by John Updike
“Smart enough,” she answered, “but he had a pugnacious way of making students feel stupid. He came from—how can I say this?—very ordinary people, near Worcester. He took me out there for Thanksgiving once, and all anybody cared about was the high-school football game, this sacred rivalry between two old mill towns; we all had to go, though it was bitter cold that year. His nephew was playing and got injured, even. They were tough, I should never have tried to be nice to him. After that Thanksgiving I knew it and tried to pull back.” Owen made noises of sympathy but she talked through them, her gray eyes gazing at that past gray day. “They were Roman Catholic, and though he was quite dismissive of what he thought were people’s attempts to cling to illusions, he once told me that we of course would be raising our children Catholic. When I expressed surprise, he became very angry. When he was angry, he would go all dark in the face, I don’t know how he quite did it, but it frightened me.”
She tried to imitate, in her fair and passionless face, Ralph’s lethal look, and the effort was like a cheap beer poured into a crystal wineglass. Owen thought for the hundredth time how fortunate he was to be with her, if only for the time being. She was an education. “And me?” he asked her. “Am I tough and ordinary?”
“Owen, don’t fish for compliments. You’re a Bird.”
In her girlhood, she and her girlfriends at Browne & Nichols, in the innocent cruelty of their adolescent clique, had classified people into three types—Birds, Horses, and Muffins. Owen could not quite grasp it, just as he could not grasp the ritual she described, acquired when she was thirteen or so, of lying in bed and, when she could not sleep, resting her eyes, with religious rigor, on each of the ceiling’s four corners. It meant more to her than she could say, or would say.
“A cute little bird?” he asked. “Chirp, chirp?”
“Not really,” Phyllis said, pursing her lips in a concentrating, solemn way he adored, crinkling the unpainted flesh of them. Making a moue, she told him it was called, when he had lovingly described this expression of hers to her. Now she told him, “A big lazy bird that hovers all day, in circles, hardly moving its wings, and then swoops to the kill.”
“Oh, dear! I sound frightful.”
“No more than anybody else. Kill, kill, kill, kill, kill, kill,” she said. She explained, “That’s from Shakespeare,” adding, “Just using mouthwash—think of all those microbes you kill.”
“I’m shocked,” he said, “that you could ever see me killing anything. I can’t even step on a spider. I have a phobia about them.” Yet he was pleased by her description, as granting him some initiative and force, when his inmost sense of himself was of an innocent witness, acted upon but not acting. He snuggled closer into Phyllis’s cool warmth and asked, “And you? What are you? I keep forgetting.”
She was shy of talking about herself, as if touching too tender or shameful a part of her body, or as if her ego was difficult to locate. “Not a Horse,” she said. “I have a Birdy look, but am really a Muffin, inside.”
“Surely not.”
She was offended. “Muffins aren’t a bad thing to be. They’re accepting. They’re non-disruptive. They don’t hurt anybody.”
He saw himself swooping in her mind, a dark shape empowered to hurt. “Not even other Muffins?”
“They don’t meet other Muffins, Muffins are too rare. Most people are Horses, clumping along.”
He laughed at the subtlety of this boast. She valued herself highly enough, but in terms so subtle as to be almost beyond him, like higher math, or the fine points of a foreign grammar.
Impatient with self-exposition, she reverted to an earlier topic: “I showed my father the most unpleasant and threatening of Ralph’s letters, and Daddy wrote him one of his own, mentioning legal action.”
Owen felt relief; he wouldn’t have to handle it, then. Her father was still in charge. “Well, good. And did that shut the creep up?”
“We don’t know yet. That was just days ago.”
“You poor angel, you’re still in the middle of this, aren’t you? Uh, did your father have to write to any other boyfriends?”
He was giving her a chance to laugh; he had not expected her to mull it over. “Last year, there was, but this was his idea, not mine. A boy—man, really, he was older than I—I used to see in the summer, who my parents didn’t think was at all suitable.”
“They didn’t, but you did?”
