Among the things beyond expression in various cultures have been the names of deities, infernal beings, totemic animals and plants; the names of an individual’s blood relatives of the opposite sex (a ban related to incest restrictions); the new name given a boy at his initiation; the names of certain organs of the body; the names of the recently dead; the names of sacred objects, profane acts, leaders of cults, the cults themselves. Double substitutes must be used. Carefully devised code words. Taboo variants. Oaths are duly taken. An entire bureaucracy of curse, scourge and punishment is set up to discourage utterance of the unspeakable. Copyists of manuscripts are prevailed upon to resort to the strictest kind of transliteral deviousness. No writing that touches on the life of a secret subject can itself escape secrecy and in time culthood is conferred on document as well as primary figure. Often more than one person is concealed in the cult leader’s generative shadow and the names of none of those who follow can be revealed except as provided by the contextural pattern itself, however primitive its design or childlike its claim to a scientific principle of arrangement.
He dropped the sock and got his pajamas. Before stepping into them he briefly juggled his testicles. This was a bedtime routine he’d lately developed not only for the common monkey sport of fingering those boiled orbs (dimeric witness to virility) but also in earnest celebration of the fact that his left testicle had fully emerged at last, making him not only whole but reassuringly asymmetrical as well, the left drooping a bit lower than the right, as decreed by nature.
Slowly he was getting accustomed to the canister’s tenuous perspectives. In his pajamas he examined the components of the limited input module. He knew this was standard equipment for the sector he was in but he had no interest in learning how to work the thing. For whatever it was they wanted he’d need pencil and paper at most.
Someone was outside the door and now a knocking sound was evident, bap bap, a sort of cartoon noise, bap, as of an oval stone dropping on a bald infant’s head. He opened the door to see a figure in oversized work clothes. The man listed slightly, giving the impression of being burdened beyond the reach of deepest fatigue, someone who sleeps in subways.
“They know me as Howie in this sector. The fume sewer man. Heard you were worth seeing. Maybe you want me to show you what’s what down there, two or three levels down, what they got down where I work down there, fume sewers, evaporators, recyclers, backup spewing filters. You think this is far down. That there is a lot farer. I could take you eight levels down. Nobody goes eight levels down without a red pass.”
“I’m supposed to go to bed.”
“You’re the only kid in this whole place.”
“There’s another one being born.”
“Eight levels down in noise is some racket. Accelerators, storage rings, proton impactors, collision machines, Howie Weeden, always glad to meet a kid.”
“They want me to get up early.”
“Let’s shake hands. People shake hands when they meet. You don’t just say nice to meet you, one person, and the other person do nothing. People shake hands.”
“I still have wet.”
“What’s that?”
“I still have wet on my hands from just washing up for the night.”
“They told me to come look,” Howie said. “They said there’s a kid over there worth looking at for the way he adds numbers in his head.”
“That’s not what I do.”
“I have a python in my room. Don’t tell anybody. It’s my best pet ever. Want to come watch it digest?”
“They have me on a schedule.”
“There’s a woman takes a bath every night at this time and you can see her in a ceiling reflector if you look through a hole in the wall standing on a bench in the workroom over near the next sector up one level. I’m the only one that knows. I call her the water woman.”
“Let’s go,” Billy said.
He put on his robe and slippers and followed Howie Weeden through the play maze to a red elevator reserved for maintenance personnel. They got off and headed down a long empty corridor. Signs of the shadow-flow were everywhere. Howie moved quickly despite a double shuffle of his right foot.
“If anything happens, grab my tongue,” he said.
“I don’t understand.”
“Just be ready to grab my tongue.”
“I want to know why.”
“I never had to tell anybody before. They always knew. You tell somebody to grab your tongue, you don’t have to say why. Just if I slam out, go for the tongue, that’s all I’m saying.”
“How often does this happen?”
“More often than not,” Howie said.
