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.