(A Modern Victorian Tale)
The shortest distance between two points is a straight line. She jerks her head up with a start and sees the clock–9:40 a.m. There just might be time! There just might be time if Nancy runs fast enough, time to see John and confess her love for him. She has been working on a proof all night and has fallen asleep at her desk and is late, is late, for a very important date, and now she doesn’t know if she can catch him before he catches his plane. But how quickly can she descend that damn staircase that begins outside her door, the staircase that is an endless Fibonacci sequence that spirals and spirals down? Those old worn stones might cause her to trip over and chip a tooth, the fragment cleaving off in a perfect right triangle. She runs faster and faster, her hair trailing behind her, her footsteps echoing off the walls. These old Oxford colleges like Magdalen are more trouble than they are worth, though they are prestigious and date back from the 13th? 14th? 15th? Century, full of lore and history and funded by the coffers of kings and dukes and marquises, for they are damp and chilly and dark, unwelcome places to call one’s abode.
The shortest distance (though not a straight line) between Magdalen College and the Mathematical Institute on St. Giles (John’s office, ETA 9:57 am) is via Longwall Street which becomes Holywell Street, then under the Bridge of Sighs onto Broad Street, which at this time might be littered with tourists and buses and bicycles and shoppers and babies, pushed along in their prams by their “Mums”–not “Moms,” as this is England–and cooed to and cosseted with nursery rhymes or digestive biscuits, just as her own mother used to do for her when they were in Oxford two decades ago. Decade from deka- for ten in Greek, when her father was on sabbatical from Rudyard University. Sabbatical. One break in seven years. A rather Biblical concept, that, seven years, seven being an important number. Seven wonders of the ancient world. Seven having the highest probability of occurring when rolling dice. Seven musical notes–do, re, me, fa, sol, la, si, or sa, ri, ga, ma, pa, da, ni on the Subcontinent. Seven years ago when Nancy and John first met.
A garden party on the “math lawn” at the renowned American university of Rudyard. Nancy was on the far side of 13, sipping her punch (a curious concoction of lemonade mixed with an unknown variable of red liquid), hoping she would not spill it upon her long white cotton lace dress that she had sewn herself, modeled after something she had seen in a Victorian storybook. But she shifted her legs, and the entire glass of punch emptied itself onto the lap of her beautiful white dress, the artificial red color beginning in the center and then spreading itself out in all directions, like a circular amoeba–fluid mechanics in action. Someone probably spiked the punch; inevitably, one of her father’s grad students would have emptied his flask of vodka or rum into the punch bowl and have therefore inebriated half (or a percentage equal to a majority) of the crowd. These students were not deviants; deviations perhaps, standard or otherwise, but they were a bunch of good kids. They were mathematicians, after all–how wild and bacchanalian could they be? Someone was talking to her father about Gauss while Nancy tried to mop up the mess on her dress.
And suddenly, there he was, directly in her line of vision, a straight line between two humans: the tall, slender, ginger-haired John Boleslavic. Though he was but 19, he was her father’s graduate student in his class on model theory, and one of the best in the class. He was listening intently as someone ranted against the latest recipient of the Field award, questioning the validity of the awardee’s proof; his pale slender fingers were resting on his chin, he nodded silently. John was present, and yet he was absent; his mind was wandering somewhere and his ideas darted back and forth in his head like a pair of goldfish trapped in a small glass bowl.
She waited till his eyes finally rested on her, those eyes that were inevitably colored blue and green with flecks of hazel, colors that she often saw in fractals or crystals; except these eyes were not fragments or jagged but rather beautiful round orbs that were perfect spheres, so that if one were to take appropriate measurements, one would find that they were paradigms of perfection. His muscles were indeed well-defined, hidden under his reddish T-shirt, which was rather informal for a garden party, but maybe Nancy was the overdressed one, a vestige from those 19th century novels she liked to read, in which the heroines spoke their minds while eating dainty finger sandwiches and playing croquet with flamingos as mallets. Yes, his eyes were finally resting on her, and in them was the genesis of a smile, the corners turning upward, like a parabola, and then the mouth followed, revealing a row of perfectly beautiful teeth. Well, they were not exactly perfect, not in rows where each tooth was suspended at a 90° angle from the gums, but they were perfectly beautiful, nonetheless. He offered to bring her a napkin from the table by which he was standing. She nodded, stood up, teetered, and crumpled to the ground, the punch having worked its effects on her, and blushed as red as the punch itself.
