About nine months after John had learnt to speak, some one gave him a child’s abacus. For the rest of that day there was no talking, no hilarity; and meals were dismissed with impatience. John had suddenly discovered the intricate delights of number. Hour after hour he pertormed all manner of operations on the new toy. Then suddenly he flung it away and lay back staring at the ceiling.
His mother thought he was tired. She spoke to him. He took no notice. She gently shook his arm. No response. “John!” she cried in some alarm, and shook more violently. “Shut up, Pax,” he said, “I’m busy with numbers.”
Then, after a pause, “Pax, what do you call the numbers after twelve?” She counted up to twenty, then up to thirty. “You’re as stupid as that toy, Pax.” When she asked why, he found he had not words to explain himself; but after he had indicated various operations on the abacus, and she had told him the names of them, he said slowly and triumphantly, “You’re stupid, Pax, dear, because you (and the toy there) ‘count’ in tens and not in twelves. And that’s stupid because twelves have ‘fourths’ and ‘threeths’, I mean ‘thirds’, and tens have not.” When she explained that all men counted in tens because when counting began, they used their five fingers, he looked fixedly at her, then laughed his crackling, crowing laugh. Presently he said, “Then all men are stupid.”
This, I think, was John’s first realization of the stupidity of Homo sapiens, but not the last.
Thomas was jubilant over John’s mathematical shrewdness, and wanted to report his case to the British Psychological Society. But Pax showed an unexpected determination to ‘keep it all dark for the present’. “He shall not be experimented on,” she insisted. “They’d probably hurt him. And anyhow they’d make a silly fuss.” Thomas and I laughed at her fears, but she won the battle.
John was now nearly five, but still in appearance a mere baby. He could not walk. He could not, or would not, crawl. His legs were still those of an infant. Moreover, his walking was probably seriously delayed by mathematics, for during the next few months he could not be persuaded to give his attention to anything but numbers and the properties of space. He would lie in his pram in the garden by the hour doing “mental arithmetic” and “mental geometry,” never moving a muscle, never making a sound. This was most unhealthy for a growing child, and he began to ail. Yet nothing would induce him to live a more normal and active life.
Visitors often refused to believe that he was mentally active out there for all those hours. He looked pale and “absent.” They privately thought he was in a state of coma, and developing as an imbecile. But occasionally he would volunteer a few words which would confound them.
John’s attack upon geometry began with an interest in his brother’s box of bricks and in a diaper wallpaper. Then came a phase of cutting up cheese and soap into slabs, cubes, cones, and even into spheres and ovoids. At first John was extremely clumsy with a knife, cutting his fingers and greatly distressing his mother. But in a few days he had become amazingly dextrous. As usual, though he was backward in taking up a new activity, once he had set his mind to it, his progress was fantastically rapid. His next stage was to make use of his sister’s school-set of geometrical instruments. For a week he was enraptured, covering innumerable sheets.
Then suddenly he refused to take any further interest in visual geometry. He preferred to lie back and meditate. One morning he was troubled by some question which he could not formulate. Pax could make nothing of his efforts, but later his father helped him to extend his vocabulary enough to ask, “Why are there only three dimensions? When I grow up shall I find more?”
Some weeks later came a much more startling question. “If you went in a straight line, on and on and on, how far would you have to go to get right back here?”
We laughed, and Pax exclaimed, “ Odd John!” This was early in 1915. Then Thomas remembered some talk about a “theory of relativity” that was upsetting all the old ideas of geometry. In time he became so impressed by this odd question of John’s, and others like it, that he insisted on bringing a mathematician from the university to talk to the child.
Pax protested, but not even she guessed that the result would he disastrous.
The visitor was at first patronizing, then enthusiastic, then bewildered; then, with obvious relief, patronizing again; then badly flustered. When Pax tactfully persuaded him to go (for the child’s sake, of course), he asked if he might come again, with a colleague.
A few days later the two of them turned up and remained in conference with the baby for hours. Thomas was unfortunately going the round of his patients. Pax sat beside John’s high chair, silently knitting, and occasionally trying to help her child to express himself. But the conversation was far beyond her depth. During a pause for a cup of tea, one of the visitors said, “It’s the child’s imaginative power that is so amazing. He knows none of the jargon and none of the history, but he has seen it all already for himself. It’s incredible. He seems to visualize what can’t be visualized.”
Later in the afternoon, so Pax reported, the visitors began to grow rather agitated, and even angry; and John’s irritatingly quiet laugh seemed to make matters worse. When at last she insisted on putting a stop to the discussion, as it was John’s bedtime, she noticed that both the guests were definitely out of control. “There was a wild look about them both,” she said, “and when I shooed them out of the garden they were still wrangling; and they never said good-bye.”
But it was a shock to learn, a few days later, that two mathematicians on the university staff had been found sitting under a street lamp together at 2 a.m. drawing diagrams on the pavement and disputing about “the curvature of space.”
Thomas regarded his youngest child simply as an exceptionally striking case of the “infant prodigy.” His favourite comment was, “Of course, it will all fizzle out when he gets older.” But Pax would say, “I wonder.”
John worried mathematics for another month, then suddenly put it all behind him. When his father asked him why he had given it up, he said, “There’s not much in number really. Of course, it’s marvellously pretty, but when you’ve done it all—well, that’s that. I’ve finished number. I know all there is in that game. I want another. You can’t suck the same piece of sugar for ever.”
During the next twelve months John gave his parents no further surprises. It is true he learned to read and write, and took no more than a week to outstrip his brother and sister. But after his mathematical triumphs this was only a modest achievement. The surprising thing was that the will to read should have developed so late. Pax often read aloud to him out of books belonging to the elder children, and apparently he did not see why she should be relieved of this duty.
But there came a time when Anne, his sister, was ill, and his mother was too occupied to read to him. One day he clamoured for her to start a new book, but she would not. “Well, show me how to read before you go,” he demanded. She smiled, and said, “It’s a long job. When Anne’s better I’ll show you.”
In a few days she began the task, in the orthodox manner. But John had no patience with the orthdox manner. He invented a method of his own. He made Pax read aloud to him and pass her finger along the line as she read, so that he could follow, word by word. Pax could not help laughing at the barbarousness of this method, but with John it worked. He simply remembered the “look” of every “noise” that she made, for his power of retention seemed to be infallible. Presently, without stopping her, he began analysing out the sounds of the different letters, and was soon cursing the illogicality of English spelling. By the end of the lesson John could read, though of course his vocabulary was limited. During the following week he devoured all the children’s books in the house, and even a few “grown-up” books. These, of course, meant almost nothing to him, even though the words were mostly familiar. He soon gave them up in disgust. One day he picked up his sister’s school geometry, but tossed it aside in five minutes with the remark, “Baby book!”