Ratner's Star (19 page)

Synthetic figures on the glass slide moved at timed intervals in a bright clasping skater's blur of identity and division. As one microsphere parted from another, a third joined a fourth. This coincident symmetry did not astonish the lone brown eye that watched from above. Billy thought of the process as a simple one, that of artificial objects being rearranged on a limited surface. There was something wholly touching about these microspheres, these subcreatures of polypeptide origin. They possessed the innocence of small things viewed from a distant point.

“Shouldn't you be getting back to work?” the woman said. “I feel guilty about letting you linger. So much depends on you.”

He raised his head from the eyepiece. Desilu Espy in her starched close-fitting tunic and high white socks resembled a puffy schoolgirl whose age had somehow doubled before she'd found time to don appropriate clothing. She and Billy stood in a glass booth in an area set aside for research in extramolecularism. Beyond the enclosure, in every direction, were all the elements of modern laboratory swamplife—electron microscopes, optical rotation instruments, rows of precision devices for measuring, photographing and synthesizing the unseeable, everywhere a sense of insomnious acids. He put his eye to the microscope once more.

“We're analyzing a giant molecule,” she said. “It's more complex than anything ever found in the spectral lines in the Milky Way. Perfectly stable under heat and light. This is a good sign in terms of do we or do we not find the building blocks of life beyond the solar system. Don't you have work to do?”

“I'm not finished looking at this.”

“Sometimes I wonder wouldn't it be simpler if the Ratnerians just turned up one day. Or wouldn't it be almost as simple if we used an enormous topographical marking to indicate to any visual monitoring device that there's intelligent life on Earth. Somebody thought of a huge pine forest planted in Siberia in the form of a right triangle. The monitoring device would see it and report back to its people. Ideas like that really appeal to me. They're such human ideas. Only humans could think of ideas like that. Radio emissions are impersonal. What can you learn about a civilization from pulses and gaps? We could plant a right triangle of pine trees with a square of blue spruce attached to each side. The extraterrestrials would be charmed by it. If not, we wouldn't want to know them anyway.”

She stood five feet away, watching over him with a clear concern for the object entrusted to his secular pleasure. Without raising his head from the instrument he closed his scope eye and simultaneously opened his free eye. He shielded this action from Desilu Espy by putting left hand to forehead in a pretense of deep concentration. As she continued
to talk, he stared at her knees, the only items discernible under the circumstances. Very clean. Clean knees. A clean-kneed woman.

“Are you sure you shouldn't be getting back to work?”

“I worked last night.”

“Here comes whosis himself. What's-his-name. He's probably going your way. He can take you back.”

“I didn't know I needed taking.”

“I've put together a tiny discussion group for this evening,” she said. “The gymnasium just around the corner. You have to come. They'll want to see you.”

“Haven't they seen me yet?”

“Your wrong eye's open.”

He raised his head and stepped down the small aluminum ladder he'd been using to position himself at microscope level. A man was standing outside the glass booth, smiling ironically. He was small and seedy-looking, dressed in a wrinkled ill-fitting suit that gave the impression it had just traveled thousands of miles, perhaps with him inside it, at the bottom of a steamer trunk. He was so close to the booth when he spoke that his words made small clouds on the glass.

“Tea more noot.”

“Now I remember,” the woman said.

“We meet at last.”

“Who?” Billy said.

“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
n
th 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.”

“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?”