“Here you are.” He handed her two large square napkins and a glass of water. “Shall I get you a cookie as well?”
Nancy nodded and began dabbing the stain on her dress with water.
John presented her with a disk of oatmeal studded with morsels of chocolate.
“3.5 inches,” Nancy said, after examining the cookie.
“Were you to measure it, it would measure 3.5 inches in diameter exactly.”
John laughed heartily. “By God, you are a mathematician’s daughter! No time wasted on imprecision.”
“Imprecision is the death of exactitude, which is something mathematics demands.”
Mathematics: (noun) from the Greek máthema, “knowledge, study.” Nancy is gasping, panting, as she runs past the courtyard of Magdalen College. She must stop to catch her breath, reclaim the white puffs of atmen that are visible against the cool, damp morning air. But this will cost her time, for she must reach him by 10:00 a.m. Greenwich Mean Time. The arches and pillars around the grass form a sort of cloister in which, at an earlier time, a beautiful nun swathed in folds of linen would have languished over her lost lover, thinking of him incessantly during matins and vespers, questioning her decision to enter religious life, and leaving it a year later when her knight in tarnished armor returned, world-weary from fighting in the Crusades in Greece. He is her knight in shining armor, John, ever since maidenhead, and she has waited for him, cloistered in libraries and studies and rooms with high ceilings and wood paneling and worn tables into which students have carved their names or their amours or their indiscretions, immortalized in oak or mahogany for the youth of the academic world to see.
Oscar Wilde, too, has languished over the love of a man in this courtyard here! Perhaps he had been in the very same spot in Magdalen College this morning 100 years ago, or perhaps 150 years ago, chewing on the end of his pencil while writing his immortal witticisms, brilliant words that could not transcend a country’s laws forbidding sodomy. Oscar Wilde knew of love, wrote of love, loved things Greek, from Greece, the birthplace of so much mathematics. Greek, like Pythagoras. The Pythagorean theorem: a² +b²=c². But isn’t the whole greater than the sum of its parts? Do two individuals who meet, copulate, love, and reproduce create something that is greater than their two discrete selves? John is agape, perfection to her, her very own kouros, her very own Greek god. He has been more than her kouros here: he has been her advisor, Professor Kouros, during a period in which, though sitting parallel to each other daily, poring over number theory, she has not been able to intersect with him, due to decorum and propriety. She has studied with him two years, he has been her mentor. But she could say, handing him a ticket, “John, shall we fly away to the Hellenic world–three hours ahead of Greenwich Mean Time due to the longitudinal division of our planet into time zones–explore the ancient wonders and columns Ionic, Doric, and Corinthian, visit the birthplace of Archimedes and Euclid, make love, and live happily ever after?”
Integrate. From the Latin integratus, past participle of integrare, to “make whole.” ‘Integer’ has the same root. A whole number, not a fraction thereof. Again Nancy is running, rounding the gate past the porter, and free of the confines of the college, she is on the High Street and maybe she’ll not take Longwall Street after all and will take Queen’s Lane instead. Queen’s Lane is more medieval and mysterious. Here, she is Guinevere or Eleanor or Elizabeth or any variety of female sovereign for a brief moment as she flies down the well-worn path where perhaps Oscar Wilde walked, en route to visit a lover of the male persuasion. There are clouds piling up overhead–she has forgotten an umbrella. She may end up drenched, soaked, saturated. Should she return to her room to fetch an umbrella? A strange invention, that; six or eight spokes emanating from the center, like an octopus or a spider. But if she goes back, she may lose time, lose the possibility of professing her love. There are but 12 minutes left, 12, a significant number to demarcate the months in a year, the hours on a watch, signs of the zodiac.
