Half and Half Again

In the fifth-century BC, in southern Italy, there lived a philosopher called Parmenides, who believed that ontological pluralism—the belief that our existence is made up of many moments—was a misapprehension. Parmenides believed that our existence was one single, unchanging reality, in which the passing of time, space and motion, was an illusion. According to him, milk might sour, and loved ones might die, but the world was actually continuous, indivisible. We live in a world in which we are all simultaneously unborn, alive, and dead. Parmenides is with us, and we are and were with him.

It’s easier to understand Parmenides’s sense of indivisibility if you imagine Italy in summer. There, the senses are sympathetic to an unchanging reality; the days have a rhythm, the pulse of a sleeping heart. Olive trees, sunshine, water; the sound of the wind in the leaves. Insects cry out, clinging to the bark.We live within a oneness of comprehension, where everything—even the things we have not yet experienced—is still inside our horizon line of understanding. We may not be able to see this, but that doesn’t mean it doesn’t exist.


All of this is nonsense on some level, but these days, I am starting to sense a sphericity in me. Right now it is very slight. I feel it on the days I write in cafes in New York City. There will be three, ten, fifteen people there. A few have laptops. Others sit in twos, talking. Sunny dialectic; they’re telling stories to each other. One is dressed in nurse’s scrubs, and a second’s father has just died. A third wears very large hoop earrings, shaped into large hearts. Sitting at the bar, a woman has a flock of starlings tattooed on her back, which are mostly hidden by her shirt. The fan is turning and The Smiths are playing; that moaning voice, Cassandra in the body of a man. Out on the street, people walk by in the soft light, inspecting their phones. When you become hyperaware, your sense of predestination rises like sap in a plant. These people belong to me. I am newly compassionate; this is my sphere, for better or worse. It takes an infinity to walk to the bathroom.

You could call it a slowing. You could also call it an adult thing, Parmenides’s sphere, when you start to sense an inevitability to the shape of your existence. Olives, water, wine. A girl sits down and tells a boy that nobody likes a man-child. I could go to a different café, could come back here on another day and though the details—the food, customers, weather, and song—would be different, the feeling wouldn’t have changed. I am sensing a thickening tradition in my own life, a kind of hardening. The plates of my experience are fusing together. I am living within my own horizon line, and I have not departed from it for some time.


On March 8, 2014, Flight MH370 took off from Kuala Lumpur airport. It was supposed to land in Beijing, but less than an hour after takeoff, the communication transponder was manually turned off. Just before that, Malaysian radar picked the plane up turning abruptly left, deviating from its northerly flight path and heading out over the Gulf of Thailand.

It took less than seven hours for the media to pick up the story. Everyone assumed the plane had been hijacked, but as the hours passed, no terrorist group came forward to claim responsibility. One morning stretched into one day. None of the neighboring countries had spotted the plane on their radar systems. There were no cellphone calls from passengers. That first night stretched into two, then three, then more.

In that first week, MH370’s disappearance was the story to follow; experts in aviation, satellite, terrorism and South East Asian geo-political ambition speculated endlessly on T.V. about why and how. This talk was all anyone had, because the plane refused to materialize. It had to have landed (its fuel would have only lasted until midday of the first day) but without any contrary information, the plane kept on flying in people’s minds. The television show Lostdidn’t help. Neither did the sense that the world seemed too small to lose a giant plane. Satellite tracking is ubiquitous, our digital handshakes instinctive and incessant (I must register on a satellite hundreds of times of day), but still—227 passengers and 15 crewmembers had vanished into the blue, along with all of that steel and fabric and plastic, suitcases and food carts and pillows and blankets and toys and clothes. Matter vanished into thin, high, blue air.

At the time, I was using a gym to train; it was too cold outside to run. I grew up in New Zealand, and have never owned a television, so this was the first time I’d really encountered the phenomenon of an American 24-hour news cycle. As each day passed, even with the sound off, I found it harder and harder to watch the monitors suspended from the ceiling. The media couldn’t bear to look away. They reported on their not reporting.

