by BRIAN HALL
Still no one has sat next to her. However, the buses since Chicago have been considerably less than full, so probably it doesn’t mean anything. How asymmetrical of her that she cares, since she loves pretending she’s the only person in the world. Asymmetry, thy name is human.
Remembering her gooseneck lamp, her nights of reading in her happier youth, she rummages in her pack and pulls out the first Newman volume. She turns it over in her hand. Impossible to describe how much comfort she gets from these books. The four volumes together weigh six pounds, fourteen ounces, the mass of a newborn baby, more fulfilling, less demanding. Slate-blue, full cloth, sewn bindings, a summation symbol stamped in copper on the front and spine, the title on the spine in gold: The World of Mathematics. The volumes are sixty years old, but the binding is tight, the pages seem new. Bravo, Simon and Schuster.
She still remembers opening the present. Her twelfth birthday. She and her mother were still living in that apartment in Astoria she loved so much. The present had been mailed from her father. He’d used Christmas paper—candy canes—at which her mother rolled her eyes. The note said he’d found the books among his own father’s things. “Thought you might be interested. Love, Your Father.” She opened the first volume and read the subtitle, A small library of the literature of mathematics from A’h-mosé the Scribe to Albert Einstein, presented with commentaries and notes by James R. Newman, and knew on the spot that a fine project for the next few weeks of her life would be to read the series from cover to cover to cover to cover to cover to cover to cover to cover.
She had never met her father’s father, nor wondered about him. But now she wishes she could write him a letter of thanks. She wonders if he loved Newman as much as she does. Whoever he was, he took good care of his books. Bravo, Mr. Vernon Fuller.
At night, under her cone of silence, she breezed through Newman’s first selection, “The Nature of Mathematics,” by Philip E. B. Jourdain, in two days. Since this was an overview, she nodded at the math she understood and hopped over everything she didn’t, trusting it would be elaborated on later. The second entry was “The Great Mathematicians,” by Herbert Westren Turnbull, and here was where she realized that her plan to peruse the entire series in a mere few weeks would be unworkable. On the first page there was a reference to an Egyptian priest of around 1700 BC named Ahmes who—she turns right now to that very page—“was much concerned with the reduction of fractions such as 2/(2n + 1) to a sum of fractions each of whose numerators is unity. Even with our improved notation it is a complicated matter to work through such remarkable examples as: 2/29 = 1/24 + 1/58 + 1/174 + 1/232.”
Adding fractions was a cinch, of course, she’d been able to do it since she was five. But this notion of reducing them to sums of unit fractions had never occurred to her. Indeed, a good deal of her attraction to Ahmes derived from sheer puzzlement as to why he wanted to do it in the first place. Did the Egyptians have some idea that unit fractions were more fundamental? Were they? And what would “fundamental” mean in this context?
Starting with 2/3, she assumed that reducing it to 1/3 + 1/3 was not allowed. So instead she quickly came up with 1/2 + 1/6. 2/5 and 2/7 were just as easy: 1/3 + 1/15 and 1/4 + 1/28, respectively. By the time she got to 2/9 she could see that all of these fractions could be reduced simply by subtracting the largest possible unit fraction; the difference would always be another unit fraction. 2/9 = 1/5 + 1/45. 2/11 = 1/6 + 1/66. 2/13 = 1/7 + 1/91. In each case, the quotient of the denominators of the two unit fractions was equal to the denominator of the original fraction. And if you generalized the math, you could easily see why this would always be the case. So there was a much better solution to 2/29 than what old Ahmes had come up with, namely 1/15 + 1/435. Discovering that she was smarter than the greatest of all the Egyptian mathematicians was highly gratifying. (Only later did it occur to her—maybe, for Ahmes, complexity was the point? Maybe the challenge was to string out as many unit fractions as you could? Was that more “fundamental”?)
