All the same, he begins to try persuading himself otherwise, looks for reasons why of course he won’t do it, and finds them, reminds himself of Weinberg and his “That’s what you think”—sheer madness! He hasn’t even been able to prepare for it, hasn’t revised the work they have done since the semester began, would be making straight for that Unsatisfactory if he went to school tomorrow. But come to think of it, Weinberg sits beside him, Weinberg is good at cheating, he’ll be able to get hold of something of Benda’s, one of his solutions to a problem, one of Weinberg’s; that will be enough, he may be able to solve one for himself, after all, he understood a lot of what they’d been studying about progressions and differentiations. In a few hours he has almost come to the conclusion that he’s not so totally dependent on his neighbours after all; if Mertens and Linke and Severin and Blank can solve these problems then so can he… What you’re saying is lazy, very lazy, my dear Gerber, because if that were so you would have nothing to fear from a supplementary test on your own later. You don’t know anything. You don’t know the first damn thing about it.
“Not the first damn thing!” says Kurt out loud, and the strong language makes him feel calm and peaceful for a brief moment. But then it all comes back to him, nagging him, won’t leave him alone; he tries to recite a few formulae from memory, the integral of x to the power of n times dx equals x to the power of n plus 1, x—whew!—n plus one, say the n plus one very fast, remember that, so that anyone can tell it all belongs together, otherwise it might be thought that you meant x to the power of n minus plus one, which would be a bad mistake—so what’s the formula? He repeats it as fast as he can… now then, Geeeerber! That’s what God Almighty Kupfer always did. He went up and down between the rows of desks, and after every word there was an endlessly long pause, he dragged out the final syllables; if he was at the back of the class he looked at the front, as if to choose his victim there, and then suddenly called the name of someone sitting in an entirely different place, or tapped the student beside whom he was standing on the shoulder with his forefinger; and the student, thus taken by surprise, naturally stammered and couldn’t answer, even if he had just memorized the formula fluently. During the pauses between Kupfer’s words—sadistic pauses, the students called them—some of the good mathematicians, those with nothing to fear, sometimes amused themselves by timing the length of those pauses with a stopwatch; the record to date was sixteen seconds, and it had gone like this: work out… (eight seconds)—in your head… (twelve seconds)—whaaat… and that pause lasted for sixteen seconds, and then Gerald had fallen for it, that was God Almighty Kupfer’s way… What was the formula? Kurt writes with his finger on the white bedspread:
if n is larger or smaller than minus one, and how does the second formula go?
But he can get no further; he traces the equals sign a couple of times with his finger, as if on the board at school, and finally, in a bad temper, turns the bedspread over. He wants to get it all out of his head.
But a decision has to be made; and he has to think again after all, and he can’t get to the end of his thinking, realizes that his thoughts are going round in circles once more. In addition, at last he feels very tired. Just before sleep overcomes him, he decides: if he wakes up in the morning early enough to get to school and take the test in comfortable time, yes, and if his leg isn’t hurting, not a bit—then he will take that as a divine judgement and he will go to school…
Only when Kurt saw the school building did it all come back to his mind, sombre and terrible: waking up at nine-thirty, his mother’s anxious questions, his answer, always the same, like a formula: quick, quick, I have to get to school or I’ll fail… and now he was really standing there, heart thudding, trembling in sudden fear: what he intended to do—and would do, for he was going through with it, wouldn’t turn back—suddenly seemed to him so incredible that he couldn’t believe it was true. No, no, it can’t happen, it’s impossible, the test is postponed, Kupfer is unwell…
But there lay the big blue exercise books, gaping at the air with a single rectangular eye.
