by Carole Maso
“OK,” he says, and he goes over the formulas again and again until I know them, until I am exhausted. I put my head on the desk. I move my chair closer to his.
“Chaos is subdued here,” he says, as he draws shapes on the board. “Copy them down,” he says quietly. Burdens lift, things simplify, reduce. “We can block out the world outside the classroom,” he says, sitting down at his desk, tired, too.
“I love you the distance of the focal length squared,” I tell him. When I reach for him under the desk he pulls away. He removes his glasses.
“Miss Turin,” he says, “I never make love with my students. It’s a rule.”
I reach for him again, put my hand on his thigh. “Prove it,” I say.
He stands up. I fidget with his belt. He steps back. “Prove it again,” I say, unbuttoning my schoolgirl blouse.
He unties my ponytail. “It’s a rule,” he says. “We must be serious.”
What he is teaching me is that what we must do will not be easy, and we will have to work hard to get there. We must be diligent, we must not be afraid to work, sacrifice. It will take the greatest effort even to make the slightest progress.
“Is this a metaphor for something, Jack?”
“This is math class,” he says.
He buttons up my blouse, buckles his belt. I am his student today and the rules of the classroom must be respected, the lessons of the classroom must be learned. He’s not ready to give up on me so soon.
“Now for a quiz,” he says, drawing yet another shape on the board. He trembles, I think. We must be strong, discipline ourselves. These are only exercises, quizzes—yet preparation, nonetheless, for the real tests still to come.
“You must not be afraid, Vanessa. It means us no harm. It’s even more beautiful than a swan.”
I shivered. Great sadness filled the room. Her hand trembled on my forehead.
“You must fly with it—wherever it asks you.
“Sometimes,” she said, holding my hand, “it will take you on its luminous back to places that seem bad—dark, cold, lonely places. But you must not be afraid. It is all for a reason. You must believe that you will come back.”
“But most of the time,” I said, “the places you go are filled with light, beautiful, bright, like nothing else in the world.”
My mother closed her eyes. “That precious, precious bird,” she whispers, “that bright bird of topaz.”
She follows it into darkness. She follows it into places where nothing is familiar, no one stops to talk, and it seems she is lost. She follows it into the center of sorrow, into places of great pain. She follow s it where no one else dares to go. That’s when the men usually come.
She put her head on the pillow with me “They are dressed in white,” she said, “and they carry hypodermic needles. But even then I stay. They want me to look away, to leave the Topaz Bird behind They think they can make me see what they want. But they can’t. Even then I stay.
“You must not listen to them,” she said, and her voice was raised. “You must not look away,” my mother insisted. “There is no way to stay safe.” My mother saw that I was frightened. She sat up. “You must try not to look away,” she smiled. “You must try. Always remember, Vanessa, that the Topaz Bird is special and we are lucky to see it. Always remember: it means us no harm.”
She looked so lovely in that last moment before folding the covers around me, right before turning out the light, and I thought, falling into sleep (or was I already sleeping?), that I would not look away if I saw it. If it would make me more like her, this magnificent woman who surrounded me with her saving breath, wrapping me in it, I would not hesitate.
When I go to Paterson in my head, when I finally get to the right street, identify the house, number four fifty-eight, and open the front door, I walk down a long, dingv hallway, past the dark kitchen and left into a small bedroom. A big man sits on a chair next to the bed in his undershirt, and I know I am in the right place. In front of him the Paterson Sunday News is open to the travel section. A towel is draped over the lampshade to block out excess light. A frail, blonde woman with eyes like glass sits in the bed propped up against a pillow. She looks so tired.
As I look more closely and my eves adjust to the darkness, I see children, two children, two girls, nearly the same age, one light, one dark, huddled in a corner, their bony knees up against their chests, hair falling in their eyes.
“Where will we go today?” the woman in the bed asks; a slight smile, almost a smirk, comes to her face.
“Let’s see,” the man says in the dark. “How about Savannah?” And he begins to read.
“Savannah,” the woman sighs. This is the last thing she will say. She is too weak to talk much. This reinforces the man’s notion that women are quiet, women are always meant to be quiet. The girls, too, will just sit and listen quietly, like their mother.
Who falls asleep first, it’s hard to know. He reads until each pair of feminine eyes has closed—Lucy, the dark girl, the youngest, sometimes first; sometimes the sick woman; last of all my mother, the other little girl, the light one, safe in a dream of magnolia.
The man gets up and closes the paper, leaving the sleeping room for his second job, necessary even on Sundays for heart money—medicine money.
But in my house Grandma Alice lives. She lives to take trips on planes to Savannah and Paris. She lives to watch her daughter grow famous. She lives to work with us in the garden, to dance with us under the chandelier of the sun. She helps me to see the Topaz Bird. She’s the one I tell about the golden rectangle.
One afternoon in late October while looking for my snow boots I stumbled upon the great, mysterious shape of my childhood: a golden rectangle.
