by Don DeLillo
“Timur Nut’s his name.”
“You in your area of mathematics. I in mine. The two colossi. You with your loyal supporters. I with my own fervent assemblage. We bestride the mathematical firmament like colossi. Each with his own following. Each able to refute the accepted formulations of the past with laughable ease, no? Keen sense of competition to be sure. But we are never less than gentlemen. Mutual respect. The true beneficiary is mathematics itself. You with your pure preoccupations. I with mine. Our combined genius beggars everything, including description.”
Billy had never heard of Timur Nut. He didn’t know how to respond. Almost anything he said might be taken the wrong way. The man seemed very sure of his position. Someone this seedy and foreign, smiling ironically, couldn’t be taken lightly. There were two possible ways to proceed. One was to say little or nothing. The second was to attempt a systematic destruction of the man’s imagined stature. He felt two things could happen if he took the second approach. His devastating arguments would cause Nut to break down completely, leading to one of two responses. Either an embarrassing plea for mercy or an episode of semiphysical retaliation. This latter possibility might include recriminating looks, one, and maybe abusive gestures, secondarily. But an attempt at systematic destruction could have an alternate effect, one much more likely than a breakdown and very terrible to contemplate. Timur Nut by logical means would prove he was indeed a renowned mathematician, the equal of any. Using both inductive and deductive reasoning he would demonstrate an astounding verity, the kind of undislodgeable truth that would render absurd everything Billy had previously believed to be true. He had the seediness to do it.
“Okay, what’s your specialty?”
“Nutean surfaces.”
“Never heard of them.”
“They’re pseudospherical.”
“Zorgs.”
“I know them well,” Nut said. “We’ll be a match for each other. Two massive intellects. It’s only natural we meet on the field of battle. I must warn you, however. I never take prisoners.”
“How do we do this?”
“Two out of three,” the small man said.
His face had disappeared behind the vapor made by his breath on the glass. With his index finger he drew an ironic smile on the shapeless second face formed in steam. Desilu Espy unlocked a panel in the glass booth and Nut led the boy to the nearest corridor. The elevator door opened.
“Come in,” a voice said.
There was a chubby man standing in a corner of the elevator. Billy and Timur Nut got on. The passenger introduced himself as Hoy Hing Toy. The door closed.
“I ask three questions and then you ask three,” Nut said. “If there’s a tie, a neutral observer asks three more. Two series out of three is the winner. Don’t answer too quickly. There are layers of meaning here.”
“I’m ready.”
“Question one. An equation of the nth degree may have how many solutions?”
“It may have n solutions.”
“Don’t be so quick to answer correctly. Tragic mistakes can result.”
“It’s pretty obvious. The answer is n.”
“Question two. Remember, layers of meaning. Using no more than one hyphen, how would you characterize a geometry that is not Euclidean?”
“Non-Euclidean.”
“Question three. You’re answering too fast. How many dimensions am I talking about if I’m talking about umpteen dimensions?”
“Dimensions that are many in number but the exactness of said number being left unsaid.”
“Syntax counts.”
Hoy Hing Toy nodded his head slowly. Billy couldn’t tell whether he was agreeing with the answers or paying silent tribute to the subtlety of the questions. There was nothing very distinctive about the questions, he felt, aside from their childishness. The questions strongly supported his conviction that Timur Nut wasn’t what he claimed to be. Of course, he’d twice said something about layers of meaning. This indicated a logical trap of some kind. Questions so simple they were all but unanswerable. He recalled the questions one by one and they were simple all right but in the dumbest of ways, especially the one about umpteen dimensions, although non-Euclidean with one hyphen wasn’t far behind. He stopped wondering about the questions and turned his attention to the elevator. It should have arrived in his sector long ago. These were highspeed elevators. Soundless, free of vibration, extremely rapid.
“We’re not there yet,” he said to Hoy Hing Toy, asking a question in effect.
“I seem to agree.”
“Is it because we haven’t arrived, you think, or because we’re stuck?”
“I know what you mean.”
“If we’re not there yet, it could be because we just had to slow down for some reason. But if we’re stuck, we’re not moving at all.”
