“I, uh...I... Allow me to explain how I see it.” The others smiled ruefully at his attempt to sound mature, and the second son produced his famous jeering cackle, but the youngest forged ahead.
“I think this elderly gentleman must be a great mathematician. Yes, I’m sure of it. A great and renowned mathematician. A Doctor of Mathematics, naturally, and a world-class scholar. Mathematics is changing drastically these days, as I’m sure you’re all well aware. It’s going through a transitional period. This has been underway for the past ten years or so—since about 1920, to be more precise, or just after the end of the World War.”
It was painfully obvious that he was parroting, word for word, a lecture he’d attended at school the day before.
“If one looks back on the history of mathematics, one can see how the science has evolved in concert with the times. The first stage in this process came with the discovery of differential and integral calculus. That spawned what in broad terms we might call modern mathematics, as opposed to the traditional Greek variety. New territory had been opened, and directly afterward we had a period of, not refinement, strictly speaking, but expansion. That was the mathematics of the eighteenth century. As we move into the nineteenth century we find, sure enough, another rash of new ideas, and this too was a time of sudden change. To choose one representative figure, we might mention Gauss, for example. That’s G, a, u, double-s. But if we define a transitional period as a time during which continual, rapid change takes place, then the present is, indeed, a transitional period to end all transitional periods.”
This was of no use whatsoever—least of all as a story. The youngest son was nonetheless positively triumphant, convinced that he was beginning to hit his stride.
“Things have become extremely complicated. We are now awash in a deluge of theorems, and mathematics as we know it has reached a dead end. It has been reduced to a science of mere rote memorization. And the one man who at this crucial juncture has dared to stand up and proclaim freedom for mathematics is none other than our elderly professor. He’s a great man. Had he become a detective, he undoubtedly would have solved even the most difficult and bizarre case after nothing more than a quick stroll through the scene of the crime. That’s how brilliant he is. At any rate, as Cantor himself has put it,”—here we go again—“freedom is the very essence of mathematics. This is certainly true.
“Our word for ‘freedom’—jiyusei—was coined as a translation of the German Freiheit. But it’s said that the Japanese word was originally used in a strictly political sense and may not be an exact equivalent. Freiheit is a simple concept that means ‘not enslaved,’ ‘not subject to restraint.’ Examples of things that are not frei are to be found in any number of familiar places... so many, in fact, that it’s difficult to choose a single illustration. But take our telephone number, for example, which, as you all know, is four eight two three. How do we write it? With a comma between the first and second integers. Four comma eight two three. Now, if we were to write it with a slash, as they do in Paris—four eight slash two three—one could see the logic, but this custom of separating each group of three digits with a comma is nothing less than a form of slavery. Our elderly professor is making every effort to smash such corrupt conventions. He is a great man. Poincaré tells us that the only thing worthy of our love is truth, and I heartily agree. To grasp the truth in a concise and direct manner is the highest of human endeavors. There is nothing superior to it.”
So, what about the story? The other brothers and sisters were by now exchanging disconcerted looks, but the youngest son remained oblivious to them as he plowed ahead with his wobbly thesis.
“To enter the realm of empty academic theory is to run the risk of digressing from the point, but if I might ask you to bear with me for a moment, it so happens that I am currently engaged in the study of mathematical analysis, and since it is rather fresh in my mind, I should like to present a certain problem inherent in this field as an example of what I’m trying to say. These days it has become customary for treatments of mathematical analysis to begin with a discussion of the theory of sets—a questionable tendency in and of itself. Tradition, it would seem, can inspire in people an almost religious faith, and this sort of blind dogmatism has even begun to infiltrate the world of mathematics. It must be driven out at all costs. And that is precisely what our elderly professor has taken it upon himself to do—to rise to the battle against tradition.”
The youngest son was growing noticeably excited. Everyone else was bored to tears, but he had roused himself to a righteous fervor worthy of his elderly professor.
