Ratner's Star (40 page)

“Assuming you're asleep,” D'Arco said, “your task at the moment is to wake yourself up. Just assuming, of course. Assuming you're asleep. The idea is to wake yourself up, assuming you're asleep, and identify the sound that corresponds to my voice. There's a specific matching operation that goes on.”

“I admit I don't like this kind of talk.”

“Of course, there's always the chance you'll wake up with diplopic vision. This will happen if your sleep, assuming you're asleep, is lacking in rapid eye-movements. You'll open your eyes to a world in which everything is paired. No unpaired things in the whole world. Countable objects. A set of sets associated with the number we call two. Assuming you're awake, which is no less likely, I should mention that this is the ape whose EEG tracings we thought were yours.”

“The arms on him.”

“His habitat is rigged exactly like your canister.”

“Fingers, the toes.”

“I think it's time both of you were returned to your respective EEG stations. Assuming one of you isn't already asleep and being recorded.”

“If I had a scissor, I'd like to cut his toenails. Something about toenails that long makes me want to start cutting. What about you?”

“I'm a busy man,” D'Arco said.

Tree Man looked at Billy and spoke, with grim effort, biting off the syllables as they emerged, slowly, units of digestive turbulence.

“All in finite sets are in finite but some are more in finite than others.”

From D'Arco came an avuncular chuckle, little spit-divots sailing through the air.

“The whole is e qual to one of its parts.”

D'Arco wheezed at that, nearly doubling up.

“Pretty droll bunch, those folks over in Zoolog,” he said. “I guess the brain adjustments and other work they did on the chimp could use some refining. But in the meantime I'd like you to take my other hand. Want to be sure you get to your canister and into the twofold.”

As D'Arco moved toward him, hand extended, Billy felt ready to cower and spring simultaneously. There was a noise in the corridor, someone running, the sound of a voice delivering essential news, and they moved into the doorway to see Knobloch coming toward them at top speed, his mouth forming words as he ran.

“They're sending,” he cried. “They're sending again. They're sending.”

Fifty feet from the door he lost his balance and fell but rolled over smartly on his shoulder and was up and running again in the same motion, minus one shoe. He hobbled panting to a stop in front of them.

“They're sending, they're sending.”

“Who is sending and what is being sent?” D'Arco said.

Knobloch looked at Billy.

“I hate you,” he said.

“Why?”

“You saw me fall.”

D'Arco clapped his hands a single time.

“Who and what?”

“Radio signals. Extraterrestrials. They're sending again.”

“What's the nature of these signals?”

“Fourteen pulses, a gap. Twenty-eight pulses, a gap. Fifty-seven pulses.”

D'Arco sagged visibly. Slightly lopsided, Knobloch merely sweated and tried to catch his breath. Billy stepped back into the hobby room, certain this was the end of all menace run amuck.

“I think we learned something here today,” he said.

In the doorway the two men conferred. Billy wandered over to a small window in a far corner of the room. He looked down to one of the lawns and saw what appeared to be an impromptu parade. Two ragged lines of people. Some of them apparently carrying instruments. He was too far away, however, to hear any music. What he did hear, behind him, was Tree Man II padding down the corridor. When he turned he saw that D'Arco had also gone. This left Knobloch, stocky with pustules, to lead him to his canister, not before retrieving the lost shoe and putting it back on. In the canister he tucked Billy into the twofold and departed. In a matter of minutes his voice filled the room.

“Say ‘I read' if you read what I'm saying.”

“I read.”

“Who discovered zero and where was it discovered?”

“Hindu, India.”

“That concludes our voice check,” Knobloch said. “Preparing to record stage-four functions. Preparing to record, preparing to record. Is subject ready?”

“No reply.”

“Preparing to count down. Subject is counting down. Subject is closing his eyes and counting down from zero. Subject's eyelids are terribly heavy. Subject is drowsy as he begins to enter stage one. We have low voltage activity at this time. Decreased amplitude, increased frequency. We are recording at a paper speed of fifteen millimeters per second. Preparing to receive stage-one tracings. Preparing to receive, preparing to receive.”