The little note-cards had already been made out. Kurt recognized Ditta Reinhardt’s steeply sloping handwriting (so Severin had retired from the job of secretary) and read the words long familiar to him over a period of seven years, with only the Latin numerals for classes changed: High School XVI, 1st Semester, Class VIII, Name: Gerber, Kurt; Contents: mathematical tests—it was so cold and indifferent. Kurt opened his exercise book at random and found the poor-quality sheet of bright red blotting paper between the pristine pages of blue graph paper, one after another, open wide and ready. Suddenly hope came to his aid: as he is so self-sacrificingly doing his duty, he thinks, dragging himself to school while he isn’t well (the leg is hurting again), Kupfer will show clemency, will close an eye if Kurt tries copying from someone, will mark his work leniently, may even let him off the geometry test…
Kurt has arrived in the middle of break; he is greeted by only a few, and fleetingly by those few, the eighth-year students are short of time, feverish restlessness fills the whole room. Some students are pacing nervously up and down, replying impatiently if anyone addresses them, others are scribbling figures and letters on thin strips of paper in tiny, tiny writing; most of them are whispering formulae to themselves with their eyes closed, in tones of urgency, each on his or her own, and yet all bound together. The formulae are like magic spells, like prayers—and now Kurt knows what the scene reminds him of, something he recently read that occurs to him: it was about a pogrom in a synagogue, and there the congregation sit in fear, in terrible anxiety, waiting for the Cossack hetman to come in with dreadful news. Kurt can imagine them all bursting out weeping and wailing—but no, that probably won’t happen, after all they have “prepared” for the test, learnt their lessons, some are so sure of themselves that they even chat to one another—those are the experts, they inconsiderately talk out loud. Kurt listens: “And I know for a fact that we’ll all be getting different problems,” claims Klemm. “God Almighty Kupfer will bring along thirty-two papers with four different questions on each.” That doesn’t bother Klemm’s friends. “Let him!” says Pollak dismissively, and Schönthal says quickly, cuttingly, showing his teeth, “Well, if anyone has the nerve to try copying—” Then he feels Kurt’s eyes on him, ducks his head and makes a sign to the others. They look surreptitiously and with malice at Kurt, darkly afraid of that alien gaze; it makes them uncomfortable to see anyone who has the time and inclination to look like that now, they feel that such a glance comes from a place where all the mathematics tests in the world disappear into ridiculous insignificance—and that won’t do, it is bold, it is even impudent, arrogant, particularly from someone who would surely give much to be able to talk lightly in their own carefree manner…
The bell rings. They all fall silent for a moment, look up, startled, and then plunge headlong into their work again, as if under the lash. Now the stragglers arrive; some have been smoking, Kaulich is among them, then Benda comes in, quiet and thoughtful, taking long strides, and Weinberg as well. He expresses no surprise at seeing Kurt there, just smiles. “It will be all right.”
“But I haven’t done any preparation,” says Kurt, pointing to the students still revising hard around him; even now he has not been able to get anything into his head—then the door is opened, stands open briefly—there’s a breathless silence—careful—and in comes Kupfer.
The class stands in tense silence, like the silence it preserved in the first lesson of term. What now?
Kupfer sets about taking the register. Else Rieps, who always hands him the pen, shifts impatiently from foot to foot. Kupfer says, almost under his breath: “I take it the same as yesterday are absent? That’ll be Lewy, Nowak, Kohl, Gerber.” He writes quickly, in a businesslike manner. Else hasn’t noticed Kurt’s presence, she nods…
“I’m here, Professor Kupfer, sir!”
Kupfer looks up. And what a look. It slowly makes its way towards Kurt.
Impossible to describe the mixture of avid amazement, wily triumph and malicious expectation in it. “Well, well,” says Kupfer slowly, striking out the name Gerber in the register again. “So you thought better of it in time.”
“Yes.” Kurt has no idea where this is leading.
Kupfer nods. “There would have been unfortunate consequences for you if you had persisted with your fraudulent claim to be sick, thus missing the test.”
“It wasn’t fraudulent, and I’m here, Professor Kupfer, sir.”
“You don’t say so!” remarks Kupfer sarcastically. “I seem to remember that you were out and about in town in perfect health during lessons on Wednesday. And you were away sick on Thursday? And today you’re well again? Strange.”
