Bright Shards of Someplace Else

by Monica McFawn

  This sent the butterflies aflutter. The light of his desk lamp was angled so the butterflies created huge flapping shadows like stingrays on the back wall whenever they moved. There were about fifty butterflies in the net-cage; their purpose was to bring in customers. As he leaned over to examine them his first day, the owner explained:

  “These are the ones that aren’t fit for flight. See the notch out of the viceroy’s wing? That’ll make it fly off sideways. See how that painted lady’s missing an antenna? That throws them out of whack, too. Cast-offs always go in the cage.”

  Aaron had been working for Final Release for a few years now. The company sold butterfly releases, that is, releasing hundreds of butterflies at pivotal events such as weddings, ribbon-cuttings, funerals. Usually there was some kind of crisis Aaron had to deal with—this morning it had been a complaint about faulty release pods. He had seen one of these botched releases firsthand when the owner went to show him how well they worked. “I don’t get what all the complaints are about. These have been rigorously tested,” the owner said and pulled the ribbon. The little paper box flattened down and then opened, so the butterfly, a monarch, pinwheeled down to the warehouse floor in the wake of the scale crushed from its wings.

  Aaron had offered to redesign the pods, and for a few hours he was in his blissful element. He sat on the concrete floor with a monarch mount, a compass, a calculator, a piece of string, and four stacks of sturdy cardstock in various dimensions. He drew diagrams, he folded and unfolded paper, he slipped the dead monarch in his prototypes, he experimented with the opening mechanism, the amount of force needed to pull the paper envelope apart without the string breaking or the paper ripping. Soon he had a new release-pod design, one that would be safe for the butterflies, cheap to produce, and able to be operated by the frailest hands of their clientele. The owner and his wife were thrilled, but Aaron was not—there was an unsightly crinkle in the way he had ordered the folds, something that wasn’t as tight as it could be. He kept refining the way the folds collapsed into each other and had stayed on into the evening to balance the books.

  It was late. Some of the butterflies began to roost, stiffly adhered to the sides of the net cage, except for a periodic slow pump of the wings. The effort it took to balance the books left him wide awake; after a moment he reached into the box of crumpled receipts and sale orders and pulled out a scrap. He leaned his head on his hand and began writing out some kind of equation, with square root signs, symbols, numbers, letters, arrows, and circles. Aaron knew exactly where his calculations would lead—they always led to the very same dead end—but there was something meditative in making a fresh attempt.

  He worked and worked and finally paused, looking upward. The Birch and Swinnerton-Dyer Conjecture was centered on a long list of variables, in fact, it could best be described as an attempt to play out seemingly infinite possibilities to a fixed end. This kind of math was necessarily so abstract that the theorist needed to create some solid stakes in his mind to keep the whole thing from rising into the ether. “You just need to find your tether,” Dr. Bajpai would say, “some system to keep yourself rooted and organized. Because once you wade into a problem …” and then he would trail off and gesture to his own system, the strips of crepe paper, covered with numbers, that he hung from the office ceiling. Aaron looked over at the butterflies again. The cage was small, the butterflies flawed and therefore poor fliers, but they were all centers of possibilities, small little suns whose linear rays represented every possible flight, every downward dive their life cycle–end might take.

  Pursuing a conjecture had a particular appeal for him. Dr. Bajpai liked to say that the work of a mathematician was not discovery but validation, and therefore the most affirming type of work one could do. The funny thing about conjectures, Aaron thought, was how beautifully simple they were. In fact, they often seemed laughably obvious to anyone familiar with advanced math. But they could not become official theorems until someone did the legwork to show, beyond any doubt, that they were correct in all cases, which meant, Aaron knew, that you needed to find a system to try out all cases. He liked the thoroughness of it, the clever ways one could circumvent a million calculations with a crisp equation, the elegance of condensing reams and reams of numbers and possibilities into a few simple, perfect steps.

