education in physics, which, as it turns out, is a study in much more than equations and methodology; I learned a much deeper appreciation for what comprises the scientific attitude. Among other things, to study physics formally is to learn that there is an art and a skill to wondering: we can wonder successfully, we can wonder profitably, we can wonder fruitfully. There also, I learned that I would never become a physicist.

Physics demands precision, and it is, you learn, unacceptable to compromise our assumptions and our methods by playing fast and loose. A physics professor approaches her subject with a caution beyond compare. When I first came to the university, I was prepared to be dazzled by the sight of a physicist in action. I had heard it described, encounters with the greatest of the great minds—physicists wiping the chalk off their hands after deriving a brilliant truth in a tiny office, unconcerned with success or reward. Physicists, I believed, wondered gracefully and with ease.

But instead I saw day in, day out, physics professors stopping in mid-sentence at the blackboard, drafting and revising statements in their minds before settling on claims about the arbitrary nature of coordinate systems and mathematical methods we use to study phenomena. Coordinates—the grids we map our physics on—come in all shapes, literally. We left the neat Cartesian flat plane from high school behind us to map numbers to points in spheres and cylinders. From there one could abandon Euclid and explore countless other manifolds, where parallel lines do what we had been told was impossible: move toward or away from each other. Whether you opt for spherical coordinates, or canonical coordinates in Hamiltonian mechanics, or others among a myriad of choices, you’re dealing with an abstraction. In principle, any choice will do. Similarly, you could discuss quantum theory in terms of Heisenberg’s matrix mechanics, or Schrödinger’s wave mechanics, or Dirac’s unification of both, or Feynman’s path integral formulation. I was swimming in an ocean of law. Rather, I was teetering on the shore, terrified to dive in, of the possibility that one system really was better than the others—of making the wrong choice.

Feynman began a famous lecture on gravitation by pointing out that we love to marvel at others’ minds. If you have only a superficial admiration of a scientist’s mind (gee, Einstein was a genius), you won’t fully appreciate the discovery or insight that makes that mind worthy of admiration. These guys—my professors—weren’t supposed to hesitate. It was awkward. I can’t say I wasn’t disappointed at first, but from this I gathered the magnitude of the difficulty these physicists were confronting, and eventually I came to enjoy the philosophical stammering.

Formal physics is an incredibly intimidating discipline. Few of us have the resources, especially in mathematics, to keep up. (Just mention math or physics at a cocktail party. You’ll be astounded by the number of confessions you’ll hear about not getting past high school algebra.) When Barbie said, “Math is hard!” I like to think she was talking about phase portraits in the trace-determinant plane, and complex separable Hilbert space, and eigenspaces, and Fourier transforms, and tensor algebra. Physics, and the math that goes along with it, is just hard for most people. I count myself among them.

And if you are a woman, there is another kind of intimidation to contend with. I learned quickly that women are still, by and large, not encouraged in the science academy. In a freshman orientation for the Women in Physics organization at my school, one of the senior members, a female graduate student, approached several apprehensive new women students, including me. She said to the group of us, “Promise me that one of you will graduate with a physics degree.” It seemed a dramatic thing to say, but that was before my own male professors told me I was “wasting my time.” In the first semester, the females outnumbered the males 6-4. By the second semester, when half of the entire class as a whole dropped out, the ratio of the remaining students was 7-3 in the men’s favor. The trend continued over the next four years, with finally only three women from my year graduating with a B.S. in physics. I don’t believe for a moment that this reflects true cognitive discrepancies; no credible study has produced a shred of evidence that men have more aptitude than women in the math and sciences, only that there is a difference in the performance of men and women after a certain age. Certainly the thinning out of women cannot be attributed to a loss of interest in physics as they gain more exposure. That would suggest gender-determined propensities, a notion as absurd as a cat at once dead and alive, and with side-pockets. The fact in my own case is, although I managed to finish the degree, I never felt welcome.

