Page:Popular Science Monthly Volume 32.djvu/271

 shapes and orders in which the digits or numbers arrange themselves, of which a considerable variety have been described by Mr, Galton and his correspondents, and by M. Jaques Bertillon. One correspondent reported to Mr. Galton that when a child he counted by imaginary cards from one to ten, and his little boy in the same way used an imaginary domino; another pictured numbers in groups of so many dots; to the same person, the numbers, from the part they played in the multiplication-table, had been personified. Thus, 9 was a wonderful being of whom he felt almost afraid; 8 was his wife; "and there used always to seem a fitness in 9x9 being so much more than 8x8"; 7 was masculine; 6, of no particular sex, but gentle and straightforward; 3, a feeble edition of 9, and generally mean; 2, young and sprightly; 1, a commonplace drudge. "In this style the whole multiplication-table consisted of the actions of living persons, whom I liked and disliked, and who had, though only vaguely, human forms." Mr. George Bidder, who was known in early life as "the calculating-boy," saw the numbers arranged in their order along a concavely-scalloped curve, the first part of which, comprising the first ten numbers, followed the arrangement of figures on a clock-face.

Another person's experience was to see the numbers arranged in association with certain colors up to 108. After 108 the notion of place became hazy and indistinct, though visualization was still possible, with effort. This writer as a child had a great liking for 6, arising, possibly, from his desire to be six years old. He was also very fond of blue, the color which he associated with 6. One of this writer's sisters saw numerals in a differently arranged diagram, and the figures themselves colored, each its own color. Another sister and a brother saw the figures in diagrams, but less clearly. The effects of heredity were strongly marked in two families of cousins. A sister in the first family saw the figures up to 200 in a rather complicated arrangement in a kind of cloud-land of different degrees of shading; another sister saw them ascending in a directly perpendicular line in front of the eye up to 1,000, when they became vague and seemed to turn to the left. A brother saw them in a straight line from left to right, black, on a ground varying in illumination—the millions in a vague, bright distance to the right. Other members of these families associated them with figures or with linear arrangements peculiar to themselves.

To another writer the figures presented themselves in an intricate curve, in which "the zero-point never moves; it is in my mind; it is that point of space known as 'here,' while all other points are outside, or 'there.' When I was a child, the zero-point began the curve; now it is a fixed point in an infinite circle." To another, who saw the numerals arranged for the most part in a regular row, like park palings, they appeared as far as 12 to be concealed in black shadow; from 12 to 20 was illuminated space, in which he could distinguish no divisions.