“Let’s examine the case of absolute convergence. In the past, ‘absolute convergence’ meant that a sum was conditionally constant irrespective of order or sequence—the operative word being ‘conditionally.’ What it means nowadays, on the other hand, is simply that progression series of absolute value must converge. It’s said that if progression series converge and progression series of absolute value do not converge, one can change the order of the terms to make them tend to an arbitrary limit, so it turns out that... that they converge anyway, so... so it’s all right.” Suddenly he was losing his grasp on the subject. He felt terribly alone. He thought of the textbook by Professor Takagi sitting on the desk in his room, but he could hardly stop here and go get it. Everything was explained clearly in the book. He was on the verge of tears. His voice faltered, his breast was trembling, and in a tone so shrill it resembled a shriek he said: “In short...”
The brothers and sisters all sat with bowed heads, giggling to themselves.
“In short,” he said again, suppressing a sob, “the problem with tradition is that it can cause even an error of great magnitude to go unnoticed, but there are a lot of problematic little details involved that we don’t have time to go into here. In any case, I would like to express my fervent wish for the publication of an introduction to mathematical analysis that has a freer point of view and is more accessible to the layman.”
And here the youngest son’s part of the story ended. What a mess. A chill had even fallen over the room. There was simply no way to continue the story, nothing to graft onto. Everyone seemed lost in morbid contemplation. The elder daughter, however, being the compassionate person she was, wanted to come to her youngest sibling’s aid. She stifled a final giggle, composed herself, and began to speak in a quiet voice.
“As the preceding discussion has amply demonstrated, our elderly professor is a man of lofty character. A lofty character is always shadowed by adversity. This is a rule with no exceptions. The old professor doesn’t fit in. Forever regarded as strange or eccentric by his neighbors, he can’t help but feel miserably lonely at times, and on this particular night he is, as usual, alone, as he picks up his walking stick and heads for Shinjuku.
“Our story takes place in summer. Great crowds of people throng the streets of Shinjuku. The professor presents a heartrending sight in his old, wrinkled, cotton yukata, with the sash tied high above his waist and the loose ends dangling down almost to his heels, like the tail of a rat. What makes things worse is that, although the professor is a man who perspires a great deal, he has forgotten his handkerchief. At first he wipes his brow with the palm of his hand, but this method proves no match for such a prodigious amount of sweat. It gushes from his forehead like water overflowing a mountain pool, streaming down his nose and temples, washing over the entire surface of his face, and dripping from his chin to his chest, and he feels perfectly wretched, as if he’s had a jug of sticky camellia oil dumped over his head. He finally begins to use the sleeves of his yukata, swiftly passing one sleeve over his face, walking a few steps, then surreptitiously doing the same with the other sleeve, and before long both sleeves are drenched. The professor is by nature indifferent to appearances, but this flood of perspiration is just too much for him, and at last he decides to take refuge in a beer hall.
“Inside, the air being pushed around by the fans is warm and damp, but at least his persp
iration subsides somewhat. The radio in the beer hall is blaring a lecture on current affairs, and suddenly the professor takes notice of the voice delivering the lecture. It’s a voice he’s heard before. It sounds like that weasel, he thinks, and sure enough, when the lecture ends, the announcer comes on to pronounce the name of ‘that weasel,’ attaching the honorific title ‘His Excellency.’ The professor wishes he could wash out his ears. The weasel is a man who studied alongside the professor throughout higher school and university—a calculating schemer who climbed to a lofty position in the Ministry of Education. Now and then the professor and the weasel have occasion to come face to face at class reunions or academic conferences, and each time they meet, the weasel heaps gratuitous derision upon him. He delivers a series of boorish, banal jibes, and although nothing he says is the least bit funny, the members of his entourage laugh uproariously at every word, all but slapping their knees. On one such occasion the professor kicked his chair back and rose to his feet in a rage but unfortunately stepped on an orange he’d dropped earlier, squishing it and allowing a startled, feeble shriek to escape his lips. ‘Eek!’ he cried, at which the entire company exploded with laughter. Thus the professor’s righteous anger ended in a sad and pitiful farce. But he is not about to give up. He’s determined to punch that weasel in the nose one day.
