“Tell me about your mathematical dreams.”
“Never had one.”
“Cardano did, born half dead, his inner life a neon web of treachery and magic. Gambler, astrologer, heretic, court physician. Schemed his way through the algebra wars.”
“Can I see the baby?”
“Ramanujan had algebraic dreams. Wrote down the results after getting out of bed. Vast intuitive powers but poor education. Taken to Cambridge like a jungle boy.”
Though never less than stunned by her presence, all sepia and hoarfrost blush, he thought this woman slightly strange to be delivering such a grand harangue in the middle of a wood. Her remarks were somewhat formal and even vehement, as if she were trying to convert him, but as much as he liked the clear morning chime in her voice he knew he’d have no trouble resisting the force of her propositions on the extramathematical content of mathematics. A shadow-tailed arboreal rodent sat on a limb. The breeze freshened, creasing the gauzy fabric that covered the baby carriage. A sudden impulse made Billy want to run in circles around the woman and her perambulator. Run and whoop for the sheer stupidity of it, the utter dumbness, making a fool of himself for the sake of foolishness alone. A lancer’s battle cry. A coon hunter’s halloo. Run and shout and fall. But Myriad’s beauty precluded this kind of nihilistic spree. He would have to stand and listen. Disagree if need be. Pout with ankles crossed like a mud-smudged little kid. The only thing that seemed inevitable was his presence at the lesson.
“Sonja Kowalewski wasn’t allowed to attend university lectures. We both know why. When her husband died she spent days and days without food, coming out of her room only after she’d restored herself by working on her mathematics. Tell me, was it Kronecker who thought mathematics similar to poetry? I know Hamilton and many others tried their hands at verse. Our superduper Sonja preferred the novel. Did I get it right this time or backwards? I think I got it backwards.”
“What’s my chances at seeing the baby?”
“It has all its parts,” she said, “and they’re all in the right places. Still, it won’t do to show it. ‘Nothing,’ said Napier, ‘is perfect at birth.’ ”
“He was talking about logarithms.”
She smiled and touched him briefly, the back of her hand, his brow, the trees and fruit, yin hsing, silver apricots, his life and hers, sequence of mephitic decay, the leaves, the bark, the tissue, the humus, the manure, tall, a drifting walk, hair blown back now, wind shift, as she glided behind the tiny carriage, their lives and hers, eldest sons and storied daughters, sand-reckoners, pursuing mathematics to its evanescent cave.
Rose-white woman, I want to die among your petals.
He went back to his room and waited. Then he practiced his signature for a while. He kept expecting someone to turn up. Or a note to come under the door. Or a drawing or poem. Or a message scrawled on the teleboard screen. Or a videotape delivered in some extraordinary way. But things stayed quiet except for a remote monotonous sound, as of people engaged in minor construction, coming from somewhere beyond the exit grating in a corner of the wall.
12
PAIRS
Robert Hopper Softly was a child-sized man with glaringly fair skin and a gift for leading people into situations they would never have entered on their own. There was a distinct sense of authority about him. His body, pathologically stunted as it was, possessed to full extent misfortune’s power to reproach not only nature but symmetry itself. Softly in fact assigned supreme meaning to arrangement, proportion and equivalence but only insofar as these terms applied to abstract constructions. For himself, he did not wish to correspond. He was not part of a collection. With no adult in plain view could he be called reciprocally unique.
Head was disproportionately large, heavy brows shading his gray eyes. Hair was white-blond with pink tinges nestled at the roots. He had a shallow jaw and exceedingly wide mouth, a thumb-sucking machine, aggressively sensual, too much palpitating lip. It was clear he experienced pain with every step he took.
Being an important force at the Center for the Refinement of Ideational Structures he was hardly the sort to be attracted to fashionable schools of superstition, to mysticism as science’s natural laxative, to gymnastic meditation or standard mantric humming, and yet that residual smile on his face, that bare trace of masterful nasty charm, derived from a memory of his own early identification with (the magical aspects of) numbers. He recollected his naïve delight on establishing a relationship between his name—the letters of first, middle and last able to be correlated one-to-one-to-one—and the cardinal number six. This same number, viewed a bit differently, was a special element in the set of positive integers, being a mathematically perfect number, equal to the sum of its divisors. Here was the kind of coincidence a child of subnormal growth might be disposed to treasure like a flawless stone. Odd that he’d recall it now and even stranger the vestigial thrill he felt.