She pursed her lips again, this time keeping silent. She did not like, beyond a point, being probed, and had already taken him in so much deeper than he would have dared hope a mere year ago, when she had been to him just a vision, floating through the halls. “You did,” he concluded.
She didn’t disagree. So: he had rivals lodged in the exterior world, like Jake and Ralph, and rivals lodged in her heart, her secret being, like the tremulously clever Klein and this unnamed man her parents objected to. Owen was learning when to change the subject, encountering a closed door in the corridors of her past. “Was it your parents’ idea to have you become a math major?”
“No: they were rather horrified, they’re such humanities snobs. Literature and the arts are all they care about. To them make-believe is life. Science is vulgar. My father’s specialty is the English Renaissance—the sixteenth and seventeenth century—”
“Thanks,” he interrupted, nettled by their previous conversation and this summer lover she was refusing to talk about. “I know when the English Renaissance was.”
“Of course. Some people don’t. My father doesn’t do just the poets and playwrights, Shakespeare and so on, that everybody knows about, but these prose writers nobody can bear to read any more, Sidney and Bacon and Lyly and Lodge, always writing about Arcadia in this elaborate way—he loves them. That’s where my name came from; all those old poems are full of Phyllises—sprightly Phyllises, naughty Phyllises. I turned out to be a dreamy Phyllis, rather disappointing.”
“Not to me. Nor to a number of others, it sounds like.”
“About ten years ago,” she went on, on her preferred topic, “when the man who teaches eighteenth-century prose had his sabbatical, Daddy took that on, too—Dryden and Bunyan, Addison and Steele, Boswell and Johnson—and he revelled in it, working it up, shelves of this impossibly dry old stuff. He hides in books, my mother says.”
“My father hid in numbers.”
“So do I; I’d love to meet him some day.” Owen shied from trying to imagine it, poor beaten-down Floyd Mackenzie with his tender stomach and penny-ante job, and this cosseted Cambridge princess. It would make a meeting as awkward and painful as the one between his mother and Elsie. Our parents hatch us but cannot partake of our work in the world. Phyllis explained to him, trying to give of her deeper self, “Don’t you find it so beautiful, math? Like an endless sheet of gold chains, each link locked into the one before it, the theorems and functions, one thing making the next inevitable. It’s music, hanging there in the middle of space, meaning nothing but itself, and so moving, Owen.” Did he need this nudge? Had he been falling asleep beside her long, soothing body? True, he relaxed when with her, as if home at last. “It used to make me cry,” she said, “when I was a teen-ager, having a problem come apart for me—the way it cracks open at a certain point, goes from being all outside to all inside, if you believe the equations and follow through on them. It’s like, at the beach, turning a horseshoe crab upside down, all the little legs wriggling and the tail flipping to turn it all over. No, my parents didn’t encourage me. They thought science was for plodders, grubby guys usually from the Midwest. I tried to tell them, math doesn’t do useful work, it does useless work. Which of course isn’t exactly true; physics and technology depend on calculus. And set theory.”
“Do you understand,” he asked her—and such a question must have demanded a more intimate setting than a corner, however dimly lit, of the visitors’ lounge at 120 Bay State Road; it might have been in her Bexley Hall room, against the rules, on one of those weekends when her roommate,
Sally Fazio from Providence, was back in Rhode Island or off skiing in New Hampshire—“set theory? I mean, why it’s so wonderful?”
“I think I do. It is wonderful, so elemental and original. It’s one man’s invention, you know. Newton and Leibniz invented calculus independently, Lobachevsky and Bolyai did the same for non-Euclidean geometry, and if they hadn’t Gauss would have—it was just sitting there waiting to be picked up—but without Cantor set theory might not have ever come into being. Hilbert said nobody will ever expel us from the Paradise Cantor created. Isn’t that nice? To create a Paradise nobody will be expelled from?” Talking of mathematics, Phyllis became more animated and precise—quicker-voiced, wider and more reckless in her gestures. Her blood ran faster beneath the thin fair skin.
“It is,” he had to agree.
“And he did it, a lot of it, in a mental hospital. His brain snapped, set theory was so powerful.”
