That same day Törless asked the mathematics master for permission to call on him, in order to discuss some points in the last lesson.
The next day, during the noon break, he went upstairs to the master's little apartment.
He had gained an entirely new respect for mathematics, for now it seemed all of a sudden to have ceased to be a dead school subject and to have turned into something very much alive. And arising out of this respect he felt something like envy of the master, who must be on familiar terms with all these processes and relationships and who carried the knowledge of them about with him always, like the key to a locked garden. But above and beyond this Törless was also impelled by curiosity, though it was, to be sure, rather diffident curiosity. He had never before been in the room of a grownup young man, and there was a certain titillation in wondering what things looked like in the life of such a person, a different person, one who knew things and yet was composed and calm, 'it least so far as one could tell from the external objects surrounding him.
He had always been shy and withdrawn in his relations with both teachers and believed that as a result he was not particularly well liked by them. Hence his request, as he now paused in agitation outside the door, seemed to him an act of daring in which the main object was less to get some further light on his difficulties-for at the back of his mind he had already begun to doubt that he would get any-than to cast a glance, as it were, past the master and into this man's daily cohabitation with mathematics.
He was shown into the study. It was a long narrow room with a single window; near the window was a desk spattered with ink-blots, and against the wall was a sofa covered in some scratchy green ribbed material, with tassels. Over this sofa a faded student's cap hung on the wall, together with a number of photographs, the size of visiting-cards, brown and now grown dark with age, dating from the master's university days. On the oval table with the knock-kneed legs, which were of a would-be grace and prettiness that had somehow gone wrong, there lay a pipe and some leafy, crude-cut tobacco. The whole room was permeated with the smell of cheap tobacco-smoke.
Törless had scarcely had time to make these observations and note a trace of discomfort in himself, as on contact with something unsavoury, when the master came in.
He was a fair, nervous young man of no more than thirty, and quite a sound mathematician, who had already submitted several important papers to the academy.
He at once sat down at his desk, rummaged about a little among the papers strewn upon it (later it struck Törless that he had positively taken refuge there), then, crossing his legs, he began to polish his pince-nez with his handkerchief, and fixed an expectant gaze on Törless.
Meanwhile Törless had been scrutinising him too. He observed a pair of thick white woolen socks and saw that over them the bands of the underpants had been rubbed black by the blacking on the boots.
In contrast the handkerchief peeping out of the breast pocket was all white and dainty, and though the tie was a made-up one, it counterbalanced this by being as magnificently gaudy as a painter's palette.
Törless could not help feeling further repelled by these little observations; he scarcely found it in him to go on hoping that this man was really in possession of significant knowledge, when there was nothing whatsoever about either his person or his surroundings to suggest that it might be so. He had been secretly imagining a mathematician's study quite differently and as somehow expressive of the awe-inspiring matters that were excogitated there. The ordinariness of what he saw affronted him; he projected this on to mathematics, and his respect began to give way before a mistrustful reluctance.
And since the master was now shifting impatiently on his chair, not knowing what to make of this long silence and this scrutinising gaze- even at this stage there was already an atmosphere of misunderstanding between the two people in the room.
“And now let us. . . now you . . .I shall be pleased to tell you whatever you want to know,” the master began at last.
Törless then came out with his difficulties, exerting himself to make clear what they meant to him. But he felt as though he were talking through a dense and gloomy fog, and his best words died away in his throat.
The master smiled, now and then gave a little fidgety cough, said:
“If you don't mind,” and lit a cigarette, at which he took hasty puffs. The cigarette-paper-and this was yet another thing that Törless noticed and found incredibly sordid-at each puff became greasy and crumpled up, crackling a little. The master took off his pince-nez, put it on again, nodded . . And finally he cut Törless short. “I am delighted, my dear Törless, yes, lam indeed delighted-' he said, interrupting him, “your qualms are indications of a seriousness and a readiness to think for yourself, of a . . . h'm . . . but it is not at all easy to give you the explanation you want. . . . you must not misunderstand what I am going to say.
“It is like this, you see-you have been speaking of the intervention of transcendent, h'm, yes-of what are called transcendent factors.
“Now of course I don't know what you feel about this. It's always a very delicate matter dealing with the suprasensual and all that lies beyond the strict limits of reason. I am not really qualified to intervene there in any way. It doesn't come into my field. One may hold this view or that, and I should greatly wish to avoid entering into any sort of controversy with anyone . . . But as regards mathematics,” and he stressed the word 'mathematics' as though he were slamming some fateful door once and for all, “yes, as regards mathematics, we can be quite definite that here the relationships work out in a natural and purely mathematical way.
“Only I should really-in order to be strictly scientific-I should really have to begin by posing certain preliminary hypotheses that you would scarcely grasp, at your stage. And apart from that, we have not the time.