  Even before he had become interested in math, he had operated with a certain efficiency and directness, a notable lack of superfluity. When first charged with dressing himself, he wanted a faster method than putting on each cumbersome piece at a time, so he clipped his whole outfit together with clothespins (jacket to shirt to pants to socks), suspended it off the ladder of his bunk bed, and jumped in. Routes and paths were of particular importance to him, and every time his mother drove him to school (he could not cope with the bus), he formulated a new route or departure time for her to try, clapping his hands in the back seat and laughing when all the lights were green and his stopwatch read a few seconds less. His father was an inventor of household gadgets who was always streamlining and combining (he invented the kitchen knife with the vacuum handle to pick up the scraps), so he of course approved, while his mother, a Realtor, appreciated having a child who completed his homework and chores so quickly, leaving her free to make calls, bragging all the while that her son could probably close on a house in an hour.

  He saw, in all quick and smooth motions (a cat grabbing a bird from the air, a car swerving around a bike swerving around a squirrel, all synchronized, all moving forward) not just efficiency but beauty, but his life thus far had progressed in disappointing fits and starts. In high school he had been clearly talented in math, but his practical gifts caused everyone, including his parents, to push him into business, where his organizational abilities would be of use. During the senior year of his undergraduate degree at Penn State, he had gotten into a car accident that left his upper body in a stiff cast for the better part of a year. The feeling of that cast—the way it restricted him—seemed to hover over him even when it was finally removed, so he still got up from a chair with an extra burst of energy, as if anticipating a debilitating weight. Once he graduated, a year behind, he had gotten a job as assistant head of supply for a kitchen-supply manufacturer, but it was quickly obvious that he wasn’t right for the job. He hated the burdensome reporting that accompanied any change he proposed, the roundabout corporate gibberish he was forced to adopt.

  After being fired, he floated around, picked up freelance accounting work, played online poker for money; he even visited two county fairs and won, both times, the jelly-beans-in-a-jar counting contest. He moved back home and helped his father test blenders and automated ice-cream scoops, he worked in his mother’s garden, he went for walks with his grandparents who lived across town, he applied for jobs in statistical analysis but was turned down. He finally took the job at Final Release, beginning as a butterfly packer but soon taking on their accounting after his boss heard him calculate a complicated return off the top of his head. It was around this time that he became involved with “recreational math,” the term used when lay people try to solve age-old mathematical conjectures. He had first been introduced to conjectures in high school, when his math teacher had the class all work on Fermat’s Last Theorem before it was solved. When Andrew Wiles discovered the proof in 1995, Aaron had sent away for the journal it was published in and curled up with it for hours as if it were a novel. Just a few months ago he began looking through his old math textbooks for some still-unsolved conjectures and settled on the Birch and Swinnerton-Dyer Conjecture, which concerned itself with rational points on elliptical curves. He began working on it in all his spare time, even mailing what he thought was the proof to the Clay Institute for Mathematics, which offered a prize to whoever solved it. He received this letter back, with his name and specifics in the blanks:

  Dear _______________,

  Thank you for submitting your proof for the _______________ conjecture. Errors appear on page(s) _______________, rendering it inv
alid.

  Professor Abdu Bajpai

  This night, like so many others, found him at another impasse with the problem. He made a notation on his paper where he left off, then grabbed his coat and went out the back door for a break. Behind the office, behind the refrigerated shipment van painted with a blue butterfly trailed by hearts, past the shed filled with torn nets, the release-butterflies resided in what was nothing more than a small cement outbuilding with a sliding door latched with a padlock. The whole area was dark. Aaron swung the flashlight back and forth in front of his feet, the store’s main set of keys swinging on his belt loop. The arc of the light left a brief trace, sometimes demarking the beginnings of a plateau curve, a parabola, a bicorn.

