Home > Essays > Of Emptiness, Nothingness, and Asymptotic Freedom
Christopher Livaccari
Published: Sat Apr 15 2006
Art: Paul TheriaultSwimmers (detail), 2019, acrylic and found paper on scavenged wood
Of Emptiness, Nothingness, and Asymptotic Freedom

A word devoid of thought is a dead thing, and a thought unembodied in words remains a shadow.
        —Lev Semenovich Vygotsky (1896–1934)

For me, it all started with British accents. Doctor Who, Monty Python, The Avengers, The Royal Shakespeare Company. I would walk around the house speaking for days in nothing but British accents—sometimes cockney, sometimes posh—the different rhythms so thrilling to me that I just couldn’t go back to my slightly ridiculous Long Island dialect (it makes me shudder to hear my teenage self pronounce words like “water” and “coffee”). Later on, in high school, I would do the same with Spanish and Russian, and annoy my monolingual parents incessantly. “English, please!” “Sure. BBC News, Irish, or Scots?”

I don’t think it was anything inherently interesting about British TV, but I watched far more of it than the American version and spent most of the time recording inventories of words in my head, trying to make sure I could pronounce each one exactly right, and making lists of correspondences between British and American English. Thus began my lifelong devotion to speech patterns—rhythm, stress, intonation, and all the mysterious beauties of prosody, the sonorousness of the stop, fricative, affricate, nasal, liquid, and glide.

I fancied myself a young Champollion but was perhaps more a J. R. R. Tolkien, creating fantastic languages in his head, or Francois Gouin, one of the unsung heroes of applied linguistics. A late-nineteenth-century French teacher of Latin, Gouin attempted to learn German by memorizing a grammar book, a table of 248 irregular verbs, and 30,000 words from a German dictionary, along with works by Goethe and Schiller. He was fascinated by the structures, syntax, and morphology of the language, and, armed with this impressive body of knowledge, set out for a university in Hamburg—Don Quixote charging the windmills—but found that he could not understand a single word of German. Gouin saw in German grammar an elegance beyond the banalities of everyday speech. And though he eventually found a new approach to language-learning in the model of his three-year-old nephew’s natural and effortless acquisition of French, Gouin could not escape the beauty of the patterns he’d found in those German grammars.

The novelist Gene Wolfe writes in his Book of the New Sun that “certain mystes [one of his delightfully archaic word choices] aver that the real world has been constructed by the human mind, since our ways are governed by the artificial categories into which we place essentially undifferentiated things, things weaker than our words for them.” But those categories, and the models that represent
them, have held as much fascination for me over the years as they did for Gouin.


Before resigning from the U.S. Foreign Service, I spent a full year of Sundays studying the Chinese poet Qu Yuan with one of my bosses at the U.S. Embassy in Tokyo, a former professor of Chinese history. Qu Yuan is China’s first real poet. Like many of the other great poets of ancient China, he was a scholar-official who turned from the social world to pursue a life of simplicity and contemplation. He was also a political dissident and exile, whose lament “How can I live with men whose hearts are strangers to me?” has echoed in the voices of two thousand years of Chinese poets. Qu Yuan’s poetry is some of the most difficult Classical Chinese I have ever attempted to read—as different from the language of Confucius as Dante’s Italian is from Virgil’s Latin. It is written in a language utterly foreign to a modern Chinese reader—and yet the strangeness of the language is precisely what makes the text so illuminating.


I first learned about this kind of illumination as a young boy. Lying in the comforting darkness of my bedroom each night, I would hear my father in the room next door. “Five times seven,” he would say, and there would be a pause as my little sister went through the times tables in her head. “Thirty-five,” she would say. And then, more enthusiastically, “Another one.” “Eleven times eleven.” A longer pause.

A few minutes later, if she hadn’t fallen asleep, my sister would probably hear a somewhat different conversation coming through the wall from my bedroom. “So if aliens exist…?” or “If the universe has an end what’s on the outside?” I could never understand the idea of an expanding, bounded universe, and got caught up trying to figure out what that “nothing” outside it could actually be. Of course, it was just that—”nothing”—but how to understand the absolute lack of identity or existence?