“You know, I am quite prepared to admit that, for instance, these imaginary numbers, these quantities that have no real existence whatsoever, ha-ha, are no easy nut for a young student to crack. You must accept the fact that such mathematical concepts are nothing more or less than concepts inherent in the nature of purely mathematical thought. You must bear in mind that to anyone at the elementary stage at which you still are it is very difficult to give the right explanation of many things that have to be touched upon. Fortunately, very few boys at your stage feel this, but if one does really come along, as you have today-and of course, as I said before, I am delighted-really all one can say is: My dear young friend, you must simply take it on trust. Some day, when you know ten times as much mathematics as you do today, you will understand-but for the present: believe!
“There is nothing else for it, my dear Törless. Mathematics is a whole world in itself and one has to have lived in it for quite a while in order to feel all that essentially pertains to it.”
Törless was glad when the master stopped talking. Since he had heard that door slam it had seemed to him that the words were moving farther and farther away from him . . . towards that other, indifferent realm where all correct and yet utterly irrelevant explanations lie.
But he was dazed by the torrent of words and the failure, and did not instantly grasp the fact that now he should get up and go.
So, in order to put an end to it once and for all, the master looked for one last, convincing argument.
On a little table lay a volume of Kant, the sort of volume that lies about for the sake of appearances. This the master took up and held out to Törless.
“You see this book. Here is philosophy. It treats of the grounds determining our actions. And if you could fathom this, if you could feel your way into the depths of this, you would come up against nothing but just such principles, which are inherent in the nature of thought and do in fact determine everything, although they themselves cannot be understood immediately and without more ado. It is very similar to the case with mathematics. And nevertheless we continually act on these principles. There you have the proof of how important these things are. But,
” he said, smiling, as he saw Törless actually opening the book and turning the pages, “that is something you may well leave on one side for the present. I only wanted to give you an example which you may remember some day, later on. For the present I think it would still be a little beyond you.”
All the rest of that day Törless was in a state of inward upheaval. The fact that he had had the volume of Kant in his hand-this quite haphazard circumstance, to which he had paid little attention at the time-now worked mightily within him. The name of Kant was familiar enough to him, though only as a name, and its currency value for him was that which it had generally among those who even remotely occupied themselves with things of the mind-it was the last word in philosophy. And this authority it had was indeed part of the reason why Törless had hitherto spent so little time on serious reading.
For very young people, once they have got over the stage of wanting to be cab-drivers, gardeners or confectioners when they grow up, in their imaginings are inclined to set their ambitions for life in whatever field seems to hold out most chance for them to distinguish themselves. If they say they want to be doctors, it is sure to be because some time, somewhere, they have seen a well-furnished waiting-room crowded with patients, or a glass case containing mysterious and alarming surgical instruments, or the like; if they dream of a diplomatic career, it is because they are thinking of the urbane glamour of cosmopolitan drawing-rooms; in short, they choose their occupation according to the milieu in which they would most like to see themselves, and according to the pose in which they like themselves best.
Now, in Törless's hearing the name Kant had never been uttered except in passing and then in the tone in which one refers to some awe-inspiring holy man. And Törless could not think anything but that with Kant the problems of philosophy had been finally solved so that since then it had become futile for anyone to concern himself with the subject, lust as he also believed there was no longer any point in writing poetry since Schiller and Goethe.
At home these men's works were kept in the book-case with the green glass panes in Papa's study, and Törless knew this book-case was never opened except to display its contents to a visitor. It was like the shrine of some divinity to which one does not readily draw nigh and which one venerates only because one is glad that thanks to its existence there are certain things one need no longer bother about.
This distorted relationship to philosophy and literature in due course had its unhappy effect on Törless's development, and to it he owed many of these miserable hours. For in this way his ambition was diverted from the subjects to which he was really most inclined; and while, being deprived of his natural goal, he was searching for another, his ambition fell under the coarse and resolute influence of his companions at school. His inclinations re-asserted themselves only occasionally and shamefacedly, each time leaving him with a sense of having done something useless and ridiculous. Nevertheless they were so strong that he did not succeed in getting rid of them entirely; and it was this unceasing conflict that left his personality without firm lines, without straightforward drive.
Today, however, this relationship seemed to have entered a new phase. The thoughts that had just caused him to seek in vain for enlightenment were no longer the baseless concatenations produced by the random play of his fantasy; on the contrary, they created upheaval in him, holding him in their grip, and with his whole body he could feel that behind them there pulsed an element of his life. This was something quite new for him. There was within him now something definite, a certainty that he had never known in himself before. It was something mysterious, almost like a dream. It must, he thought to himself, have been very quietly developing under the various influences he had been exposed to in these last weeks, and now suddenly it was like imperious knuckles rapping at a door within him. His mood was that of a woman who for the first time feels the assertive stirring of the growing child within her.
He spent an afternoon full of wonderful enjoyment.