“Hearing his loathsome, grating voice on the radio has put the professor in a most unpleasant mood, and he gulps down a beer. Never having been one to hold his liquor very well, he grows tipsy almost at once. A young girl selling fortunes enters the beer hall. The professor calls her over and in a soft, familiar tone of voice says: ‘How old are you, dear? Thirteen? You don’t say. That means that in another five years... no, four years... no, no, in another three years, you can get married. Now listen carefully. How much is thirteen plus three? H’mm?’ And so on. Even a respected professor of mathematics can behave rather inappropriately when drunk. Now, however, having been somewhat overly persistent in teasing the girl, he realizes he has little choice but to buy one of her fortunes. The professor is not a superstitious man, but tonight, partially because of the radio broadcast, he feels somewhat vulnerable and has a sudden urge to consult the fortune as to what will become of his research, and where his destiny will lead him. When one’s life begins to unravel, one is tempted, sadly enough, to cling to the thread of prophecy.
“The fortune is of the invisible ink variety. The professor heats the paper with the flame of a match, opening his bleary eyes wide in an attempt to focus on the words as they appear. At first he’s uncertain what he’s seeing—it merely looks like some sort of design—but gradually the lines resolve into clear-cut characters written in a flowing, old-fashioned style:
JUST AS YOU WISH
“Seeing this, the professor beams. Well, no, ‘beams’ is hardly the word. Our noble professor erupts with a vulgar-sounding chuckle—‘Er, her, her, her’—then thrusts out his chin and looks about at the other drunken customers. None of them take any particular notice of the professor, but that doesn’t stop him from nodding to each of them and producing a series of silly laughs—‘Ha, ha. Just as you wish! Hee, hee, hee. Excuse me. Ho, ho!’—as he strolls serenely out of the beer hall, his self-confidence thoroughly restored.
“Outside, a slow-moving river of people flows over the street. It’s quite a crush. People jostling and shoving, all of them dripping with sweat but trying to look composed and indifferent as they shuffle along. They’re walking with no goal or destination in mind, to be sure, but precisely because their daily lives are so dreary they are harboring, all of them, some faint flicker of hope that compels them to stroll through the Shinjuku night with looks of cool composure on their faces. Walk up and down those streets all you like, not a single good thing will come of it. This much is certain. But happiness is being able to hope, however faintly, for happiness. So, at least, we must believe if we are to live in the world of today. Discharged from the beer hall’s revolving door, the professor totters and dives into the city’s sad current of migrant souls and is at once jostled and swept downstream, floundering and flailing as if he were drowning. Tonight, however, of all the members of this vast throng, the professor is quite possibly the one with the greatest confidence. The odds of his obtaining happiness are better than anyone else’s. Recalling his good fortune from time to time as he walks along, he smiles or nods to himself, or raises his eyebrows to give his expression a grave and dignified aspect, or makes inept and rather uncouth attempts at whistling.
“Then, suddenly, he collides head-on with a young student. This, however, is only to be expected. In a crowd this size, it’s natural that one will bump into someone else occasionally. Nothing comes of the encounter; the student merely walks on. But a short while later the professor collides with a beautiful young lady. Nothing comes of this either, though: she merely continues along the street. It is not yet time for happiness to arrive. The new development is to come from behind him. Someone taps the professor lightly on the back. This time it’s no accident.”
The elder daughter stopped there. She’d been speaking all this time with downcast eyes. Now she snatched off her glasses and began vigorously polishing the lenses with her handkerchief—something she always did when self-conscious.
The second son continued.
“I’m afraid I’m not very good at doing descriptive passages. Or, rather, it’s not that I’m not good at it, it’s just that it seems like too much trouble today. So I’ll keep this brief and to the point.” Such cheek.
