The strange thing is that a moment later I heard it hit the tree on the far side. When I turned, the leaves of the beech were rustling. A few of them floated down. I blinked. I looked back into the air above the river. In my eye, the fireworks continued. Shimmering translucencies of white ember arcing within an oscilloptic polygon, still poised at the apogee. Then they began organizing themselves into a wavering, sinusoidal curve — first dully, then brightly — like an old TV coming on. Finally they peaked. For those who wish it described mathematically — and I still remember it mathematically — I then observed, for perhaps a second and a half, a mobile Lissajous figure continually transforming itself, first homotopically, then homeomorphically, then entirely, into a strange, scattering set of flaming runes, the entire white-hot conflagration sparkling and growing brighter as it fell.
It persisted until I turned my head.
—
WE CALL IT intuition because we don’t have a better word for it.
A few days after I quit Physico, when I was still wandering Manhattan during the daylight hours like a man let out of prison, Audra suggested I go back to see my father. At that point, I’d been home from my second visit for less than a week. I couldn’t decide whether I felt the way I did because of Dad or because I didn’t have a job anymore.
“Well,” she said, “why don’t you just go out there again and find out?”
Two days later, when I pulled into the cove, I could see Cle and Paulie and Mom inside the cabin, preparing the feast they’d promised me if I came back. All three of them were in the kitchen, sidestepping one another as they gathered the dishes. Dad was outside, standing in a haze of smoke at the end of the dock, waving a pair of barbecue tongs at the car. When I walked down to him, he raised his glass. “The prodigal son returns.”
“Yes he does.”
He took a polite-sized swallow of bourbon. “Here’s to you, then.”
“And to you, Dad.”
A longer swallow. “And here’s to our singularities!”
“Which singularities would those be?”
“Well,” he said. “You quit your job, didn’t you? And your old man still feels like a million bucks.”
In mathematics, singularities are reversals — the points at which the graph makes a sharp turn.
“To our health,” he said. One more gulp. “And to our new freedom.”
Not a half hour later, as I was loading silverware into the picnic basket in the kitchen, I watched him hurry along the dock to help Cle and my mother, who were walking down with their platters. At the stairs, he reached forward and guided them up. (Mom first, then Cle — the order all of them always acknowledged.) He didn’t know I was watching — or maybe he did — and as they moved out toward the grill, he stayed at the top of the steps, gazing after them. I have to say, he did look well again, eyeing the women who’d just waltzed him back into his life.
Paulie left the house then, carrying a pitcher of lemonade, and as she came up the beach, Dad waited for her, too, at the top of the stairs. She didn’t look happy, exactly, but I remember that she looked optimistic. I hadn’t seen her like that in a while. She’d been out here now without me for the week, and she and Dad seemed to be friendly in a way that they hadn’t ever been before. She climbed a couple of steps, and he reached forward from the edge of the dock and held out his hand. She looked up for a moment, then grinned shyly and took it. Something about the expression on her face — the hopefulness in it — made me look back down into the picnic basket. That’s why I didn’t see it happen.
I wish it hadn’t been Paulie.
The sound was like a branch breaking off somewhere in the woods. Then the smash of the pitcher. When I looked up, Paulie had fallen onto the sand. On the dock, Dad was staggering backward. He looked down at his hand, which stuck out strangely from his sleeve. For a moment he seemed confused. Then he let out a howl. My mother came running. Dad grabbed his elbow, bellowing now, and careened forward to the top of the stairs, where he stumbled, missed the railing, and fell sidelong onto the beach.
THE SCAN CAME up covered with blots: metastases too numerous to count. In the emergency room, Dr. Gandapur steadied my mother with his hand.
The arm had snapped when he’d tried to help my sister up the stairs, then shattered when he’d landed on the ground.
They didn’t operate. Instead, he was put in a cast that went all the way over his shoulder. Only his fingertips showed at the end. They were purple. The doctor hadn’t even been able to straighten the bones, so the cast bent a second time, midway up the forearm, as though he’d been given another elbow.
But the next day, when we brought him back to the cabin, he sat down on the couch with a cigarette and a glass and used his good hand to light the cigarette. He dragged on it, set it down, and lifted the glass.
—
IN THE DRIVEWAY, Dr. Gandapur reached out the window of the old Mercedes and handed me a bag. “He’ll need this now. As you know, I cannot return every day.”
I looked at the label. “He won’t like it.”
“I know he won’t. But I will keep the dose to a minimum.”
“Thank you, Doctor.”
Glancing back at the cabin, he said, “Pardon me for asking, but are Mr. and Mrs. Biettermann still visiting?”
“Mrs. is.”
“And Mr. — is he around at all?”
“He’s back in New York.”
The doctor remained still for a moment, looking carefully up at my face. Then he said, “Just make sure you keep it upstairs.”
—
AUDRA, I KNOW, thinks I have a hard time speaking about the things that matter to me. And Matthew, at Stillwater, thought the same. I know they both believe that I don’t want to reveal myself, or perhaps that I don’t know what my feelings truly are.
Well, they’re right: I don’t.
But not because I don’t think about them. I do. A mathematician goes to great lengths to define things. A plane in mathematics is not merely a flat surface but a flat surface of infinite thinness and size. Trivial? Not to us. When I say plane, I’m not thinking of a tabletop or sheet of glass or a piece of paper. You might point to any one of these objects; but all of them are precisely that: objects . They exist in the world. And because they do, they are defined by their breadth and reach. To a mathematician, a tabletop is no more a plane than a slice of rum cake is. In the world we know, in fact, the only thing that can actually be called a plane — or a portion of one, anyhow — is a shadow.
You see?
Words fail us. Even the world fails us.
Are there not a thousand forms of sorrow? Is the sorrow of death the same as the sorrow of knowing the pain in a child’s future? What about the melancholy of music? Is it the same as the melancholy of a summer dusk? Is the loss I was feeling for my father the same I would have felt for a man better-fit to the world, a man who might have thrown a baseball with me or taken me out in the mornings to fish? Both we call grief. I don’t think we have words for our feelings any more than we have words for our thoughts. I don’t even believe that we actually do the things we call thinking and feeling . We do something, but it is only out of crudeness that we call it thinking; and when we do the other thing, we call it feeling. But I can tell you, if you asked Archimedes in the third century B.C., or Brahmagupta in the seventh A.D., or Hilbert in the twentieth, when they’d first known that they’d solved their great problem, I suspect they’d all say they had a feeling .
Maybe that’s why mathematicians like blackboards. Words steer, while equations mostly follow. When the terms of mathematics fail, we invent new ones. Euclid. Diophantus. Viète. Descartes.
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