There was an abstract force to the extremity of this feeling, a kind of pure aversion. On waking, my first thought was whether they had found out what had happened during the night, but I was always reluctant to turn on the radio; I knew that finding out would not be as painful as being told that, yet again, no one knew. My gait felt off. I kept on tripping on the treadmill. It wasn’t a paradox, but it felt like one: the crunching sensation of the mind as it persists in a belief that can no longer be true.


Parmenides’s lover was (reputedly) Zeno of Elea, another philosopher. You might recognize his name because Zeno’s paradoxes are one of the few pieces of Greek philosophy that persist in popular culture today. People remember the gist of it: a space—a football field, an arrow and target—and talk about moving from one end to the other in steps, each time dividing in half the remaining distance. You can move half of the way there, they say, and then half that, and so on and so forth. Yet because you can halve the distance an infinite number of times, it takes an infinite amount of time to reach the target. We should never get there.

Such thought experiments survive as a kind of stoner’s delight, as a story told by one college student to another, ambling along St Mark’s Place. We’re so confident in our empiricism that the scenario seems a pseudo-intellectual amusement rather than a real proposition. But Zeno was serious. That an arrow didhit its target suggested that those who thought the world was divisible were just plain wrong. Parmenides’s thought that all was indivisible might seem difficult to swallow, but to Zeno, so too was the idea that all of our actions were truly divisible. His paradoxes were thought experiments designed to defend Parmenides. What we perceive as multiplicity was really a singularity wearing the mask of many. The thought dogs humanity. It is also the basis of spiritual belief.

What seems more surprising is that we remember Zeno’s name. There is something about his thought experiments that is singular enough to name it, a quality in his stories of division and non-attainment that we still find distinct. They are analogies for a thought process we seem to have a hard time explaining any other way.

In some kind of asymptotic echo of his paradox, most people trail off before they get to the end of their retelling; they’re confident of the bit about division, hazy about the conclusion. Our fuzziness about the paradox is part of the paradox now. His is the line of a song that everybody in a bar somehow knows to chant, in unison, even if they don’t know the singer’s name. “Oh! We’re halfway there. Oh-oh!” It may be that Zeno’s paradox persists because beyond his name, there is no single word that can accommodate that delicate sense of the finite and the infinite. Like oil and vinegar, if left alone long enough, they’ll insist on separating. The paradox whisks them together.


Eight days after flight MH370 disappeared, I flew to Los Angeles with my boyfriend and drove to Joshua Tree National Park. I had booked a cabin in the desert for five days; I wanted to write, and run outside.

One night, as we lay in bed together, looking out through a large window onto the desert, which stretched away for miles, the rocks and yucca lit by the moon, the highway lights flickering in the far distance, my boyfriend asked me to marry him. I felt something snap or spring tight in me, as real as a pulled tendon: guilt and love.

We spent the next few days talking about what marriage meant. I had no interest in being joined to another person for legal or religious reasons, but there was that romance of extremity, of settling down, of never being technically lonely again. There was the hunger for being loved so much that someone would do such a thing. Our paths had crossed rather randomly, and now there he was, whistling as he made the coffee, or standing on the porch, stretching, looking out at the mountains. I choose you. I declare something is permanent, even though I know nothing really is. The distance between yes and no seemed a chasm a foot wide and thousands of feet deep.

So we began to divide the distance up. Talk of a ring. Talk of children. Half the distance, then half again. Summoning our nerve. I do. Impossibility and inevitability go so well together. Walking across a room used to feel like the easiest thing, but now when I moved across the cabin, bringing him wine, taking dishes to the sink, their air seemed to crackle.

Zeno wrote approximately 40 paradoxes featuring Achilles, chariot races, and tortoises (among other objects), but I’m surprised he didn’t use the trembling distance between lovers.

At Joshua Tree, I followed the news on MH370, and registered the fact that two of my countrymen were on the flight. The New Zealand Heraldpublished a profile of one of them, Pauly Weeks, an engineer who had been on his way to a new job in Mongolia. Just before boarding, he had texted his wife Danica Weeks to tell her that she and the kids were the most important things to him in the world. Since then, Danica said, she had woken every morning expecting to find Pauly lying in bed next to her. She could not shake the certainty of his weight, and so every day, she had to unlearn. All of her senses told her something that could not be true. She had started writing poetry about him, rhyming couplets, whichthe Herald published.