  He unlocked the door and flicked on the light. The room resembled a mausoleum, the walls lined with stacked steel drawers filled with packed boxes of butterflies, all tucked in their little paper wontons for release. The temperature was maintained at forty degrees to keep the butterflies in an inanimate, ready state; nothing moved in the room, nothing could. Aaron pulled open a drawer marked “Viceroy,” then selected the sharpest key from the bunch at his hip and pressed it along a length of shipping tape. The flaps sprung open, revealing twenty-four cardboard compartments. In each one, a linen-paper pod inscribed with something—these were inscribed with “Jan & Mike June 23rd”—was wedged in a slit of foam. Aaron lifted a pod out, held it before him, and pulled the string carefully—these were the old, flawed pods. The butterfly did not fly out, but walked out with groggy casualness as if debarking a plane; it made its way down Aaron’s arm with its two wings clamped into one dimension. Upon reaching his fingertip it did a slow, labored turn, its legs adhering to one another and tripping it up like the loop of a shoelace.

  He watched the butterfly, thinking about an idea that came up in his most recent conversation with Professor Bajpai. After he had received that first form letter, he had continued working, and when he set out on what he considered a radical new approach, he sent a letter detailing it directly to Dr. Bajpai, on a whim. Surprisingly, the professor wrote back to him personally, effusively praising his efforts and pointing out the potential significance of his method. From there, they began a correspondence, first over the mail, then over the phone, and finally Aaron visited his office a few times, lugging a portfolio filled with all his handwritten notes and calculations. The professor seemed to like talking to Aaron, and Aaron liked being able to talk math with anyone. Dr. Bajpai, as old and respected as he was, had an irreverent streak which had at first flummoxed Aaron. Sometimes he ribbed Aaron by pretending not to understand prime numbers and forcing him to explain them, or he would, after hearing Aaron’s rapid-fire explanation of a complicated string of algebraic computations, ask in a deadpan voice if A+A+R+Zero+N had any part in what he just said, or if Aaron had been overtaken fully by a mathematical muse. Once he had even answered the phone when Aaron called with a grand announcement that he himself had solved the Birth, Sin-a-Ton, and Die Conjecture, using the pattern of his own life as the primary proof. Aaron used to simply wait it out when Dr. Bajpai got on these tears, but he had recently learned to enjoy them, sometimes even planting amusing mistakes and messages in his work in response.

  Aaron bucked his wrist, encouraging the thing to fly off. The creature fell dramatically until it came to, opened its wings, and began flapping inches before it hit the ground. He watched as it flew upward and tapped the buzzing lights, landed on the highest shelf, walked along its edge, then took a long, looping flight back down to the concrete floor, where it pressed its wings together and zipped itself into a single plane.

  The butterfly clinches it, Aaron thought in the shorthand of thoughts. Something in the precise delineation of the butterfly’s flight—or the way it clenched shut at the end, or the way its wings parted the air, or the way it interacted with the box corner, or its broad relation to all the geometry in the room—something had done it, and Aaron was now as sure as he would ever be that he had the means to prove the conjecture. He bent over the box top and made furious notes, for, as sure as he was, he knew it could still get away; like all great ideas, it manifested itself by zooming by.

  He returned to the office and continued working on the problem, startled by the simplicity that now stone-skipped over what he once saw as irrevocable complications. He was calculating so fast he pulled scrap after scrap out of the box, filled it, then tossed it in a box top. The lone desk lamp glowed on his face, his hairline was beginning to sweat, and his thigh was vibrating under the desk, sometimes bouncing high enough to hit the underside and cause his pen to slip. On the wall behind him, the large shadows of the butterflies rioted and undulated as if in a breathless dance-off with his leg. In an hour, he had all but solved it. There were some straightforward calculations left to go, but these were formalities. He was sure he had found the proof.

  It was so quiet in the office that he could hear the buzzing of his own head—the faint vibrations of the air over his eardrums, the clicking of breath in his throat. He put his pen down and was completely still for a moment, then looked outside. The whole area was dark but for a strip of light at the warehouse door. He forgot to lock up, again. The last time he did that raccoons pried open the doors and tore into some of the boxes. It was a nasty scene, bits of boxes and butterfly wings all over the floor. He tapped the papers that comprised the proof into a neat stack and went outside. Around him fireflies pulsed in the sky, seeming to Aaron to be fixed points of light flicking on in a vast switchboard.

