"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."

"I thought we weren't staying."

"It depends on events," Softly said. "We'll be here in general but elsewhere in particular, I suspect."

They began to walk again. It was still possible to hear an occasional parade sound, very faint at this distance, tiny rips in the air, the brief repeated pop of tearing seams. Softly kept the jacket over his head.

"I think we're free to break off, split away, to follow a new course. In line with the rigorous approach I'd like everyone to stop using expressions like 'Ratnerians,' 'superbeings,' 'extraterrestrials' and so forth. It's a radio source we're in touch with. If Moholean relativity is the real thing, the source isn't even where it seems to be. So why assume it's a planet orbiting a star? Remember the homely old adage: 'Belief in the causal nexus is superstition.' So let's from now on be sure to use the term 'artificial radio source.' And let's find a more precise name for the so-called beings who are presumed to have initiated the transmission. How about 'artificial radio source extants'? ARS extants. Just so we know what's what."

"Getting tired?"

"From talking more than walking. Hard to adjust to the fact I'm walking with someone who doesn't tower over me. The size we share makes it easier for me to imagine you in the palsied grip of middle age, hee hee, which in turn makes my own years fall away like dry leaves. The fate of man, recto verso, is to go to his grave in a rented hearse-o."

In time they returned to the vicinity of the cycloid structure. A woman opened the gate that led from a small enclosure known as the abstract garden. She walked toward them, carrying a small piece of luggage and some books.

"Look at the ass on that."

"What ass?" Billy said. "She's coming toward us."

"I like to anticipate."

Softly put his jacket back on and they settled into adjacent chairs in the abstract garden. The paraders had evidently passed this way, leaving tokens of their frolic. A man with a pointed stick jabbed daintily at pieces of paper and stray fragments of costume.

"So in conclusion," Softly said, "what we've got to do is restate and strengthen our method of reasoning. Make it exact and supremely taut. Introduce distinctions and fresh relationships. Argue our propositions in terms of precise ideographic symbols. Submit our mathematics, in short, to a searching self-examination. In the process we'll discover what's true and what's false not only in the work before us but in the very structure of our reasoning. There's been no concerted attempt to eliminate slackness and ambiguity from the work you've done up to now. I've got news for you, mister. The goddamn fun is over."

They were alone in the small garden. The afternoon had lost some of its rabid glare. A smell of mown clover rose from the earth. It summoned a special presentness, that particular time-sense in which animal faculties conspire to rouse the spirit, the ordering force of memory, and Billy was stirred to relive some elemental moments separately blessed within the flow of past events. They could be counted, the times in which he'd guided a length of string through the hole he'd nail-scraped in a chestnut, the lumps of clay he'd thumbed and gouged into some amorphous model, the cherry pits he'd buried and people he'd learned to believe. They could be counted, the times in which he'd flexed his toes in dense wet sand, the bites of ice cream he'd chunked out of dixie cups with a flat wooden spoon, the caves he'd made in his mashed potatoes, the pages he'd detached from his composition notebook, tearing down along the row of wire rings, and the white flakes that bounced down out of the air as a result, also distinct and countable. They could be named and listed, the places he'd hidden from danger, the nights he thought would never end.

Softly got up, stretched and headed abruptly toward a remote rear entrance of the building. The boy followed, carrying the briefcase. It wasn't until he walked toward the reflecting surface of an electronic door, now sliding open, that he realized he was still wearing the false mustache.

 

REFLECTIONS

 

Logicon Project Minus-One

 

Everywhere dense the space between them seemed a series of incremental frames that defined their passion's dark encompassment, man ostensibly engrossed in dressing, woman nude and on her side (a horizontal dune anagrammatized), neither failing to be aware of the sediment of recent links and distances, that variable material suspended in the air, living instants of their time within each other, sweat and re-echoing flesh serving to confirm the urgent nature of their act, the industry involved, the reconnoitering for fit and placement, the fundamental motion, the pursuit of equable rhythm, the readjustment of original position, the effort of returning to oneself, of departing the aggregate, and in the slightly pasty daze in which they now remembered their fatigue, their sense of well-merited weariness, it was possible for each to examine even further the substance of that space between them, so reflective of their labor, the odors transposed, the strand of hair in the mouth, the experience of whole body breathing, the failure (or instinctive disinclination) to produce coherent speech, the bright cries, the settling, the eventual descent to slackness, the momentary near sleep in milkiness and cling, the recapturing of normal breathing tempo, the monosyllables and blocks of words, the raw awareness of the dangers of exchange, the oddly apologetic uncoupling, mutual recognition of the human demonol-ogy of love. She rose from the bed, not without a glib tickle of the springs, this done with a bounce of her amazing buttock, the left, notable for its star-shaped birthmark. He sat atop a footstool, engaged in double-lacing his shoes, taking time between knots to watch her dress, an operation that seemed to portray the correspondence between position and time, one action generating the next, step-in, shake-into, hoist-on, her limbs and torso covered now, fluidly moving woman, her eyes appearing to follow the delicate pebbling sound of Softly's voice. She sat back on the bed as he spoke, the bottoms of her feet identically smudged with dust, arms enfolding her raised knees to form a body-hut that wobbled. Softly rubbing his pale stubble took time to glance inside the folder she'd left propped against the footstool. He spoke a moment longer (about terms, formulas, sentences and proofs), then got up and hurried out of the room, moving with his customary lurch. Had he happened to turn, a step beyond the doorway, for a final word or sweet and simple farewell nod he might have found himself a trifle mystified by the wry smile on his lover's face.

 

I  TAKE  A  SCARY  RIDE

 

The boy was packed and waiting when Softly arrived in his canister. His pants were pressed and he wore his good sport coat and tie. His fingernails were clean. The part in his hair was nearly straight.

His shoes were shined. The mustache was gone. While Softly nosed his way around the room as though they were about to move in rather than vacate, Billy picked up his suitcase and headed toward the door.

"Not that way."

"What other way is there?"

"Straight down."

"Explain please."

He watched Softly approach the metal grating located near the base of the wall. This, of course, was the emergency exit point for the whole sector. Softly unclasped the grating and set it on the floor.

"We can't go in there except for man-made or natural disaster," Billy said. "They told me that. I nodded my head to show them I understood their statement. Floods, fires, wars, earthquakes."

"Do I get to pick one?"

"I don't like going down there for no reason."

"There's an emergency all right. I thought all along this would happen and it has. Cable traffic is heavy beyond belief."

"So what is it, some kind of alternate physics situation or the bottom is falling out of space or water doesn't boil at the boiling point anymore? Because around here that's the kind of emergency you get."

"Tensions," Softly said.

"What kind?"

"The worst kind. International tensions. Mounting international tensions. First there were states of precautionary alert. Then there were enhanced readiness contours. This was followed by maximum arc situation preparedness. We can measure the gravity of events by tracing the increasingly abstract nature of the terminology. One more level of vagueness and that could be it. It's not just a localized thing either. We're dealing with global euphemisms now. Exactly how soon it'll break out depends on when x, representing the hostile will of one set of nations, and y, the opposing block, slip out of equilibrium in terms of capability and restraint coefficients. We could frame any number of cutie-pie equations but we've got more important work to do."

"So how far down do we go? Is there a basement with a shelter right under here?"

"We go deeper."

"Where they keep the proton accelerators? I think that's about as far down as the building goes."

"Deeper."

"I know where. Where the balloon is that they keep in that big room, the balloon for astronomy. That's about thirteen levels down. Or the Great Hole. We go to the Great Hole, right?"

"Deeper," Softly whispered.

"Deeper than the Great Hole?"

"What I find most satisfying about this structure is the fact that it comes in more than one part. The first, naturally, is the cycloid. The second is the first in reverse, completely below ground level. Same shape upside down. Same distance down as up. Nothing goes on down there in the sense of official goings-on. It's nothing more than an excavation. But it fulfills the concept."

"I think I'll stay here."

"I call it the antrum. Just a fancy way of saying hole in the ground. I've had the floor of the excavation fixed up a bit. Just the bare essentials. And I've selected the very best people to help us in our work. Every one a supersavant. It took all the persuasiveness I could muster. I think the world tensions helped. In this kind of chancy muddle everybody agreed the only way to stay intellectually fresh was to put ourselves in a state of total isolation. Consider yourself lucky to be working with these people."

"I'll take my chances with the global phrase-calling."

"Follow me down," Softly said.

On his hands and knees he backed into the exit hatch. Billy handed down his suitcase and followed. After descending a long metal ladder they had to step over a series of sewer pipes to the edge of a catwalk. It was hard to see, the only light being provided by a dusty bulb. To one side was a stack of beams and thick boards set on sawhorses, all apparently left by workmen. They crossed the catwalk and headed toward another light, avoiding puddles as they went. This time the bulb was inside an open shaft. Softly cranked a lever and eventually a small elevator ascended and stopped, roughly at their level. It was really the frame of an elevator, much of its wiring exposed, no paneling at all, a few yards of hexagonal mesh closing in all but one side. In this lame cage they were lowered into the excavation, a journey that took them through storage and maintenance areas, restricted sectors, down along porous shale and rock, past timber underpinnings and assemblies of masonry and steel that formed support for subtunnels and emergency access routes, the elevator suddenly dropping into open air, free of its shaft, cabling into the darkness of the inverted cycloid, air currents, oscillation, a bucketing descent through drainage showers and rubble-fall, the cage shaking so badly that Billy sought to convince himself there was a pattern to the vibrations and changes of speed, a hidden consistency, all gaps fillable, the organized drift of serial things passing to continuum. Gradually the elevator slowed down, steadying its descent. Then it fitted into its housing, a sort of armored toy-box located on a platform about a dozen feet off the ground. The riders stepped out and walked down makeshift wooden stairs to the "very bottom of the vast excavation. An awful lot of trouble, the boy thought, just to fulfill a concept.

