Tactfully, diplomatically, she renewed her negotiations with Carlo. The boy, she put it to him, had genius. It was the foreign gentleman who had told her so, and he was the sort of man, clearly, who knew about such things. If Carlo would let her adopt the child, she’d have him trained. He’d become a great maestro and get engagements in the Argentine and the United States, in Paris and London. He’d earn millions and millions. Think of Caruso, for example. Part of the millions, she explained, would of course come to Carlo. But before they began to roll in, those millions, the boy would have to be trained. But training was very expensive. In his own interest, as well as in that of his son, he ought to let her take charge of the child. Carlo said he would think it over, and again applied to us for advice. We suggested that it would be best in any case to wait a little and see what progress the boy made.
He made, in spite of my assertions to Signora Bondi, excellent progress. Every afternoon, while Robin was asleep, he came for his concert and his lesson. He was getting along famously with his reading; his small fingers were acquiring strength and agility. But what to me was more interesting was that he had begun to make up little pieces on his own account. A few of them I took down as he played them and I have them still. Most of them, strangely enough, as I thought then, are canons. He had a passion for canons. When I explained to him the principles of the form he was enchanted.
“It is beautiful,” he said, with admiration. “Beautiful, beautiful. And so easy!”
Again the word surprised me. The canon is not, after all, so conspicuously simple. Thenceforward he spent most of his time at the piano in working out little canons for his own amusement. They were often remarkably ingenious. But in the invention of other kinds of music he did not show himself so fertile as I had hoped. He composed and harmonised one or two solemn little airs like hymn tunes, with a few sprightlier pieces in the spirit of the military march. They were extraordinary, of course, as being the inventions of a child. But a great many children can do extraordinary things; we are all geniuses up to the age of ten. But I had hoped that Guido was a child who was going to be a genius at forty; in which case what was extraordinary for an ordinary child was not extraordinary enough for him. “He’s hardly a Mozart,” we agreed, as we played his little pieces over. I felt, it must be confessed, almost aggrieved. Anything less than a Mozart, it seemed to me, was hardly worth thinking about.
He was not a Mozart. No. But he was somebody, as I was to find out, quite as extraordinary. It was one morning in the early summer that I made the discovery. I was sitting in the warm shade of our westward-facing balcony, working. Guido and Robin were playing in the little enclosed garden below. Absorbed in my work, it was only, I suppose, after the silence had prolonged itself a considerable time that I became aware that the children were making remarkably little noise.
There was no shouting, no running about; only a quiet talking. Knowing by experience that when children are quiet it generally means that they are absorbed in some delicious mischief, I got up from my chair and looked over the balustrade to see what they were doing. I expected to catch them dabbling in water, making a bonfire, covering themselves with tar. But what I actually saw was Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Kneeling on the floor, he was drawing with the point of his blackened stick on the flagstones. And Robin, kneeling imitatively beside him, was growing, I could see, rather impatient with this very slow game.
“Guido,” he said. But Guido paid no attention. Pensively frowning, he went on with his diagram. “Guido!” The younger child bent down and then craned round his neck so as to look up into Guido’s face. “Why don’t you draw a train?”
“Afterwards,” said Guido. “But I just want to show you this first. It’s so beautiful,” he added cajolingly.
“But I want a train,” Robin persisted.
“In a moment. Do just wait a moment.” The tone was almost imploring. Robin armed himself with renewed patience. A minute later Guido had finished both his diagrams.
“There!” he said triumphantly, and straightened himself up to look at them. “Now I’ll explain.”
And he proceeded to prove the theorem of Pythagoras—not in Euclid’s way, but by the simpler and more satisfying method which was, in all probability, employed by Pythagoras himself. He had drawn a square and dissected it, by a pair of crossed perpendiculars, into two squares and two equal rectangles. The equal rectangles he divided up by their diagonals into four equal right-angled triangles. The two squares are then seen to be the squares on the two sides of any one of these triangles other than the hypotenuse.
So much for the first diagram. In the next he took the four right-angled triangles into which the rectangles had been divided and re-arranged them round the original square so that their right angles filled the corners of the square, the hypotenuses looked inwards, and the greater and less sides of the triangles were in continuation along the sides of the square (which are each equal to the sum of these sides).
In this way the original square is redissected into four right-angled triangles and the square on the hypotenuse. The four triangles are equal to the two rectangles of the original dissection. Therefore the square on the hypotenuse is equal to the sum of the two squares—the squares on the other two sides—into which, with the rectangles, the original square was first dissected.
In very untechnical language, but clearly and with a relentless logic, Guido expounded his proof. Robin listened, with an expression on his bright, freckled face of perfect incomprehension.
“Treno,” he repeated from time to time. “Treno. Make a train.”
“In a moment,” Guido implored. “Wait a moment. But do just look at this. Do.” He coaxed and cajoled. “It’s so beautiful. It’s so easy.”
So easy…. The theorem of Pythagoras seemed to explain for me Guido’s musical predilections. It was not an infant Mozart we had been cherishing; it was a little Archimedes with, like most of his kind, an incidental musical twist.
“Treno, treno!” shouted Robin, growing more and more restless as the exposition went on. And when Guido insisted on going on with his proof, he lost his temper. “Cattivo Guido,” he shouted, and began to hit out at him with his fists.
“All right,” said Guido resignedly. “I’ll make a train.” And with his stick of charcoal he began to scribble on the stones.
I looked on for a moment in silence. It was not a very good train. Guido might be able to invent for himself and prove the theorem of Pythagoras; but he was not much of a draughtsman.
“Guido!” I called. The two children turned and looked up. “Who taught you to draw those squares?” It was conceivable, of course, that somebody might have taught him.
“Nobody.” He shook his head. Then, rather anxiously, as though he were afraid there might be something wrong about drawing squares, he went on to apologise and explain. “You see,” he said, “it seemed to me so beautiful. Because those squares”—he pointed at the two small squares in the first figure—“are just as big as this one.” And, indicating the square on the hypotenuse in the second diagram, he looked up at me with a deprecating smile.
I nodded. “Yes, it’s very beautiful,” I said—“it’s very beautiful indeed.”
An expression of delighted relief appeared on his face; he laughed with pleasure. “You see, it’s like this,” he went on, eager to initiate me into the glorious secret he had discovered. “You cut these two long squares”—he meant the rectangles—“into two slices. And then there are four slices, all just the same, because, because—oh, I ought to have said that before—because these long squares are the same, because those lines, you see….”
“But I want a train,” protested Robin.
Leaning on the rail of the balcony, I watched the children below. I thought of the extraordinary thing I had just seen and of what it meant.
I thought of the vast differences between human beings. We classify men by the colour of their eyes and hair, the shape of their skulls. Would it not be more sensible to divide them up into intellectual species? There would be even wider gulfs between the extreme mental types than between a Bushman and a Scandinavian. This child, I thought, when he grows up, will be to me, intellectually, what a man is to a dog. And there are other men and women who are, perhaps, almost as dogs to me.
Perhaps the men of genius are the only true men. In all the history of the race there have been only a few thousand real men. And the rest of us—what