The interview was brief, but it stuck with me. I would think about her most days when I went running along the dusty roads. It felt good to run into the desert holding nothing but my iPod. There was no track, no one else about. I kept an eye on my odometer watch, on distinctive rock piles. Cacti, sand, blue sky. I felt like a different woman: an American, who drove a car, who lived near by, who was married. For the first time I felt like I was in my mid-thirties. Here was another future, knitting itself now, spooling itself out ahead of me: a red thread out or in. My skin was drier. My weight bounced off and onto my joints differently each time my foot hit the sand. There would be a time in which I would come to expect this man’s weight in my bed too, when my sense memory might grow stronger than reason.

Ironically, neither Parmenides nor Zeno wanted us to develop a taste for such speed, such transformation. Zeno wanted to divide and divide simply in order to show the absurdity of the motion. But what seems to have lasted is not just the impossibility, but also the pleasure that comes from division. How exponential the function of dividing by two is! How quickly we seem to move away from our beginning! There is a charm and terror to the sheer rate of change, to the ever-diminishing room in which we have to move, and how we can continue to move in it. One step, two step, three—and the sky is suddenly darker, the cliff a different kind of stone. I could return to New York with a rock on my hand.

Regardless of what Zeno intended, this is part of the pleasure of the paradox now; it leans both ways, towards completion, towards dissolution. The closer you get, the more aware you are of the edges between things. That awareness is a pleasure, an acquired taste. It sets you on your tiptoes, gives you balance in any high wire act of fatalism.


I can’t remember when the disappearance of MH370 became bearable. I flew back to New York and continued teaching. The first day it was warm enough to run outside, I pulled my left piriformis, which is a small muscle deep within your ass, partially veiled by your glutes. It attaches to multiple muscle groups, including the ilia-sacral nerve. It turned out to be very painful. For weeks I couldn’t balance my body weight on my left leg, which meant that every second step down, every time the femur pushed up into the hip socket, I felt a jolt of pain.

Online, I watched many dissection videos of left back legs, part of a flourishing sub-genre of online medical dissections. I was always looking out for the piriformis. Faceless men narrated the names of the muscles and tendons, pushing them this way and that with a silver pointer. Whenever they reached the piriformis, I felt a rush of feeling. There it was! It was like the face of a relative who doesn’t recognize you on the street. Sitting at the computer, I’d raise my left cheek up off the seat and prod at the glutes, trying to part them, my fingers digging. That’s what it looked like inside I’d tell myself: redder, twitchier, but just as blind, just as instinctive.

Through spring and summer, I sat in bars facing my boyfriend drinking wine, talking through the early evening. I so wished him to know how I felt, swaying with happiness; how it felt to sweat, or exhale, to feel my tongue at the roof of my mouth, how the ring he gave me felt on my finger: gold, with a diamond that had a smear of orange at the center. I wanted him to know what the pain felt like in my ass, and how it slowly ebbed. But how could I? The impossibility of knowing another, from the inside out, from the blood and gastric juices and neural pathways, is the despair of love and the excitement of the world.


On a mathematical level, Zeno’s paradoxes have been solved, and rather easily. Zeno didn’t understand that we could move through an infinite set of points in a finite amount of time. He failed to separate the finite number of real things a runner has to accomplish from the infinite series of numbers we can use to describe what the runner does. Zeno was dealing with what looks infinite rather than the actual mathematical infinite.

I barely know how to treat infinity; the word mostly lingers as a trace of my eight year-old self, discovering swearing brinkmanship. You’re infinitely worse.You’re infinitely worse plus one. But as Bertrand Russell has pointed out, we can’t understand the infinite if we have “habits of mind derived from the consideration of finite numbers.” Nothing is gained if “we pass its [the infinite’s] terms in review one by one.”

One fall day, when I read this sentence, I stopped, and took a big breath. A thought came to me, and I could not unthink it. Zeno’s arrow, its clumsy impossibility, was also an analogy for a finite love that is trying to be infinite.