“It’s impossible to tell,” Hoy said. “You know how these elevators are. We must take them on faith. I have always suspected they never move at all. There is simply a new backdrop erected and then the door reopens.”
“It’s an interesting sensation,” Nut said. “Always we have stood in the elevators without seeming to move. Now we are really not moving and there is no change in sensation. It’s absolutely the same whether we move or stand at rest. Something is being violated here. Some rule of motion or logic, no? Perhaps we’re not stuck at all. We’re moving with infinite slowness. There are three of us in an elevator that by law holds no more than twenty-one people. We are one seventh then. Zero point one four two eight five seven, one four two eight five seven, one four two eight five seven, on and on and on. Multiply decimal by number of people. One becomes four as four becomes two as two becomes eight as eight becomes five as five becomes seven as seven becomes one. Infinite place-changing. I don’t like nonrepeating decimals. Pi makes me furious. To how many places have they calculated pi? And never any semblance of lawful progression. Over one million decimal places. A book-length whimper. Your turn now. Three questions. No more or less.”
“I’m concentrating on getting out of this thing.”
“I’m sure they’ve been alerted either above or below,” Hoy said. “The alert mechanism is almost certainly automatic. Wouldn’t you think? In a building like this? Even as I speak, they’re probably working feverishly to repair the cables.”
The fact that Nut was aware of recurring decimals disturbed Billy almost as much as the stalled elevator did, assuming it was stalled. The monologue on decimals supported the haunting possibility that Nut was exactly what he said he was. True, the support was slight but it was enough to be worrisome. And of course he’d chosen to discuss a decimal that had the same digits, in the same order, as the number array transmitted from Ratner’s star. A person could do a fair amount of multiplying without changing these digits—merely their order. Nut had already demonstrated what happens when the array is multiplied by three. Were the Ratnerians trying to indicate something about multiplication? About the fraction one seventh? About original digits rearranged? If so, why hadn’t they put the first gap after pulse one instead of pulse fourteen? He slouched in his corner, arms crossed on his chest, each hand clutching the opposite shoulder.
“Two great savants,” Timur Nut said. “You in your rarefied specialty. I in mine. You have flung down the gauntlet and I have taken up same. Your turn to make the questions. Cluster of three.”
“I’m in no mood right now with the way this elevator’s been behaving.”
“Very well, I ask again. Be prepared for hidden levels. Question one, second series. What word leaps to mind when I say that one hypercomplex number times a second hypercomplex number is always equal to the second such number times the first?”
“ ‘False.’ The word ‘false’ leaps to mind.”
“No extra credit for speed of reply.”
“Come up with something tougher. Maybe that’s the way to slow me down.”
“Do your dreams exceed your grasp?”
“Wait a minute.”
&nb
sp; “Question two, second series. Do your dreams exceed your grasp? I am counting off the seconds.”
Billy looked at Hoy Hing Toy. Hoy was tugging absently at his necktie as though the fiendish complexity of the question had reduced him to inane reverie. It would be interesting to see how Nut justified the question on mathematical grounds.
“If dreams don’t exceed grasp, all human life is futile. Science offers many basic differences between man and animal. We have symbolism, organized speech, self-awareness. We are more often than not repelled by our own vomit. But the most important difference is that man’s dreams exceed his grasp. There is no future for mankind unless this is so. Think of a Dedekind. Or a Riemann. Think of a Riemann. These men fulfilled the dreams of an earlier mind. They were dreams in living form. That a Riemann was able to do original work on n-sheeted Riemann surfaces was hardly accidental when we consider how very well the way had been prepared for him. That a Dedekind was able to formulate the Dedekind cut was due in part to a non-Dedekind influence. In their mentor’s intellect was the first white flash of the mathematical existence of these men. They exceeded his grasp.”
“I think we’re moving,” Hoy said. “Are we moving?”
“Inability to answer duly noted. Your dreams most certainly do exceed your grasp.”
“We’re moving.”
“How do you know?” Billy said.