By this time she had realized that to do Newman properly, it wouldn’t be enough to read every page, she would need to reproduce every result. Next came Thales of Miletus, 640 to 550 BC, who proved (as Mette proved again) that a circle is bisected by any diameter and that the angle inscribed in a semicircle is always right. After Thales came the Pythagoreans, a large subject. Mette proved the Pythagorean theorem three different ways. She studied triangular numbers and square numbers. Everything Turnbull mentioned led her down branching paths beyond what he himself covered. For example, she figured out all by herself that, since every odd number could be expressed as the difference between two squares, then every odd number was also the lowest term in a unique Pythagorean triple, in which the two larger terms were consecutive integers: 3-4-5; 5-12-13; 7-24-25; 9-40-41; 11-60-61; 13-84-85; etc. In this kind of Pythagorean triple, not only would the sum of the squares of the two lower terms equal the square of the largest term, but the sum of the two larger terms, unsquared, would equal the square of the smallest term. It felt like magic.
She spent a week studying the five regular solids and their properties, getting lost in calculations of their internal angles. She spent another week trying to square the circle and trisect the angle, in case somebody had missed something. She spent hours with a compass and straightedge drawing nested pentagons and pentagrams, continuing their fractal recursions down to infinitesimal points—or anyway, points smaller than a sharpened pencil point. She proved once again that the legs of a regular pentagram are golden triangles. She drew a nested recursion of a golden triangle and marveled at its beauty, the way the successively smaller triangles and golden gnomons called one another into existence like divinely matched pairs, like “turtles all the way down.” This led to the logarithmic spiral, to Robinson triangles and Sierpinski triangles, to Penrose tilings. She fooled around with Ruth-Aaron numbers, Smith numbers, Carmichael numbers. She spent several weeks filling page after page with numbers subjected to the 3n + 1 rule, graphing the results. (Mathematician Jeffrey Lagarias: “This is an extraordinarily difficult problem, completely out of reach of present day mathematics.”) She found something calming in repetitive calculations, something deeply satisfying in the slow emergence of an inexorable pattern.
She always eventually returned to Newman so that, while exploring alleyways and jungle paths, she wouldn’t miss continents. Six months after her birthday she had reached Diophantine numbers (an extremely large subject), which at page 113 out of a four-volume tally of 2469 pages, not counting the index, represented only 4.58 percent of the whole. At this rate, it would take her 10.92 years to complete the project. And that was under the unlikely assumption that the material would not get more complicated as it went along. So maybe it would take her fifteen years, maybe twenty.
The thought of a twenty-year program of Newman study filled her with unutterable happiness.
Now (3:45 a.m., breathing with the bus) she misses that happiness. She misses youth. She misses the youthful idea that a subject really might be conquered, that all the gorgeous order lying hidden under disorder could be unearthed like sacred bones, laid out in neat rows on pristine sheets, labeled in a neat hand. She misses the youthful delusion that conquering a subject would validate her existence. She has the impression that her father still has it, this belief, this happiness. And though she just now thought of it as a delusion, isn’t it true that if you still have it, then it does validate your existence, and therefore is not a delusion? An Epimenides paradox. She has the impression that her father doesn’t need anyone else. He has remained pure. Whereas she opened her gates, she welcomed disorder, she gave it a parade. She’ll never get it back, will she? Peace of mind. The thought fills her with a terrible fear.
She’ll be in Seattle in three hours and fifteen minutes. What then? A ticket back to New York would be to make the futility of her situation obvious. She could go on a random walk through the Seattle streets, let a dark alley decide. She
could check into a hotel, pay two weeks in advance, decline all room service, nail the door shut. A simple burrow. She could go up and then come down from the Space Needle.
She’s been sitting on a text from her father that came in between Missoula and Spoke-ann. I guess I’m a little worried. Could you send me a note? It made her feel bad. It’s nearly 7:00 a.m. where he is, so he’s probably awake. She takes out her phone and forces herself: Please don’t worry. taking time to think. Life choices.
1984–2002
When she was a lonely and strange twelve-year-old, she wrote her autobiography, whose sole purpose was to convince its sole reader that her life had meaning. During its composition she happened to make a friend, a plot development so astonishing she decided to end her story on it: “And thus it came to pass that Saskia White and Jane Singh lived happily for many years, until the Last Days and the destruction of the world.” (Or something like that; she was enamored of Tolkienesque High Hokum.) The ink, as they say, wasn’t even dry when a note arrived out of the blue from her long-absent father, inviting her on a summer camping trip in Norway. Jane came along and terrible things happened, not a few of them Saskia’s fault, and the friendship was destroyed.
