Page:Popular Science Monthly Volume 42.djvu/531

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In all these forms the figures and letters appear to me in my own handwriting, except in the divisions of the day. In these, I have the abstract idea of morning, etc., in mind, but with the distinct divisions as in the diagram. All the plans are very much larger than here represented. The figures begin at my left and cross to my right before me, curving at 8; and 1,000 seems about my fingertips when my arm is extended straight before me. The circle of the seasons is about as large as would lie between my arms extended straight before me. The days of the week occupy a line at my left, about a yard long. The divisions of the day are perpendicular, as though hung on a wall, and morning begins at a level with my hand.

The number form in Fig. 18 is peculiar in this respect, that it reads from right to left. The seer is an artist, and it may be worthPSM V42 D531 Color related calendar visualizations.jpgFig. 17. mentioning that she is not left-handed. Other features of her form she describes as follows:

The line of the figures runs down to 8, 18, 28, 38, 48. They turn and ascend to the multiples of 10, but after 40 I see only the numbers found in the multiplication table—42, 48, etc. The numbers 18 and 19 form a very dark corner; 20 is quite light; 24 again is dark, the darkness continuing to 30; 30 is again light, and the numbers following are all quite light. The source of light seems to be 60, which is much higher than the rest, the light touching those on either side; 75 is very distinct.

Number forms being all unlike, adequate explanation of them becomes practically impossible. Speaking very generally, however, their origin may be traced to one great cause—namely, the attempt or necessities of children to give a concrete form to the abstract. Now, numbers are among the first abstractions that children have to wrestle with. Our earliest abstract ideas, perhaps also our later ones, are, as it is now well known, either mere samples of individual things, or else a kind of composite picture of them. The child's concept of boy, girl, dog, horse, are nothing more than visual pictures of some particular boy, girl, dog, horse, or else a composite picture of a limited number of individuals. Now, numbers do not admit of such composite pictures. They are bald abstractions that the poor child must manage in some way. In most cases, if he be an eye-minded child, he merely visualizes the Arabic numeral. He may give it

vol. xlii.—34