584 PRIMITIVE NUMBER SYSTEMS. 



in wliic'li a cliild when learning to oonnt makes nse of his tingers. 

 Cliihlren have for ages done the same; and the cliildreu of the human 

 race, the savages of pre-historic times, unquestionably counted on their 

 ten digits just as the African, the Eskimo, and the South Sea Isl- 

 ander do to-day. So universal has the finger method of counting 

 always been that many investigators, prominent among whom is 

 Grimm, have laid it down as an axiom that all numeral Avords arise 

 from names of the fingers of the hands. Savage races employ, as 

 might be expected, a great variety of methods of recording their count- 

 ing — as splints, pebbles, shells, kernels of grain, knots, etc. Then 

 come simi)le scratches, notches cut in a stick, Robinson Crusoe fash- 

 ion, and other similar devices. But back of all these, and forming a 

 common origin to which all may be referred, is the universal finger 

 method of counting, the method with which all begin, the method 

 which is too convenient to be entirely relinquished, even by civilized 

 races. 



This universal recourse to the fingers often resulted, as might be ex- 

 l)ected, in the development of a more or less extended pantomime 

 number system in which tlie fingers wei'e used in much the same way 

 as in the deaf and dumb alphabet, though the signs actually employed 

 were very difierent from those employed by unites. A system of this 

 kind was much in vogue among the ancients, by means of whicli any 

 number up to 10,000 could be expressed : units and tens by inflections 

 of the fingers of the left hand, linndreds by siniilar inflections of the 

 fingers of the right hand, and thousands by a repetition on the left 

 hand of the signs used to denote units and tens. The Chinese still 

 employ a finger method of expressing numbers less tlian 100,000, and 

 among nearly all Eastern jjeoples a digital arithmetic of one sort or 

 another is to be found. Of so common use is this sign language that 

 traders are said to communicate to each other the price at which they 

 are willing to buy or sell, and at the same time to conceal their otters 

 from bystanders, by putting their liands under each other's cloaks and 

 touching each other's fingers. 



Recent anthropological research lias developed many interesting 

 facts respecting the limits to which the number systems of the various 

 uncivilized races of the world extend. As a matter of course, all races 

 can indicate numbers as liigli as 10, the fingers serving as a means of 

 showing what they have no words to express. In nearly all cases we 

 find this limit extended to 20, the second 10 being told off on the toes, 

 or on the fingers of a second man. But savages have in very many 

 instances no words for numbers higher than 2, 3, or 4. The Botocudos 

 have no definite number beyond 1. For 2 they say "urahii", many. * 

 The Puris and the Watchandis stop at 2. The former express 3 by 

 ''prica", many, and the latter express the same number by the combi- 

 nation 2, 1. 1 The Andamans have only two numeral words, though 



* Tylor : Primitive Culture: vol. i, j). 2iH. t Ibid. 