No time to waste, for John is to catch a flight bound for the states, back to New York or Newark or one of those homophonous major hubs, to depart after two years of research at Oxford, one half of which has overlapped with her sojourn as an exchange student. A flight on a 747 or 767 or alternately an Airbus; the difference lies merely in the degree of automation upon which the pilot relies. What makes a plane fly? It takes so many pounds of thrust and so many pounds of lift and so many pounds of drag, as Signore Bernoulli explained and Sir Newton as well, with the help of Monsieur Coanda. What makes the soul fly? How many pounds of–well, she will blushingly acknowledge it–thrust from a man’s body does it take when they integrate their bodies? How much lift, when he takes her in his arms and lifts her up to be able to see the newborn robin babies in their nest, “Look, Nancy, how tender and fragile they are!” he whispers, “Not there, there!” and she sees them, downy and peeping, their mouths wide open for their mother’s regurgitation? How much drag, how much drag is there in her legs right now as she is skipping over the sidewalk and stones, wondering whether or not she should tell him, offer her body and soul to him.
Integrals often have a finite limit to their summation. But her love is a function of all of her previous life experiences summed up, Σ, her love continuous except for a finite number of finite jumps in a finite interval called her life, like Riemann’s Theorem, or is she really going mad now? She recalls a rainy afternoon with John, one of those incessantly gray days where the rain simply pelts the windowpanes and yet refuses to come to a boil and let itself out in a thunderstorm.
“Nancy, is it? A literary-sounding name,” he said. John was standing in her father’s study in their house, a room filled with books and papers from the floor to ceiling and everywhere in between, poring over a tome on the integral. He was clad in a T-shirt bearing the name of some mathematical association. “It sounds like the sort of name that should belong to a clever young woman in a book in the 19th century–Middlemarch, perhaps,” to which Nancy nodded, speechless. Conceivably he mistook her age for younger than she really was. After all, she had barely just become a woman, was still pale and slender, with limbs that like those of a filly. “Don’t you talk?” he asked, with a smile twitching at the corners of his eyes.
“Yes,” said Nancy. “I’m Nancy,” and at once realized how foolish her elliptical conclusion to the conversation sounded.
“How old are you, Nancy?”
“I beg your pardon,” he apologized with a bow. “I thought you were younger; 13, perhaps.”
“But 13 is such a distasteful number: it is prime, its multiples are rarely found, and of course, it is very unlucky in the Western world. It is even more distasteful than high school, an institution which I abhor.”
“But you don’t find mathematics distasteful, I assume?”
“Oh, no, not at all! In fact, I think I should be happiest in the world were I curled up on the couch with the cat by a roaring fire reading about the history of calculus.”
“The history of calculus? That’s quite an advanced subject for such a young girl,” he said incredulously, but not condescendingly. John went on to add, “But I am not surprised that you are investigating the history of calculus. What else would one expect from a mathematician’s daughter? We have heard all about your precocious numerical talents in the department. Of your awards. Of your recognition by mathematical scholars as a budding math genius. You, too, are a mathematician.”
Nancy was speechless at such a compliment. She was being called a mathematician at such a young age, called a mathematician in a way that was an accolade rather than an epithet in the schoolyard. After all, she couldn’t help it if she had been the sort of girl who spent recess poring over a copy of Flatland rather than suspending herself upside down from the monkey bars, her knickers in full view, or singing silly rhymes while holding hands and running around in a circle–a rather imperfect circle, at that.
“But a young woman like you needs to have other pursuits other than mathematics. One must have friends, or other people of interest.” John’s face was glowing with warmth, his hand gently on her shoulder. “One must not bury one’s head in books too much. One must, shall we say–integrate people into one’s life.”
For the first time in her life, something was ignited within Nancy and she smiled, really smiled, smiled at being admired by a man who was not a schoolteacher or a mathematician or her father. It was a handsome young man not 40 years old or 50 years old, but 21. Lucky 7 times 3.
“But I’m not sure people can understand mathematics very well–unless they are mathematicians. My books keep me company. Wouldn’t it be absolutely divine to have high tea with Jane Austen or Lewis Carroll?”