Only now does Kurt see the trap. Kupfer is baiting him with malice aforethought: maybe he will yet be led to commit a punishable offence. He swallows all the retorts already on the tip of his tongue and says calmly, “I’ll bring a doctor’s certificate to school.”
Kupfer makes a dismissive gesture: “Yes, we know about that sort of thing.”
Some of the class are beginning to shuffle their feet impatiently. They are afraid of a long argument and, stimulating as that might be some other time, today every minute counts. Kurt says nothing.
“Well?” Kupfer tilts his head to one side and drums his fingers on his desk. At that, Kurt slumps forward, his throat swelling; something appalling is about to happen—but Weinberg has already grasped Kurt’s clenched fist under the desk, and he holds it firmly. His jaws are working, but otherwise his face shows nothing.
Making a superhuman effort, Kurt regains control of himself.
“I have nothing else to say, Professor Kupfer, sir.”
But Kupfer trumps him with his closing point. “You astonish me. Please sit down.”
Kurt drops back into his seat, shaking, his fists opening and closing. Weinberg claps him on the thigh and says—Weinberg always knows the right thing to say, he can turn a situation right round with a few words—says quietly, as he concentrates intently on writing “1st Maths Test” and the date in his exercise book, “The hell with Kupfer!”
Kupfer writes an Arabic numeral 1 on the board with a flourish. First question. So much for the prophecy that he was going to bring thirty-two different questions in order to prevent any copying. God Almighty Kupfer needs no such precautionary measures. That would look like weakness. Like fear of someone cheating. Kupfer and fear? No one cheats in Kupfer’s test. Not God Almighty Kupfer’s.
There are already several white letters on the blackboard. Mysterious signs, like those Chinese magic flowers that unfold in water. Does anyone know what they’ll turn into? Does anyone know the particular meaning of that letter x? x can mean so much! x is not just a letter of the alphabet or even a mathematical sign. x takes many forms. For instance, x can have a small number 1 under it, and then it is the co-ordinate of a point of intersection with the axis in the general equation of the circle. But x can also be arithmetical, for instance as a factor in an endless geometric series of the first order. For while the geometric series is pure arithmetic, the arithmetical method is pure geometry. And x is everywhere. There is no fraction line on which x will not thrive. x, in general, is a modest little thing. If you treat it properly, it will let you bend and twist it as you like, and then, out of the thousands of fruits it can bear, just the right one will fall into the lap of its careful handler. All ways pass through x. Without x there is no life. And if it wasn’t there from the start it is sure to come along later, forcing itself through a tiny crack in the calculation, crossing its spidery legs in peaceful enjoyment of its existence and waiting—often waiting only to be dismissed again, to be “eliminated”. And often waiting for something that is equal to it. There are factors whose whole purpose is to be equal to x. For love of them, you often have to fetch x back from infinity. It hasn’t been around all this time, there didn’t seem to be any necessity for its presence, but suddenly it comes along, with a little equals sign hitched to it, the team of horses pulling a carriage, and wants to be treated accordingly. That’s x for you. By what right? Why? To what end, for what purpose? Who gave it this rank? And why x in particular? And how is it established that x equals this and that? There’s something not quite right. There’s a gap somewhere. x starts out like an amusing toy, lending itself to all kinds of tricks, and then suddenly turns bitter and incomprehensible. x = . Equals what? Some quiet agreement? There are some people who don’t get asked. They were ignored when the agreement was being concluded. Suppose they now refuse to consent to it?
Only they can’t. Because x is stronger. Its extremities grow and bend, wind around the body and throat of the agreement, until they have acknowledged the existence of x and manipulate it as it demands.
And suppose they still won’t agree? Or they want to, but they can’t? Suppose they toil, sweating with torment and misery, in the iron embrace of the great unknown, and can come to no conclusion? Suppose they suddenly run out of breath?