He was wearing two thirds of his three-piece suit. His shirt sleeves were rolled up and he carried his suit jacket over his shoulder, index finger through loop, as he walked along the corridor. In his other hand was a belted leather briefcase, scraped raw in places, old enough to have been his schoolbag in third or fourth grade, an object of sufficient romance, distinction and authenticity to be described as possessing moral and ethical substance. Inside were his hand-washables.
Billy at this point was sitting in pajamas on the edge of his twofold, pinky finger at belly level, idly mining some navel sludge. He blinked a few times, his body trying to respond to the fact that it was technically awake. A moment later a voice filled the room. It seemed to have no definite source. It simply filled the room (or was the room), an immense buzzing voice accompanied by a tiny echo.
“This is Knobloch reporting that a terrible mistake has been made. You were accidentally assigned to an experimental canister. The canister you’ve been occupying is actually a giant sensor. It records your heartbeat, your electrical brain activity, your oxygen intake, your eye movements, your cerebral blood flow and countless other functions that can be studied on EEG and similar tracings. Say ‘I read’ if you read what I’m saying.”
“I read.”
“Nobody’s supposed to occupy that canister except on an experimental basis. You were put in there accidentally. The room is extensively shielded from outside interference. The walls, the floors and all the furniture are equipped with extremely superfine sensing devices. The only way you could avoid being traced would be to suspend yourself in midair. Literally everything you’ve done has been recorded, measured and studied. Except we didn’t know until now that the tracings we’ve been getting belong to you.”
“I read but do not understand.”
“There’s a signal output terminal that processes all the EEG record runs from various clinical sites. We were interested in the tracings of a particular EEG subject located in a high scrutiny habitat. We were very interested in this subject. We monitored around the clock. But evidently the output terminal sent us your functions by mistake. We weren’t interested in your functions. You’re not even supposed to be in that canister. That’s an experimental canister.”
“Who is this other EEG subject?”
“Tree Man II.”
“I do not read.”
“The ape. The chimp. That’s what they call him over in Zoolog. The chimp whose phonetic structure they’ve rebuilt. We thought we were reading Tree Man’s tracings. But apparently we were reading yours.”
“What do they say, my tracings?”
“That kind of information is confidential,” Knobloch said. “But now that we know you’re in the experimental canister, we might as well take advantage.”
“Take advantage how?”
“This is Knobloch preparing to de-transmit. Please remain in your present position for further voice contact. Do not move except as necessitated. Excess movement causes static.”
There was a pause.
“Good morning,” a second voice said. “This is D
’Arco speaking. I am tall and rather fit, with finely chiseled features and eyes that bespeak a certain amount of worldly fatigue. Knobloch is stocky with pustules. While we’ve got you there, we may as well try a little something scientific. What I’m interested in is a person who hasn’t strayed too far from his archaic collective memories. A child, in other words. It would be perfect if you were half your age. But I’m willing to grab what I can.”
“I would rather I went back to work on the code, deciphering the code.”
“No need to raise your voice,” D’Arco said.
“I just want to be sure I am heard.”
“By common consent the star code is no longer an ongoing project. I’m amazed anyone took it seriously in the first place. Radio signals that weren’t even repeated. A jumble of pulses. How can you do serious work with that kind of unreliable data? What I’m interested in is a particular segment of your stage-four sleep.”
“I have just now woken up.”
“Sleep is a very active state, part of your waking life really. At times your heart rate and blood pressure soar. Your neural activity increases. There are rises in spinal fluid pressure and stomach muscle activity. Your little pee-pee-maker gets hard and fluttery. Under closed lids the most important thing of all is happening; your eyes are getting periodic exercise. Their rapid movements are coordinated in terms of conjugate function—a paired mechanism supplying a single vision. Without this exercise you might wake up to a double world. Which is the object, which the image? They are paired one-to-one.”
“Sleep is part of waking?”
“When you dream in stage-four sleep, you connect with your own racial history. You glimpse a portion of your earliest being. Perhaps this is why there is no stage four after a person reaches seventy years. This stage just drops off, like a rocket booster. The segment I’m particularly interested in is called stage-four primal, which is characterized by a total lack of dream recall on the part of EEG subjects. Brainwave tracings indicate that dreams do occur in stage-four primal. But no one has been able to remember one. With pregnant EEG subjects, we find bursts of fetal activity in this substage. Is there a connection between the subject’s primal dream and the fetus’ emergence from the uterus? The structure of the atom was conceived in a dream. But it wasn’t a stage-four primal. Pure fable, myth, archetype, model, mold. This is how I characterize a primal. Dreams so shatteringly primitive the memory withdraws from them to relieve itself of responsibility.”
