“Where are you from?”
“United States.”
“Whereabouts?”
“Hundred Thirty-eighth Street.”
“I’ve heard of it.”
“Ever been there?”
“Never been there. Just heard of it.”
“Good and peeved,” she said. “All my life I did without. I launched my professional career so I could stop doing without. Doctor has a house with grounds. I always know when he’s trying to impress somebody, because that’s when he tells me to step off an elevator or get out of a moving vehicle. Business, industry and the corporation. Nothing under an executive vice-president gets into that office. We run checks so nobody can falsify their title. Doctor looks up their fannies and tells them they’re doing just fine. When we get their waste specimen reports back from the lab, he calls them up and says fine, doing fine, keep it up. If they’re out of town on business, he wires them about their specimens. Nice, fine, beautiful. He gives them encouragement. He praises their specimens. Oldest trick in the world but it always works.”
“I guess that’s how you get a house with grounds.”
“Always I’m the one’s got to make room, understand. But no point you and me swinging the heavy gloves. We got a long flight ahead. It’s doctor and the beard I’m peeved off at.”
“I’m not going back.”
“Mean to tell me you’re staying here?”
“I guess so.”
“You standing there and telling me plane or no plane you are not hot-trotting your body away from this locale?”
“I stay until somebody says leave, I guess. Nobody’s said anything as far as I know. I guess I stay.”
“That fazes me. It really does. That fazes my whole composure.”
“You think it’s that bad here?”
“It’s not a question of bad,” Georgette said. “An accident is bad, which I’ve been at a hundred before I went into private practice. This place is no accident, no. But it’s got such separate parts, seems like to me. Maybe it’s just too new. All I know is one thing doesn’t lead to another the way it should. I’m glad I’m going. I just wish this elevator had a button I could push so a light come on and we get out of here fast. See, that’s what I mean about one thing not leading to another. Whenever you have an elevator with no button to call it with, that’s when you wake up in the middle of the night with the menses cramps.”
The freight elevator descended and kept right on going. Through the gate they watched it pass their level. A few minutes later they heard it coming up. When it stopped finally, Evinrude was aboard. He still carried the torch he’d been holding when Billy had encountered him in the vicinity of the jagged hole. This time the torch was unlighted. Georgette unlatched the gate and they stepped into the elevator. Evinrude lifted a projecting handle, starting them upward. He gave the two passengers no more than a grudging nod before directing his attention to the floor between his feet. After a long climb he depressed the lever and the elevator came to a stop.
“You, the nurse, you step off. The boy stays until we reach his stop. Stand back for the moving gate, watch your step stepping off, walk don’t run.”
They ascended again, two of them, moving in remarkably smooth fashion considering the fact that this was a freight elevator and not the smaller vibrationless kind. “And so irrational numbers were defined as convergent sequences of rationals,” the manuscript had said. “The deft manipulation of such polar extremes, with resulting approximate values, may drive the purely logical observer to seal himself in a brickwork privy as a means of perverse defense against the cries of ‘poetic truth’ that so often accompany sequential definitions and (to cross the mathematical brink this once, and briefly) approximations of any kind.” Evinrude stopped the elevator, opened the gate and led Billy into a gigantic storeroom full of equipment.
“This is where we expect them to surface,” he said.
“Who?”
“The pigeons.”
“The ones released in the ceremony?”
“They flew through a hole in solid rock and from there either back out again or into a ventilation duct that leads up eventually into this storeroom. If they flew back out into the Great Hole, that’s not so bad. If they’re in here or en route to in here, that means trouble.”
“Didn’t anyone know this would happen?”
“They weren’t supposed to release pigeons,” Evinrude said. “The subject was raised at a briefing. It was determined no pigeons. We drew up guidelines. We went to great lengths. But they released anyway, so now we have to retrieve. I happen to hate pigeons. I can’t stand being anywhere near them. But it’s my job to retrieve so I’ll just have to submerse my feelings and go do it. All this because somebody ignored the guidelines.”
“Pitkin, I bet.”
“The duct’s over that way.”
“Why do I have to be here?”
“I need someone to help me deal with the pigeons. I didn’t have the wherewithal emotionally to ask someone my own age. Besides, children know how to deal with animals. Adults have grown too far from their origins to be able to confront animals on a nonpet basis. The duct comes out of the wall behind that long row of tables.”
They pushed through a dozen stacks of shipping containers. Deal with the pigeons, the man had just said. To Billy this sounded as though either a massacre or a bargaining session was in store. Evinrude still carried the unlighted torch, a circumstance suggesting massacre.
“So you do mathematics.”
“I’m the one.”
“The very word strikes fear into my heart,” Evinrude said.
“Mathematics?”
“It goes back to early schooling. The muffled terror of those gray mornings getting out of bed and going to school and opening up a mathematics textbook with its strange language and letters for numbers and theorems to memorize. I didn’t mind any other subject. But math struck terror. Everything about it. The sound of the words. The diagrams and formulas. The look of the book. Sometimes I find it hard to believe that humans actually do mathematics, considering what’s involved. It’s like a branch of learning in outer space.”