In the workroom he stood on a bench and put his head to a metal bracket at the juncture of two cement walls. After several minutes he looked at Billy, pointed to a specific perforation in the bracket and then stepped down to the floor. Billy wasn’t nearly tall enough to put his eye to the spot in question, so Howie set himself on the bench once more, bunched up on all fours, as the boy climbed up his arched back and found a foot-grip alongside each shoulder blade. His hands were flat against the wall, head twisted, right eye almost in contact with the small vertical slit. There was a hole in the wall, perhaps half an inch in diameter, directly behind this particular level of the bracket and so he found himself peering through two openings, one punched by machine into the metal bracket and the other most likely resulting from crude workmanship or premature erosion of the wall, the sector, the level, the entire structure. Beyond both holes was a ceiling reflector.
“Just remember the tongue,” Howie said. “This weight on my back isn’t doing my skull trauma any good.”
In the tilted mirror he saw Una Braun. Wearing a loosely knotted robe patterned in mellow colors she stood barefoot on pentagonal tile, her body a bit foreshortened by the angle of reflection, combing, combing her hair. Bottles of perfume and baby oil stood on a glass shelf. His knees went weak and he thought he would fall. Both hands were dug into cement, not finger-gripping (he feared she’d hear the scratching) but pressed desperately, palm and heel, into the wall. It was she, Una, about to bathe, undress and bathe, water woman soon to drop her robe and step into that clear and distorting, dense and un-colored element. Varieties of light glanced off the surface borders of air and water, water and glass, glass and oil, the whole room a medium of nonuniform density, these propagating waves graining her body, soon to be rubbed and soaped and misted, transformed in displaceable mass, passing through itself, beauty bare, an unfalsifiable and self-blinding essence, not subject to the judgments of mirrors, what Euclid might have danced to in the summer dusk. Oooo naaa. She stood combing her hair, the big toe of one foot digging idly at the inmost pentacle on a cool blue unit of tile. Now she smiled at a stray thought, a memory of home or long buried song lyric, one hand dropping to the whimsical knot on the robe’s sagging belt, perhaps loosening it further, the other hand placing the comb on a shelf.
Do they comb their hair before they take a bath?
She lowered her head for a moment, moving partly out of his line of vision, returning seconds later. When she looked up, she saw him. That very section of wall, mirrored twice in the complex placement of the bathroom’s reflecting surfaces, was spread across the ceiling. There was his right eye, magnified.
“Who is that?”
He kicked Howie’s shoulder to indicate trouble.
“We’re caught,” he whispered.
“I heard,” Howie said.
“What do we do?”
“Ask for tits and let me know what happens.”
She hadn’t moved.
“Show me your tits.”
The sound of his voice surprised him in its unreal evenness and degree of clarity.
“Billy, is that you? Do I know that voice? It’s you, isn’t it?”
“Show me your tits please.”
“Repulsive person. Wretched little boy.”
He kicked Howie again, more urgently this time.
r /> “I tried asking but nothing got shown.”
“Ask for thigh.”
“You ask.”
“Who’s up there?”
“You didn’t tell me there’d be conversation. I expected to see things without this talk. She knows me by voice.”
“Ask for hair,” Howie whispered.
“Which area?”
“Below, below.”
“You ask this time.”
“Maybe, your age, you better stick with titties.”
She was still there, evidently defiant.
“Let’s have some boobs,” he said.
“How very sad. Yes, more than anything, sad. Tragic individual. Sad, sad boy.”
“Cheer me up with a quick tit.”
He gave Howie a very light kick, as if requesting some confirmation of the brilliance of this wit under pressure.
“Undeniably wretched person.”
“Left breast,” he said.
“Demean yourself, that’s all you do.”
“While I’m up here. Some nipple. How can it hurt?”
Howie pushed up.
“Cheeks,” he whispered.
“Nothing’s getting shown.”
“Ask for cheeks and report back.”
“She’s not showing.”
Una left the bathroom in her own time, setting things in order, replacing caps and closing lids; clearly she had no intention of scuttling away like a maiden outraged. There was nothing for him to do but climb down Howie Weeden’s back to the bench and floor. The maintenance man studied him crookedly.
“What happened?”
“Gone.”
“No bath?”