“Something has changed,” Hoy said. “I seem to believe we’re moving. I have a sixth sense in these matters. Any opinions anyone? The door will reslide open any second now. Do they expect us? Will the scene be set? Or will we walk out upon absolute void? I believe we seem to be moving. Feelings pro or con?”
They were silent for a time, listening for distant whispers or trying to apprehend whatever spectral information might be sealed into the elevator with them.
“Question three, second series,” Nut said. “Who invented Nutean surfaces?”
“That one I can guess.”
The trifling nature of this last question made Billy feel better. It was one of the sillier questions, almost as dumb as umpteen dimensions, and it tended to negate the effect of Nut’s discourse on Dedekind and Riemann. Billy didn’t like the way he’d referred to them as “a Dedekind” and “a Riemann,” as if he’d been talking about a peach and a pear. But it was true he knew their work to some extent. Doubly fortunate then his question about Nutean surfaces.
“We’ve stopped moving,” Hoy said. “What do you think? Are we still moving or did we just stop? Even as you hear the sound of my voice, I am sensing a stoppage.”
“If that’s good or bad, I think it’s bad.”
“Two men, both giants, each in his own field,” Nut said. “It now becomes the turn of the younger of the two to question the older thereof.”
“Maybe later.”
“No hidden levels.”
“Why not?”
“All meaning restricted to one layer.”
“You had extra layers.”
“Zorgs excluded.”
“They’re my field.”
“We’re here,” Hoy said. “The door is opening. The door has opened. We can step out. I knew it. I have a sixth sense. Who heard me say it? We’re here. They fixed it just in time. We won’t fall after all.”
In his canister Billy showered and washed his hair. He put on his terrycloth robe and shadowboxed a while. Then he sat down to work in purposeful isolation, tracing whatever relationships he could find between the common whole numbers fourteen, twenty-eight and fifty-seven, soon extending his search to include fractions where there had been integers alone, negative quantities where positive had prevailed, imaginary numbers to replace the real, managing in a remote part of his mind to watch himself at work, an old man (cuter than most) in a small old cluttered study, wearing a robe and peeling slippers, sitting at an oak desk rough to the touch because it was layered with the sprinkled pink grains of his brush eraser, thriving on plain food, irregular sleep, constant work, finding himself pleased by this history of his future, a factually accurate illusion, electric heater on the floor, desk lamp with crooked shade, manuscripts stacked in four corners of the room. Systematic inquiry. Precise definitions. Complete proof. Every new dawn brings paeans to his universality. Number-theoretic insights to big-game theory to post-Nutean surfaces to bi-level nonstandard analysis. Credited as the engineer of a vast shift in mid-twenty-first-century mathematical thinking. Age times six. Eight five seven one four two. He was distracted from this interlude of austere self-veneration by the awareness that the sheet of paper on which he was calculating was not perfectly flat, containing many distortions in the form of furrows and grooves, meager ravines, curvature rampant from point to point. He practiced his signature for a while and then got dressed and returned to the research area in which he’d spent part of the afternoon. In minutes he found the gymnasium where Desilu Espy, the clean-kneed woman, had gathered the members of her discussion group.
Here and there on the burnished floor men and women greeted each other with elusive half-kisses. This was something he had never seen in the Bronx, the way they darted at each other’s cheeks and ears, the custom of puckered conversation at short range. He’d expected his hostess to come sweeping toward him in stylish evening attire, laughing in the silvery lilting manner that people employ at such gatherings, dressed (he’d expected) in nonfunctional satins and moody little shoes, coming across the gym haunch by haunch in a motorized feline glide of supple perfection. But she turned out to be wearing the same canvas shoes, knee-socks and bacteriologist’s harness she’d had on earlier. Of course this wasn’t a party, he reminded himself. It was just a discussion group. They were here to discuss something. However, the lights were low and there was that pigeon-kissing everywhere he looked. She took him past the swimming pool and introduced him to Commander and Mrs. Burris Shrub. The commander was large and broad-chested. He wore a gray business suit, double-breasted, with enormous sagging lapels. His wife was decrepit, a pink-white woman who kept striking herself in the face with a lacy handkerchief. Every dreamy swipe released a pinkish mist of face powder from the outermost stratum.