A short distance away was a series of cubicles for working and sleeping. Larger units included a first-aid room, a kitchen, a primitive toilet, some field telephones. Everything was set on a slightly curved surface of clay and rock and there was nothing above but darkness. Oil drums, wooden crates and natural debris were set around the cubicles to keep dislodged rocks from bouncing in. A generator droned nearby. Water dripped, splashed and occasionally cascaded in the distance. It was cool down here but not uncomfortably so. The smell of earth was firm and gripping, mineral-rich, and humid air could be felt on the tongue like the taste of a lead penny.

"Frightening ride, I freely concede, but better this than a block and tackle descent," Softly said. "If we ever short-out down here due to flooding, that'll be next. Up and down we go, sitting in a loop of high-grade rope."

In Billy's cubicle were a cot, a footlocker, a large shiny blocklike chair and a TV table on casters, this last item meant to serve as a desk. The partitions were about twice his height. There was no door, just an entranceway; no ceiling; a clay floor. Softly left him alone to do his unpacking and Edna Lown lowered herself toward a kitchen stool, moving slowly as befitted her bulk, a cigarette aslant at the corner of her mouth. He opened the lone piece of luggage but found that only half his things could be pressed and kneaded into the locker. The rest he left in the suitcase, which remained unclosed at the foot of the bed. Then he sat in the chair, not accustomed to free time, Lown's blouse littered with pale ash from her cigarette. Softly took his ease across the table, watching her thumb through a sheaf of papers, hair fairly gray and worn in an uneven page-boy cut, clear eyes set in a broad strong face, sedately aging woman, tank-driver of the neo-logistic school, her thumb accelerating the page count now.

"Where is he?"

"Cube one."

"Will he fold under pressure?"

"He's my protege, Edna."

"What took you so long?"

"Had to talk to someone about some questions bearing on incidental matters related to the project."

"We work in absolute privacy, Rob. I won't give an inch on that. Neither will Lester. This seclusion business was your idea. Now don't start bending."

"Edna-doll."

"You've got tendencies."

"We work without outside interruptions. That was and is my formal promise."

"When do we see him?"

"Anytime you're ready," Softly said. "Is that the latest notation work?"

"I'm not happy with it."

"Of course you're not happy. This is a revolution in the making. All science, all language wait to be transformed by what we're doing here. I am the leader. Nobody's happy until I'm happy and I won't be happy until we've finished what we've come to do."

The boy did not move when they entered his cubicle. Softly sat on the bed. The woman remained in the entranceway, examining the apathetic figure in the chair. She wore glasses with dark frames and round lenses.

"We expect this will be a long and intensely productive period for all of us," she said.

"I haven't even shut my suitcase. That's how long I'm staying."

"Events aren't influenced by one's wishful application of significance to commonplace objects. Whether your suitcase is opened or closed, we'll be here quite a while."

"This is a lady dentist talking."

"Behave yourself, Willy. I told you the fun's over. Edna Lown is here at my request, my entreaty, my urgent supplication. Learn from this woman."

"Naturally I'm familiar with your work," she said. "I detect a strong computational strain running through it. Not much sense of discrimination. Not much use for logic. Paradoxically yours is the kind of intellect we need. The basis of mathematical thinking is arithmetic. The whole numbers and how we use them. On the other hand the basis of arithmetical thinking is pure logic. We can trace the foundations of arithmetic to a handful of logical propositions. It seems to be the rule for top people to come to mathematical logic only after considerable work in other areas. That's nice. I like rules, regulations, formats."

"It seems to me if I remember correctly they got me here to explain a message from outer space. Do I keep on doing that too or do I just work on this other stuff?"

"You can play with the code in your spare time," Softly said. "If you sincerely feel the ARS extants are using a nondecimal system, attack it from that angle. I think what they're using is what we're looking for. A universal logical language. Help us develop that and the code will take care of itself."

The woman spat a grain of tobacco from the tip of her tongue.

"Mathematics is a model of precise reasoning, subject only to the requirements of an inner discipline," she said. "It's an annex of logic. Nothing more. All the rules of what we call 'number' derive from logical propositions. Logic precedes mathematics. And since the fundamental elements of logic have no content, mathematics has no content. Form, it's nothing but form. It stands on thin air. The symbols we use are everything. What they represent we discard without the slightest misgiving. The focus of our thought, the object of our examination, our analysis, our passion if you will, is the notation itself. And this is what our work will involve to a large extent. It's nothing you haven't done before really. The emphasis is on classes rather than numbers. That's all."

"Is that all?"

"I enjoy listening to my logic-mongers talk," Softly said. "They make the creation of an artificial language seem anything but difficult. Remember, Willy, the greatest work is both simple and inevitable. That's my final word for the moment. I'll leave you with Edna now. See you in a few pangs."

"What's that?"

"There's no day or night down here. The body makes its own time, usually very different from what we're accustomed to. Waking time we measure in pangs. Hunger pangs. Sleep time we measure in lobsecs. This refers to a Lester Bolin snore cycle. Lester's Edna's associate. The average full-length sleep is about half a dozen lobsecs."

"Don't you think that kind of talk offends adolescents?"

"Willy, if you think Edna is sensible, there's always Lester to contend with. I remember telling him once how interesting I thought it was that the first use of zero as a number probably took place a great deal earlier than the usual estimates would have it and in Indochina no less, where we can imagine a sort of common abstract boundary between the Taoist concept of emptiness and the Hindu notion of void. He flailed, literally flailed at the air."

"Of course, there was Cantor," the woman said.

"I'm late for an appointment."

"After all the breakdowns, depressions and seizures, after he died, finally, didn't they find in his papers a statement to the effect that mathematics can't be explained without a touch of metaphysics?"

"Juju mama mumblety-peg."

"Obviously I agree," she said. "I just mean it's curious enough to be interesting, not unlike your emptiness and void. What does our young man think?"

"If it's in his papers, I guess that makes it history."

"History is full of interesting things," Softly said. "It has no worthwhile statement to make to us, however, in our current preoccupation. We're permitted to deduce, at least at the outset, that everything is either a or non-a. What we're not permitted to do is say that everything is either the Great Wall of China or something else. In our present circumstance we don't even know the Great Wall exists. We've never heard of it. So let's forget about history."

 

I  GET  A  LITTLE  BACKGROUND

 

Edna Lown spoke for a time on the possible form an interstellar vocabulary might take. She pointed out that a "grammar" would have to be communicated gradually through the medium of radio signals of different wavelength and duration. It would be a step-by-step operation, the elements of our synthetic language defining themselves as they were transmitted and, we trust, deciphered. There would be no inconsistencies or exceptions to rules. As we formulated our cosmic discourse, basing it on principles of neo-logistic thought, we could make our transmissions increasingly abstract and difficult, assuming, we hope safely, that those on the other end had correctly interpreted previous transmissions. In this way we could progress from "a plus b equals c" all the way to a definition of "truth," if indeed this word is subject to definition. The radio signals in combination would be the equivalent of a set of ideographic units written in Logicon. Connectives, binding variables, arrays of signs gradually emerge from the radio noise. The concepts of "plus," "minus," "equal to," "is implicit in," "can be interpreted as" soon accumulate in a solid body of planet Earth knowledge. He sat in the chair listening to her as Softly emerged from the shaft, hurried across the catwalk and headed toward the metal ladder. In her room the young woman sat on her bed trying to make sense of the notes she'd written earlier in the day. She seemed to have trouble expressing anything resembling annoyance or frustration; all such displays were inevitably absorbed by her utter presentableness. Well-tailored pants and shirt. Trim figure. Roundish, soft and overpretty face. Whenever she gestured in the direction of vexation, the act automatically endowed itself with a glow of tomboyish pathos, much too adorable to be taken seriously. Hair coasting over the juncture of jawbone and ear, slightly upcurled, the palest of browns. Eyes overripe with sensibility. Softly was halfway out of his pants before he'd taken a couple of steps into the room.

"Let's go," he said.

"What is this, a nuclear holocaust copulation drill?"

"I'm in a hurry."

Softly seminude resembled a Roman sculptor's serious jest. He appeared ludicrous only to the extent that parts of his body were still bound in cloth. Elsewhere nothing was in miniature and it could be maintained, as now he removed the final stretchable sock, that naked he was even more imposing than when fully dressed, his chest fairly broad, his head more closely related in size to the rest of his appendages, an illusion fostered by the balancing factor of his sex organ, a piece of equipment that seemed to hold him together, structural bond and esthetic connective.

"Rob, I'm kind of busy."

"So am I, so am I, but I took time to come up here. You don't have to undress completely. Just give me something to aim at. A suitable accommodation."

"Unfunny," she said.

"Come on, let's get moving."

"These notes are all messed up. I can't read my own notes. How will I ever get a book out of this?"

 

SEE  LESTER   EXIST

 

Lester Bolin glanced at the envelope and strolled over to cube one, where his associate was saying that any civilization advanced enough to have constructed an apparatus for receiving radio transmissions from other parts of the universe would most likely be able to interpret any series of messages based on strict logic. In fact the artificial radio source extants would probably have less trouble understanding a message from Earth than we ourselves experience every time we try to decipher fragments of an ancient language found buried somewhere on our own planet. This seeming irony, she said, merely emphasizes the absence of logic in our spoken languages.

