“Bullshit.”
She looked into the distance. “I want to save you,” she said. “I think that’s what it is. Save you from your own brilliance.” She tapped out another cigarette. “Or maybe for it.”
“What?”
“You heard me.”
“I don’t need to be saved, Cle. That’s ridiculous.”
—
AWAKE NOW FOR almost two full days, scribbling notes into the tiny cardboard pad that he’d been carrying since the meeting with Borland. To meals. To class. To every single place he went. He’d made his way deeper into the problem. Walking alone along the water one evening, he watched the cargo ships creeping south beneath the bridge. Tiny blinking cities of light on the water. Starry bottles drifting sideways in the black. Incredibly, this was where he’d stumbled upon a crack. A narrow one. A thought had reached back. Encasing sheens. Volumeless shapes. He sent his mind deliberately away, then allowed it back. The crack remained. It was real.
The Malosz was not insurmountable. It could be solved in the higher dimensions.
This is where the answer first made itself known to him, in the muddy-smelling dark on a garbage-strewn dock above the tidal flats in Emeryville. Tinge of rot in the air. Wintertime headlights streaming ceaselessly from the west, dividing north and south at the shore. Complex white curves incising themselves against a black-paper rendering of the world. The trudging ships below. It would be provable in another dimension. This was the route. His rivals would never think of it because it was so deeply counterintuitive. But the more he considered it, the more clearly he knew — this path would be orders of magnitude simpler.
He’d found it.
From a tar-soaked piling, he flicked his cigarette into the smelly sand. Pinched a drink from the flask in his back pocket and headed home to sleep.
—
“EARL AND I are mortals,” she said.
A doughnut store this time. Shattuck Avenue.
“Bullshit.”
“Mortals hang out with mortals, Andret. Do mortal things.”
“Bullshit, Cle.”
“We talk. We walk. Sometimes we trip. We don’t bother with conundrums the human mind has never breached.”
“You’re sleeping with him.”
“Maybe I am.”
“What? Cle?”
“I said maybe I am.”
“I’m begging you.”
“Don’t beg.”
“Please, Cle.”
“I said don’t.”
“Then fuck you.”
“Brilliant. Thank you.” She looked out the yellowed window, dragged on her cigarette. “If you want to fuck me, you know, you still can. Anytime you want.” The smoke lingered. “You can always do that.”
“Thanks.”
Silence.
“You don’t think I know what you did, Andret?”
“I’m sorry.”
“Don’t be. It doesn’t matter.”
“Yes, it does. I’m sorry.” He’d been waiting to say it. “I’m sorry, Cle.”
He took her hand. It was someone else’s hand.
“You think I care, Andret? I don’t. I don’t give a damn about her.”
“I don’t either. I’m begging you.”
“Look at me, Andret. Only mortals beg. You’re not to do it.” She reached and pulled his face close, held it there. “Not you, Andret. Stop following other people’s rules. You’re beyond them.”
—
THAT NIGHT, ANOTHER party: Biettermann again. Alligator smile. A girl beside him and a bumping crowd.
Biettermann said, “China White.”
The girl lifted her fist. A blue dragon, twisting across her knuckles.
“China what?” said Milo.
Biettermann laughed. The girl, too. Biettermann grabbed her mouth and kissed the full lips. The girl looked at Milo. Kissed Biettermann and looked at Milo. He turned away. When he turned back, she was still looking. Her mouth still on Biettermann’s. She nodded, tilted her hand toward him and opened it. The dragon’s fire curling into her palm.
Then, stepping from behind her: Cle.
Biettermann kissed her, then, too, right in front of him. His arm around both of them. Cle closed her eyes.
Milo stared.
All three of them looked at him now.
“White,” said Biettermann. “China White.”
They all laughed.
Then Biettermann opened his palm: a syringe. “You ready to travel, my friend?”
—
LATER, HE WONDERED why he’d refused. He could have at least stayed near her. Instead, he’d gone off by himself, walked home, and spent the rest of the evening in the bar near his apartment.
A month and two weeks. That’s how long it was before he saw her again. On his calendar he checked off the days.
China White
THERE WERE AT least two ways to solve any problem: from the beginning, which was the usual approach; and from the end, which was not. Likewise, every theorem could be proved either directly, using incremental logic, or indirectly, by conjecturing the negative of the hypothesis and demonstrating a contradiction. Thus there were at least four permutations to choose from.
This was how he began.
A pad. A room. A tiny view. Not numbers but geometry. One couldn’t draw a fourth dimension. This was a mathematical dictum, and of course he challenged it, but after days of trying to negate it he at last accepted its truth. Yet one could extrapolate.
At night he experimented. With his eyes closed he built a one-dimensional world and imprisoned himself within it. From there he imagined the second dimension — the unfathomable impingement of a greater universe. Then, after days of this, he imprisoned himself in two dimensions and imagined a third. The fracturing of experiential knowledge. It was forceful work. It was physical work. It required him to bind his thinking. He could maintain the fiction for only minutes at a time. The effort left him hungry.
In a way it was akin to idiocy — Cle was right. But he understood at the same time the radical difficulty of what he was attempting. The weight of discipline required to unlearn the world and refabricate it from principles.
Intuition mattered, too. There was no going forward without intuition.
At last he relented in his experiments and took to the problem itself, attacking first from the ordinary dimensions. This was merely underwork to confirm his approach. It was work that Akira Kobayashi was obviously embarked upon, too, in Kyoto. A month later, he was aware — though unsuccessful in articulating the particulars — that this route would lead nowhere. At the bottom of his own labyrinth of reasoning he glimpsed an infinite loop, a multibranched chain closed only by its own first tenets. A logical dead end. The realization flooded him with relief. Kobayashi was not a threat.
Marat Timofeyev, on the other hand, in Kiev, seemed to be attempting the problem from the negation of the hypothesis, working apagogically — the path that Andret now turned to. Timofeyev’s steady papers on complex manifolds, his meticulous proofs of mid-lying conjectures: this was a man laying a foundation. But soon Andret grew sanguine about Timofeyev, too. Unless his rival’s papers were diversionary, he was creeping forward by inches on a journey that was many miles long. A careerist, he realized one night in Evans Library as he unwrapped a new set of journals. A man interested only in a professorship.
At the realization, he allowed himself a weekend’s rest. A bottle of bourbon. In his apartment he sipped it from a coffee cup.
He didn’t call Cle. He didn’t want to go over a cliff.
Then he went back to work. His first task was to leapfrog what Timofeyev had done. He began by assuming the result, by starting from the proven conjecture and filling backward. If this was true, then so must have been that; for that to have been true, then so must have been this. The individual steps were simple, each requiring the smallest of conclusions. But the complexity of them all together was exhausting. It was as though in the morning he built a house of 1,000 cards, all in his mind, and in the afternoon he chose a single one to remove. Then the next morning, he would build a house of 999 cards. This was what Timofeyev had been doing, but in reverse. One morning, he realized that in this manner it would take years to reach a proof.