PEIMITIVK Nl^ir.KII SYSTEM^^. 



By Lett L. Con ant, Pli. D 



Among the speculative questions w liich aiisc in conneetion with the 

 study of luatheniatics from a historical standpoint tlie origin of num- 

 ber is one that has i)rovoked much discussion and has led to extensive 

 research among- the primitive and savage languages of the human race. 

 A few simple considerations will liowever show that such research 

 must necessarily leave the question entirely unsettled, and will indi- 

 cate that it is, from the very nature of things, a (juestiou to wliich no 

 definite, or at least no final, answer can l)e given. 



Among the barbarous tribes whose languages have been studied, 

 even in a most cursory and imperfect way, none have ever been dis- 

 covered which did not possess one or more words indicating familiarity 

 with the number concept. Some tribes ha\e been found in which 

 knowledge of luimber was so slight that the statement has been made 

 that their language contained no numerals. The Chiquitas, of South 

 America, for exam])le, have no word even whicli we can accept as a 

 distinct substitute for "one." That numeral they express by a word 

 meaning nearly the same as "alone." Here the number sense appears 

 at its lowest ebb, but still it does exist; and going lower yet, one 

 would be rash, indeed, if he were to assert that the higher animals 

 can not distinguish between 1 and 2. Xot a few tribes have been 

 found who could not count beyond two; more yet with 3, 4, or 5 as 

 their number limit, while 10 marks the boundary of the numeral sys- 

 tems of a very great number of the primitive races of the world. The 

 assertion would seem then to be a safe one that the number sense is 

 never wholly lacking. It is evident also that numerals must be among 

 the earliest words to l)C formed in any language. Tluiy express ideas 

 which arc- wholly concrete, which ])recede liunmn intelligence, and 

 which are in many ways manifested by the higher orders of the brute 

 creation. The origin of number therefore must be conceded to lie 

 beyond the proper limit of in(juiry, and the i)rimitive conception of 

 number to be fundamental with human thought. 



Historical inv<'stigation must begin not with nund)er itself, but with 

 modes of expression of number. Herein ])r('cisely the same, manner 

 as in the expression of all forms »>f thonglit, desir«% and einolion, the 

 sign language ju'eceded words. We are all familiar with the manner 



