The slanting eyes, small and dark, turned inward again. Oriental or gypsy? Many Hungarians had Romany blood. Or was the doctor—all those experts he had consulted—wrong, and Paul Mongoloid?
Names, Kadar reflected bitterly. What did they mean? In mathematics, you called something a ring, a cycle, an ideal. What you named it was unimportant; all that mattered was its place in the structure—never things, but the relations among them; those were what counted. What was Paul’s relation to the world, now and in the future?
For the present, he was only a baby; in many ways, less than a baby. Mrs. Merrit was a kind, motherly woman; not intelligent; not educated; but warm. Paul obviously liked her, if he responded to anybody, which was doubtful. His normal expression, in an adult, often suggested profound boredom.
The professor thought about the tests—the endless, expensive tests. Colored doodads, blocks, strings, geometric forms to be matched—and the brisk, young men and women who presided over the rituals. Paul had confounded all of them; Kadar felt a perverse glow of satisfaction at the thought. The boy didn’t make mistakes; instead, he simply refused to cooperate. Of course, it was nothing to rejoice over. Apathy meant even more severe brain damage, the doctors seemed to think. And Paul’s electroencephalographs certainly were abnormal, suggesting those of an advanced epileptic.
The child nibbled at his lips again, making that tiny murmur in his throat. The eyes turned outward briefly, met Kadar’s somber gaze, then Paul slipped clumsily from the high stool and padded from the room, moving with the rather unbalanced gait of a sedentary elder.
* * * *
Off for some lunch, Kadar thought. Why didn’t Mrs. Merrit call the boy, instead of letting him set his own schedule? My fault, he told himself immediately. I’m letting her raise him, while I try to forget Eleanor—yes, and him, too—in my work. On the other hand, why impose disciplines on a child who never rebels? The sweet placidity of Paul was reflected in his childish routines. He ate whatever was given him—but only if hungry. He never cried; always lay quietly in bed when put there; and seldom got out until Mrs. Merrit came for him in the morning, although she mentioned occasionally, with some wonder, that he often was awake, stretched out under smooth bedclothes, with his eyes wide open.
Aside from that, his only quirk was the tall stool. At the age of two, he had already shown his preference for the flashy thing, climbing it to overlook Mrs. Merrit at her chores in kitchen and dining room.
Then, after the professor, acting on impulse, put the stool in his study, across from the big desk where he worked, Paul had come to prefer that location. Every day, for at least three hours, while Kadar scribbled away, the child sat there, sometimes apparently fascinated by the motion and hiss of the pen on paper, but more commonly with his eyes blank and unfocused.
Mrs. Merrit, naturally, thought this scandalous and unhealthy. For many weeks she tried to interest the child in a variety of toys, but without success. What the trained psychologists had been unable to accomplish, Kadar thought wryly, was not for a woman like his housekeeper to bring about between cooking and floor-mopping.
Even retarded children may be good artists. But when given crayons and big sheets of paper, Paul had made a few tentative dabs, very awkwardly, and lost interest.
The boy must at least get some exercise, Mrs. Merrit insisted, so the professor bought a jungle gym, and, to his surprise, Paul condescended to scramble about in the thing for half an hour now and then. But Kadar suspected it was that same urge to attain purely physical elevation—did the child seek a height equivalent to that of the adults around him? Was that the only break in his apathy?
Paul came back to the study, and approached the stool.
“Come here, son,” the professor said, moved to try establishing a relationship that always eluded him.
Meekly, in silence, Paul padded over. Kadar looked into the slanted eyes, searching for some kind of warmth. There were undoubtedly little lights inside, but they conveyed nothing to his understanding. He put one hand on the boy’s silky hair, ruffling it, and Paul stepped back—not alarmed, but somehow rejecting the act. The professor felt a sudden urge to hug him, but quelled it, he couldn’t have said just why. Paul went back to the stool, scrambled up in his queerly uncoordinated way, and sat there, lumpishly, his eyes again turned inward.
It came to Kadar, then, that Eleanor had sometimes worn such a look: an expression of deep self-communion. And yet—and yet—Uncle Janos had also looked that way often—Crazy Janos, who bungled everything he tried. Come to think of it, didn’t Janos have an Oriental cast of features, too? It was all so far back, and in Hungary; Kadar couldn’t remember. Besides, Janos died while his nephew was still a child.
The professor reached for a fresh sheet of paper, and began again, searching for the high road to Paradise. Fifty pages of the most advanced research—a new field of mathematics; a place beside Gauss, Abel, and Galois— hung on his finding that path. If a certain sequence converged to an irrational number, the key theorem and all that it implied was valid. And still the proof eluded him. Enough; enough; no more today; his head was on fire. Return with a fresh mind, like Poincare and the Fuchsian Functions; that was the only hope, now. But he knew it wouldn’t solve anything. Only a fresh approach, something revolutionary, could smash through the iron wall.
