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....”
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.