"In any case Logicon is not designed to be spoken. As we go along we'll doubtless see it reveal an innate resistance to being articulated."

"By humans," Bolin said, standing in the entrance.

"Lester's been working on an experimental thing. He believes he can get it to speak Logicon."

"Sorry I'm late, all. Cut myself and couldn't stop the bleeding for the longest time. Isn't there supposed to be a limit for that sort of thing? Coagulation? Doesn't blood clot on schedule or something?"

"How'd you do it?" Billy said.

"I was opening my mail with a long thin instrument consisting of a flat-edged cutting surface terminating in a handle."

"A knife?"

"If you want to put it that way."

"Lester's notion of a joke," Edna said. "Lester's a joker. Except jokes don't work very well down here. This is dead time. You can't cut it."

Bolin was a large man who gave the impression of being unmade. It wasn't simply that his clothing fit badly; certain items either missed connections with other items or were connected in the wrong way. The back of one trouser cuff was stuck in his sock. The reckless knot in his tie failed to conceal the fact that his shirt was fastened, starting from the top, with button a in hole b and so on down to his belt buckle. Part of his shirt was tucked into his shorts, the elastic band folded over his belt for an interval of several inches. His hair was thinning up front and he seemed to want to pat it often. Softly took a cigar from the little metal box. Minor rockfall on the north slope. Mushrooms, mosses, algae, phosphorescent fungus. The trancelike sleep of sated bats digesting upside down. Bolin stepped outside a moment, returning with a chair. Edna Lown stood a few feet to one side of the entranceway. The simple act of sitting was for Lester something nearly ceremonial, his rump and thighs settling ever deeper, investigating the chairness beneath them, and Billy felt this was a man intent on compressing every second in order to discover the world-point within, a serious man, look how he enjoys his sitting, watch his scraping feet, see him exist, a man (Softly mused, of sitting men in general) concluding an infinite sequence of states of rest to begin this period of self-limiting motion. Constant temperature, humidity, darkness.

"My husband, when we were married," the young woman said, "didn't recognize my handwriting. We never left notes for each other. We never wrote letters, even when separated for months. It was always dring-dring the telephone. Isn't that remarkable? What we've come to? His own wife's handwriting. My own husband's. Both ways it worked."

"Is that why your marriage broke up?" Softly said.

"We forgot to have fun. That's what happened. No kidding, we just forgot. There he goes. A fleeting figure in the dawn."

"And now you can't even recognize your own handwriting."

"I can recognize it all right. I know it's mine. I just can't read it. So don't draw full circles."

"Remember, you don't talk to anybody unless I give the word. Edna will not like this. It will take every last ounce of my massive powers of persuasion."

"Is smoking allowed in this crate?"

"I want you to straighten out those notes so I can have a look. That's the first order of business. Then you see my friend Terwilliger. Then we go back up. I don't want to push things. I need Edna's good will. This is a smuggling operation. You are being smuggled in. When you're finished interviewing the boy, you will be smuggled out."

"I'd rather stay in the antrum."

"You will be smuggled out," he said.

Serious people. No way no how, Billy thought, to avoid them in this setup. That one sitting inside his chair. The other one standing there in a blouse, a skirt and desert boots, her age and size wearing those tall shoes, not that you can blame her, this setup down here, not even any planks over the ditches. Envelope resting on Lester B.'s knees. Serious very serious. As Lester and Edna spoke of the discipline they would all have to exercise in order to succeed in this venture, Billy put his right index finger in his mouth and bit away part of the fingernail without detaching it completely. He then used this jagged fragment to scrape dirt from under the fingernails of the other hand. Eventually he reversed the process (left index finger, right hand), feeling good about the whole thing, partly because it seemed so ecologically sound. After a while he thought of his own funeral, another favored pastime, resorted to whenever his mood needed a boost, his self-esteem a measure of support. There he is in a heartrendingly cute casket lined with napped fabric, white and velvetlike. Everyone he's ever known shows up for the wake. They stand about solemnly, shopkeepers and doctors of philosophy, dozens of boys and girls, colleagues by the score. Their sorrow at his passing mingles with his own self-pity (as he watches). It's fairly obvious. There's not much doubt about it. Guilt. They feel guilty. What they feel is guilt. They bear this terrible guilt for not having treated him better, loved him more, valued his life above their own.

Jerks.

Inside the drained body little eruptions of rot are already taking place. What once was composed of water, fat, protein, minerals, skeletal ash and assorted fluids is at this moment undergoing structural alteration of the most extreme sort. Mulch, glurrk, wort and urg. Nameless wastes. He felt a slight weakness in his upper arms, which probably explained why this part of the death reverie failed to entertain to its usual degree.

"So what's it like," Lester Bolin said, "being a radical accelerate?"

"If that's what I am, it's the only thing I've ever been, at least as far back as the time I first knew what numbers were, so I can't compare it with anything else, which is probably in general the thing you're looking for, I mean more than, less than or equal to what it's like not being a radical accelerate, if I heard the question right."

"In its own way, a remarkably exact answer," Lown said. "Note the use of 'if,' 'only,' 'at least,' 'as far back as,' 'anything else,' 'probably,'

'in general,' 'more than,' 'less than,' 'equal to,' 'like,' and finally 'if again. Good to excellent answer."

 

LESTER TELLS US ABOUT ROB

 

"I'm lowering my voice, so watch my lips. Softly. What Softly's got is a nonhereditary child-size condition. Rare sort of thing. Diagnosed right from the beginning. He was an abnormally small baby, I mean really small, lopsided as well, badly proportioned. He said considering what he looked like in infancy and early childhood he's lucky to have emerged as a 'viewable' adult. Apparently the thing was caused by a chemical imbalance in the mother's womb. As I understand it, he's not a dwarf per se. He told me this himself. I never expected to hear this kind of intimate revelation from someone like Rob. The problem with his hips was there from the start. Part and parcel. One night he just sat himself down and told me the whole thing. I admire the man more than I can say. To have accomplished what he has under such negative conditions. Here, this was delivered to me by mistake."

He tossed the envelope on the bed and followed Edna Lown out of the cubicle. They stopped off in the kitchen, where Softly was pouring tea.

"So?"

"He has to get used to us," Edna said.

"He will in time. Any trouble develops, let me know and I'll work on it."

"How long have you known him?" Lester said.

"He's been at the Center for a couple of years. I first met him several years before that."

"What about your other friend?" Edna said.

"Who's that?"

"How long have you known her?"

"What other friend?"

"There's a young woman in your cubicle."

"She's sitting on your bed," Lester said. "Surrounded by sheets of paper. Sorting them."

"No problem."

"Who is she, Rob?"

"Journalist, she's a journalist. Extremely adept and very cooperative. Doesn't do anything without checking with me first. Comes to me for verification of every note, quote and so on. Will not interfere with the work. Will not make a nuisance of herself. She is no problem, believe me. I'm orchestrating the whole thing. Nobody gets anything out of this project that we don't want to give."

"She's writing an article, is she?" Edna said. "A sort of general background article on Logicon. Is that the idea?"

"Book, she's writing a book."

"Rob, I don't like this."

"It's a little book, Edna."

"What else has she written?"

"Little books," Softly said. "All her books have been little."

 

I  READ   MY  MAIL

 

Billy decided to take a walk around the area. He got up slowly, envelope in hand, and went along the crude lane that separated the rows of cubicles. There wasn't much here that he hadn't already seen when Softly led him in from the elevator. He didn't go more than a few yards beyond the protective barrier of crates and oil drums. From this short distance the units for living and maintenance resembled a secure campsite, the only source of light in the giant earthen bowl. He was aware of the presence of water. Somewhere up on the slopes water was running along bedding planes and joints. Maybe it was right under him too, dripping into hollows, seeping, cracking rock apart, collecting and finding outlets, only yards below, wells and falls, deep pools, wide living rivers. He sat on a rock and looked for the first time at the front of the envelope Lester Bolin had given him.

 

Consortium Hondurium

c/o Liberian Ship Registry Inc.

The Guano Exchange Tax Shelter

Liechtenstein

 

Mr. William D. Terwilliger Jr.

School of Mathematics

Center for the Refinement of Ideational Structures

Pennyfellow, Connecticut

USA

 

Please forward

The thought of mail depressed him. He would have to open the envelope and read what was written inside. It seemed so burdensome. Worse, it was bound to remind him of the task ahead. Linguistic fission. Less than the measured heft of ordinary language. Less than sentences and phrases. Less than words. Less than word fragments. Less than number words. Less than the customary signs and symbols. Less than the usual graphics.

 

Space Brain Computer Quiz WIN!    WIN!    WIN!    WIN!

Magnetized plastic symbols

 

May we congratulate you on the fact that we have selected your name from a carefully guarded mailing list of some of the world's most distinguished intellects and professional people, culled from hundreds of other lists. This makes you eligible to win an unlimited number of brightly colored redeemable plates embossed with precoded symbols. All you have to do is correctly answer the enclosed bi-level quiz questions designed and formulated by the world's most famous computer-the fantastic Space Brain!