“Personally, I’d prefer a beer with Andrew Wiles at Cambridge, but I’d settle for a round with my friends.” John leaned in and smiled. “There’s the teakettle whistling. So perhaps I’d settle for a cup of tea with you instead!”
A matrix is an array of numbers in columns and rows. Nancy winds her way through the streets but she is lost in the columns and rows of Oxford’s colleges. Bees live in a sort of a matrix, for their honeycomb is an interlocking system of hexagons within which they live. Matrices of nine numbers that she had to solve as a child. Would they add up if she tallied them this way and that way? A matrix has a system and order to it, an internal logic, a rhythm to things. But no, in this matrix, the array of colleges is not in neat rows and there is no internal logic to this jumble of buildings. She is lost, having turned on the wrong street, and now this grave error will cost her time. She must find her way out of this labyrinth, left-right-left-right, but here is Radcliffe Camera, around which she must circumambulate, and now time is running out quickly. One can only count lost time. One cannot make up for it. She has lost before, and she will not lose John. Will she find him at the Mathematical Institute? Or should she try his residence, a small flat above a fish-and-chips shop endlessly belching greasy exhaust? Or worse, he has departed early and is en route to Heathrow (stress on the second syllable), dozing comfortably in the coach with his head resting on the window? No, she must not entertain a myriad possibilities, lest it send her brain into a whirl, a vortex of will-I?-won’t-I? catch him.
Probability=number of desirable outcomes over number of possible outcomes. Odds= number of desirable outcomes over undesirable outcomes. “Tell me more about integers, Daddy!”
“Well, they are whole numbers, Nancy. Like the numbers you count on your fingers, the numbers in a scale, the numbers on your ruler. And then of course, there are the negative ones, below 0.”
“Would you like to hear me count, Daddy?”
“Of course, Nancy. Let’s hear your integers.”
“I can count really high.”
Her father stops her at 33. “What can you tell me about 33, Nancy?”
“Well, it’s an integer. Not a prime number. A multiple of three. Do you know why it’s special, Daddy?”
“It was the age when Mummy died. Her name was Georgiana, was it not?”
Georgiana. A rather regal-sounding name for a simple Welsh girl who loved to make things with her hands, a girl born by the border of England in a cottage made of stone or slate or some type of rock mined out of a quarry somewhere. Georgiana Hanford Jones, a clever girl who was forever creating shapes out of paper–pyramids and origami-like constructions for her little brothers and the neighboring farm children. She’d tell stories to them, when she wasn’t knitting and milking the cows early in the morning with a book of equations upon her knee. A girl who liked to stay inside and read, which was fortunate, given her often sickly condition. A girl who hoped to escape the confines of her small Welsh village and go to university–and she did, she did escape and read math and philosophy. The pale, anemic, ginger-haired Georgiana would mesmerize her peers with her speeches, her opinions, drawing on paper napkins in the pub to make a point. Clever Georgiana, they’d say, she’s really an old soul trapped inside a young woman’s body. Her professors praised her, saying she’d either become a renowned female mathematics professor or prime minister. The thought was that graduate work in sunny, arid California would ameliorate her hapless health, her croupy cough, her pulmonary problems. She gained an American boyfriend, and a full scholarship.
But somehow the odds were against her. Odds, like in betting or gambling, what one might do in Monte Carlo or Macau. Stripes of red and black on the roulette wheel or the black and white of the blackjack board, calculating if one’s paltry sum placed in the ante will somehow miraculously multiply hundredfold, thereby allowing one to enjoy that expensive bottle of champagne, or perhaps rest at the fancy seaside hotel amongst all the millionaires, be they legitimate ones or made through illicit means. Yes, the odds were against Georgiana Hanford Jones, who often coughed while writing her thesis, coughed during her wedding ceremony, coughed when Nancy was a tiny child nursing at her breast and later when Nancy sat on her lap adding numbers before she fell into her afternoon nap, coughed when the doctors told her the statistical average for surviving her malady was quite poor. “Dearest one, know how I love you so,” were her last words to the little Nancy after folding her a small origami heart, collapsing back on her bed with a violent cough rattling her body with a seismic intensity. The only odds that were not against her were those of death–at least in one matter, she was a winner with an unfailing probability, a 100% success rate: P(death)=1.
