having become a grownup,
mature in every way,
and being the only one
who knows it.
His face resembled that of a bear cub, and the elder brothers and sisters in fact found him adorable and had always tended to pamper him. As a result of this treatment, he was a bit scatterbrained. He loved detective stories and from time to time, alone in his room, experimented with disguises. He’d recently bought a dual-language edition of Conan Doyle stories, purportedly for the purpose of studying English, but in
fact he was reading only the Japanese translation. He quietly suffered the tragic conviction that of all the brothers and sisters, he alone worried about their mother sufficiently.
The father had died some five years before, but there was no threat to their standard of living. Which is to say that they were a family of some substance. Occasionally they were all overcome with a suffocating sense of boredom, and such was the case on this particular day. It was a dark and cloudy Sunday. Summer was on its way, but first the gloomy rainy season must be endured. They’d all gathered in the drawing room, where the mother was dispensing apple juice to her five children. The youngest son’s cup was considerably larger than everyone else’s.
It was customary in this household for the brothers and sisters to relieve bouts of boredom by taking turns spinning out a collective story. The mother too sometimes joined in.
“Any ideas?” The eldest son swept a pompous gaze over the assemblage. “I’d like today’s protagonist to be a bit eccentric, perhaps.”
“Let’s make him an elderly man.” The younger daughter struck a hopelessly affected pose—elbow on table, chin on palm, forefinger raised to rest against cheek. “I gave this a lot of thought last night”—it had, in fact, just occurred to her at that moment—“and I realized that elderly men comprise the most romantic category of human beings. An old woman won’t do at all. It has to be a man. An elderly man can be merely sitting on a veranda, and that’s all it takes, it’s already romantic. Ahh...”
“An old man, eh?” The eldest son pretended to think it over for a moment. “All right, so be it. Let’s make it a nice story, though, full of sweetness and light. ‘The Return of Gulliver’ last time was a bit too dark. I mean... I’ve been rereading Brand recently, and I have to admit it makes my shoulders stiff. It’s just too harrowing.” A rare confession.
“I’ll go first!” The youngest son nominated himself in a shrill voice without bothering to pause and arrange his thoughts. He gulped down his apple juice. And then, slowly and deliberately, he began setting forth his ideas.
“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.