 

Eerie and Uncanny

 

This phenomenal control-process system-more adaptable than anything in the eerie world of science fiction-has not only designed and preprinted the deducto-magic quiz on the enclosed quiz card but is programmed to scan and grade your personalized entry. If you are a selected

winner, your redeemable wallet-sired laminated plates will be enclosed

in next month's quiz. A dozen consecutive winning entries-one for each month of the calendar year-will entitle you to redeem your plates at one of our centrally located redemption centers in your color-coded area of the world. See map attached.

 

Pay-then play

 

Every statement on the enclosed quiz card has a pair of answers. SIMPLY CHECK THE BOX NEXT TO THE WORD THAT IS MOST LOGICAL. In order to play, you must first pay the preselected entry fee for your particular mailing list. This figure is computer-stamped on the back of your quiz card. All arrangements subject to the provisions of Space Brain leasing agreement. Void where voided.

 

ENCLOSED QUIZ CARD

 

Do not use numbers to indicate logical words. Simply check (x) the correct box. Only perfect solutions win. In the event of a tie, all entries subject to disqualification.

In a tricky situation it is your best friend, above all others, who would

find it easiest to__________you.

[  ] deceive    [  ] believe

The faster you run from nameless danger, the________you get.

[  ] queasier    [  ] wheezier

For one of tender years, it is best to approach life and its logical opposite, adult constructions both, with whatever degree of__________you can hurriedly muster.

[  ] fatalism    [  ] natalism

People who live in caves eventually go___.

[  ] wan       [  ] yon

The practice of __________ would be difficult to introduce into alien

cultures.

[  ] embalming   [  ] salaaming

The radio doesn't normally give listeners a chance to hear a__________.

[  ] chap snap    [  ] lune rune

Active people are __________ than people who just mope around feeling

sorry for themselves.

[  ] healthier   [  ] svelthier

Faced with temptingly equivocal data, the annotator immediately begins

to__________

[  ] validate     [  ] salivate

Being concealed, the woman's starring ______ was difficult to interpret.

[  ] role           [  ] mole

Some children have to be______into playing certain games.

[  ] coaxed      [  ] hoaxed

Logical thought is indispensable to __________ in the midst of this, the

most ambiguous of all possible worlds.

[  ] surviving   [  ] conniving

Amusing, isn't it, how it's always the most rational of individuals, positioned securely in the dark, beyond reach of even the faintest trace of sunlight, who refuses to entertain the notion that under these or similar

circumstances he'll ever be __________ by his own shadow.

[  ] heightened   [  ] frightened

 

After observing that the introductory bulletin accompanying the quiz card was stamped with the attesting emblem of a notary public, he made his way back to the cubicle, where a young woman was waiting.

"Hi."

"H'o."

Her visit was brief and the interview she conducted, although it had its opaque moments, was pretty easy to take. She rolled the TV table over to the chair and took notes as they talked. Billy sat on the bed, his back against the partition.

"I'm Jean Sweet Venable. I'm sure Rob's told you about me."

"Terwilliger, William."

"I'm sure you were warned about a writer on the prowl."

"Never heard of it."

"Rob gave me permission to research this whole project and eventually do a book. Sounds fairly intriguing, this Logicon business. The fact that someone like you is involved makes it all the more so."

"What's your question?"

"Do you calculate in longhand or on the typewriter?"

"I use a pencil."

"What are some of your other work habits?"

"I write in the dark."

"That's exactly the kind of thing I want."

"I write in the dark."

"Give me more like that," she said. "I pounce on stuff like that. I eat it up."

"Are you something Rob keeps on the side? Because it's fine with me but you have to understand he probably doesn't take this book you're doing too seriously. Wherever he goes there's something on the side."

"I'm fairly well known in my own right."

"For what?"

"My books."

"Have I heard of them?"

"So I don't think this is a case of somebody keeping somebody else on the side. Eminent Stammerers. That was my first. Got a fair share of attention considering the limited scope of the subject matter. I've done scores of magazine pieces."

"Anything else I might have read or know of someone who did?"

"The Gobbledygook Cook Book"

"Sounds familiar."

"Fourteen weeks on the list."

"Not bad."

"So I don't think, despite appearances, that this is a case of somebody not taking something too seriously."

"Keep believing it. I do."

"What's the essence of your work?" she said. "I want to know what happens inside your mind. What is mathematics? Poincaré talked about getting flashes. Do you get flashes? He also said, I think he was the one, that mathematics is the art of giving the same name to different things."

There was a trace of hoarseness in her voice, of lightly sanded cunning, somehow at odds with her appearance. Certain words she spoke seemed almost to vibrate with the kind of ironic connotation difficult to isolate from its sexual core. There was in addition an offhand and even cavalier element to her note-taking. She scribbled what he said. Line after line of catchpenny scrawl. Not even remotely legible. Maybe, he thought, she was just thinking ahead to the next question.

"What else should I ask?"

"I write using big letters."

"I like it," she said. "Now this business of deciphering what the ARS extants are saying. Is this being abandoned in favor of the Logicon project?"

"I am keeping going on it."

"You're a good subject," she said. "Give me some more like writing in the dark with big letters. Most subjects insist on telling me about every so-called fascinating job they've had since the age of puberty, or what good athletes they used to be, or the year they spent in a beach house in shorts. I much prefer the offbeat item. Give me more, give me more."

She liked to stand clutching herself as she talked. Hands under opposite elbows. Only one hand to elbow if she had a phone or drink in the other. Leaning back against the nearest large object as she talked. Sometimes her right foot scraping the floor. Her head sometimes tilted left. Jean believed in very little. All around her all her life people went around believing. They believed in horticulture, pets, theosophy and yogurt, often in that order, flickeringly, going on to periodic meditation, to silence and daunted withdrawals. Despite their belief in staying single they all believed in marriage. This was the collectivization of all other beliefs. All other beliefs were located in the pulpy suburbs of marriage. To entertain other beliefs without being married was to put oneself in some slight danger of being forced to be serious about the respective merits of these beliefs. Dishevelment would result. True belief. The end of one's utter presentableness. Recently ex-married, Jean had not yet detected flaws in her presentableness. But this was because she had not yet experienced the onset of the danger of belief. The links were thrilling if indeed true links, if more than mere envisioned instants.

"I think we should wear uniforms," Bolin said.

So, if she had been standing and talking, which she wasn't, being encamped by now in Softly's cubicle, "sorting impressions," trying to read "notes," there would have been on display some related version of that casual posture, that sleeveless V-neck sweater, that knit shirt, the acute crease in those flannel pants. Her husband had left without warning one morning. No hint since of whereabouts. All around her people accused him of cowardice. If willing to grant this, she realized she would have had to concede the corollary, that to live with her in wedlock required courage. (Is that really logical?) A certain marital valor. An intrepidity and grit. She didn't hate him, miss him or wonder where he was. Never a thought of some swell revenge. Among the things she didn't believe was that we learn from experience. Nothing of value accrued to her from the fact of his disappearance except for one insight, that there seems to be in men a universal mechanism, a preconscious warning hum that is activated upon mention of certain details of a woman's prior life. And so each man she met, on being told of her husband's sudden departure, would himself suddenly depart. It began to take on the rhythm of a biological cycle. All of them assumed she had made life unbearable. No doubt an expert in chaos administration. A magic-wielding bitch despite her utter presentableness. Discovery of the chromosomal hum did not interest her much, being useful only when she was in bed with someone she wanted to wake up in bed without, in which case she had only to remember not to go to sleep without first mentioning that one morning without warning her husband had left. All around her all her life all the others believed, forever attending classes to solidify old beliefs and obtain knowledge that would lead to new beliefs, grown people going to school for instruction in coloring with goo, in lifting the dress to sit on the pot, in spitting out buttons to prevent strangulation, believers, flickering.

"How are the notes coming along?" Softly said.

"Accumulating nicely."

"They should be ready by now. I want to see them when they're ready."

"I'm changing systems," she said. "It's just a question of switching over to this new system. Everything's in order. It just has to be sys-temized anew."

"Do it up top."

"I want to stay."

"Edna and Lester won't like it. They want absolute assurance nobody's hovering, nobody's listening, nobody's otherwise disturbing their concentration."

 

BILATERAL  SYMMETRY

 

It had been Bolin nonstop for a solid hour. Maybe more, maybe less, hard to tell. Billy thought he saw a light high on the southwest gradient, there and gone, a pale beam shifting. He was in his chair. Lester Bolin was sitting on the ground at the juncture of two partitions. Bolin on bilateral symmetry. Bolin on symbolic notation. Bolin on the subject of uniforms. Team jerseys with LOGICON sewed across the front. His left leg was bent at the knee, the other leg stretched out flat, and he ceased gesturing in accompaniment to his remarks only to raise his left hand from time to time in order to simulate a grooming motion over the scrubby tract above his forehead.