My sister had a talent for numbers, just like my father. I, who suffered from a chronic math phobia, tended to get caught up in the ideas of science: the beauty of the metaphors and models used to describe the natural world. My father was an electrical engineer: handy, thrifty, and infinitely practical. His avocational interest in Einstein’s special and general theories of relativity was motivated primarily by a desire to understand how the equations worked, how tensor mathematics and topological abstractions could be used to quantify even the most frighteningly complex physical phenomena. The equations never took with me: what I brought away from those discussions was a photographic imprint of the wonderfully curving topological spaces used to represent relativistic ideas. I became utterly fascinated with the illustrations in my father’s copy of John Archibald Wheeler’s classic Spacetime Physics. My father gave me the book and it now sits on my own bookshelf, not far from the brand-new revised edition I bought online a couple of years ago. The mathematics still puzzles me—but the ideas are as captivating as ever. I get the same feeling of wonder from Wheeler’s spacetime diagrams that I do from the beautiful multi-colored image of the DNA helix on the cover of Richard Lewontin and company’s Introduction to Genetic Analysis, a textbook that I purchased for the sheer aesthetic power of that molecule, or from the dazzling four-dimensional hypercube on the cover of an old pre-cyberpunk Rudy Rucker popular science book. Abstractions all, they are far more beautiful and captivating than the supposed realities to which they refer, those “things weaker than our words for them.”

When my father had led me through all the science books in the children’s section of our local library, we sat staring at each other. “How about mythology?” he said, and led me to the very last row of books in the room. It was at the far end of the row, on the bottom two shelves—at the time, exotic, uncharted territory for me. If I went back to that library today, I could immediately go to the spot where my father first pulled The Children of Odin and Stories of the Gods and Heroes from the shelf. The startling line drawings of Odin and Thor, Isis and Osiris, and Perseus and Medusa that I saw on that day are as imprinted in my mind as the DNA helix, Rucker’s hypercube, or Wheeler’s spacetime diagrams. I spent that entire first afternoon with Thor and the frost giants of Jottenheim.

How many words do frost giants have for snow, anyway? These were the questions that obsessed me as a child. And when I later discovered the Sapir-Whorf hypothesis—the classic anthropological statement of linguistic relativism—I was amused to find that it had grown out of the realization that Eskimo languages had far more words for “snow” than European languages. The difference between Eskimos and frost giants, I suppose, is that all of those Eskimo words for “snow” can be translated into English—falling snow, snow on the ground, wet snow, snow packed hard like ice. What is even more fascinating is that further exploration reveals that the Aztec language has but one word for what we refer to in English as “cold,” “snow,” and “ice.” It wasn’t until I heard Chomsky declare that “colorless green ideas sleep furiously” that I began to understand that the mental worlds of the Aztec and the English speaker are by no means incommensurable: it’s all about deep structure, after all.

This kind of reflection on language, with healthy doses of science and myth, opened me to the power of metaphorical thinking. And I will never forget that it was from my father, in the soft glow of the nightlight, that I first learned to think metaphorically, those gloriously curving topological spaces hinting at the unfathomable vastness of the cosmos, and those glorious heroes and heroines—standing steadfast in the face of fear—at the inexhaustible mysteries of our selves.


I was to stand at the intersection of those mysteries of self and cosmos while contemplating words on a blackboard a little later in life. Words on a blackboard, that’s all they were, but somehow they captured my imagination. “Asymptotic freedom.” What did they mean? I wasn’t quite sure. But those words scrawled in large letters in white chalk across the blackboard brought me back from half a morning of daydreaming. Sitting in a classroom with the young luminaries who were getting ready to wow the Westinghouse Science Fair with their gene-splicing experiments, descriptions of quantum gravity, and solutions to the ozone problem made me feel just how inconsequential a suburban dreamer I was. I had been admitted to a pre-college science program at Columbia University, but I couldn’t help feeling that I was let in to bring suburban diversity to this decidedly urban—and decidedly brilliant—group of kids: the scientific equivalent of busing. Without me, the class would have been almost totally composed of students from Bronx Science and Stuyvesant. While I was struggling with the basics of calculus, these kids were questioning the very foundations of Western mathematics; while I was learning to calculate the velocity of a falling body in Newtonian space, they were adding refinements to Schrödinger’s wave equation.

