524 POPULAR SCIENCE MONTHLY. 



THE ORIGIN AND DEVELOPMENT OF NUMBER 



SYSTEMS. 



BY PROF. EDWItf S. CRAWLEY. 



"TT is generally acknowledged that we have in the number sys- 

 J- terns of the lower races to-day a means of studying the devel- 

 opment of our own system. This is based upon the assumption 

 that when the savage begins to count he does it always in essen- 

 tially 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 for- 

 ward all goes to support this view. 



Counting begins when man first forms the idea of two as dis- 

 tinct 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 contempora- 

 neous 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 concep- 

 tion 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 trav- 

 elers 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 