Nancy is lost in the maze of Oxford and must find her way out if she is to catch him before his departure. She will not see him for a year, perhaps two, for she must finish her studies here and he must return to Rudyard, their beloved university back at home. She must tell him, tell him to wait for her, to not enjoin his heart to another. She is afraid to postulate what the outcome might be should another homo sapiens of the X-chromosome variety should catch him on the peak of a sine wave of libidinous sentiment. But can she be certain that if she told what she has felt all along, that it will be reciprocal? Take a number, multiply it by 1 over that number (its reciprocal)–you end up with one! A perfect pair of numbers. Opposites create a 1. How many years of being one, through all the special moments?
A proof must demonstrate that which is always true. Yes, she had all the proofs. The late-night walk in the woods on a night where the crickets (or were they cicadas?) were chirping steadily and the air was balmy and slightly damp to show her a particular constellation that was rare during that time of the year. He told her of his love for astronomy and man’s quest to reach the stars and astral bodies, his hand grasping hers–a night that was her 16th birthday. The way her pulse would race and her nostrils would flare and her palms would sweat whenever she saw him hunched over his notebook, the pencil held in his curled hand, moving furiously across the page. Then he would look at her with an absent yet intense look and exclaim, “I’ve almost got it, Nancy; I’ve almost got it, thanks to you!” and smile at her with a most intimate, personal smile, one she never saw him flash at anybody else. The look in his eyes, upon his return from a summer holiday in Spain with a girl whom he had romanced, when he said, “I don’t know, Nancy; I just don’t think she’s for me. I think there’s somebody else,” and gazed at her with his beautiful blue-green-hazel eyes, embraced her with his sinewy arms and legs. “We’ll both be at Rudyard this fall, now that you are going to be a freshman there.”
Those sinewy legs. When he broke his right one years ago at Rudyard, playing touch football with some athletically inclined grad students (certainly they were not mathematicians, as mathematicians were generally not athletically inclined), he sat in his apartment with his leg propped up upon the nubby red couch, its casque-like plaster entombing his limb, she attended to him in her spare hours between classes and studies, serving him soup and bread, the bowl of soup teetering upon the plate as its steamy aroma emanated into the air, serving as some sort of an aphrodisiac (certainly they were mathematicians, as only mathematicians would find soup to be some sort of an aphrodisiac). She watched as he sipped it from the spoon, facing him as she sat next to his feet, his legs straddled open in a remarkably suggestive way. “You could take care of me forever, Nancy,” he said, and held her hand, and then and there she would have mounted him but for the rather cumbersome (not to mention necessary) plaster cast, and for the fact that a young mathematics student would not make for a suitable mother should she get pregnant at this moment, for neither of them had a condom on hand. So many sperm, one sole egg. The odds were so unlikely, really; bloody how did anybody get conceived?
How can one predict how a given individual, in a given circumstance, with given factors and some concrete evidence, might react? Is there at all proof when it comes to the human heart? For Nancy is sure, she is sure as she winds around the bend, where she thinks it will lead her to Broad Street, she is sure there indeed is proof, for there is evidence, and it has been replicated. Is that not one of the hallmarks of the scientific method, that the results must be replicated?
“How do you think they built the pyramids, John? How do you think they were able to envision such large geometric forms without the use of cranes or planes or computer simulation?”
He was sitting next to her, his knee touching hers, in the math library on campus, as though he were recounting a fairytale or bedtime story to her. “That’s the genius of mathematical models. They allow us to comprehend a sense of scale, a sense of proportion. We can actually predict how things will work.”
“But how accurate can a prediction be? Supposing the range that one would generate in statistical terms cannot quite accurately predict other factors when a pyramid is built, such as the wear of the stone, weather, even gravity?” How accurate can a prediction be, indeed? It would have to be a yes or a no. On or off. 1 or 0, like in binary.
