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
Christopher Knight, Alan Butler