As they got closer to the ventilation duct, Evinrude carefully inspected the floor as well as every item of equipment within reach.
“I don’t think they’re here,” he said. “Because I’ll tell you why. Wherever pigeons are, pretty soon the shithing starts.”
“The what?”
“Pigeons are known for their shith.”
“You mean ‘shit,’ don’t you?”
“Did I say it wrong?”
“Definitely.”
“There’s not something called bullshith?”
“There’s no h at the end. There’s just one h and it’s near the beginning.”
“I should be standing here frankly amazed. I should but I’m not. Because I’ll tell you why. All my life I’ve been making little mistakes like that. ‘Shith’ is just one example. I guess I learned it wrong.”
“Where did you grow up?”
“In the outskirts,” Evinrude said. “With a volunteer family. I had no parentage of my own. I think this led to oversights in my upbringing. Little gaps here and there. I’m weak in some areas. No doubt about it.”
“Shit is universal no matter which language. Use my spelling and I guarantee you’re safe.”
They reached the duct. Evinrude flicked a switch, reversing the air current.
“If they were on their way this way they can forget it because once the air is flowing the other way the only thing they can do is relax and be carried back to the Great Hole. They’re on their way down. We got here in time. They haven’t surfaced. I definitely think that entitles us to something.”
A single pigeon stood about sixty feet to Evinrude’s right. Billy pointed it out to him. The pigeon began to approach, taking little pink-footed grip-steps. Evinrude held his torch out away from his body, then placed it gently on the ground, as though signifying his peacefu
l intentions.
“Why isn’t it flying?” he said. “I can accept their presence in the air. When they walk I hate them. I just want to crumple.”
“Then let’s leave.”
“Why isn’t it afraid? It’s walking right at us. I hate the way the head goes back and forth. They’re full of disease in case you didn’t know. Look at the funny steps it takes. They’re very famous for disease. Watch out for your nervous system in particular.”
“I’m going,” Billy said. “Goodbye.”
“I consider myself terrified. I’m consciously trying to inundate my feelings but so far no luck at all. I am really scared. I can hardly bear to look at its little head gliding forward and back, forward and back. I hate the way it walks, don’t you? Those scabby little feet. It’s definitely headed this way in case you had hopes.”
“I’m running,” Billy said. “If I were you, I’d do the same. Come on. Let’s go. Goodbye.”
“I don’t know how to run.”
“Come on, hurry.”
“I never learned,” Evinrude said.
“Everybody knows how to run. It’s easy. You just move your legs and then you’re running. The brain sends a message to your legs and all of a sudden you’re running. If you don’t hurry up about it, I’m leaving. Just move your legs fast. Get your brain to send the message. Everybody can run. It’s not hard. Try it and see what happens.”
The pigeon took several more pink steps.
“It’s not hard if you know how,” Evinrude said. “I don’t happen to know how. The subject of running is foreign to me. As a child I wasn’t taught how to run and I’ve never been able to pick it up on my own. It’s something I’ve always envied in other people, this marvelous ability to run.”
11
SEQUENCE
There were times when he felt the lure of a submoronic mode of being. During such periods his mind turned opaque, making it hard for him to perceive the simplest incentive. It would be easy, he believed, to spend a lifetime in this stateless zone. Content to be organic. Content to perform only monotonous tasks. Content to forsake coherent speech. The spirit that informed him would swiftly dwindle, replaced by the soul of a plant. In time he’d dispense with voluntary motion and the natural management of his body. Content to smell himself and dream of downy molds.
This feeling always occurred when he was on the verge of solving a drawn-out mathematical problem. It seemed to mean, nearing the end, that he preferred to abandon all the structural forms, the intersecting perspectives, the entire weightless system of exact relationships; discard it all in exchange for the scantest condition of existence.
The intuition of mathematical order occupied the deeper reaches of cognitive possibility, too old and indistinct for tracing, predating even the analytical scrapings of logic and language. Because his work’s natural tendency was to provide a model of his own mind, of himself as a distinct individual, he was puzzled by the lack of an adequate vocabulary for mathematical invention, by his inability to understand what made his mathematics happen. In retaliation, as it were, against the secrecy of his own constructions, he engineered a desire to subsist on minims of specific being. It was to this, the unknown self, that the basest nature was clearly preferable.
At the module he scribbled nonsense on a pad. This surprised him, this familiar indication that he verged on an answer, because it accompanied the solution of a problem that was anything but familiar, having (he was coming to see) none of the usual shadings and gradations. Sequence, form, unsuspected relationships were not really the issue here. But the process seemed the same as always. He could feel it happening, an emptying of both modes of consciousness, the asymmetric transmapping of fact and unorganized reality.
Beings that need no intervening substance to transmit their art, able to write with their fingers, laser-paint with eyes alone, creatures such would surely know this feeling, as of nature taking part in thought, the living brain that codes its own development.