“Nothing.”
“I played a trick,” Howie said. “She already finished her bath. When I got up there I heard the water getting sucked out of the tub. I think it’s here.”
“What’s here?”
“I can feel it. It’s here. I’m getting ready to slam. The tongue. Prepare to go for the tongue. I’m slamming out.”
The boy hurried out of the workroom and got on the nearest elevator. For a long time, in robe and slippers, he walked in and out of arcades, suede sitting rooms, meditation suites, past miniature waterfalls, around ornamental fountains, under arched gardens, through reference libraries, lush saunas, empty game rooms, totally lost, thinking wistfully of his crisp little bed. An unmanned cart marked EMERGENCY LINEN SERVICE went speeding by. All was quiet until he reached a transparent bridge leading to one of the upper sectors of the armillary sphere. The enormous motion of the sphere was audible, a continual muffled utterance less of machinery at work than of overwhelming mass in friction with surrounding air. He entered the sphere and stood just above one of the elliptic bronze rings. Arciform spaces. Flowing motion. To be up so high, turning, contained in material receptive to visible light, was a liquid thrill, the night sky so clear and near and living. As he was swept gradually past the edge of a steel support he saw something pierce the sky, an incandescent object dragging vapor-light behind it and needling in and out of darkness. Aloft too long to be a shooting star, it might have been a snow-maned comet, come sunward to orbit, or a supernova’s argon shriek. In other places the sky was tranquil, although nowhere completely still, and he wondered whether the flash he’d seen was part of the process of a star being formed, point of light set within the fiery trigon, that name given to the first, fifth and ninth signs of the ancient zodiac. Twelve equal parts. Thirty-degree arcs. Earth, air, fire, water. Triplicity of fire. Fire’s pre-eminence. Equilateral triangle of fire. Men born under new stars are destined to lead revolutions.
Eventually he reached the correct sector. Workmen were placing huge acetylene devices along the walls of the corridor, presumably to keep the shadow-flow from “spilling over.” He went to his quarters, sat at the module and began looking through the manuscript he’d had in his possession since leaving the Center to make the journey here. It was a handwritten document given to him by his friend and mentor, Robert Hopper Softly—a work-in-progress detailing Softly’s observations on any number of mathematical topics. As he browsed he heard a tiny sound, ibd, and eventually noticed, to his left and just above eye level, that a message was appearing on the teleboard screen, a chalk-scrawl beamed by laser:
See me
Earliest a.m.
Space Brain Complex
U.F.O. Schwarz
“The teacher of the secret book died between the fire-pillars at Tarentum. Those of his disciples not burned to death were killed by mobs. The mathematical brotherhood was dispersed. What, we ask, did it leave behind? A sense of order in nature. The notion of mathematical proof. The word ‘mathematics’ itself. But the teaching didn’t end, spreading through the Mediterranean, maintained in formal order for over two hundred years. Numbers as the basis of creation. The religious instinct arithmetized to regrettable effect. A dream of water put out by flames.”
He went inside to brush his teeth, mis-squirting a strip of toothpaste into the wash basin, where it formed a line and curve resembling a crumpled number four. Directing the tube at the figure he proceeded to close the curve, making line and zero, or ten from four. But sooner or later he would have to stop fooling around and brush his teeth. So he spoke a password to his mouth, tetraktys, and it opened.
3
SHAPE
Remarks from Softly’s work-in-progress:
“The unattested cadence of the heavens had been based on the circles of Ptolemaic calculations, a format supported by the Polish monk Copernicus. All work on celestial events was superimposed on the mirages of animism, prophecy and the Christian occult. Motive soul drove the planets and it was held that every orbit described a musical scale. The problem of course and solution as well were distinctly mathematical, although not without some hearsay of the empyrean.”
When Billy stepped off the elevator he was in Space Brain Complex. This was a vast computer area, quiet at the moment, no one in sight. In the middle of an open space stood a small office of frosted glass, a cubicle really, and he headed toward it. Sitting inside on a swivel chair was U.F.O. Schwarz, a densely packed individual weighing well over three hundred pounds. Attempting a jaunty sort of greeting he tried to pivot in the chair. Nothing moved, however. Concentrated flesh. Eye slits. Bubblelike hands. The chair was equipped with a footstool, which Schwarz managed to nudge toward the boy, kicking it soccer-style.