The snowstorm was unexpected and we were caught off guard. I could not immediately find my hat or scarf or boots and did not consider going out without them. My mother’s only rule, the only thing she ever asked of us, was that we be dressed warmly if the weather was cold and sometimes even in hot weather she would wrap us in sweaters, fearful of some unaccountable chill that only she could feel. Now I had no idea where to find my boots. I looked through the whole house but they remained lost.
It was one of those rare early snowstorms that, occurring out of season, last only hours, an afternoon at most, and then are gone. The air returns to the air of autumn afterwards; the colorful leaves remain on the trees as if the wind and snow had never come at all. I looked everywhere that afternoon for those boots and found them finally way in the back of my father’s dark closet.
His shoes lined neatly in a row seemed impossibly odd and large. I picked up one of his brown wing tips. The father that put on these shoes and went out into the world in them was a father I did not know. I was afraid of those shoes. They seemed to me in some way testimonies of sadness—the holes around the sole, the smell of the leather, the heels unevenly worn down. Their heaviness in my hands weighed on my heart. He must have been uncomfortable in them, I thought, fie wore those shoes when he shook other men’s hands, halfheartedly, I imagined, alone in their company, too. Each quiet pair stood like soldiers on a cliff in blue morning mist.
And then I saw it—the blue spiral notebook that would make me forget that somber line of shoes and my father’s sadness. I never reached my snow boots that day; I missed that quick October blizzard. By the time I put my father’s notebook back in the corner of his closet, a place I would return to over and over, the snow had melted and the sky was filled with stars. The snow had gone as quickly as it had come. No one would have remembered the storm at all had Hetchcr not made a snowball and put it in the freezer for proof, evidence for my skeptical grandmother who lived in Pennsylvania and would want to see it.
I could never have dreamed what was in this unlikely notebook of my father’s, dated 1958, the year I was born. It seemed amazing to me that he had a notebook of his own at all. It was my mother who kept all the journals. The only things I had ever seen him write were letters to her, which he labored ov
er. But there it was, a notebook in his handwriting, and I was convinced that, to understand this one notebook, only a few pages of which were actually filled, would be to understand everything: my father, my mother, the world, all that would happen.
I continue to dream, even now, about the golden rectangle, which my father as a very young man surely must have believed meant something. The handwriting in that notebook was confident and convincing. There were loops and swirls in it, flourishes that have since disappeared from my father’s script. The notebook has disappeared now, too. All I have is the memory of that large, hopeful penmanship and the copies I made of those pages. This is w hat I found there:
January 1958
The Concept of Beauty, the Divine Proportion,
and the Golden Rectangle
Stravinsky discussing composition quotes Morse:
“Mathematics are the result of mysterious powers which no one understands and in which the unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty’s sake and pulls it down to earth.”
It is not in the clarity of things but in their beauty and mystery that music and mathematics join.
Bartók—Crucial musical events mark divisions and subdivisions of the work into golden sections.
Hardy—In great mathematics there is a very high degree of unexpectedness combined with inevitability and economy.
The unexpectedness and inevitability of such math and music are not merely formal but ultimately reflect back to the real world. Music has a concrete emotional meaning with the capacity to change a listener’s feeling. Math also has a concrete meaning. In such a reordered understanding of reality, which seems both surprising and necessary, may lie some qualities of beauty itself.
—Both are attempts to make sense of things, to shape aesthetic universes that bear directly upon our own.
Musical Qualities of Mathematics—
Hardy—“Beauty is the first test: there is no permanent place in the world for ugly mathematics.”
Potncaré—“The feeling of mathematical beauty, of the harmony of numbers, of forms, of geometric elegance.”
The Golden Ratio was considered by the Pythagoreans to be the most beautiful of proportions.
The golden rectangle with sides in that ratio has been linked with the proportions of the Parthenon.
Luca Pacioli—1509—De Divma Proportione Da Vinci
The Golden Ratio
A line is divided into a golden section when the ratio of its 2 parts is the same as the ratio between 1 part and the whole. The ratio, that is, reproduces itself within itself. The diagonals of a pentagon divide each other in this ratio.
As a fraction it is composed entirely of 1 ‘s layered in an infinite series. The number becomes a sort of arithmetic “image” of the geometric property of the ratio. It is represented endlessly within itself. If a square formed by 1 side of a golden rectangle is cut off, a golden rectangle remains. If squares are continually removed, there is an infinite spiral of golden rectangles contained within each other.
If a curve is drawn based upon the golden rectangle, it is precisely the shape of a chambered-nautilus shell. It is a logarithmic curve of continuous growth. Any two segments of the curve are the same shape; they are just different sizes.
As a snail grows, it produces shell material in the same formation. Similar curves lie in the center of a sunflower, in the shape of a fir cone, and in other natural forms that contain the golden ratio.
In the manipulation of abstract material, which reveals new relations and structures, math and music find their common formal ground.
In Beethoven piano sonatas there is the sense that a concentrated exploration of musical elements is taking place as one listens; when a theme returns in a recapitulation, it is no longer heard as it was in the beginning.
—This aesthetic has been central to the West and is implicit in the golden ratio. This concept of beauty involves proportion between various elements and a relation between parts and whole—a reproduction of macrocosm in microcosm.