Exact correspondence of form and constituent arrangement on opposite sides of a dividing line or plane, Softly thought. He rejected the idea, never proposed, that there might be someone or something on the other side of an imaginary median line to match his parts and their relationships and into which he might theoretically flow. He was bundled into his bed, thumb-sucking, trying to stifle the chill that had penetrated his body on the most recent descent. Several blankets and a thick quilt. His thermal jammies. In the kitchen Lester was boiling water for tea. Edna was out near the barrier trying to get the shower to work properly. In cube one, the boy was unwavering in his marsupial sulk. Fill fill fill. Softly thumb-sucking made a series of tiny plectral sounds, as though pinching an inflated balloon. He felt a period of depression coming on. Arrival as scheduled. Activity and high excitement. Then this immense gloom. He consoled himself with the thought that it wouldn't last long and more pointedly with the clinical knowledge that a person afflicted with cyclothymia, the technical name for this condition, was known, of all things, as a cycloid. How utterly lovely. What depths of stability and equivalence. What splendid Einheit or unity. Day and night of manic-depressive psychosis. Sun, heat, maleness. Moon, shade, femininity. Bless all Celestials and may they dualize forever. Pangs and lobsecs. He took his thumb out of his mouth, stepped from bed, opened the briefcase that held his hand-washables, felt around among the underwear and socks and came up with a small cylindrical inhalator. It was trademarked NorOmCol and had a screw cap, which he removed in some haste. He fitted the device high into his left nostril and squeezed once, I went to a Chinese restaurant to get my laundry back, releasing a colorless vapor. Whoosh. Wonder what a microscopic view would resemble. Noradrenalin transmission appearing on the slide like a neon sea. Cells unable to reabsorb. Active brain, racing pulse. Is this stuff psychoto-mimetic is the question. Or is it "madness"-inhibiting? He put on an old robe and slippers, pondering which came first, state of mind or effect produced by chemical agent, his nostril pleasurably scorched.

 

I went to a Chinese restaurant

To get my laundry back

They served it up on the half-shell

Without the usual crack:

Yan tan hoakery poke

Bloody hum de dum

Divy tivy artichoke

You are it

 

He went into the kitchen, where Bolin was pouring tea for Edna Lown, who sat before an ultraviolet lamp. Waving off a cup of tea he circled the table a few times before climbing a stool near the entrance-way. Edna wore sun goggles.

"Laughter," Bolin said.

"What do you mean by that?"

"Ha ha. Just another way of saying ha ha."

"Why don't you simply laugh?"

"I am laughing. Ha ha. A sound indicating amusement or glee. Middle English ha ha. Old English ha ha."

Heterology refers to lack of correspondence between bodily parts, as in structure, arrangement or growth. An adjective is heterological if it denotes something that doesn't apply to the adjective itself. What about the adjective "heterological"? Is it heterological (this is Softly thinking) or not heterological? Let's work our way through the successive reflections of this logical dilemma. The mind that makes it to the other side needn't concern itself with bodily parts and whether they match or not. For isn't it true, historically (I permit myself to slip, this once, through my own blockade), that people have maintained a fascination for the subplot of erotic potential in small bumpy misproportioned men (not that I wish to exaggerate my own unevenness), perhaps suspecting us of possessing cyclic drives and impulses traceable to our more "natural" state of being; that is, our obvious lack of grace (which means, here, both effortless movement and divine favor, stressing the latter); or believing us capable of providing something deeply feared and longed for, nightmarish fulfillment, incubus asquat on the belly of a sleeping woman.

"Sign over Spanish barber shops," Lown said. "Algebrista y sangra-dor. Bonesetter and bloodletter. Trying to solve the flow."

The slope was dark. There were matches and candles in the pack, however. A crack of flame by the light of which a man might refuel a carbide lamp. At her desk Edna removed the heavy glasses she wore and then reached down and unlaced her desert boots. An unspoken sigh rose through her frame. The easeful stress of mellow bodies settling. Eyes closed now. Lips moving: broad-stroked Mayan lips moving slightly. What we conclude must be true in all possible worlds. True false. Tautological contradictory. Easier to reason without a sense of passing time. No systematically recurring event such as sunrise to provide a means of measuring an interval. Rest now rest. Continuous variable. Limit of an infinite sequence. Cut ever nearer the true value. Close in. Klõz in/n/n/n/n. Edna had grown children; that is, sons and daughters now adult, living with husbands, wives and real children in suburban Bellevue or some slight variation thereof. (Where's gramma, dad? She's living in a cave, shut up.) This piece of furniture was all that could be scavenged in the way of a desk, being a former chair taken apart and put back together by Lester Bolin inventively rearranging.

Despite the constant need for enterprise, the lack of material comfort, she liked it here. This was true work, what her life was all about, a summation, the terminating act of a long career that had often verged on greatness. The careers of each of them-Lester, Rob, herself-had proceeded along fairly similar routes, touching here and there, pausing to curl one inside the other, ever so lightly, never before this close to braiding together in a significant way. The atmosphere of crisis would prompt them to work harder and better. The lack of comfort. The imposed proximity. Rest now rest. It was all so enfolding. Across the fiction of pure space they studied each other intently, parents of their own bodies, listening to the listener, all gravid with formal deduction. She opened her eyes. Maurice Wu. And put her glasses back on. Yes rested well rested. Time to shake off the dross of ordinary language. Maurice Wu squatting in the guano fields. She heard Bolin begin to snore. What she found truly remarkable was the fact that it had taken her so very little time to adapt to these ridiculous living conditions. On a typewriter stand in Bolin's cubicle was an old Royal portable with a sheet of paper sticking up out of the roller. Set on the ground between the legs of the typewriter stand was a shortwave radio. Next to the stand and the radio was a small plastic desk. On the desk was a framed photograph of Lown and Bolin formally posed on a small lawn on some campus somewhere, each of them half turned toward the camera and half facing the other person, hands behind their backs, Edna's left leg extended a bit, Lester's right leg likewise set forward, the photographer's insistence on balanced composition (whatever the level of humor intended) evident most of all in the centering element of the entire picture, this being a waist-high twin-handled jug of indeterminate markings, each handle pointing (as it were) toward one of the standing figures. Above the radio, the stand, the antique machine, the desk, the photograph, draped across the full length of one partition, was a banner inscribed as follows:

 

BREATHE! GLEAM! VERBALIZE! DIE!

 

He completed the mixture, relighted the lamp, fitted it once again to

the miner's hat. He put his work gloves back on. He snuffed the candle.

He put the candle back in the pack. Getting to his feet he shouldered into the pack and put the hard hat back on his head. Besides the gloves, helmet and pack, he wore coveralls, kneepads, high socks and climbing boots. He carried a canteen and sleeping bag separately from the pack. After several heavy shrugs to redistribute the weight on his back, he began the long passage down the southwest slope to the tired lights at the floor of the antrum.

 

ROB  DOES  A  TRICK

 

Softly fully dressed went to cube one. He was thinking of Jean Sweet Venable aswarm in bedsheets hundreds of feet straight up. Of her works he had read only The Gobbledygook Cook Book, deeming it serviceably useless; a good example, in other words, of what he expected (and would demand if need be) of her current assignment. He found his protege in the stiff gleaming chair, sitting with legs crossed, a novel posture for the boy.

"Is there anything I can do to cheer you up?"

"Stand on your head."

Softly did this, fairly easily, not without first putting a folded towel on the spot where his head would settle. Showing little strain he righted himself. Then he sat on the towel, an act evidently requiring more effort than the headstand did.

"What else?"

"That's enough for now."

"I want you to be happy, Willy."

"I'm trying."

"We need you. You wouldn't be here otherwise. This is the most important thing any of us has ever attempted. Otherwise you wouldn't be here. Let's trust each other, you and I. A secret pact. Mutual love, trust and brotherhood."

"I trust you."

"Then why aren't you cooperating with Edna and Les?"

"I'm here when they want me."

"You have to show a willingness, an enthusiasm. This isn't some boring homework assignment in junior high. Show something. Make me proud of you."

"I'm here for the asking."

"You're a mathematician," Softly said. "You work till you drop."

"That's pretty much what Endor told me."

"Sure, sacrifice."

"The hole he's living in is equipped with a hole of its own."

"You have to put yourself on the line, everything forever, and you haven't been doing that, Willy. Let me tell you why we're lucky, you and I. Something you've never thought of. Size, our size, because of our size we don't have to pump blood nearly as far as most people. Most people have to pump to much greater heights. We save squillions of miles of blood-pumping effort. Don't have to worry about high blood pressure or arteries popping open. Cheery news, don't you think?"

"Does the outside world know about any of this?"

"The outside world? What do you mean by the outside world?"

"The people anywhere but here who might be interested in this project. Do they know what we're supposed to be doing here?"

"I don't know what you mean when you say what we're supposed to be doing here."

"I'll start with the way it's been happening up to now."

"Sure," Softly said.

"The signal from Ratner's star. The people who tried to figure it out before I got here. Endor leaving for the hole. My getting here. The events. My working on the code. My being told the signals are not coming from Ratner's star and that it's all because of a mohole. More events. The second signal the same as the first. Your getting here. The Logicon project."

"So what's the question?"

"Do they know about this out there? Other people in science? Does anybody know what's going on here?"

"Absolutely no one."

"How come?"

"Pressures, because of external pressures," Softly said. "The last thing we need is a whole bunch of people commenting, jumping up and down, making judgments. The last thing we need is coverage."

"Stand on your head," Billy said.

When he was seated again Softly took a newspaper clipping out of his wallet. He unfolded it and waited for the boy to reach over and take it.

"Meant to show you this earlier. Nothing very important. Just thought you'd like to see the kind of company you've been keeping."

 

Make Formal Prize Announcements

 

STOCKHOLM This year's Nobel Prizes were made official today after delays owing first to the local outbreak of hostilities and subsequently to internal disputes surrounding the awards for peace, economics and physics. The appropriate Swedish and Norwegian committees jointly released the official list without comment.

 

CHEMISTRY-Walter Mainwaring, Canadian; Cosmic Techniques Redevelopment Corp.; for research in exo-ionic sylphing compounds.

 

PHYSIOLOGY/MEDICINE-Cheops Feeley, Kurd; the Cheops Feeley Foundation; Field Experiment Number One; for developmental work in the scar-free implantation of microcomputerized electrodes.

