THE ORIGIN OF NUMBER SYSTEMS. 525 



as an indefinite term for a great many. Spix and Martins say of 

 the low tribes of Brazil : ' They connt commonly by their finger 

 joints, and so up to three only. Any larger number they express 

 by the word many' In a Puri vocabulary the numerals are given 

 as 1, omi ; 2, curiri ; 3, prica, ' many ' : in a Botocudo vocabu- 

 lary 1, mokenam; 2, uruhu, 'many/" It is needless to multiply 

 these examples. 



The next step in advance in the development of a number sys- 

 tem is taken when the fingers and toes are brought in as aids in 

 the art of counting. The advance is now comparatively rapid up 

 to the point where, these means being exhausted, there is no fur- 

 ther natural aid conveniently at hand. It is popularly believed 

 that finger-counting represents the very earliest stage of the art, 

 but the existence of tribes who can not count as far as five, as 

 already cited, would seem to be conclusive evidence of a stage 

 which antedates this. The etymological character of the numeral 

 words in most of the known languages points to the same conclu- 

 sion. Prof. Levi Leonard Conant, in a book recently published 

 under the title The Number Concept, has collected and analyzed a 

 great number of the numeral systems of savage and semicivilized 

 tribes. He says (pages 98 and 99) : " Collecting together and com- 

 paring with one another the great mass of terms by which we find 

 any number expressed in different languages, and while admitting 

 the great diversity of method practiced by different tribes, we ob- 

 serve certain resemblances which were not at first supposed to 

 exist. The various meanings of 1, where they can be traced at all, 

 cluster into a little group of significations with which at last we 

 come to associate the idea of unity. Similarly of 2, or 5, or 10, or 

 any of the little band which does picket duty for the advance 

 guard of the great host of number words which are to follow. A 

 careful examination of the first decade warrants the assertion 

 that the probable meaning of any one of the units will be found 

 in the list given below. The words selected are intended merely 

 to serve as indications of the thought underlying the savage's 

 choice, and not necessarily as the exact terms by means of which 

 he describes his number. Only the commonest meanings are in- 

 cluded in the tabulation here given : 



" 1 = Existence, piece, group, beginning. 



" 2 = Repetition, division, natural pair. 



" 3 = Collection, many, two- one. 



" 4 = Two twos. 



" 5 = Hand, group, division. 



" 6 = Five-one, two threes, second one. 



" 7 = Five-two, second two, three from ten. 



" 8 = Five-three, second three, two fours, two from ten. 



" 9 = Five-four, three threes, one from ten. 



