Page:Popular Science Monthly Volume 32.djvu/272

 A person who was described as a mathematical astronomer, of rapidly-rising reputation, saw the numbers in a straight row, while he would be standing a little on one side. They went away in the distance, so that 100 was the farthest number he could see distinctly. The row was dusky-gray, and paler near to the observer. The tens were marked by a kind of fleecy lumps.

M. d'Abbadie made a communication on the peculiarities of numerical vision to the Anthropological Society of Paris, and this led M. Jaques Bertillon to relate his experiences in the matter, beginning with the time when he learned to count. "I connected," he says, "each of the numbers as it was taught me with some object in our garden, so that when I went over the series I would in imagination walk along an alley that led from the house to the end of the garden. Thus, an indestructible association of ideas arose between the figures and the plants in the garden: the figure 1 became attached to a chestnut-tree that marked the beginning of the walk, the figure 5 to a bench near it, the figure 7 to a tub farther on, the number 14 to a little laurel; 30 and the following figures were lost in a dark avenue of trees that terminated the walk; while beyond 40 the numbers ceased to be associated with any object, probably because I had not learned to count further when I made the pleasant associations. If I wished to add 14 and 5, I would in fancy go to the place (the laurel-bush) that 14 occupied in the garden, and go some steps farther to 19. The puerile work was wholly involuntary; and I well recollect when my tendency to proceed thus was almost invincible. I had another process for fractions: the idea of ¼, for example, was directly associated with the idea of a quarter of an hour marked on the clock; and if I had to add ¼ and ⅓, I imagined the hand pushed forward twenty minutes, or one third of an hour, and I immediately had the result,. I was not able, however, to calculate any fractions in this way the denominators of which were not factors of 60."

A professor of mathematics in Geneva saw the numbers in a zigzag line which made turns at 10 and at 60, up to 116, and no further, and added to his description that when young he likened some sounds to colors: a grave sound was black, a less grave one, red; an acute sound, yellow; a very acute one, bright yellow.

Another correspondent saw the numbers arranged in their regular orders in a system of lines—the first 10 in a horizontal line, the next 10 in a line perpendicular to it, the third 10 in a line running diagonally from right to left, the numbers from 30 to 90 in a perpendicular line parallel to the line of the second series, and the larger numbers to 1,000 in a line running from right to left parallel with the first one. The vision stopped at 1,000.

To another correspondent of M. Bertillon's the numbers presented themselves—not very clearly distinct from one another—in a descending column, quite narrow down to 10, where it doubled in width;