 

ECONOMICS-No award.

 

PHYSICS-Orang Mohole, Austro-Mongol; Relativity Rethink Priorities Council; Sexscope Gadgeteer Inc. (consultant); Field Experiment Number One (visiting member); for theoretical work in the Moholean structure of the value-dark dimension.

 

MATHEMATICS-William Terwilliger Jr., American; Center for the Refinement of Ideational Structures; Logicon Project; for studies in zorgal theory.

 

PEACE-No award.

 

LITERATURE-Chester Greylag Dent, unaffiliated and stateless; for what the Swedish Academy described in its original announcement of the award as "recognition of a near century of epic, piquant disquisitions on the philosophy of logic, the logic of games, the gamesmanship of fiction and prehistory, these early efforts preparing the way for speculative meditations on 'the unsolvable knot' of science and mysticism, which in turn led to his famous 'afterthoughts' on the ethereally select realms of abstract mathematics and the more palpable subheights of history and biography, every published work of this humanist and polymath reflective of an incessant concern for man's standing in the biosphere and hand-blocked in a style best characterized as undiscourageably diffuse."

 

"How come they have me down for Logicon? I haven't been here long enough for any Swedes to know where I am."

"They made a routine request for information," Softly said. "As usual in matters pertaining to you, this material passed across my desk at the Center. All anybody knows about Logicon is the name. I had to account for Lester and Edna being here. Also for our absence from the Center. But nobody knows the actual nature of the project."

"But what if I said no I'm not going."

"I felt you'd trust me enough to come with me. Trust. Let's trust each other, Willy. Let's help each other be."

"I'll try."

"Incidentally I'm negotiating with Mainwaring. I want to get him here if at all possible."

"Who's that?"

"First name on the list," Softly said.

"Chemistry. Walter Mainwaring. Canadian. Cosmic Techniques Redevelopment Corp."

"He may be the only person in the world who understands the full implications of sylphing."

"How does that help us?"

"You never know, he might come in handy, somebody like that. We're negotiating now. I want him here badly. He's the last one I need. The final one-of-a-kind mind."

"Edna, Lester, me and him."

"Lown, Bolin, Terwilliger, Mainwaring and Wu."

"Who's Wu?"

"Oriental gent," Softly said.

Sooner or later he had to get up and go to the toilet. On his way back he heard his name called. It was Lester B,olin speaking from bed. Billy approached the entranceway of Lester's cubicle. He saw the banner, the photograph, the typewriter, the radio, the man himself, the narrow bed consisting of canvas stretched on a collapsible frame, the sheets and blankets at one end of the bed, bunched up, supporting Bolin's head. Lester wore a sport shirt and pajama bottoms.

"How do you like it down here?" he said. "Like it?"

"Hate it."

"Intensity," Lester said. "Everything's so concentrated down here. I'm having a great time. Want to go up with me later? I have some work to do on the model. Sources of power are handier up there. It'll be computer-driven. Parts will operate electromechanically on instruction from Space Brain. This is preceded and followed by an operation called logic rendering. The result, with luck, will be a control system that speaks Logicon. Of course we have to perfect the language first. That's our primary job. Take that paper out of the typewriter and look at it."

 

"What does it say?"

"If the word 'proof in this context applies only to arrays of sentences that make an assertion about an object language L, then in fact the proof itself, as opposed to the word 'proof,' shall be evident only in terms of the language M, or metalanguage, in which we draw necessary conclusions about the object language L, this method M also being subject to formal study through investigations carried out in M prime, or meta-metalanguage, the purpose being to preserve selectness by using only those statements that consistently refer to themselves," Bolin said.

The boy went back to cube one and got into bed. Isochronal rock-falls. Cave openings all along this route. More guano for my artifacting. The caves set into the slopes of the excavation contained a number of megaderma, or "false vampires." These were cannibal bats that rampaged among the roosting species, all of which were covered with tiny bloodsucking insects which themselves provided asylum for even smaller parasitic blood-fleas. Whole lot of sucking going on. Which could be the reason, thought Wu, why medieval gnome-worshippers in the mountains of central Europe believed that the crystal mixture of hydro-magnesite and water possessed distinct medicinal properties and may have been right, they might, for wasn't it used centuries later to stop the flow of blood? Moon milk. Dehydrating agent and coagulant.

 

EDNA   GETS  ANNOYED

 

"I don't know what to call you," he said. "What do you want to be known as?"

"Mrs. Lown."

"Maybe I'll get out of bed later and come talk to you. Right now I'm in bed."

"We have work to do."

"Being in bed is the work I'm doing right now."

"Don't be smart."

"I think I have a fever."

"I'll leave this material on your desk," she said. "Then I'll come back for it."

"What's the point of that?"

"I expect you to read it in the meantime."

"How will you know if I do or not?"

"Really this is childish."

"I could fake it," he said.

"You've no reason to behave this way."

"Okay, I'll read it."

"We're professionals, after all."

"I'll read it right away."

"Please read it," she said.

"I will."

"Do you really have a temperature?"

"They're common for my age," he said. "Growing takes place with a fever."

"That's quite a stack of reading you've got before you. I'm afraid you have to put up with my handwriting. If your eyes get tired, close them.

As long as your eyes are closed, you might as well sit in front of the radiation lamp Lester Bolin brought on down. It compensates for lack of sunlight. You can borrow my goggles if you promise to return them."

"What does Lester Bolin want to be known as?"

"Mr. Bolin," she said.

Once she'd been a character in a novel. How distressingly strange it was. The woman in the book wasn't like her at all, at all. Yet she'd recognized herself immediately. Such essential differences. The name he'd given her. Impossible to think of herself with a name like that. The one word of dialogue he'd written. Nothing at all like something she might say. But she'd seen herself at once. Jean Sweet Venable. The mind of the character was completely unlike her own. The clothing. The body. The mannerisms. A carefully wrought set of individual mannerisms. Carefully. Wrought. But they weren't hers, you know? No resemblance whatever. Still, she'd seen herself at once despite the differing circumstances, setting, dialogue, mind, body, clothing and mannerisms. What was it he'd done to bring her face to face with this representation she tried so forcefully to deny? How did he manage it? Son of a bitch. What did he know? Nothing more than anyone could learn by sleeping with someone. My star-shaped mole. That was the only thing she'd recognized as being literally hers. The character sat in cafeterias. The character was disheveled. She sat at tables still wet, bearing the elliptical traces of a washcloth. People talked to themselves. They pushed food into their mouths with their hands, pecking at their own fingers, never less than watchful of the possibilities of theft and death, poised cunningly over free glasses of water. They all carried shopping bags. The character was surrounded in her cafeterias by men and women with shopping bags and none of them shoppers, none at all, not one. It said so in the book. Collectors. Epicures of refuse. People tired and hungry after days of poking through trash cans. Collectors (talking to themselves, force-feeding) of bottles, cartons, bags, paper cups and other terminal necessities. Those without empty dented milk cartons will learn how foolish they've been when the time comes. Emblematic birthm?.n. on the buttock. This was the only thing, superficial or otherwise, he'd used as perceived. This and her inclination to predict. Jean loved to make predictions. On marriages, divorces, breakdowns, booms and crashes. It was not these similarities, however, but other things, merely superficial in the book and resembling nothing she'd ever said, done, thought about or looked like, these other things, it was these that impressed on Jean a sense of resemblance between her and the character based on her. How painfully strange it was, searching the pages for signs of her own persona. Surfaces, guise and conscious intentions. The kingship of printed fiction. Its arbitrary power. Its capacity to gain possession of a person or thing by ineradicable prior right. The character had fainting spells. The character sometimes sat all night in doorways. The character's underwear stank. The character was never far from the presence of ugliness, the physically ugly, from the plane of mis-shapenness. She, Jean, carried air-mail stamps in her handbag. She had a shoetree for every shoe. What did he know? How much and how? Son of a bitch bastard.

Softly pushing in and out.

Defenseless love is suicide. Under that open sky nothing falling survives the rigors of identification. Where once men and women sought communion in sexual love, innocent of the need for programmatic valuation, they now deploy themselves across a level of existence composed of silences and daunted withdrawals. The theme of modern love is isolation. No longer is the lover prepared to experience sentimental pain, that traditional embellishment that gives desire a degree of symmetry. We did not fall into the trap of matter in order to be redeemed by love and thrust upward into the world of pure form. Clearly we did not, she thought. No longer can lovers regard sex as the mysterious chrism of their life together, as nature partaken, the rayed balsamic flowers worn by a woodland god. Sex is painted on the very walls, spread on white bread. Lovers, then, once their secret language has been despoiled by synthetic exchange, are forced to disengage their love from biology and keep it in seclusion. What replaces erotic language? Oral sex, she answered brightly. Tongues wagging in appointed crannies. Lap, pal, left to right. Unsuspecting mouth devoured by the genitals to which it presumes to communicate its moist favors. Defenses must be built to save the lovers from what unfolds around them and then again within their love itself to shelter each from the other's patent treachery. What is defenseless love but an invitation to nipple-pricking pain? Knowing the rules, we all shout at the jumper to jump. On the other hand, she thought, love does not speak to theorists.

"Evil pelvis," Softly said. "Unscrupulously seductive mouth. Belly a bowl of fruit. Labyrinthine navel. Resilient milky thighs. Cute pudendum, hee hee. Lickable armpits. Predatory eyes. Surging breasts. Hair rare. Smile terribly foudroyant. Backside a-twinkle."