Exponential growth is the inverse function of logarithmic growth. But no, love could not be binary; there was too much ambiguity in it. Rather, it was a spectrum, a Richter scale (which is logarithmic) in which each gradation of love was much greater than the previous, a range of feelings and emotions that were endlessly dazzling and endlessly confusing. “He loves me, he loves me not.” Could she take care of him forever, forever like infinity that endlessly looping number eight lying upon its side? She suspects she feels a drop of water as her feet pound the pavement, the clouds look menacing. But it turns out to be a single droplet, as though someone has emptied a celestial chamber pot onto her head.
But no, it was John who had taken care of her forever, his presence becoming exponentially more significant in her life. Yes, John was like the sun. She would always feel the warmth of his presence extend to her wherever he might be. No matter where in the world he was, he wrote her a letter or a postcard or perhaps even sent her a small packet containing souvenirs: a seashell, candy, a bead necklace. “I am teaching at Oxford, Nancy. It is stunningly beautiful here, fairy-tale beautiful. Not to mention the academics are superb. I could get you a fellowship to study with me here, if only Rudyard would release you for a year or two.” And so those words scrawled in blue ink on a postcard, with a verdant view of Christ Church College prompted her to scurry into the Office of Overseas Studies to obtain an application for studying abroad. The woman dressed in white sitting behind the white desk in the white room smiled and encouraged her, her presence radiating benevolence, an Administrative White Queen.
As she quickens her pace, in a quick glance at a window above the shop on Broad Street, Nancy sees a cat sitting contentedly. Is it smiling, grinning, like a Cheshire cat, slyly trying to mislead her and tell her she is jolly well not on her way? She always feels like a cat next to John, contented and purring. They solve problems together, they scratch out solutions on chalkboards, argue, dispute, confer, discuss. But what is the solution? Why, all the books in world famous Blackwell’s just to her right cannot possibly content her or provide her an answer. They cannot explain to her the mysteries of the human heart, cannot console her loneliness or ache; no box of Cadbury’s procured from the stationer’s she has just passed could rationally answer life’s profoundest questions, the chocolaty goodness providing only a sweet momentary escape from her deepest woes.
She nearly knocks over a woman and her child who have just exited the Oxfam shop, the woman’s plastic carrier bags from Boots slithering to the ground and the woman shouting an expletive. “Sorry!” she calls out as she runs by, but then feeling guilty, turns around to help the woman pick up her purchases that have spilled: paracetamol tablets, wine gums, pencils for the child, cotton wool, rubber gloves, a new eyeliner pencil in “mahogany brown,” shaving cream for the Mr., a ladies’ magazine printed on cheap paper with tips on how to brighten her day, add highlights to her hair, tell if her husband is cheating, plus the news of a pop singer’s successful battle with breast cancer, and the bonus of her own horoscope. Yes, the mundane things of life are maybe a more pleasant way of passing one’s time, rather than pondering differential equations or number theory.
Infinity continues without limits. But this infinitely long journey to reach him needs an end, and the amount of oxygen (measured in pascals) is certainly dwindling in her respiratory system. She remembers the note that came through the pigeon post saying he is leaving around quarter to ten and so she desperately hopes that St. Giles shall lead her directly to her beloved with a minimum of tourists and traffic and students and academics pondering and pontificating as they walk by with their leather satchels and glasses and tomes thick as bricks. John is immortal to her as the stones that construct Balliol College, the stones that she runs her hand along as she flees down the sidewalk, stones that scratch her hands and rough them up a bit, very unladylike indeed. The cold damp air is getting to her lungs, she is going to wheeze, but her persistence keeps her going, for she does not know his exact moment of departure, when the van will come, though he will not be sitting on a cornflake waiting, as in the Beatles’ song.