“What my brain doesn’t quite get,” Owen persisted, elevating himself to Cantor’s class of mental fragility, “is why it was such a big deal when Russell and Gödel found these internal contradictions or paradoxes—as Klein points out, the confusion is basically semantic. I don’t see what undecidability has to do with the history of the computer.”
“You don’t?” said Phyllis, unable to quite conceal her disappointed surprise, as if her own clarity of mind had been conferred upon Owen by her regal act of accepting him as her boyfriend. The two of them met before class and rejoined afterwards; they shared mid-morning coffee and a dragged-out late lunch at the Student Center across Mass. Ave.; they went to movies together in Harvard Square or on Washington Street in Boston; sardonic Jake and menacing Ralph had been banished to the rim of the circle at whose quiet center Owen found himself. In the evenings, unable to be away from each other for more than four hours, the two reunited amid the smoke and misted mirrors of the little restaurants where students huddled in overheated symposia.
“I mean,” he said, insisting on his own obtuseness, thrusting it upon her, “so what if there exists a set of sets that are not members of themselves, which makes it a set that both is and isn’t a member of itself?”
“But, Owen dear,” Phyllis said, “the antinomies—the paradoxes—undermine classical logic, but the way they have to be phrased brings us to symbolic logic, which brings in Boolean math and the Turing machine and algorithms. Undecidability is like knowing you have a swamp and having to invent methods to build on it anyway. It’s like the Back Bay on all its pilings,” she said, so pleased with her own analogy that her face for the moment was more a Bird’s than a Muffin’s.
Phyllis inhabited an attenuated realm where he longed to join her. Her very air of absence pulled him up, led him on; at times he had the sensation that the void which the rigors of post-Aristotelian logic discovered at the very roots of arithmetic existed also in her—a refusal to be obvious, an implacable denial beneath the diffident, compliant surface. “You know I don’t love you yet,” she said after they had been going together for a year and were already considered a couple by their peers.
Owen was shocked, especially since they were lying stretched out together somewhere, on a bed or floor—it must have been in her senior year, when she moved back to her parents’ house, giving them some sneaky privacy. They didn’t shed their hot clothes but were, in those inhibited, swaddled times, “making out.” Owen had assumed he was lovable, though beneath the regard of the Ginger Bittings of the world. His mother and Elsie had loved him.
He betrayed no feeling, simply hugging Phyllis tighter and saying, “Really? Well, I love you. Maybe you love me but don’t know it yet.” At the same time he felt his own body drifting away, washed backwards by the thought that he should not be directing his life to flow through this other, alien body.
“Maybe,” Phyllis ambiguously agreed, in a voice thickened by regret that she had revealed so much. Her face was inches from his in the shadows of the room, which in his memory of the moment he felt to be on a high floor, perhaps her brother’s room in her parents’ house. He had been kissing her, those lipstickless numb lips, as if to press blood to their surface, while individual strands of her mussed hair tickled his face with the exasperating persistent delicacy of flies’ feet on a muggy day. Sometimes it seemed that she was the one being tickled; more than once, as a spasm of love drove him to a flurrying multiplication of kisses on her lips, and her high blushing cheekbones, and her fadeaway eyebrows, and her lids with their squirming pulse, the whole marvellous silverpoint precision of her, she laughed aloud, disconcertingly, deflatingly. He read these moments of rejection as his clumsy, premature rupture of the delicate barriers she had erected in twenty-one years of being so fine, so solitary. He tried to imagine what motion within her, what minute climate change, would persuade her that she loved him. She had let slip, at moments in their courtship which stuck in his mind as illuminations of her obscure inner life, that she and another girl at Browne & Nichols used to hold hands and that the unspeakable boyfriend that her parents agreed would never do had been, in a way that made her hands fly apart in memorial measurement, “enormous.” He had been a creature of summer camp and perhaps had acquired for her the mythic stature of the mountains, the great rough-barked pines, the distant granite outcroppings, the thunderheads on a still summer day blazing white above the dark evergreen ridge. Hank—his name, which she let slip—had been head of maintenance at the camp, captain of the battered pickup truck, master of the trash dump and the pine-needle-covered roadways, and though he had spent a few semesters at the University of New Hampshire, he professed no ambition but to continue in Nature, hewing and hauling and spraying DDT on mosquitoes and black flies. His lack of ambition had included placing no claim on her, though they knew each other through several summers. Perhaps she had been the suitor, the shy aggressor, like Owen setting up the Monopoly board for Buddy Rourke. Phyllis’s face, when she thought of Hank, shed its absence, its indolence, and somehow steeled itself, though she tried to hide her feelings behind a pensive moue. Owen comforted himself that, if he was less intelligent than she, Hank had not even competed.