Maurice Wu unencumbered by equipment and heavy clothing crossed the path to cube one. He was still a fairly young man, slender, appearing cheerfully relentless atop a long informal stride.

"Unfunny, ass, and totally inaccurate needless to say."

"Call me names and see how far you get."

"I want to see Edna next."

"Next we do this."

"We just did that."

"We do it again."

"I'll settle for Lester."

"How lucky for me to be so crudely unattractive. What tinctures of wetness it loosens from your innermost loam."

"God how horrible."

"Admit it, bitch; my titmanesque frame, my gross and pettish mouth, collapsing jaw, unnatural skin pigment, my eye color; admit the jingle you feel. I kiss my own thumb every day on waking. Think what little chance I'd have as an idealized Hollywood dwarf. Get used to my lewds and moods, sweet Jean, foul runt and lecher that I am, because I control the flow of material and nothing of note gets said to the likes of a keen journalist like yourself without my considered okay."

"You don't have baggy flesh," she said. "It's baggy flesh I count on for my cheapest thrills."

"You think this is a lark, don't you?"

"You're firm, Rob. I give you credit, your age."

"You think you walk in here and just talk to some people and organize some notes and there it is, the whole story, all ready for the bookbinder's tools."

Bolin and Lown left their cubicles.

"This area of the world is rich in caves," Wu said. "Up on the slopes there are openings, if you look closely enough. Some of the caves they lead to are first-rate. Tons of guano. Just a question of burrowing under."

"You go in it and look?"

"Countless decades of accumulated bat shit."

"What do you find underneath?"

"In this particular excavation, nothing that goes back very far. Pottery and bones mostly. I've found stuff in other places that goes back so far your flesh would crawl."

"Fifteen centuries."

"Don't make me laugh," Wu said.

Bolin put the pot on, nodding to Softly as he passed. In the boy's cubicle Maurice Wu stood leaning with his elbow up high against the partition, hand on head.

"Understand you're running a fever, Willy."

"Hello, Rob," Wu said.

"Hello, Maury. Hi, Willy. Understand you're running a fever."

"It's not much."

"Starve it," Softly said.

"Okay."

"What do you think of Maurice?"

"I barely met him just now."

"What I value most about Maurice is this flair of his for syncretistic thinking. Sweet and sour pork. Diametrically opposed entities partaking of each other's flesh. It permeates all his thinking. The reconciliation of opposites. Childish and dumb but I love it. Did you read the notes Edna gave you?"

"It's like Weierstrass wanting to take things like continuity and limit and base them on the integers."

"I told you never mind that stuff, mister. Forget about historical figures. Pretend you never heard of those people, places and things. Besides it's not 'wire-strass.' Did you read the notes Edna gave you? Edna gave you notes to read."

 

I   GET  INTERVIEWED  AGAIN

 

Bolin was intent on composing the whole of Logicon on his old portable typewriter. Why not? If he and Edna and the youngster were sufficiently stringent in their methods, a handful of symbols would suffice. That plus the alphabet. More than enough to work with, ideo-graphically. This sort of notation would appear at times to resemble cartoon obscenities. Nevertheless the meanings and relationships concealed by ordinary language would stand out sharply. In normal times Lester lived with his wife in a converted barn. The horse stalls they'd turned into dinettes. The haymows were now sleeping lofts. They'd found a hand-cranked washing machine and made an end table out of it. Elevator descending. A plant stand was formerly a butter churn. They bought Tiffany glass for their spirit lamps. A Civil War whiskey barrel became a pre-Revolutionary soup tureen. Conclusions must follow necessarily. We must compel acceptance of conclusions.

"Did you know you'd get the prize?" Jean said.

"I had a hunch."

"Where were you when you heard the news?"

"At Rob's house."

"Give me more."

"I was sitting in a chair. He came in and told me. Then we shook hands."

"That's not too terribly interesting," Jean said. "Give me something better."

"That's what happened."

"I want better than that. You have to give me better."

"How come you keep riding back and forth? Why don't you just stay down here?"

"I'm not allowed," she said. "The logic-mongers might object. Come on, slyboots, give me some more."

"Rob said I wouldn't have to make a speech. Then he did this trick he does with turning his jacket inside out without taking it off. That's all that happened."

"I understand whenever Rob lectures at the Center, the place swarms with mathematics groupies."

"Who do you want to know about, me or him?"

"You're not giving me anything to pounce on. You were a better subject last time."

"Talk about pouncing, better not bring your husband around if you have one. Rob doesn't care what he says in front of husbands."

"Our marriage failed for lack of fun," she said. "Fun is the only way to survive. A marriage is doomed without it. Think of all the time you have to spend alone, the pair of you. You have to renew, renew, renew. It's time that wrecks marriages, obviously. For a long while we managed well. This is because we made sure we had fun. We played- tricks on each other. We stuck out our tongues. We called each other on the phone and used funny voices. These weren't necessarily impulsive acts. Often there was a great deal of premeditation involved. We thought it was essential to do these things and so we worked at it, we worked at it very hard, so very hard. And it was successful for the longest time."

"But then you ran into trouble."

"We used to scare each other a lot," Jean said. "Of all the kinds of fun, this was probably the one that worked best. Jumping out of doorways at each other. Pretending to be dead. Screaming into the telephone. I loved pretending to be dead. I was terrifically good at it. He was never completely sure it was just fun. There was always an element of doubt in his mind. When he'd lean over me for a really close look, I'd jump up screaming. That would keep our marriage going for another week."

"I'm surprised it wasn't longer."

"I know it sounds foolish. Between us, we totaled I don't know how many years of very expensive higher education. Still, we felt we had to do these things to keep from going stale, you know? One morning he got up and left as usual. He always left before I did. I can barely remember his face but I know he left early, he liked to leave early, he liked to be the first one in the building to hit the streets. That was the day I realized we'd had no fun in a long time and I knew at once this was the reason we hadn't been getting along. I made it a point to get home first that evening. Emptied a large bottle of aspirin. Hid the tablets. Put the bottle next to the bed. Got into the bed-torso nudo for documentary shock effect. I sprawled and waited, trying to look puffy. But he never came home. That was the day he'd decided to leave for good."

"Sure it wasn't sex that caused the trouble? Maybe you just never brought it out in the open."

"Sex was fine," she said. "It wasn't sex at all. Sex was the least and best of our worries."

"How many times a night?"

In the kitchen unit they worked and talked. Cigarette ash was scattered over Lown's blouse. She slipped her feet out of the desert boots and discussed Lester Bolin's latest work on notation, which she considered far too cumbersome, overburdened with content. It was pleasant to sit with Rob and Lester, exchanging ideas and objections, seeking to extend the technical possibilities of their method by making it ever more reductive.

"It's like doubling to get half," she said. "A negative number doubled yields half the original value. A series of doubled reflections gets continually smaller by half. I don't think we'll be rewarded with a sense of genuine precision until we get as close as possible to a kind of beneficially corrective infinite regress. Lester, I think you'd profit immensely by clearing your work through our young man."

"I showed him some stuff very recently. He just walked out. It seemed to depress him. I'm anxious to work with him but he just isn't interested. I wonder if we really need him. Do we really need him?"

"I'm reminded of a family that lives across the road from me in Pennyfellow," Softly said. "Years ago they adopted a very small child, an Asian girl, orphaned by the bombing. In a matter of days she became the focus of that home as none of the natural children in the family ever did. This is because she possessed something unique. Moral authority. Time and again I heard one member of the family chide another for piggishness, insolence, bad grammar, always saying in effect: 'What will Phan think of us when she's old enough to understand?' Remarkable, the sheer authority of that small round object. Because she was tiny, virtually mute, because she was Asian, an orphan, a victim of war, Phan was the ultimate moral force in that household, a living contradiction of nearly everything the family had once held to be eternal; that is, justice, truth, honor, so forth. Now I don't say my pal Willy is a moral force exactly. But I do believe his presence here has extramathematical significance. True, as Edna says, mathematical thinking is based on the whole numbers, Willy's specialty, and it's also true that his powers extend to related areas and that once he gets deeply involved in what we're doing here he'll probably put us all to shame, his mind working like a beam of light searching out a target. But Lester, when Lester asks whether we really need the boy, that's a valid point. After all, we're dealing with a form of mathematics that substitutes classes for numbers. This is what makes him reluctant to enter. He knows he may have trouble finding his way around. Nevertheless I maintain we absolutely need him. He's our living contradiction. His intransigence speaks against us. We need him to balance things. He's the listener, the person we need to judge what we do. This is the power of the young. They know what's right, if not what's left."

"It's unlike you to put things on a human level," Edna said.

"Does it erode my formal authority?"

"It's a pleasant change, truth be known."

"Jean Venable would like to spend some time with you and Lester. Journalist I told you about. Briefest of interviews. In and out. Give her a feel for the subject."

"Sorry," Edna said.

"Everything she writes crosses my desk."

"That's not the point."

"Lester-pet, what about you?"

"I don't think so, Rob, no. The last thing we need is that kind of distraction."

"I'm going back to work," Edna said.

"How's it coming?"

"Fair to good."

"The boy will respond," Softly said. "He's very young. These are strange circumstances. He'll come around. Wait and see."