“Is that all one computer out there?”
“Space Brain.”
“Whose office?”
“Kind of cramped.”
“I have the feeling you carry it around with you.”
“That’s about as funny as a dead kid’s toy,” Schwarz said. “We’re waiting for Nyquist but I guess I can bring you up to date in the meantime. We chose this time and place because we knew we’d have complete privacy. I’m the person who arranged with Professor Softly to bring you out here. Spoke to him in person. Reported certain recent events. He talked at length of your extraordinary abilities.”
Schwarz had a glass of orange juice in his right hand. He tilted the glass slightly now, the surface of the liquid assuming an elongate outline. Billy began guessing the large man’s weight, keeping the figures to himself.
“What do you know about space?”
“Not much. Maybe even nothing.”
“Stars and planets.”
“Last night I saw a comet or something. I don’t even know what it was. That shows how much I know.”
“Doubt it was a major comet,” Schwarz said. “One’s long gone and the other’s not due for a while.”
“Pure mathematics is my field.”
“We’ve been contacted by someone or something in outer space.”
“I do pure work. A lot of it is so abstract it can’t be put on paper or even talked about. I deal with proof and nonproof.”
“Beings in outer space. Someone or something. An extraterrestrial civilization.”
“What about it?”
“They’v
e contacted us. We picked them up on the synthesis telescope. They transmitted and we received. Pulses. Signals were transmitted in irregular pulses. We happened to be tuned to the right frequency. Space Brain has printed out a tape covered with zeros and ones. Mostly ones. The message was not repeated. This is unfortunate but not disheartening. One hundred and one pulses and gaps. The pulses we interpret as ones. The gaps or pauses as zeros. There are only two gaps. The transmission was fourteen pulses, a gap; twenty-eight pulses, a gap; fifty-seven pulses. Total of one hundred and one information units. One zero one is binary five, which may or may not mean something. One hundred and one is also the lowest three-digit prime. Then we have the arrangement of pulses—fourteen, twenty-eight, fifty-seven. Plenty to work with, don’t you think? At any rate we are not alone. Something is out there and it is talking to us.”
“What is it saying?”
Schwarz paused here, locked into the framework of his petrified baby fat. What was odd about his way of speaking was the fact that nothing moved but his lips. Independent animation. Now, however, he raised the glass to his pouched face and nibbled at its rim. Billy heard a faint metallic tapping coming from well beyond the perimeter of the small office, less faint a moment later, then less again.
“That’s our problem. We don’t know what the transmission means. Space Brain has printed out hundreds of interpretations without coming up with anything we can call definitive. Dozens of men and women have also failed. Radio astronomers, chemists, exobiologists, mathematicians, physicists, cryptanalysts, paleographers, linguists, computer linguists, cosmic linguists. I’m sure you know Endor. We got Endor here to decode the message. Endor seemed the one man who couldn’t fail. Famous the world over. Well versed in all aspects of extraterrestrial communication. A first-rate mathematician. A brilliant astrophysicist. Science prizes hand over fist. He worked at the message for a great many weeks. Then he worked some more. He kept saying it’s probably so simple we can’t see it. One day he stopped working and just sat in a chair in his room for about seventy-two hours. Finally he went to live in a hole in the ground. That’s where he is at latest report. He’s living in the ground. He eats plants and worms and refuses to talk to anyone. You’re our last hope, it looks like. When Field Experiment Number One became a functioning entity we never in our wildest dreams thought we’d be lucky enough to receive signals from a supercivilization so early in the game and then unlucky enough to be unable to unravel them. We feel certain it’s a mathematical code of some kind. Probably a number code. Mathematics is the one language we might conceivably have in common with other forms of intelligent life in the universe. As I understand it, there is no reality more independent of our perception and more true to itself than mathematical reality.”