Midway through D’Arco’s recitation, Billy got up and jogged around the room, testing Knobloch’s statement that excess movement causes static. It was true. The sound of D’Arco’s smooth deep enveloping voice was interrupted by random bursts of noise. He tried standing still and quickly raising his hand. A small crackling warp in D’Arco’s voice. He tried kicking his foot backward. A little hiss.
“Being a nonadult EEG subject,” D’Arco said, “you haven’t had time to drift away from your psychic origins, whatever these may have been, however replete with terror, darkness and fetal shrieks. Routine horripilation. We’d like you to sleep. Nothing more than that. You simply get into the twofold and sleep. Nothing will be attached to your body. The canister itself is sensor enough. All we want to do is record your stage-four primal. We want to learn what kind of dreams you have in that stage.”
“But you said they’re never recalled in that stage, being the shattering kind of dream.”
“Very good,” D’Arco said. “You’ve been listening.”
“Also I have slept here ever since arriving. This means you already have plenty of tracings of mine.”
“We thought your functions were Tree Man’s, which means we didn’t activate the current that could electrically stimulate the flash points in your temporal lobes, thereby enabling you, on awakening, to experience flashbacks of scenes from your primal dream.”
“Is that the same as remembering?”
“It’s better,” D’Arco said. “The details are much sharper.”
“So what happens now?”
“You go to sleep.”
“I’m not sleepy.”
“Knobloch will read to you,” D’Arco said.
There was a brief silence.
“The history of zero is both interesting and informative,” Knobloch read. “It is thought that zero was discovered in India by a Hindu many, many years ago. It is the shadow of pure quantity. On one side of it are the positive integers; semicolon; on the other side the negative integers. Plus and minus, minus and plus. You are getting sleepy. Your eyelids are getting heavy. You are falling into stage-four sleep preparatory to entering an undiscovered primeval dreamscape. Zero is an element of a set that when added to any other element in the set produces a sum identical with the element to which it is added.”
He dressed quickly and walked out, hearing, before he closed the door, the static caused by his movements across the room. He gave his body a moment to replenish its supply of oxygen, energy and whatever else had been disrupted by the prospect of simple sleep—a prospect that caused decided terror, delayed or not. Then he went to the nearest elevator, waited for the door to open, stepped inside and pressed a random button. When he stepped off he saw two workmen hurriedly installing an office door and another man disappearing around a corner with a paint can in his hand. Billy went the other way. Something about the area seemed familiar but it wasn’t until he walked past a barbershop that he realized he was in the vicinity of the hobby room. Pure luck, he concluded. Since this was a time of threat and since Endor’s room was padlocked, the hobby room represented a welcome refuge, even if second best. Stage-four sleep recorded and traced. His brain waves on paper. Bursts, flat lines, spindles, jagged flashes. Dropping off. Falling to an alternate surface. The hobby room looked the same as it had when he’d encountered Siba Isten-Esru, the name shaman, Seven Eleven. Even the neon organ used in Ratner’s torch-lighting ceremony had been returned from the Great Hole. He sat on Endor’s tricycle and looked around. There was an eerie restfulness attached to being alone in a room of solid objects, this shadowy attic haunt so thick with reveries and dust. Weapons of holy wars. Pieces spilled from jigsaw puzzles. Trick decks of cards. Catgut, bamboo and iroko wood. He got off the vehicle and wandered into the depths of the room, passing among Victrolas, soda fountains and mummy cases. These last were very small, stamped OMCO RESEARCH, apparently designed for children, each case decorated with a chipped and faded likeness of the individual it once contained. In a steamer trunk he found a makeup kit. Among various pastes, wigs and cosmetics was a small black mustache, very somber, an emblem of anonymity more than a decoration, fit for a man who gravitates toward the darkest corners of rooms. He placed it over his lips and used his index fingers to press down. It seemed to stick fairly well. He pressed again several times as he strolled past the organ and tricycle back toward the door. Standing there were D’Arco and Tree Man II, the latter flat-footed, long-limbed, head thrust forward, jug-eared, a quizzical look on its face, profoundly self-mocking, the very expression Billy had come to associate with scholarship, distinctive mastery in learning. Not that the ape was so nakedly akin to some master of the classics. Just ambiguous was all, or appearing to be, teasing the known world, reluctant to share its puzzlement. One paw was held by D’Arco, who was well past middle age, his neck veins extending like bridge cables from his throat to the point of his chin. Wispy hair grew on his autocratic knuckles.
“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 every
thing 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.