All roads possess at least one rusted, rickety bike that is anchored to the railing (Theorem: There does not exist a single bicycle in Oxford that is not rusted and rickety), a simple machine that multiplies the force applied by pedaling and allows man to move at a much faster pace than walking. Most of the bikes are not locked, what difference does it make if she should borrow one? Here is a perfect specimen: brown, rusted, wide-framed, and entirely ancient, its two wheels forming the two round halves of the infinity symbol. The rate of change of technology is an incredible thing. From walking to a bicycle and eventually to the jet airplane. A bicycle built for two. A tandem bicycle for two lovers, rolling past the Isis or Seine or Donau or Rhine, perhaps. She must roll along and declare that she should spend an eternity with him, eternity is infinity, that endless loop like a number eight lying on its side, widening then coming to a point and widening again then coming to a point, endlessly undulating itself. What is an eternity after all?
She can see them strolling side by side in Oxford 40 years from now, retired after several years of academic service. They duck under cow carcasses hanging in the Covered Market or stroll down the path alongside the Isis past Merton College with the view of Christ Church behind the meadow. “Would you hold this a moment, Nancy?” he would say, handing her the camera case. “I’d like to get a picture of this, the light is simply beautiful.” His fingers would possibly tremble, as is often the case with the elderly, and perhaps the picture would come out crooked and Nancy might chide him that he was holding the camera on an angle, 15° or 17°. And they might sit at the breakfast table, littered with crumbs from crusty rolls and their plates greasy from the eggs, the gray morning light filtering in through the sheer once white curtains. Nancy would be reading a mathematics journal or doing a crossword puzzle, and John working out a proof for his own entertainment, chewing on the eraser end of the pencil and reworking one line of it over and over again. Then Nancy might finally glance over briefly and say, “You forgot the multiplier.”
“There, in front of that X. See?” and point to a variable. A dawning of recognition would pass across John’s face, his handsome blue-green-hazel eyes still no less keen in his now wrinkled face, which would be surrounded by a halo of gray hair.
“Oh, yes,” he would say, and then continue to scratch away while Nancy smiled smugly with the pride of knowing that it was she who really provided the correct answer and solved the proof.
But could eternal love ever die? Or did it simply transform itself, youthful passion transformed into middle-aged comfort transformed into elderly tenderness? Sexual ardor dissolved into mature companionship? Would she still love him as much 30, 40, 50 years from now, or would she simply love him in a different way? Certainly, for all her life, she could differentiate him as being her only true love, with two brief interludes. One was a flame-haired boy who followed her around the math department during spring of her freshman year, pestering her with questions about differential equations. The other, a German exchange student last summer, with whom she had an extended flirtation that culminated in a soggy weekend trip to a cabin by the lakeside, full of spiders and disputes over returning to Rudyard before the roads got too muddy to drive on and the need for mortal comforts such as toilet paper.
A sine wave shows a repeated oscillation. Life is one endless sine wave of up and down, happy and sad, doubt and assurance, varying only in amplitude. Her love and obsession are causing her to gasp in a rather orgasmic way, in rhythmic cycles exactly like a sine wave that one could easily plot on a graph until she reaches her climax, la petite mort, “A thousand deaths I’ll die, A thousand deaths I’ll die”–is it Dowland, or Purcell?–sung by clear voices in motets echoing off the walls of the chapel in Magdalen College, paeans of courtly love sung by the beloved to his Lady Fair, in French or English perhaps or in some dialect of the vernacular? For she must, she must, she must have it out, she must free herself of this torture in her breast, this years-long pining she has harbored for this man, this good man who has been her lover, her mentor, her source of torment, her friend, her idol, the son of Zeus–no, merely the son of Mr. and Mrs. Zeus somewhere in a respectable suburb with leaves on the trees and verdant foliage on their lawns. “He loves me, he loves me not.” She is his, he is hers, and now it is time, for they are in their prime, the prime of life, the end of the first quadrant of a century coming near.
May 1, May Day, on Magdalen Bridge: the all-night revelry and merriment had reached a climax, and hundreds of people stood on the bridge at 6 a.m., their tired and drunken faces looking up with great anticipation of hearing the Magdalen College choir sing from the top of the tower. The sine waves of pure sound, pure voices, the peaks and troughs, what could be better than the graph of a sine wave, but actually hearing it? “John? John? Where are you?” It was nearly impossible to find someone in the crowd once you let go of him.