Independent of the social obstacles presented by my gender, there was the problem of my individual limitations. It wasn’t long before I noticed a major disparity between the level at which I grasped my newly acquired mathematical tools and the insight that was needed to know when and how to use them. I grew more painfully aware at every turn that I did not possess the qualities requisite to be the kind of physicist I aspired to be.

It has become parlance that scientists divide into two categories, experimentalists and theorists. An experimental physicist must be patient. I have friends who spend long hours in laboratories and particle accelerators, recording data and interpreting it. This involves a great deal of equipment, and equipment is prone to error. Because I have no research training as a physicist to speak of, didn’t intern in a lab or complete a research project in my final year, I only understand second-hand the kind of endurance that it requires to engage in long-term experiments. To lose data in an instant that was diligently and painstakingly collected over days—even months. This dedication to exact results is part of the integrity of science. Arguably, patience is a quality one can cultivate, but I am not a very patient person by nature, and I made no significant effort to change this fact about myself.

A theoretical physicist must have the uncommon gift of intuition, and this, unlike patience, does not seem to be a quality one can nurture. The theorist can inhabit more mental territory than it seems the human mind has evolved to comprehend. I remember hearing a student say that he heard some physicists (where?) could actually picture the universe in ten dimensions because they looked at a set of equations that told that particular story. I imagined it just like that: she could just read an equation and become endowed with this higher knowledge—an image!—of a way the world could be. Now, I’m somewhat comforted to hear a physicist with this specialty as successful as Lisa Randall say that no one can actually visualize multiple dimensions; what I had heard was myth. Still, the glorification of this “other” kind of mind proved impossible to resist.

While I war with the concept of innate ability, I find it unavoidable to invoke it when discussing theoretical physicists. In high school, I knew there were the Feynmans and the Hawkings, who saw things differently from the rest of us. There were the Newtons and the Einsteins, who could overturn centuries of learning and revolutionize our conception of the world. With the kind of naïve arrogance only a teenager can have, I thought I’d try to be that kind of person. Then I realized it had little to do with trying.

Besides possessing patience and intuition, even the modest physicist—theoretical or experimental—must find the right balance between the audacity it takes to tackle extremely meaningful and far-reaching projects, and the appropriate amount of trepidation it takes to do the same. Physicists are indeed made of special stuff.

My formal education in physics regrettably exposed my limitations, naked and conclusive. In my own paradigm, I fell short somewhere in the neighborhood of innate ability. For me, a formal education in physics was a lesson in humility.

And so I shifted—a natural progression (or was it a leap?)—from one passion to another. The move from physics to poetry isn’t easy to explain, but I deeply suspect that metaphor plays an important role. I recognized it as an indispensable pedagogical tool: we need metaphors to grasp certain concepts, or at least to explain them. And, having been seduced by the nearly-fanatical devotion to rigor of formal physics, I was troubled by the notion that metaphor somehow stood in the way of truth. Yet, at the same time, I was irresistibly drawn to their beauty and their playfulness. Were rigor and playfulness mutually exclusive? Perhaps if one could ‘play’ responsibly, the most cherished values in science would not be compromised.

Where wonder is pure speculation, science excels. To wonder well, we usually assume, you should not be confined or restrained. But Richard Feynman called the scientific imagination “a terrible straightjacket.” To investigate regularity in a world of apparent chaos is a tough chore. The choice of what to speculate about is in itself a choice that can be made well or not.

Another sense of wonder is amazement, and here, both scientists and poets dwell, never tiring of the search to know the universe. This amazement is anything but passive. It is the singular kinetic feature of a mind confronting—not confronted with—a fact. The physicist and the poet do more than wonder about something. They wonder in. The difference between in and about measures the cleaving of the wonderer and the wondered.