He got out of his locker all the poetical scribblings that he had stored away there. Taking them with him, he sat down by the stove, where he remained quite alone and unseen behind the huge screen. He went through one copy-book after another, afterwards slowly tearing each into small shreds and throwing the pieces into the fire one by one, each time relishing the exquisite pathos of farewell.
In this way he meant to cast away all the impedimenta he had brought with him from earlier days, just as though he must now travel light, giving all his attention to the steps that had to be taken, on into the future.
At last he got up and went to join the others. He felt free, able to look at everything squarely. What he had done had actually been done only in a quite instinctive way; there was no surety that he would really be capable of being a new person now, none at all unless the sheer existence of that impulse was surety. 'Tomorrow,' he said to himself, 'tomorrow I shall go over everything very carefully, and I shall get a clear view of things all right somehow.'
He strolled about the room, between the separate desks, glanced into copy-books lying open, at the fingers moving swiftly and busily along in the act of writing on that glaring white paper, each finger drawing along after it its own little brown shadow-he watched all this like someone who had suddenly waked up, with eyes for which everything seemed now to be of graver import.
But the very next day brought a bad disappointment. What happened was that first thing in the morning Törless bought himself the cheap paper-bound edition of the book he had seen in his mathematics master's room, and made use of the first break between lessons to begin reading it. But with all its parentheses and footnotes it was incomprehensible to him, and when he conscientiously went along the sentences with his eyes, it was as if some aged, bony hand were twisting and screwing his brain out of his head.
When after perhaps half an hour he stopped, exhausted, he had reached only the second page, and there was sweat on his forehead.
But then he clenched his teeth and read on, and he got to the end of one more page before the break was over.
That evening, however, he could not bring himself even to touch the book again. Was it dread? Disgust? He did not rightly know. Only one thing tormented him, with burning intensity: the mathematics master, that man who looked so thoroughly insignificant, quite openly had the book lying about in his room as if it were his daily entertainment.
He was in this mood when Beineberg came upon him.
“Well, Törless, how was it yesterday with the maths crammer?” They were sitting alone in a window-bay and had pushed the long clothes-stand, on which all the coats hung, across in front of them, so that all they heard and saw of the class was the rising and falling hum of voices and the reflection of the lamps on the ceiling. Törless fiddled absent-mindedly with one of the coats hanging in front of him.
“I say, are you asleep? He must have given you some answer, I suppose? Though I must say I can imagine it got him in quite a fix, didn't it?”
“Why?”
“Well, I dare say he wasn't prepared for a silly question like that.”
“It wasn't a silly question at all. I haven't done with it yet.”
“Oh, I didn't mean it like that, I only meant it must have seemed silly to him. They learn their stuff off by heart just the way the chaplain can reel off the catechism, and if you go and ask them anything out of turn it always gets them in a fix.”
“Oh, he wasn't at a loss for the answer. He didn't even let me finish saying what I wanted to say, he had it all so pat.”
“And how did he explain the thing?”
“Actually he didn't explain it at all. He said I wouldn't be able to understand it yet, these things were principles inherent in the mode of thought, and only become clear to someone who has gone on deeper into the subject.”
“There you are, you see, there's the swindle of it! They simply can't put their stuff across to someone who just has his brains and nothing else. It only works after he's spent ten years going thr
ough the mill. But up to then he's done thousands of calculations on the basis of the thing and erected huge constructions that always worked out to the last dot. What it means is he then simply believes in it the way a Catholic believes in revelation-it's always worked so nicely. And where's the difficulty, then afterwards, in getting such people to believe in the proof as well? On the contrary, nobody would he capable of persuading then' that though their construction stands, each single brick in it evaporates into thin air as soon as you try to get hold of it!”
Beineberg's exaggeration made Törless feel uncomfortable.
“I don't think it's quite so bad as you make out. I've never doubted that mathematics is right - after all, the results show that it is- the only thing that seemed queer to me was that every now and then it all seems to go against reason. And after all it's quite possible that that only seems to be so.”
“Well, you can wait and see at the end of ten years, and perhaps by then your brain will be properly softened up and receptive to it. But I've been thinking about it too since we talked the other day, and I'm perfectly convinced there's a catch in it somewhere. Come to think of it, you talked about it quite differently then from the way you're talking today.”
“Oh no. It still seems pretty dubious to me even now, only I'm not going to rush off into exaggerations the way you do. It certainly is thoroughly queer. The idea of the irrational, the imaginary, the lines that are parallel and yet meet at infinity-in other words, they do meet somewhere-it all simply staggers me! When I start thinking about it, I feel stunned, as though I'd been hit on the head.” Törless leaned forward, right into the shadows, and his voice was low and husky. “Everything was all so clear and plain in my head before. But now it's as if my thoughts were like clouds, and when I come to these particular things, it's like a sort of gap you look through into an infinite, indefinable distance. Mathematics is probably right. But what is this thing in my head, and what about all the others? Don't they feel it at all? How does it look to all of them? Or doesn't it look like anything?”