“I’m right here, right here.” He took hold of her hand, small and pale in his larger, stronger one. The feeling of the moment was beyond beautiful; something welled up inside of her, about to burst. The cool air of the morning, the joys of celebrating nonstop for the past 10 hours, the years of longing:
“Look! They’re about to sing!” And with that, the choir launched into some moral madrigal or wholesome hymn, barely audible as they stood dozens of feet high up in the air, ethereal, as though they were channeling the divine from their lofty vantage point, delivering a holy message.
Bifurcation is a separation of a structure into two parts. The road has now split into Banbury Road and Woodstock Road, and Nancy has chosen the former–when you come to the fork in the road, take it!–and she is almost there, at the Mathematical Institute, University of Oxford. She pedals faster and faster but the damn rusted thing has reached its maximum velocity. The Institute is most certainly not what Matthew Arnold had in mind when he referred to Oxford as the city of “dreaming spires,” its ugly rectangular brick façade a poor imitation of Bauhaus or some variation thereof, and had Oscar Wilde seen it, he might have revised his witticism from “No object is so beautiful that, under certain conditions, it will not look ugly” to “Some objects will look ugly under all conditions.” The clocks are striking 10 and all of Oxford is chiming, metallic oscillations from belfries everywhere. Ding-dong, ding-dong…Ding-dong, ding-dong: an interval of a third, followed by a fifth, then another fifth, and then a third. It is too late! The bike can only go so fast, cannot outdo the taxis or lorries. She reaches the building, haphazardly rests the bike along a wall (but it collapses), runs up the stairs, but–she is panting, in need of water and a good English fry-up.
She bursts through the doors and hopes to see him, waiting patiently with his suitcases and backpack, his passport and itinerary stuffed away in some pocket somewhere. But he is not there. She begs a colleague of his who is passing by for news of John, but he says John is not in his office. She turns back out through the doors. He is not there. He is not there!
She collapses just like the bicycle, her legs give way. Her best efforts have failed her; time has been against her, the Venn diagrams of their lives have not overlapped this morning. Warm tears flow from her eyes, first slowly, then quickly. All of her calculations have been off. She rests her head on her knees, her arms wrapped around her shins, and feels utterly, totally defeated.
The sound of footsteps and something rolling are coming near, the Doppler effect in action, but it is not until the noise stops that Nancy looks up. At John! With his luggage in tow!
“You’re still here, thank God!” she madly embraces him as he embraces her, and begins to sob.
“Yes, I’m still here, darling! My watch stopped last night. I guess we can’t rely on numbers for everything, can we?”
“I guess not. Wait–can’t we?”
“No, darling. Numbers have their limits. As does math.”
“I came to tell you something. John, you can’t leave. You can’t leave me here alone. I–I–can’t explain!” She buries her head in his shoulder again.
“I know what you’ve come to say, Nancy.” John caresses her face.
Nancy draws a deep breath. They kiss.
“I’ve known all along.”
She pops her head up, like a marionette. “How, John, how?”
“Intuition, Nancy. The most precious thing that is beyond numbers, the thing calculations can’t explain. I could never tell you how I felt about you, because your father was my advisor, and then I was your advisor. Wouldn’t have been right.”
Nancy is silent.
“There is something called timing, which is different from time. It means the appropriate sentiment at the appropriate moment. Just like the men in all those Victorian novels you used to read. He loves her as a girl, and then later when she becomes a woman, he becomes her lover. Not quite in step with this century, though.”
“Guess I was born in the wrong century. I didn’t want to do something improper. Didn’t want to abuse your trust.”
Nancy nods. “But do we know it will all work out, John? Everything seems–”
“I don’t know.”
They are silent in their embrace.
Two people can be indivisible, for love defies all reason and logic.
John laughs. He pulls out a mobile phone, pushes a button, and shows her a screen. “See this quote by Oscar Wilde, sent to me by a friend this morning. ‘The very essence of romance is uncertainty.’”