  The door was ajar and he could hear the rustling and scrapes of what sounded like a whole family of raccoons. He pulled the door open and shouted “Get out! Get out of there!” But instead of raccoons, he saw men. They wore low ball caps under dark, hooded sweatshirts. Their blades were stopped in mid air above the shipping tape of a box seam, while crushed boxes and spilled Styrofoam peanuts arrayed around them. Butterflies flapped and flew around the floor like looters in the wake of disaster, while others, broken, spun as they tried to take off on one wing. “Is there anything but bugs in these boxes, fucker? Is there?” The man stood—Aaron could see he was the larger of the two—and moved toward him, waving the knife in front of his face as he approached. A long reddish beard grew down his neck and shot into his shirt like the tail end of a creature diving for cover. “You deaf?”

  Aaron stood in the doorway. He assessed the benefits of running, of putting up his hands, of pulling out his wallet and throwing bills; but all of these actions had drawbacks and he was still factoring in the variables when the man was upon him. He curled up and covered his head; his body slid forward and back on the floor as he was kicked; he was a curve, his path was demarking a series of overlapping curves, the boots swung towards him on the axis of the hips in arcs, all this lightly warped, like soft wax, on the curvature of the earth. His face was pressed down by one boot to steady him, as the other kicked his back. “There’s nothing but butterflies,” he gasped. His left eye felt as if it were spreading flat on the concrete. The view was so low he could see the legs of two butterflies, monumental as the legs of his parents appeared to him when he hid under beds and tables.

  “Nothing but dirty fucking bugs; what the fuck …” He felt another hard kick to the head as if he were to blame. His vision narrowed and all he could see was a butterfly, a painted lady, moving on its needle legs like a dancer, encircled by a field of black and backlit as if it were the star of the show. “Get his wallet, man, his wallet.” They turned him over, held his neck down, then pulled his jacket off from behind; yanked it off like playground boys pulled off the wings of bugs; he would cry and point and tell them to stop until the lunch lady made him take a time out for carrying on. His head hit the metal support of one of the shelves, and a box slid down and settled on the small of his back.

  The men ran off. The door was open and a breeze swept through, whipping the butterflies, dead and alive, aloft like fall leaves. Aaron began to curl and uncurl, trying to get the box off his back, convul
sing like a worm poked with a stick. The box rolled off and he sat up, lifting his hand to his head, where he felt a stickiness combined with something soft and detached. When he pulled his hand away there was a crushed buttercup wet with blood, only a pinprick of yellow left on its wing. He looked at his hand a long while, then tried to stand. He kicked out his right leg; he tried to push up with his left hand; he stood up with his legs splayed and wobbled before falling to his knees. Another draft came in, and he wanted badly to be outside. The night air would fix it, he thought, like people going to the sea in the old days to cure things. He crawled forward, pulling with his elbows, pushing packing material, boxes, and paper release pods in front of him, often stopping and putting his head down. Blood dripped from him and spotted the bits of Styrofoam, creating small red eyes that watched him as he lurched forward again, dragging a sheet of bubble wrap with his toe. He reached the door and with a strong kick tumbled out in a wave of debris. The grass felt so good that he lay for a moment in the healing dirt.

  “Right elbow,” he told himself, and put it down. “Left foot,” and he tried to push off of it, though it slipped back in the dirt. “Left hand,” and he reached forward and closed his fist around a clump of grass. “Right leg,” and he dug his knee in. He chanted these commands to himself, even when he lay flat, unable to organize himself for a moment. He was afraid; he tried to think of the proof. The proof! He had discovered it. He tried to remember his first attempt. When was it? He put his elbow down. It had been after he had started at Final Release; he had been sitting on the floor in his childhood bedroom, rifling through the bottom drawer of his dresser. He found his high-school math textbook, the one with the picture of thousands of crayons moving down the assembly line on the cover. It contained a very basic description of the Birch and Swinnerton-Dyer Conjecture in a purple sidebar titled “Math Mysteries!” He wrote a few things in margins. The act of writing in a book from his past felt strange. When he looked up his dad was standing in the doorway. “Watch,” he’d said, and fired up a turkey carving knife made to look like a tiny chainsaw, complete with a pull.