Saskia has thought about story endings ever since. There’s that logical fallacy, post hoc ergo propter hoc, and she wishes her Latin were good enough (ha! she doesn’t really know any Latin at all) to know how to express an analogous idea (well, mainly, to show off her Latin): the emotional fallacy that later occurrences in life have more meaning than earlier ones. If you read a story about a person with a sad childhood and a happy adulthood, you tend to think of it as a happy story, n’est-ce pas? Whereas a life that begins happily and ends sadly seems like a sad story. But why shouldn’t all periods of a life have equally weighty—or for that matter, evanescent—meaning? If only the present moment exists, chronology is not important. (She has a feeling Epictetus talks about this somewhere, where’s her copy? Or maybe it’s Vonnegut.) However, people are addicted to narrative, and the last line of a story feels like a provisional title for all the blank pages that follow.
Starting when she was thirteen, she cultivated the habit of occasionally asking herself the question, What if my story ended here? It was a way of affirming that whatever was happening at that time, whatever she was feeling, no matter how brief or provisional, had its own validity, which subsequent events could not alter. She tried it for the first time when she returned home after having run away. (Long story short—her friendship with Jane destroyed, her revered father unmasked, her share of guilt undeniable, she jumped on a bus, clung for a few weeks to an ebb-tide reef in Brooklyn, discovered like so many others before her that she could not escape herself, floated back home on the flow tide like an unsinkable plastic bag, hey, jetsam, here comes flotsam.) She noticed, as her bus descended into Ithaca, that she was feeling kind of glad to be coming home. She was even glad to see her mother, Lauren, who had been more or less invisible to her during all the years she’d fabulated about the whereabouts of her heroic dad. So when she hugged Lauren in the cold winter kitchen, she thought, “The End.” This story was about reconciliation. Of course she and Lauren went right back to fighting and playing dirty—but that was a different story.
Since she could choose when to step back and announce “The End,” she preferred to wait for the rare good moments, so that her generally lonely, often miserable teenage years became a series of YA books with the kind of plot teenagers—hell, adults, too—prefer, beginning in angst and obstacles, sinking lower into destructive behavior and despair, then turning unexpectedly upward in the final pages, finishing on a quiet moment of connection, redemption, or awareness of wisdom gained. The quieter and more ambiguous that final moment, the more literary the YA, correct?, so her imagined row of books—let’s call it A Series of Saskia Events—were all Newbery Award winners.
And thus it came to pass that one tempestuous April night, far into the wee hours, both a little high, Lauren and Saskia listened together to the storm and talked about many personal things, and did not once, either of them, take advantage of a glimpsed chink in the other’s armor to slip in a dirk. The End.
And thus it came to pass that Mr. Anderson, tenth-grade history teacher, who hated Saskia for despising his educational methods and basically ignoring everything he said all year, accused her of cribbing her final paper, “Intentional Communities in Seneca County, 1967–1978,” from some other student or paid factotum, but was thoroughly told off, nay, publicly shamed by Ms. Schwartz (Pretty Good Teacher of English, MA, OBE), who assured him that Saskia could write a paper like that with one hand tied behind her back. The End.
And thus it came to pass, after two years of awful silence, that one January afternoon there arrived in the mail a letter from Jane’s boarding school, with Jane’s name on it, at the sight of which Saskia’s face went numb with dread, but Jane said that she was doing all right, that Saskia shouldn’t blame herself too much, that Jane’s therapist had helped her see that Saskia had also been a victim of Thomas, and although Saskia didn’t believe in her own innocence for a second, still, the fact that Jane was willing to write her a letter and offer such compassionately false reassurances filled her with indescribable relief. The End.