* * * *
Swaying a little, almost like Paul in his gait, Kadar left the room. He mixed a stiff Martini, drank it slowly, and felt some of the tension go out of his muscles. Mrs. Merrit hastily made him a hot snack; she was resigned to his behavior, and knew better than to try changing it.
“Tell me,” he asked her, “has Paul ever tried to say anything yet? Anything at all?”
“No,” she said, her eyes full of sympathy. “Just little noises in his throat. But he understands; I’m sure he understands. You know how good he is about doing what we tell him.”
“I know,” Kadar said darkly. “That’s hardly normal, either. No mischief; no rebellion; nothing. A vegetable— sweet, insipid; like a spoiled melon.”
And he thought of Eleanor—vital, alert, bubbling: beauty without slickness or affectation; warmth without sentimentality. This was the child not of Eleanor and himself, but Crazy Janos: that was a typical joke of heredity—genes and DNA and Janos ending in Paul Kadar, whose father had five paragraphs in “American Men of Science.”
He left most of the lunch untouched, and went back to the study. I won’t work, he told himself; but maybe just glance over the equations again. Let my mind refresh itself; no use to keep prodding it. Deep inside his brain a tiny alarm bell was ringing. What if the theorem is false? What then? Fifty pages of meaningless squiggles: a magnificent structure with no foundation.
He entered the study, and walked to the desk. The top sheet lay there, mocking him—but what was this? The last equation was crossed out, and above it there was a long line of pencil marks. Almost like mathematical symbols, but not—by God, upside down!
Bewildered, he reversed the sheet. For a moment the writing still seemed without content, then Kadar felt his heart contract like a clenched fist. A new integral transform—powerful, elegant, and startlingly original. It would crack the tough kernel of the problem as lightning shatters an oak.
He looked up, wild-eyed. Paul met his gaze squarely. The slender throat was working; the lips moved.
“Like that ... it has to be like that. Other way ... the pattern is ugly,” the boy mumbled, his voice a queer, high-pitched stammer, as if he had to claw the words out of a diaphragm never before used.
Kadar, still uncomprehending, stared at the writing again. Upside down—because that’s the way Paul, on his high perch, always saw the symbols. Their validity didn’t depend on how they were written, of course.
An illiterate might conceivably, while listing words, write a simple declarative sentence. With luck, he might even hit upon a compound one, perfectly grammatical. But what were the odds against his writing immortal poetry, like: “Rough winds do
shake the darling buds of May”?
Kadar looked at Paul again. The boy didn’t need blocks or crayons because his mind saw every concept with perfect and immediate clarity. Just sitting on the high stool, he had absorbed a complete mathematical education from Kadar’s work. Before that, he had overlooked Mrs. Merrit, but found nothing to stir his intellect. As for speaking, no doubt that, like his gait, was a matter of physique, and relatively unimportant to such a mind.
The professor felt a great surge of joy; yet, in a moment, it was tempered with sorrow. Paul was a monster, but a superior one. He was probably above—or beyond—love in the human sense. But their minds could commune, and maybe that was the best communion of all.
<
* * * *
A short time ago, I attended a dinner meeting of the literary society, PEN, at which the subject of the evening was “The Two Cultures.” Arthur Clarke, as one of the speakers, delivered an eloquent argument to the (mostly) editors and publishers assembled, on the status of science fiction as a bridge across the gap.
I think this is largely true. But listening, that evening and since, to scientists and science writers, and to literary-academic people, I have come to feel even more strongly, with Max Beerbohm, that, “There are not two cultures, only half-cultured individuals.” Happily, I have also seen an increasing number of individuals reaching out from their culture-halves to complete themselves. I think I should prefer to say that SF is an area where such people often meet—and more and more often, contrive to communicate.
Arthur Porges and Donald Hall, juxtaposed here, come from opposite ends of the academic range. Porges is a retired college teacher of mathematics; in literature, an admirer of Kipling, London, Mundy, Edgar Wallace, T. H. Huxley. Hall is a member of the faculty of the Department of English Language and Literature at the University of Michigan, and a former editor of the Paris Review.
What they both have to say, each one says very differently.
* * * *
THE WONDERFUL DOG SUIT
Donald Hall
Lester was terribly intelligent and only nine years old. He was especially good at mathematics. “Hey, Lester,” his father would say to him, “if
Lester would come back with an answer, quick as Jackie Robinson.
So when he graduated into the fifth grade at the head of his class, his Uncle Fred gave him a dog suit. It was the best dog suit you ever saw, and it fitted Lester perfectly. The minute he put it on you’d swear it wasn’t Lester at all but some big fat mongrel.
Lester worked over his dog act until he was very good. He taught himself to shake hands, roll over, play dead and everything. Then he learned how to bury a bone, lift a leg against a bush and chase cars. When he was perfect, he showed his parents and they were impressed. “You are a Wunderkind, Lester,” said his father.
“Bow wow,” said Lester.