He scribbled calmly, oblivious to everything but one emerging thought, feeling the idea unerase itself, most evident of notions, an idea with a history, scribbling, rule of ancient numeration. What breathless ease, to fall through oneself. Rudimentary being. Leaflikeness. A condition scaled down to noncomplex sensation. No, there was no way to name the process. Mathematical ideas exist between adjacent points on a line segment. He got up and walked around the room, unaware of sound and color and yet knowing, touching, seeing, hearing, breathing, sheer certainty, feeling it inside him, watching his own feet (what a funny word, hearing it, “feet,” for the first time) move him ever more surely around the room. Thus the simple answer surfaced, deprived at first of linguistic silvering. In the seconds that followed he knew it in words.
Notation by sixty.
That had to be it, a positional notation system based on the number sixty. He knew that thousands of years ago two systems of numeration were used in Mesopotamia. Decimal and sexagesimal. The latter used a base of sixty instead of ten. Because the Sumerians had divided the year into three hundred and sixty days, they found the number sixty to be a more workable base in their astronomy. Notation by sixty also had the advantage over the decimal system in all work involving fractions because sixty has more divisors than ten. The vertical wedge used in Mesopotamia to denote the number one was also used for sixty. In the decimal system a given three-digit number is a way of expressing a quantity in terms of multiples of ten. Schoolchildren know that the number three hundred and twenty-four means three times one hundred (or 102), plus two times ten (101), plus four times one (10°). In sexagesimal notation, the tens become sixties.
The message had been received in the form of fourteen pulses, a gap; twenty-eight pulses, a gap; fifty-seven pulses. He realized now that the total of one hundred and one units was not important. This total viewed differently, as one zero one, or binary number five, was equally unimportant. The fact that one, four, two, eight, five and seven are the digits of a recurring decimal had no significance whatever. The pulse total alone (ninety-nine) and the number of blank intervals (two) were also meaningless.
All that mattered was the original series of pulses: fourteen, twenty-eight, fifty-seven. In notation by sixty these are not three numbers but a way of expressing a single large number. To discover this number it is necessary only to multiply fourteen by thirty-six hundred (602), twenty-eight by sixty (601), fifty-seven by one (60°). What was being transmitted then was the number fifty-two thousand one hundred and thirty-seven.
A man stood in the open doorway.
This, in our terms, was what the extraterrestrials were communicating. Their natural way of expressing this quantity, since they used powers of sixty, was in the form of the number 14,28,57. There was no reason why an advanced civilization should use a place-value system based on ten. Maybe they’d overcome all the problems inherent in a sixty-system and used it to much greater advantage than we use the decimal method. Of course, it remained for Billy to discover the importance of fifty-two thousand one hundred and thirty-seven. Now that he knew how to interpret the transmission, he could begin the task of decoding it. What did the new value mean? Obviously this constituted the second half of the problem.
For an unreal moment he imagined that the man in the doorway was an extraterrestrial, here to confirm his arithmetic. But there was nothing very exotic about the man and when he introduced himself as Dr. Skip Wismer, a NASA consultant on loan to Field Experiment Number One, Billy thought it a mere coincidence (of the nonexotic type) that he was associated with astronauts. Wismer went on to explain that since he had to pass this way to get to the demonstration, he thought he’d stop by and pick up Billy.
“I’m halfway done with the reason they got me here for. I guess it’s okay to take a break.”
“How do you know it’s halfway?” Wismer said. “You won’t know where the halfway point is until you’re able to look back on the entire solution. Since you can’t know what’s ahead, you don’t know how much you’ve
done. This is plain common sense.”
“It’s a feeling. Very definitely says half. When I get it this strong I know it’s true.”
“You’re claiming in effect to be digging half a hole. Can’t be done, can it? Besides you’re not even supposed to be working on the code. The source of the transmission is what we’re primarily concerned with for the time being. In addition to which is the fact that the message was never repeated. Repetition in a case like this is essential. Without it, there’s no reason to believe the pulse array is correct. Not to mention the computer retrovert we’ve just run that indicates error in the receiving equipment. Probably the switch-frequency generator.”
“What’s this demonstration you mentioned?”
“The Leduc electrode,” Wismer said.
This didn’t sound very promising. But since there was nothing else to do right now, he thought he might as well attend. First there was something he was determined to get rid of, namely the large green pill that Orang Mohole had forced him to accept in his apartments on top of the armillary sphere. He knew if he carried it around long enough, it would get him into some kind of tricky situation. He excused himself, went into the bathroom, closed the door, lifted the top of the toilet tank, dropped Mohole’s greenie inside and was about to replace the porcelain lid when he realized something was floating in the water. It was a tiny cardboard matchbox. He took it out of the tank and slid it open. Inside was a tightly folded piece of paper, wet at the edges. He removed it from the box and unfolded it.
Dr. Skip Wismer led him over a footbridge high above a miniature recycled waterfall and then into a sector called Med Comp.
“Large questions come to mind,” Wismer said, “whenever I’m in the presence of someone with your kind of vast mental capacities. For instance, do you believe in someone or something larger than yourself?”