And thus it came to pass that, following months of skirmishing in which Saskia never knew exactly what was up, or even approximately what was up, she and Shelly Landis went to the Junior Prom together and laughingly stared down the stares of the homophobic hordes that crowded the hallowed halls in those benighted yesteryears, and subsequently spent a fair fraction of the night fooling around in Shelly’s bedroom. The End.
Almost sounds like a happy childhood, doesn’t it? Saskia would like to teach this trick to everyone, perhaps offer an online course: “Ringing Down the Curtain: How to Know When to End It All, sans Gun, Cliff, or Razor.”
YA Newberry honorands (honorees?) yielded in the fullness of time to National Book Award nods. Or maybe by this point she was thinking in terms of film. For example, there was the low-budget sleeper about her ill-conceived affair with her professor (first act), followed by her ill-conceived conception (second act), with a third act of paralysis and fear—lots of staring out windows, beautifully shot by the DP in wintry rural whites and grays—but lightening in the final minutes with the birth of a beautiful baby, garnished with parsley-sprig adumbrations of a new and deeper mother-daughter bond.
She hates to say it (she really does), but that first year with Mette and Lauren on the shitty old property north of Ithaca was in some ways the happiest of her life. Just being a mother with a baby . . . For that brief season, the otherwise veiled meaning of her life became clear. If Mette hungry, then nurse. If Mette stink, then clean. Saskia’s fear and self-doubt in the first week gave way to the realization that there were two things she could demonstrably do better than any other human being on the planet, namely, intuit what Mette wanted and supply same. An ego boost, for sure. But in the service of the sweetest human interaction imaginable. (Did she already say she hated to admit it? To be clear: she believes that men might also find it incomparably fulfilling, if they’d only try it, the fuckwads.)
Of course she sometimes felt stifled, bored. The space she was asked to occupy was so small. But it reminded her of an idea that had once thrilled her, when she was a teenager, but hadn’t thought of in a long time—that fitting into a space that was defined for you, dwelling in it with acceptance, partook of the timeless and “right” actions of Homeric epic, in which formulaic language bodies forth a world of humans living by an unchanging code. Pouring water from a splendid and golden pitcher into a silver basin, generous with her provisions, she put her hand to the dirty diaper that lay ready before her.
Everything she had always disliked about her mother—her vagueness, her determined air of unreality—started to look, when helping with the baby, like gentleness, “present”ness. Saskia saw that Lauren loved babies, and since Saskia
was discovering that she also loved them, it was the first time she could acknowledge that she and her mother had something positive in common. Lauren’s boyfriend Bill, another cold-molasses dreamer, also turned out to be great with Mette. She would fall asleep on him while he read on the couch, and he’d happily lie there for hours, gingerly turning the pages above her head. When Lauren went out to work in the field—she sold produce at the Farmer’s Market on weekends—she’d pop Mette in a sling around her waist. She never tired as she weeded or culled, expertly cradling Mette’s head as she bent over, continually murmuring who-knew-what to her, adjusting her sun bonnet, passing her a fresh pea pod or string bean to nibble on.
By this period, the clutch of pseudo-siblings whom Saskia had helped raise had all decamped. Melanie’s wolf in pastor’s collar had carried her off to San Jose after the hurried nuptials, and at twenty-three she already had a two-year-old boy and a baby girl, glimpsed only in cherub-trumpeted birth announcements and doe-eyed-Christ Christmas cards that arrived with neither invitations to visit nor photos of the mother. Shannon and Austin had moved out the previous year, and were currently living farther up the lake in a decrepit farmhouse that seemed part group home, part 24/7 party house, part two-level garage for the ever-reformulating grunge band. Hopelessly slow Quentin was a sophomore at Yale. The brood mother, Jo, still lived in her trailer on Lauren’s property and still shared dinner with the other adults, but back when Saskia was pregnant Jo had declared, with an air of nipping in the bud any selfish notions, that she had already done her share of raising children. To which Saskia longed to retort, “Whose names, by the way, are . . . ?”
So in effect it was just the four of them—Saskia, her mother, Bill, and the baby—and for fifteen months it formed enough of an idyll that no one would ever have made a movie out of it. The year of living somnolently.