“I’m Calliope Shrub,” she said. “Are you one of us?”
“Depends what you mean.”
“She means outsiders,” the commander said. “I’m here merely to observe. Possibly learn a thing or two about hypothetical weaponry. Mrs. Shrub is vague at times. Pay no mind. Happens to people married to dominant figures. I understand you’re planning to do some tricks with matches and coins.”
“She’s hitting herself in the face.”
“Historical inevitability has changed since my day,” Shrub said. “There’s no longer any grand sense of sweep to the affairs of men. Where are the complex historical forces, the tides, the currents? What happened to the wide canvas on which we were supposed to play out our roles? It was simpler in my day. We could talk about the surge, the tragic pageant.”
“Does your wife know she’s hitting herself with that hanky?”
“No and I don’t want you telling her.”
“I won’t.”
“She’s better off not knowing.”
“Why does she do it?”
“That’s something I hope I never find out.”
“Nervous habit maybe.”
“I’d rather not know.”
“I won’t say a word.”
People moved through the dimness, touching and murmuring. He took a walk around the gym, finally choosing the parallel bars as his vantage point and sitting in a folding chair that was set beneath them. Involuntarily he began thinking about the code. It had never really left his mind of late. It was part of him now. It was distinct from everything else but just as much a part of him, conditionally equal, the problem located in whatever neocortical region nurtures the intuition, that contrapuntal faculty his mathematics relied on. It was as though he had two existences, right and left terms in an equation, and was obliged to face the danger that one of them, the mathematical,
might overwhelm the other, leaving him behind, name and shape. To consider invisibility as a skill. To forget your own existence in the will to persist. He’d always felt, Billy had, that thinking constantly about a problem was tantamount to solving it. A neatly dressed man with a thoughtful goatee squatted alongside his chair, whispering a name, Haroun Farad, knees creaking as he settled into his crouch. He wore a black armband. Risks in this system of fixed idea.
“In my dog-ravaged land they would rip each other apart to drink as we drink here.”
“I was told discussion. Is it refreshments too?”
“My voice whispers,” Farad said. “The book in the inside pocket of my suit coat is in very feverish demand here. Three-dimensional photos. Babies with tails. Antlered men. A woman with a pouch. Meet me at an arranged site and we’ll discuss terms.”
“Let’s see some samples before I say.”
“A duck-billed lady.”
“Who died if you’re wearing that black on your arm?”
“It’s for the aborigine,” Farad said. “A little joke we started up.”
Desilu Espy approached the parallel bars with a glass of eggnog wobbling on a tiny saucer. Billy retreated into shallow darkness a few yards away. People stood in small groups, speaking quietly. He watched Haroun Farad get to his feet and accept the glass.
“Milk content?”
“Someone said you were thirsty.”
“What is the milk content?” Farad said. “If the number of drops is more than there are letters in the world Ilah, the drink must be re-purified. Take it out please. Remove the milk.”
“And they told me you had no sense of humor.”
“I’m serious when I say this thing to you. Take the milk out or I won’t drink of it.”
“Terrific, the richness and variety of native forms of humor.”
Nonintersecting straight coplanar lines, he thought. Given a straight line and any point not on this line, it is possible to draw through this point only one line that is parallel to the given line. Once upon a time, he thought.
“In my dog-ravaged land we don’t make cheap gestures in the direction of friendship. The dogs make such things impractical, shall we say. They roam the country in packs of ten thousand or more. At the smallest provocation they’re at each other’s throats, snarling and ripping. In this environment of large thirsty dogs there is not the time for gestures. We live, those few of us who still live, in a state of concurrent but separate existence vis-à-vis the dogs. The land is lean and bare. So is the conversation. Submission to the rightly guided one is the only accepted form of behavior. Milk is the subtlest of insults. These are the realities. The dogs have made it so. We don’t expect others to understand. In our ability to coexist with the ravaging dogs, we have made the beginnings of something mysterious.”