When knowledge arrives whole, it has a singular flash to it. For an instant, a scene is illuminated. The English philosopher Alfred C. Whitehead argued that Zeno’s paradox was an attempt to isolate precisely this experience. Wesley C. Salmon summarized his point this way:

Whitehead maintained that the physical world is an extended          spatiotemporal continuum, but he believed that it came into existence in chunks; these pieces came into being as whole entities or not at all. In retrospect they can be conceptually subdivided into parts—even infinitely many parts—but the parts do not represent entities that can come to be by themselves. An act of becoming is an indivisible unit; if you subdivide in any way the resulting parts are not smaller acts of becoming.

What I suddenly understood was that my love for this man was a divisible unit. In my relationship, there was no mathematical infinite. No matter how many steps I took, I still wouldn’t reach him; even if I said, “I do,” the arrow of my heart would keep on flying.

A future spooled back, retracted like the cord on a salad spinner. I returned the ring. I felt sick about it. I still feel sick. But the thought had the inevitability of a cake; I had made this thing, and here it was, rising in me.

The filmmaker Andrei Tarkovsky thought art a way to comprehend the infinite, writing, “An artistic discovery occurs each time as…a hieroglyphic of absolute truth. It appears as a revelation, as a momentary, passionate wish to grasp intuitively and at a stroke all the laws of this world—its beauty and ugliness, its compassion and cruelty, its infinity and its limitations.” His emphasis on the instant is in line with Whitehead’s. It is an insight that cuts through rather than points at. To me, poetry does this particularly well. It crystallizes emergent thought, aims at that sensation of endless becoming. There is nothing—and then there is suddenly something, a thought, like a piece of space rock. It is no surprise to me that Danica Weeks began to write poetry as she began to mourn her lost husband. She was mourning an absoluteness.

Rather than thinking of the infinite in terms of addition, we might understand an infinite set of numbers by its characteristics; how that set of numbers operates rather than how big it is. One way to imagine this multiplicity might be to think about uncountable forms in nature like a flight of birds, a beach’s worth of sand; groups of which it makes no sense to think about what happens when you add one more of that thing. The salient feature is how that group of infinity moves: how they tumble, how they separate. My problem was that I could not think or imagine how my love for this man moved.


More than a year later, I read this out loud for the first time to a group of people. It was in the evening, and we had just finished dinner. Olives, water, wine. The light was soft and warm, and I could hear my voice in their ears. As I read, I realized that all of this had become a thought experiment, a paradox to tell other people; an analogy for something else they might feel altogether. The reality of what had actually happened had begun to drift away from me. The thought had completed itself; the cake had stopped rising. They had found a piece of MH 370 washed up on a beach on Réunion in the Indian Ocean. The details of the crash were still fuzzy, but the end was absolute. The arrow had hit the target.

The next morning, over breakfast, one of these people who had listened asked me if I thought all love was finite. “No,” I said. “I don’t think so. Even if I never thought about it this way before, I can imagine my feelings for others as infinite sets.”

She nodded, and disagreed. “I think all love is finite,” she said. But I did not ask her if she sensed Parmenides’s sphericity in her own life, if there was a quality to her consciousness that persisted, which could not be divided. I suspect there is. She has that quality to her; like a statue that may have eroded over time, the acuity of her lines still springs forth; that brow, that eye. She said she was looking for a paradigm shift. She had given up her apartment, was going to stay in a different place every two months or so for the next year. She had seen a bird in her dream that she had never seen before, and having looked it up on Google, she knew which country to visit. She was departing, moving, swiftly traveling into the dusk.

Right now I can imagine her waking in the morning, and watching the world, seeing the way people swarm and separate, rise and fall. She will notice how she isn’t surprised, even when she ought to be. The shift may come, but it was already part of her. It is silly that I see in the infinite in someone who believes in the finite, and the finite in someone who so badly wants the infinite: as silly as a racing tortoise, or a chariot that never arrives. The clumsiness turns out to be vestigial, a tail I cannot shake. The sphericity, a hidden muscle, a hidden intuition, hardens and grows.