Then… well, then they can always go and shoot a bullet into their temples out of a small black object resembling a trapeze with a half-ellipse attached to it, or they can drink some kind of fast-acting fluid from a cylindrical vessel, or they can put a noose round their necks and attach the other end to a rectangular window frame, or they can throw themselves on two iron rails tracing exemplary parallel lines and allow several massive wheels with a circumference of 2rπ to pass over them—death itself is an explicitly variable quantity, and even x is not so merciless as to prescribe one particular solution in this case…
All four questions were up on the board now, and intent expectation gave way to busy activity. All the students were keen to show that they were able to begin on the questions at once without pondering them for a long time. It was not a good idea to be visibly thinking. Kupfer might notice, and draw conclusions that were either wrong or, even worse, right. So activity was called for.
Kurt immersed himself in the exercises, wanting at least to try making something of them on his own. He soon gave up. Not one of the questions came from those areas of the subject where he was reasonably knowledgeable. No probability calculus, no differential quotients, no series. All integrals, by the look of it. And he had no idea, as he realized after briefly looking at the exercises, of the way to deal with them.
He let his eyes wander round the room. They were all working, except for Zasche, who was chewing the end of his pen with a vacant expression. Even Mertens and Severin and Hobbelmann were writing busily, drawing lines, scribbling on the wood of their desks. What were they doing? Where did all this briskness come from? It was alarming.
Weinberg was also writing. Kurt squinted at his exercise book in the row in front of him—he couldn’t see anything. A pang of fear that his friend might let him down overcame him. He craned his neck—
“Gerber! If I see that once again I shall confiscate your exercise book. Move to the corner!”
No, God Almighty Kupfer knows no mercy. He isn’t interested in the fact that Kurt’s mere presence here is an achievement in itself.
Meanwhile Weinberg is placidly writing on, as if none of it was anything to do with him.
“Zasche! You move to the corner too! You can drop these ridiculous attempts to dupe me. I notice everything. And now I don’t want to be disturbed any more.”
Kupfer leans back in his chair, takes a newspaper out of his briefcase, and immerses himself in reading it.
After a few minutes some of the students begin moving, surreptitiously at first and then, as Kupfer does not seem to notice them, more and more openly. Kurt watches what each of them is doing anxiously; so far as he is concerned, much may depend on their success.
Suddenly Kupfer raises his head—all the students freeze where they are at that moment—and looks enquiringly round the class. Has he seen anything?
No. Nothing. He simply says, “Quiet there!” and goes on reading. (Another teacher might have stationed himself by the wi
ndow at this point. Checking up on them with mirrors? God Almighty Kupfer can do without such simple tricks.)
Again, some time passes before work is in full swing again. But it is mainly the mathematical experts who are getting in touch with each other, full of chivalrous civility. There is unpleasant derision in the caution with which Scholz and Brodetzky begin conversing, probably about the more elegant calculation of an instance of volume, and beside them Mertens is shifting back and forth in growing fear—his early activity was just bluff, he hasn’t answered a single question yet—and as Scholz ignores him he is trying to pick up something from their quiet conversation. He does not succeed; the few words he hears lead him to no kind of conclusion, and he is pale with useless effort.
Kurt sees that there are only twenty minutes left. He clears his throat.
Weinberg nods three times and goes on writing. All Kurt’s senses are on edge—help ought to be coming now—then Weinberg leans to one side, just for a moment, straightens up again—and halfway between them a small note is lying on the bench.
Slowly, Kurt puts out his arm.
As he does so, he keeps looking at Kupfer so that he can spot the slightest danger.
But Kupfer is holding the newspaper, opened right out, in front of his face. Another few seconds, and Kurt will be safe.
His arm, moving little by little, comes ever closer to the note.
Mustn’t hurry, a hasty movement can ruin everything, his ruler could fall to the floor, or something else happen.
Another second. Kupfer is still reading…
Kurt has the note in his hand. Done it! And as slowly as he retrieved it, he brings it close to him. Everything is all right. He will pass the Matura.
The note lies in front of him. He carefully unfolds it, holding the refractory sides of the paper down with his spread thumb and forefinger. There are two of the problems on it, all complete and solved, he has only to write them down in his exercise book –
Young Gerber Page 9