I never asked my father about the golden rectangle. I wonder if he still thinks about that divine proportion now as he stares out to sea and the waves crash against his ocean liner and the sky begins to darken for what will seem like forever.
It is too late for me to ask him, and, even if he were here, I probably would not dare to. I violated his privacy that day, the method of his life. I stepped right into one of his unspoken obsessions, though I did not mean to do so. I was only a child that day looking for boots, only a curious child who loved this kind stranger called Father.
Now the dark is coming on. My father bends down and puts his hand in the frigid water. The snow starts to throw the towers and gables of the Baltic into romantic relief. Ships move about the harbor. A waltz plays. My father in a white tuxedo stares mesmerized by the dance of shadow and light.
Daddy, I would label every leaf on every tree for you. I would wedge my fingers into the wind and bring it to your ears so that you might hear what it whispers. I would build fires around your cool body and teach you to sing. I would shape your soft skull into the fleshy bulbs of lilies or tulips that bloom, then rest, then bloom again. I would make the daylight fluid and let you swim in its secrets, if I could.
“She is princess twice,” my father reads from the paper, “a duchess four times, nine times a baroness, eight times a countess. However, since a majority of the prince’s domain now exists in name only, her kingdom, in reality, is indeed a small one, covering three towns and 22,000 people.”
He comes forward. He hesitates. He stops. He must be walking in his sleep again. He barely looks like my father. He seems shorter somehow—older. “Daddy,” I say, hoping he might speak more easily in his sleep, hoping he might tell me what dream makes him this way.
My grandfather lilts his ax. When it is poised above his head, my father, just a boy, freezes the scene. He is afraid to watch the ax drop, for my grandfather is not chopping wood as one might expect. My father pulls himself from the bed and moves closer to the window. He rubs his eyes just to be sure and then he sees it: his father is cutting down the beautiful tomato plants, grown from seed, hacking them down to the ground. Earlier that season they had put up stakes together for those fragile plants to hold on to.
Is this what my father means when he says there are things it is better to forget? Is this what he is forgetting—his own father out in the garden chopping the tomato plants into pieces, insisting that they are Americans now, not Italians? Did his father announce that there will be no more Italian spoken in his house? No more wine drunk with lunch, as he burned the grape wines? Did he tell his wife there would be no more sad songs from the old country? How much she must have wept, hugging her small son to her breast!
My grandfather takes his ax from the toolshed, and when he lifts it above his head the scene freezes—but only for a moment. He hacks down those sweet tomatoes while the small boy looks on from his bedroom window and the eggplant and the peppers cower in terror.
“Vivaldi,” my father says. “Albinoni.”
“Albinoni,” I say.
“Paganini.”
“Paganini.”
“Corelli.”
In November the turkey industry presented a fifty-five-pound turkey to the President, but Kennedy spared its life, my father read.
“It’s local fair time in Ashtabula, Ohio,” the fat man reads from the newspaper, “where you will find the prize bulls, homemade pies, merry-go-rounds, animal freak shows, vegetable contests—prize pumpkins.
“Pumpkins,” the fat man puzzles.
“You know, Father,” the girls shout, “what we carve and put in the windows at Halloween.”
He turns the page to the next article. “Ah, yes,” he says.
“Alabama,” the father reads.
“Alabama,” Christine says. Such a pretty name, she thinks. She says it out loud, “Alabama. Alabama.”
<
br /> I picture my father being an avid newspaper reader once, opening it over a breakfast of cereal and eggs and folding it expertly so as not to get it in our faces. I seem to remember that: his daily origami ritual as he routinely turned the New York Times into a square, a rectangle, a bird, while we watched.
We had a television in those days, too, I think, and he liked to watch the news in the evenings until the news event occurred that made all other news unnecessary—the news event so great that it allowed his mind to wander around it tirelessly for years.
He sits transfixed, watching the six gray horses draw the caisson that holds the flag-draped coffin Behind the caisson is a riderless, chestnut-brown horse. Empty boots pointing backwards hold themselves somehow in the stirrups. A beautiful mother in a black veil holds the hands of two small children.
My father moves to the piano, a giant dwarfing the keys. Hunched over, he plays the Goldberg Variations with a heavy-handed deliberateness. He moves back to the television.
I grew up regretting in a mild way the death of our handsome president but mourning the realization that my father was not a happy man and that he probably never had been. I have linked in my mind, unfairly, the death of President Kennedy with my father’s great sadness because I never really noticed it before that day. Surely at that moment as my father sat listlessly in front of the TV set, his head in his hands, he must have abandoned the dream of the golden rectangle forever. Still—he did not destroy the notebook. It was there for me to find on that fleeting, snowy afternoon a few years later.
My father reads: “Catholics who attended the luncheon that Friday in Dallas were given a special dispensation and were allowed to eat meat.”
My father reads: “The presidential office was being redecorated in red and white. The change was planned months before. The red carpet was being laid down when the news of the death was received.”
My father reads that Jackie put her wedding ring on her dead husband’s hand but, unable to get it past the knuckle, she left it there, halfway down his stiff finger.