Lacing her boots she thought how close they'd be coming in the final stages to the rudiments of primitive number systems. Repetition, order, interval. Lester's shoes were scuffed and battered and she could see them pressing into the earth, which was his way of thinking and working, a concentration downward. Softly's shoes were quite immaculate, set neatly parallel, almost touching, his feet swinging in little arcs several inches off the ground. She began to rise, cigarette in mouth, as Billy went through the handwritten notes she'd left him. The first phases of communication would center on the integers. The symbols that compose Logicon will eventually have to be receded in the form of suitable radio signals. What we have then, he read, is English to Logicon to radio-pulse idiom or systematic frequency fluctuations. The statement "every number has a successor" becomes asterisk-N (or some such) in Logicon; this in turn, pending advice from the technical end, becomes something like pulse-pulse-gap, the point being that with a few key modifications, a juxtaposition here, a repetition there, we can establish a scheme of affirmation and negation, assent and denial, giving simple "lessons" in number and following up with some kind of basic information as to where we are in time and space. The most likely thing we'd have in common with the ARS extants is interest in numbers and in celestial events. Earth people, who differ widely (spoken and written languages, etc.), share use of the Hindu-Arabic number system. Also it's instructive to note that calendar-making is one of our earliest cognitive labors and evidence of interest in lunar cycles, eclipses, so on. Strange, she thought, how the integers, which are discrete, and our attempts to chart time, which is continuous, may well combine to give us a common area of reference with extraterrestrials. However, if she correctly interpreted the remarks on Moholean relativity made by Softly some time earlier, it was plain that we here on Earth do not know the location of the artificial radio source. So either we must figure it out or wait for them to tell us. In fact she didn't really care whether we ever replied to the original signal. She viewed the Logicon project as an intellectual challenge and nothing more. An advance in the art of mathematical logic. A breakthrough in economy and rigor. The transformation, in Softly's phrase, of all science, all language. She had no strong conviction that Logicon was essential to celestial communication. It would be, in her view, a breathtaking addition to the body of human knowledge, period. As far as she was concerned it might be easier to step directly from English to radio-pulse idiom without an intervening form of discourse, no matter how strictly logical. Her handwriting began to collapse and he read only one more section, this being Lown's estimate of how the expression "a plus b equals c" might actually be transmitted. There would be a pulse followed by a double time interval to indicate an operation pending, in this case addition, the plus sign itself signified by a particular kind of beep or dash. Repetition, order, interval, she thought, continuing to rise from the kitchen chair.

 

FEMALE  HAIR  DOWN  THERE

 

He heard Lester Bolin begin the first snore cycle of this particular sleep period. His things, Billy's, were still divided between the footlocker and the suitcase and he didn't know and had no intention of finding out in which of these containers his pajamas were located. There was a single light in the antrum right now and it originated in the cubicle farthest from his, a periodic surge of candleflame, Softly's quarters, diagonally across the path. He heard a sound above the snoring, very faint at first, a gentle impact somewhere on the slopes, repeated more than once. He stepped out onto the path and immediately saw something come over the barrier and bounce several times, barely visible, its forward motion ending in the gravel and soft clay, the object spinning in place, a rubber ball, eating out a slot for itself, unmistakably a Spalding Hi Bouncer, still rotating as he walked toward it past Maurice Wu lodged in a sleeping bag in a corner of his cubicle, past Edna Lown motionless in her bed, past Lester Bolin asleep on his cot; a spaldeen, as it was commonly known, just an ordinary faded-pink rubber ball that had bounced down from the top of the excavation. He picked it up and turned toward the opening of Softly's cubicle, detecting motion in the shallow glow and knowing what it was before he actually sorted out the allusive shapes. Jean Sweet Venable was in bed with Rob, moving over and around him, uncomplexioned in the dimness, a fine-grained and purposeful figure. Billy was stilled by the sight of her. The very notion of "female hair down there" had long been a source of contemplative ache and wonder; to see it, actually set eyes upon a woman's pubic hair, filled him with a stunned hush, a reverence for the folklore of the body. But what they were doing now, man and woman, had no connection to beliefs, legends or culture. It seemed to him that the sex act was something no one could make up in a story. He watched reluctantly, afraid they would perform some variation of the act, assume a position of such deft fury that he might once again grow feverish, his mind and body unequal to the burden of sexual possibility. That people might do nameless things to each other caused him some concern; he did not care to witness the unimaginable, particularly as it applied to crypts and fissures of the body. For the moment, at least, the lovers remained within the limits of his own borrowed knowledge. It was hard work, sex. Jean was breathing through her mouth, Rob through his nose. They seemed to be striving toward something that existed beyond a definitive edge. Her legs were ill-adapted to this event, too long, the sole flaw in the composite. Odd how the force of Softly's physical innocence produced abnormality from model proportion. Jean's breathing became more rapid and she began to speak as though in tongues. It was here that the lovemaking abandoned its industrious manner, its claim to uniformity and craft, and started to resemble an act of appalling power, an incoherent labor meant to be performed in the dark or near-dark. He was in awe of what they were doing because they themselves seemed driven to it and lost in it. Her head at a slant, her body moving loosely beneath the impetus of Softly's more systematic cadence, Jean continued to utter fabricated babble, terrible for Billy to hear because he did not associate it with intensely compiled delight but rather with an obliteration of self-control and the onset of an emotional state that bordered on prophetic frenzy. There was no sequential meaning to this, no real process of thought and repetition. The sex act did not have organized content. It was unrelated to past and future time. It was essentially unteachable. It did not represent anything or lead necessarily to a conclusion, a sum, a recognition that someone or something has been part of a structured event.

No one could have made this up if it hadn't actually been known to occur, whatever it was, whatever the body's need for this brief laboring void. He began to back away now, Jean's voice winding down, Softly thinking:

 

Olleke bolleke Rubisolleke Olleke bolleke Knull

 

Back in cube one he tossed the ball into the open suitcase and sat in the chair. Bolin had stopped snoring and stared into the darkness directly above. He and his wife were the kind of people other people liked to describe as being devoted to each other. But he rarely thought of her now. She was in the converted barn and he was in the antrum.

"Say something."

"I thought you wanted me to shut up," Jean said.

"Then shut up."

Maurice Wu slowly dressed, thinking of the slopes, the bat caves set within the slopes, the guano fields spread across the bat caves. He hummed a smudge of breath on each lens of his spectacles, then wiped the glasses on his shirttail before slipping them on. Man more advanced the deeper we dig. This revolutionary thesis was beginning to develop urgency. He'd seen evidence of it in the field over the past several months -elaborately notated bone objects, increased cranial capacity. But the notion itself-that at a certain layer of soil the signs of man's increasing primitivism cease abruptly, to be replaced by a totally converse series of findings-this idea had been too radical to take firm hold in his mind until recently, when, in Softly's presence, he'd felt the first trifling stir of implication. Wu had assumed the entire series of layers had been disarranged by haphazard burial practices or some kind of earth spasm in the area of the dig. He realized, however, that the findings showed far too much consistency and sense of progression (however negative) to be explained away in this fashion. The indications were in the field. Man's mental development shows signs of surging upward as we dig past a certain point and continue down. Layer by layer there is evidence of greater complexity. Working in the area of the Sangkan Ho strata, he and his colleagues had traveled farther back in "primatial time" than anyone before them, a fact confirmed by potassium-argon dating. Eventually they'd come upon the partial skull of an adult hominid of small brain capacity and only the most elemental toolmaking skills. Considering what they'd previously found, the appearance of these remains was not surprising. But several feet deeper, and about half a million years earlier, were decorative tusk fragments. Below these were signs of fire maintenance, signs of complex tool types and weapons, signs of pottery making, signs of elaborate costumes. Below these was clear evidence of a culture versed in seasonal processes and number thinking. There were tools that bore lunar notations-systematic chartings of the phases of the moon. There were bone objects engraved with planetary observations. There were limestone slates that carried records of pregnancy and birth. All these patterns had been verified in the laboratory through microscopic analysis, the markings clearly indicative of a culture that perceived the notion of time itself as a nonrandom process that enabled humans to reckon their acts and conduct their lives against a fairly predictable setting of climate, geography and celestial event. Deeper, there were clay huts and drainage systems and below this was a flat stone that could not be clearly analyzed as decorative or notational; it was marked with a quartz engraving tip as follows:

 

Bats in flight, Wu concluded, pleased that the engraving suggested his avocation. Then it occurred to him that he might be holding the stone upside down. It was at this point that he was lured from the site by Softly's abrupt summons, later to be informed by colleagues that below the stone they'd found skull fragments, vertebral and pelvic components, hand and foot bones, teeth and an upper jaw-all of which pointed to a male "hominid" who not only had a brain capacity equivalent to modern man's but also (judging by his noncranial parts) resembled us in body size, manual dexterity, posture, locomotion and even the way he chewed his food. So it was that Wu speculated as he crossed the path to Billy's cubicle: what would the remaining levels reveal: bronze, iron, plastic, neoplastic? He entered striding.

"Tell me about mathematics."

"What's to tell?"

"I understand it's a crazy way to live."

"What are you doing here anyway?"

"Visiting," Wu said. "Saying hello."

"I mean here in the antrum. Rob has us here for different reasons for each person. What's your reason?"

"He hasn't told me."

"Why not?"

"I don't know."

"How will you find out?"

"He told me to ask Mainwaring when Mainwaring gets here. But he hinted Mainwaring wouldn't tell me either. Wouldn't or couldn't. I don't mind waiting. I like it here. I go artifacting and study the bats. Hobby of mine for years."

"What do you learn from bats?"

"Bat lore."