I recently read an article in Scientific American called “The First Few Microseconds.” This piece provided an overview of the development of particle physics and cosmology since the 1970s. The descriptions of the particles and forces thought to be present at the earliest stages of the universe are unlike anything familiar to the human experience. The authors explained that the theory of the strong force between quarks (quantum chromodynamics) postulated a “shadowy cabal of eight neutral particles called gluons” darting around and between the quarks. I had heard of gluons, and hadrons, and the whole family of particles, but that doesn’t mean I truly understood much about that world. Since the discovery of the subatomic—protons, electrons, and neutrons—physicists make sense of particles in terms of what holds them together. Among the most elegant discoveries of the twentieth century is that there are four fundamental forces, and that these connect in deep ways. In the 19^th century, we learned that electricity and magnetism are aspects of one force. In the early 20^th century, we developed a remarkable theory of the gravitational force. The strong and weak nuclear forces that hold elements of the nucleus together, make up the other two. The Scientific American article points out something “especially intriguing” about the strong force between quarks: unlike gravitation and electromagnetism, the strength of this force diminishes as objects draw nearer to one another. Try wrapping your mind around that, and then treat yourself to the metaphor Riordan and Zajc provide: “Only when a quark begins to stray from its partner does the force become truly strong, yanking the particle back like a dog on a leash.”

Or take another example: the mysterious dark matter that comprises most of the universe. We can’t see it, so we infer it from other observations. The New York Times told us this August that just as a football player tackled hard enough may lose his helmet, two clusters of galaxies collided so hard that one of them has lost its halo of dark matter. The same paper reported elsewhere that astronomers have now witnessed a separation of visible and dark matter. Here, we’re asked to imagine two crowds of pedestrians on a collision course. Some people in both groups, dressed in black, refuse to engage with anyone and keep moving. The ordinary people—the ordinary matter—often stop to chat. In this way, the people in black push ahead, separating themselves from the rest.

Neither of the New York Times pieces claimed an author. Metaphors in science are often free, principally because their chief function is not ornamental, but to aid in the understanding of a concept. Still, some metaphors are so outstanding that we’re compelled to credit their originators, like the following—perhaps the most beautiful physics metaphor I have heard—provided by the physicist John Wheeler on the existence of black holes.

Imagine a dimly lit ballroom dance in which the ladies wear white gowns and the men wear black tuxedos. We can’t see the men, but we know they are there as we see the women twirl around them. In the same way, we can see in the behavior of the stars their interaction with black holes. Wheeler provided this metaphor, but we can all profit from and take pleasure in its elegance. For this astounding image of white coiling around black, animating those distant points of light and setting them in grand motion, for the physical tug I feel when contemplating the pulling of light from dark, I thank the collective human imagination. It is imagination that allows us to understand the world, and to enjoy it.

And those black holes, the deep-space singularities that digest all matter and light which approach them, eventually radiate all of their energy away and “evaporate.” But what happens to all of the stuff that went into the black hole? Does it simply disappear? Our physics is built on principles of conservation, so the scenario where information is lost is troublesome. I recall an article on this so-called information paradox suggesting that a black hole doesn’t behave fundamentally differently than a bucket of water: when the water evaporates, the information isn’t exactly retained, but it is disguised in the water vapor particles that carry it away. The problem, the theorists noted, is that Hawking radiation does not come from a black hole the way water comes from a bucket.

Here, the author is forced to destroy the analogy he had just set up. So it is with science. Metaphors can mislead. Much has been written about the problem of metaphor in science, far too much to rehearse here. Scientists and philosophers often reach the sensible conclusion: to resign to the inadequacy of metaphor—at least in the short term—as sometimes, it’s all we have.

But poets revel in the metaphor. And the notion of playing “responsibly” is distasteful. If the nuclei in Fermi’s uranium chain reaction can be described in terms of mouse traps and ping pong balls flinging around the room (that was Alan Lightman’s), it’s all the better. It’s fun. Because of science, we can picture space-time like a giant rubber sheet that warps in the presence of massive objects like enormous bowling balls, or the C₆₀ molecule as a soccer ball. Because of science, we can compare pulsars to lighthouses, and light bending around galaxies to the refraction of light that causes a pencil to appear broken in water. Because of science, we can imagine the expansion of the universe by picturing dots on a balloon; we can even, as my childhood encyclopedia did, describe the age of the earth by comparing the amount of radioactive material in rocks to the length of time it takes to wear pencils to their erasers.