Now when his parents had company, they asked Lester to get into his dog suit and fool everybody. He imitated a dog’s nyeh-nyeh-nyeh-nyeh-nyeh so that grown-up ladies would clap their hands and exclaim, “Oh, listen! He’s trying to talk.” He frisked and romped and they rubbed his ears. Then he would unzip his dog suit and step out of it, and everyone would be very surprised.
He liked his dog suit so much that he no longer studied all the time. “Lester is more of a normal boy now,” said his mother sadly. He took to putting on his dog suit after school and going out to play with the kids in the park. He chased balls or sticks for them. Sometimes he played tag or ran around the bases or wrestled. It was a lot of fun for Lester, who had never belonged to a group before. The kids thought he was a smart dog and petted him all the time.
One day in the park Lester heard some kids talking about him.
“Hey, this mutt doesn’t belong to nobody,” said one.
“What do you want, a reward?” his companion answered.
“Nah, I’m going to take him home.”
Lester thought it would be great fun to surprise the kid and his family when they took him home, so he went along. He played all the way, pretending he saw cats and things, and when he got to the kid’s slum-clearance project, it was someplace he had never seen before. He was lost.
The kid took him upstairs and into a kitchen. “Hey, Ma,” he said. “I brought home a mutt.”
“You get that frigging mutt out of here before I cut you open,” said the kid’s mother absentmindedly. Lester slunk off into another room with his tail between his legs. In the other room there was a man drinking out of a bottle who kicked Lester in the side.
Lester went out into the hall. He decided he didn’t like it here and that he ought to get out of his dog suit.
But the zipper was stuck!
He tried and tried, but he couldn’t make it budge. What could he do? Maybe if he went home his Uncle Fred could take him back to the factory. Anyway his mother could always call the fire department. But he didn’t know how to get home. He would have to ask the kid and his mother for directions.
He padded back to the kitchen. He laughed to himself as he thought how surprised they would be to hear him talk! As he came into the room he heard the mother say, “Okay, okay, okay. But he’s got to eat garbage and nothing but garbage.”
He said, “I realize this will come as a shock to you, but I am not a dog at all. I am a boy named Lester and I live at 2331 Hummingbird Crescent and I am entering the fifth grade next autumn. Uncle Fred gave me this dog suit but the zipper is unfortunately stuck. May I inquire directions to my house? I want to see my mother and father again.
The mother clapped her hands together and said, “Listen, he’s trying to talk!”
<
* * * *
Mr. Kagan will say no more about himself than that he is a graduate student of mathematics. I can add only that, in his first year of publication, two of his stories were selected for annual “Best” collections.
What follows is what I did persuade him to say something about. If your math, like mine, extends only to a vague familiarity with words like vector, tensor, set, and Riemann space, Mr. K’s glossary should help you determine where the mathematical facts leave off, and the fun-and-fantasy begins.
Metamathematics: Study of the underlying structure of math.
Nonosecond = one billioneth of a second.
Gogol: 10100 (10 with a hundred zero’s.)
Googolplex: (10100)100
Degenerate: (in math) a trivial or simple case—a point is a degenerate circle.
Isomorph(ism): A correspondence between two math systems which preserves structure.
Hausdorf Space: A “mathematical space” where any two points can be separated (“housed-off”).
Communitivity: The mathematical condition: a x b = b x a
Set: A collection or bunch
Class: A set
Group: A mathematical structure: e.g., the integers with addition as the operation.
Ring: A group with multiplication defined as a second operation.
Field: A group under addition and under multiplication, too.
Composing: Doing in a row: e.g., doing one operation, then a second, then a third.
Transformation: mapping a math structure from one place to another.
Orthogonal Transform: A transform that preserves lengths.
Inner Product Transform: A transform that preserves “inner-product.”
Degenerate Transform: A transform that doesn’t preserve anything in particular.
Well-Ordering Principle: Any collection of sets of a set can be ordered (but in a sequence).
Axiom of Zemelo: Assuming the well ordering principle.
Bolzano Weirstrauss Points: “Limit Points” of sequences—the values certain sequences of numbers approach infinitely closely.
* * * *
THE MATHENAUTS
Norman Kagan
It happened on my fifth trip into the spaces, and the first ever made under the private-enterprise acts. It took a long time to get the P.E.A. th
rough Congress for mathenautics, but the precedents went all the way back to the Telstar satellite a hundred years ago, and most of the concepts are in books anyone can buy, though not so readily understand. Besides, it didn’t matter if BC-flight was made public or not. All mathenauts are crazy. Everybody knows that.
Take our crew. Johnny Pearl took a pin along whenever he went baby-sitting for the grad students at Berkeley, and three months later the mothers invariably found out they were pregnant again. And Pearl was our physicist.
Then there was Goldwasser. Ed Goldwasser always sits in those pan-on-a-post cigarette holders when we’re in New York, and if you ask him, he grumbles; “Well, its an ash tray, ain’t it?” A punster and a pataphysicist. I would never have chosen him to go, except that he and I got the idea together.
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