It was at this point that Softly entered the room. There was a second
of brilliant stillness. Sensational, Billy thought. Colossal, tremendous, stupendous. The special presence of the man, his ascendancy, the seeming contradiction of painful quaintness, were never more evident. He put down his jacket and briefcase. Then, as Knobloch's voice continued to deliver technical data, he approached the limited input module, stepped on a chair, reached into a small compartment high above the videophone and turned a silver dial. Knobloch's voice went dead and the room was totally silent. He stepped down from the chair, picked a loose thread off his shirt cuff and then put on his jacket. Billy climbed out of the twofold, moving at once to his side. It was over, over, over.

They walked together on the grounds. Billy carried Softly's briefcase, as he'd often done at the Center. It was a mild and windless day, sky high and bright, a day modeled on the rhythmic symmetry of a period of light before nightfall. When they entered the topiary garden they heard the ample blare of the parade as it steadily developed, then saw the marchers, dozens of men and women strutting in and out of the monkey hedges, most of them in costumes of various sorts, all wearing masks, men in one rank, women in the other, moving in twos, their masks improvised from newspapers, napkins, towels and sacks. One of the marchers shouldered a tuba, his paper mask fitted with a mouth-hole, and other people played banjos, trombones, drums, clarinets and flutes. The noise produced was sufficiently dissonant to confirm the spontaneous nature of the event. In opera hats, bedgowns, bonnets, yellow slickers, periwigs, knickers and snoods they paraded under the sun, some of the “women,” seen now at closer range, appearing to be men in women's clothing, as though to correct a deficiency and even up the pairings. A ten-foot muffler connected several necks.

“I'm willing to believe this is International Children's Day,” Softly said. “There really is such a thing, you know.”

“I didn't.”

“They've kept it from the children.”

“I didn't know you were expected, Rob. You never told me a thing. What do you think of this place?”

“Needs a fluted column or two. But don't get depressed, we won't be here much longer.”

“Where are we going?”

“I'm working out the details.”

“Somewhere together?”

“Sure, together, absolutely. This whole operation needs to be drastically altered. When I agreed with U.F.O. Schwarz that you were uniquely suited to unravel the transmission, I didn't know things would be handled so casually. There hasn't been enough systematic thought put in on this.”

“But I'm a lot closer than anyone else got to a solution. The number they're transmitting is what we would call fifty-two thousand one hundred and thirty-seven. I'm sure of that and all I have to do is go on from there.”

“From there to where?” Softly said.

They walked slowly across a level expanse of grass. Softly, forced to move in mechanical tick-tock fashion because of permanently dislocated hips, lifted a tin of small cigars out of his side pocket and lit one up. He seemed to haul himself over the ground, hitching with every step, his stomach working as hard as his legs to produce some locomotion. Fields. Number fields. Algebraic number fields. Star fields. Electrical fields. Metrical fields. Field equations. Unified field theory. The grass had recently been cut and possessed that nearly toxic freshness of nature in recuperation, a savor of arrow poison more seductive than the wildest lime. The two moving figures were about a hundred yards from the building, which was hard to look at in this midpoint hour, having been designed to play with light, to magnify and angle it in veering octaves so that the whole structure resembled a burst of solar art.

“They mixed up my tracings with an ape's.”

“What kind of ape?”

“Chimpanzee.”

“They're the most intelligent,” Softly said.

They sat on the grass to rest. Billy stretched back, face lifted to the sun. After a moment he became aware that Softly had taken off his jacket and placed it over his head so that his face was in shadow beneath the upturned collar. Always doing things like that, the boy recalled. Usually these things were funny, dumb and strange and it was
only after some time had passed that he would realize there was an element of intelligence at work. In this case, he decided, it was Softly's pale coloring that provided the motivation, his susceptibility to sunburn.