K. C. Cole, a science journalist and author of The Universe and the Teacup: The Mathematics of Truth and Beauty, recently described the chasm between quantum theory and Einstein’s theory of gravity with fantastic imagery. On a small scale, “matter, energy and motion are a choppy mosaic of jittery bits,” and we’re asked to imagine a scene by pointillist painter George Seurat. On the other hand, the large scale universe is smoother, seamless, and warps around massive objects—a Salvador Dali universe. “Where the two realms meet, the quantum jitters shatter the glassy surface of spacetime like a child cannonballing into a pool.” This is the language of poets.

Like the harmonic oscillator that models so much of the universe’s phenomena, (picture a mass on a spring) science and poetry compress, and expand, and compress again. Physicists strive toward the general, the law; it is an achievement to represent all of electricity and magnetism with Maxwell’s four equations, even better to collapse those into a compact, pregnant field tensor. But “as far as poets are concerned,” the poet Charles Simic wrote, “only fools are seduced by generalizations.”

To reduce the two disciplines to the pithy formulas, poetry is the particular and science is generality, is to wage war between them. Italo Calvino describes this conflict in a discussion on science and literature: “...on the one side, the reduction of secondary events to abstract patterns according to which one can carry out operations and demonstrate theorems; and on the other, the effort made by words to present the tangible aspect of things as precisely as possible.”

We are immersed in an ocean of instances. There is elegance in disruption as well as in uniformity—we populate our poetry with the particulars precisely because of their arbitrariness, and because of what Charles Bernstein calls “the truth of details and their constellations.”

Yet we must comfortably sail the ocean of instances to the ocean of law, and be able to navigate our way back. If science strives toward the abstract and poetry toward the concrete, they both begin with observation. We cannot arrive at the general without first the specifics—a ball sliding in a wagon, the juggler’s rotating trajectories of apples, bananas, swords cycling through the air, precariously carving what cannot be carved.

The straitjacket of the scientific imagination strikes again. I seek out patterns in nature (patterns in the grain of my wooden desk—dispersion, like the developing zebra, lion, zucchini, squash?). I want to believe something grand and universal about patterns. But against that impulse, the idea of caution comes up again and again, because I’m nagged by an acquired awareness that the temptation to infer beliefs hastily is powerful. I spent years learning to recognize and sort out this seduction, and to look down upon inferences that weren’t hard won.

Physics and poetry are both vast oceans for us to wonder in. Poet Arthur Sze wrote, “No single method can describe the world.” How one arrives at knowledge makes the difference—following mental leaps, considering theories and relationships along the way. I want to sail the oceans of instance and law, to see the tree, as well as its blueprint, as invitations to wonder. Still tethered by gravity and a respect for logic, to skip and dance across the sea of ideas. I want it, but I will never be fully equipped.

Imagine that you are blind, or in some other way cut off from the world of sensory impressions. People tell you stories about what they see. They describe the landscape—sometimes carefully and accurately, sometimes they embellish, and sometimes they just plain get it wrong. But, while you can compensate for your handicap in other ways, you must rely on these stories to fully flesh out the terrain. Sometimes it seems like a tragedy: we are, most of us, blind in this way.

One metaphor that comes up repeatedly in science is that of the black box. There is a box filled with assorted objects—the more diverse, the better—and our task is to guess at its contents. Nature has secrets, and we must find them out. While it might be overly-simplistic, it’s romantic to think that there are at least some people out there who are endowed so that they can peek inside the box and report back to the rest of us.

Perhaps I was wrong about innate ability. Perhaps, if I had worked harder and to the exclusion of other things, I might have been an adequate physicist. But, and this is just a matter of fact, I believe that my contribution to physics would not have been of real consequence. I’m betting there’s something to my conviction that some people are extra-special. So what do I do, since I am not one of those fortunate few given the chance to peek inside the metaphorical box, and out at the world? I read, like I did when I was bed-ridden in high school. The world is out there; and I am in here, only hearing second hand what the universe looks like. The thing is, though, I’m beginning to reconcile my relationship with the external world. It’s not a bad deal at all. I get to hear some pretty great stories.