“Asymptotic freedom.” It was the first and only piece of text that had intruded into the long rows of equations and symbols covering the blackboard. Perhaps that’s why the words became seared into my memory. Or perhaps it was just the first thing on the board that morning that made any sense to my numerically challenged mind. “Asymptotic freedom.” What beautiful words.

The dictionary defines them as “a property of the forces between quarks, according to quantum chromodynamics, such that they behave almost like free particles when they are close together within a hadron.” You would probably need a graduate course in quantum physics to truly understand the concept, but its rudiments are fairly simple. An “asymptote” is a line on a graph that extends into infinity.

Quarks, the point particles that make up neutrons and protons, are held by attractive forces that get stronger as the particles move apart. At extremely short distances, the forces between them are infinitely, or “asymptotically,” weak, and the particles act as if they are totally free and not bound by forces of any kind. Because of a complementarity between distance and momentum in quantum mechanics, and a correspondence between small distances and large momenta, and between large momenta and large energies, the quarks also behave “freely” at high energies.

What this means for the behavior of quarks and the forces that bind them I will leave to those talents from Bronx Science. What it meant to me was something totally different. Here was an example of freedom so complete that it could meet the mathematical definition of infinity—perhaps the only true freedom to be found in the universe. Except for those quarks at extremely short distances or high energies, everything in the cosmos is bound by forces of one kind or another: the more complex the system, the more multitudinous the forces acting on it. When you get to systems as complex as the human brain or human behavior, you are dealing with forces that range from gravity and electromagnetism to social anxiety and peer pressure. As some Freudians would argue, we are the sum of all the forces that act upon us.


“Asymptotic freedom.” Where to find it? I am still not sure, but I discovered some clues a bit later in life, in the faces of Buddhist figures that I dearly loved. It was in the expression of a sculpture of Maitreya, the Buddha of the Future, that I first glimpsed what achieving asymptotic freedom might look like. Its long, handsome face—thin lips, straight nose, perfectly angled eyes—was in perfect symmetry. This was a face absent of tension, anger, sadness, or want—the eyes of a world truly without form, feeling, perception, consciousness, or volition, as the Buddhist philosophers once defined the five components of reality.

Except for a handful of professional philological and philosophical Buddhologists, most Western interpreters of Buddhism have focused on the mystical qualities of that religion—the sound of one hand clapping and the sudden enlightenment to be achieved through meditation, chanting, and ritual. As a psychological system, however, Buddhism has far more to offer. Indeed, its formula for attaining asymptotic freedom is as rigorously scientific as the equations describing quarks: Buddhism offers the concept of emptiness.

“Emptiness” is a philosophically loaded term in Buddhism variously misinterpreted as nihilism or a sort of radical relativism. It is neither. In my reading of the term, “emptiness” refers to a psychological state, a way of looking at the world that reads every experience as “open,” “empty,” or “unwritten.” It expresses the kind of interpretative power we have over those things weaker than our words for them. In this way, I would not hesitate to call it a scientific
concept, as wonderful a metaphor as the billiard-ball model of particle interactions or the curving ladder of the DNA helix.

In the end, I am not sure which is more meaningful to me—the elegance of the concept or its instructive power. Perhaps asymptotic freedom begins in the sounds we make when pronouncing the word “emptiness”: from the middle front unrounded lax vowel all the way to the voiceless alveolar fricative. Without this grand phonological symphony, our world would be merely void—rather than gloriously “empty.”


I am reminded that astronomers recently reported that black holes make music—they emit a B flat fifty-seven octaves lower than middle C. After spending a lifetime marveling at spacetime diagrams, I now know that to really hear the music of the spheres, you’ve got to get out and listen to it. But without Gouin’s ear for German, black holes will remain nothing but those undifferentiated things, weaker than our words for them.

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