They no longer shared Introduction to Digital Computer Coding and Logic. She, a senior, disappeared into the counterintuitive exotica of advanced topology—differential manifolds, invariant Betti groups embedded in Euclidean space, duality theorems. Her senior thesis sounded suspiciously like Projective Geometry: she said it had to do with “the topological classification of manifolds of dimensions greater than two.”
“How high can dimensions go?” he asked.
“To n, obviously.”
“I can’t picture it.”
“You can’t, but numbers can. Calculations can encompass however many. Don’t look so disapproving, Owen. Relax. It’s elegant, it’s fun.”
“Fun for you, I can almost believe.”
“I’m at a point where I’m not sure Riemann was right, in the case of some local curvatures.”
“The immortal Riemann of Riemann surfaces? You’re going to refute him? Baby, you’re too much.”
“He wouldn’t mind. He was a saint, of sorts. His father was a Lutheran pastor. He himself died at the age of thirty-nine, of tuberculosis. He left behind notebooks and papers full of ideas he hadn’t had time to publish. The whole universe, you know, is a kind of Riemann surface, according to general relativity.”
Her eyes wore that expression of abstracted steeliness with which she guarded the thought of those she truly, intuitively loved. A set from which Owen was excluded, even as biology and society swept them together. Always Phyllis was to harbor, as she and Owen travelled together in the thorny common world, memories of an Arcadia populated by that rarefied troop of exalted spirits, whether mathematicians or poets, Spenser or Cantor, Hilbert or Keats, to whom Cambridge in its soul was dedicated. Such a dedication does not guarantee the storms of creativity that are posthumously honored, but it curses all tamer weather as second-rate, and makes the real world a rather anticlimactic insubstantial pl
ace of exile.
While she rendezvoused with Reimann among curving surfaces unto n dimensions, Owen was grinding away at the practical subjects that went into a degree in electrical engineering—power-system analysis, non-linear impedances as power modulators, wide-band amplifiers, photoelectric transducers, insulators, transistors, microwave triodes, reflex klystrons, power relations in an electron beam under small-signal excitation, and such formulas that render invisible electrons visible, audible, and convertible to useful work. One advanced course took Owen for a week to Raytheon in Waltham, and another on repeated visits to the Harvard Computation Laboratory, where Mark I reigned in its lordly bulk and overheated obsolescence. As the Korean police action bogged down in cold and bloody mud, Owen and his schoolmates maintained exemption from the draft by passing a government test only cretins could fail: in the lecture hall called 10-250, at a signal, they presented aloft their pencils like tiny substitute guns. Brains won wars. IBM was enlisting manpower in a massive push to counter Remington Rand’s triumphant UNIVAC; a business market as well as an industrial-military one was dawning for computers. Amid these heady promises of the future, while technical breakthroughs were coming faster than the professors of electrical engineering could teach them, Owen’s overprogrammed neurons began to hum with brain-fatigue. It was like a message emerging from a veil of static when Phyllis, the week after she graduated (her honors thesis, questioning a nuance of Riemannian topology, having been cited for its originality and rigor), said to him, at a table for two in the tiny smoky Indian restaurant, just before he was heading south for another summer surveying with the crew and probing Elsie’s responses, “My parents kept bugging me about what I was going to do with myself now, so I told them I was engaged to you.”