“I think we have to attack the code in a radically different way. However we look at it, this is one of the most important events in the history of mankind. It has to be dealt with in the purest way possible. Do you see what I'm getting at? We have to be absolutely lucid. We have to be exact to a degree never before attained. The slightest intuitive content has to be eliminated from our finished work. See what I'm leading up to?”

“Let's have the gory details.”

“One way of viewing mathematics is in terms of number. I guess you know what the other way is. I'll say the word in a more expressive language just so there'll be no doubt exactly what it is we're talking about.”

“I wish you wouldn't.”

“Logik,”
Softly said.

That distinctive quality of parade music, a summons to come running, to gather together in public and allow whatever loyalty imbues marchers and band members to quicken likewise the communal spirit and reduce all colors to one; that special emotion, as the music drops into time and distance, is swept pathetically away, to be replaced by a faint wonder at the depths of regret that often follow such fleeting revelry.

“I think I feel sick.”

“Logic is the scrub brush the mathematician uses to keep his work free of impurity. Logic says yes or no to the forms constructed through intuition. So-called intuitive truths have to be subjected to the rigors of logic before we can take them seriously, much less use them in our work. Remember, we're dealing with beings of extraordinary capacity. How can we expect to communicate without a ruthlessly precise system of symbolic notation? Now I know your accomplishments. I understand your feelings—don't think I don't. But you have to admit that much of what you've done as a mathematician has been devoid of true depth. Brilliant instinctive skimming, to be sure. Unprecedented, in fact. But skimming nonetheless. We have to eliminate contradiction and go beyond
all those lax attitudes that make true scientists want to crumple up whimpering.”

“I don't like the sound of it.”

“Neo-logistic, it's called, technically.”

“I definitely feel sick.”

“Don't get your balls in an uproar,” Softly said.

Cigar smoke drifted out of the gabardine tent, not quite concealing Softly's faint smile. In slow motion his left arm emerged from the jacket to give the boy a chummy cuff on the shoulder.

“I find it interesting that Gottlob Frege produced his first landmark work on the logical foundations of mathematics exactly one hundred years ago. Almost as interesting is the fact that Einstein was born that same year. And that Dodgson published a book on non-Euclidean geometry—organized in dream form. Of further interest is the coincidence that a critical split in mathematics resulted from work being done on infinite sets about that time.”

“Why is this interesting?”

“Because I find it so.”

He dug a little hole for the cigar and gently buried it. Funny, dumb and strange.

“As we redefine and strengthen, I think we'll get closer and closer to the prospect of a genuine exchange with the extraterrestrials. We have to seek a level deeper than pure number. That much I'm absolutely convinced of. So let's not drag it out.”

“I got halfway there, Rob. I found out they use a system based on sixty. I know it didn't take any complicated work to figure this out but that's exactly the reason we don't need this big change in our thinking.”

“Even if you sit down and solve the code later this afternoon and solve it in a manner convincing to one and all, this still wouldn't mean we've found an effective way of exchanging information with the extraterrestrials. What we need and what I'm trying to get the groundwork started on is a logistic cosmic language based on mathematical principles.”

“It'll take years and years until long after we're kaput to even reach them out there with an answer. So what's the difference?”

“That's not the point, mister. Field Experiment Number One may smell like a brand-new shower curtain but its aims are important ones. If we're going to behave as a single people, as rational human beings who inhabit the same planet, we desperately need goals and pursuits that can unite us. Finding a way to speak to intelligent beings on another planet is one such pursuit. This place wasn't called Number One accidentally. Others are being planned. Beacons in the shit-filled night. If we succeed here, we'll be providing impetus for similar projects throughout the world. One, two, three, four, five.”

“I need this speech?”

“You can make it work,” Softly said. “You with your one-of-a-kind touch, your fantastic grasp of connective patterns, of relationships and form, of hypothetical states, of the ways in which an isolated concept ties into the whole body of mathematics. Think of it. A transgalactic language. Pure and perfect mathematical logic. A means of speaking to the universe. Whatever small forays have been made in this direction in the past are about to be completely overshadowed by our efforts at Number One.”