“The professor turns to see a plump woman of about forty. She’s holding a small dog with a remarkably ugly face. The two of them have the following conversation.
“‘Happy?’ she says.
“‘Sure, I’m happy. Since you’ve been gone, everything’s fine. Everything’s, well, just as I wish.’
“‘H’mph. I suppose you’ve got yourself some young thing?’
“‘Something wrong with that?’
“‘Yes, there is something wrong with that. Didn’t you promise me that if I only gave up dogs I could return to you any time I pleased?’
“‘That’s not likely to happen, though, is it? God, this one’s a real horror. Just horrible. It looks like a creature that eats larvae or something. What a monstrosity. Ugh. It’s nauseating.’
“‘You don’t have to go all pale in the face for my benefit. Isn’t that right, Pro? Is the bad man making fun of you? Bark at him. Go on. Woof! Woof!’
“‘Stop that. You’re as contrary as ever, aren’t you. You know, just talking to you sends chills down my spine. “Pro”? What the hell is that? Can’t you come up with a name with a bit more class? Idiot.’
“‘What’s wrong with “Pro”? It’s short for “Professor.” I named him in honor of you. Isn’t he sweet?’
“‘I can’t stand this.’
“‘My! You still perspire as much as ever, don’t you? Goodness! Don’t wipe it off with your sleeve. How do you think that looks? Don’t you have a handkerchief? Your new wife must be an awfully careless person. I never once forgot to see that you had three handkerchiefs and a fan whenever you went out in summer.’
“‘I won’t have you finding fault with my hallowed home. It’s most unpleasant.’
“‘Well, excuse me. Here. Take this handkerchief.’
“‘Thanks. I’ll just borrow it for the time being.’
“‘You’ve become a complete stranger, haven’t you?’
“‘When two people separate, they become strangers. That’s just the way it... Wait... This handkerchief Sure enough, it has the same old... No. No, it smells of dogs.’
“‘What a thing to say. The fragrance brings back memories, doesn’t it?’
“‘Don’t be stupid. You know what your problem is? Ill breeding.’
“‘Me? What about yourself? Do you insist on your new wife babying you too? You mustn’t, you know, at your age. How do you think it looks? She’ll grow to hate you. Having her put your socks on you wh
ile you’re still in bed, and—’
“‘I told you I won’t have you finding fault with my hallowed home. Listen, I’m happy now. Everything’s going splendidly.’
“‘And do you still have soup in the morning? With one raw egg? Or two?’
“‘Two. Sometimes three. I have more of everything now than I did with you. I’ll tell you, when I look back, I get the feeling there can’t be many women in this world with a tongue as sharp as yours. Why did you have to yell at me so much? I felt like an unwanted guest in my own home. Dining ill and supping worse. I haven’t forgotten that. I was working on some very important research in those days, you know. You didn’t understand that at all. Nagging me from morning to night about the buttons on my vest, or my cigarette butts... Thanks to you my research, and everything else in my life, was a shambles. As soon as I split up with you, I ripped every button off my vest and started throwing all my cigarette butts into coffee cups. That was a wonderful feeling. Absolutely exhilarating. I laughed so hard, all by myself, that tears came to my eyes. But the more I thought about it, the more I realized how I’d suffered at your hands. Afterwards, I just grew angrier and angrier. Even now, I’m plenty angry. You don’t have any idea how to treat a person.’
“‘I’m sorry. I was young. Forgive me. I... I... Now I understand. The dogs were never really the problem, were they?’
“‘There you go, wringing out the tears again. That always was your way. Well, it won’t work anymore. Right now, for me, everything is just as I wish. See? You want to have a cup of tea somewhere?’
“‘I can’t. I...Now I understand perfectly. You and I have become strangers, haven’t we? No, we always were strangers. Our hearts were in different worlds, a thousand miles, a million miles apart. If we were together, we’d only be miserable, both of us. I want to make a clean break with you now. I... You see, I’m going to have a hallowed home of my own soon.’