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Page:Popular Science Monthly Volume 51.djvu/538

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POPULAR SCIENCE MONTHLY.

THE ORIGIN AND DEVELOPMENT OF NUMBER SYSTEMS.
By Prof. EDWIN S. CRAWLEY.

IT is generally acknowledged that we have in the number systems of the lower races to-day a means of studying the development of our own system. This is based upon the assumption that when the savage begins to count he does it always in essentially the same way. This is, in fact, more than an assumption. An analysis of the number systems of many races scattered all over the globe shows that such a similarity exists, and there is no reason to suppose that our own ancestors followed any other method. Indeed, such evidence as it is now possible to bring forward all goes to support this view.

Counting begins when man first forms the idea of two as distinct from one and more than two. We may perhaps go back even one step further, and say that it begins when the idea of one, as distinct from more than one, is formed. If this be taken as the starting point, the distinct conception of two forms the second step. It is difficult to realize that such ideas are not contemporaneous with the birth of intelligence, but there is evidence to show that such is not the case. According to Dr. Charles Letourneau, we have one example of a race which has not yet taken even this first step. He says in his book on Sociology (translated by Henry M. Trollope), page 582: "The Weddahs of Ceylon, who seem to be the least intelligent of men, have still no mathematical faculty whatever; they have no name for any number." To say that they have no name for any number probably does not imply that they are unable to realize that one group of objects contains more individuals than another group of the same objects. They could even determine which of two such groups contained the greater number of objects, by placing in succession one from each group in pairs until all in one group were exhausted. Such a process, however, is not counting, and the race which finds it necessary to resort to such an expedient may fairly be said to have no conception of number as such.

We find other races who have taken only the first two or three steps. These are chiefly the South American forest tribes and the bushmen of Australia. Speaking of these tribes, Edward B. Tylor says (Primitive Culture, London, 1871, Vol. I, page 220): "Five is actually found to be a number which the languages of some tribes do not know by a special word. Not only have travelers failed to get from them names for numbers above 2, 3, or 4, but the opinion that these are the real limits of their numeral series is strengthened by their use of the highest known number