THOMAS] ORIGIN OF NUMBER NAMES 875 
gist, October, 1899, and to the preceding paper in this volume. This 
author points out that while the count of many primitive peoples 
has been by the fingers and hands, giving rise to the quinary and dec- 
imal systems, and sometimes by the toes and feet also, leading to the 
vigesimal system, yet the evidence derived from the method of count- 
ing by tribes in the lowest status seems to demonstrate that these sys- 
tems are far from primeval. 
He suggests that numbers of the lower scale, beginning with 1, rep- 
resenting the Ego, were the outgrowth of mysticism; 2, growing out 
of the lateral or the fore and aft aspects, being the first pausing point, 
and 4, the Cult of the Quarters, the second pausing point, beyond 
which a number of systems never advanced; to this the Ego being 
added gave the number 5. However, for a more complete and clear 
understanding of the author’s suggestions on this interesting subject 
the reader is referred to his papers. 
That the quinary system, or counting on the fingers and hand, could 
not have taken its rise until 5 had been reached by some other process 
appears to be self-evident, and is proved by the numerous systems in 
which 5 is not reached, and by others in which it does not form a basis. 
It would seem necessary, therefore, in order to obtain a satisfactory 
explanation of the origin of the primary numbers, to look for some 
other solution than the supposed method of counting on the fingers. 
The hand would not be likely to come into use in this respect until 5 had 
been reached and the attempt made to rise above that number; then 
the advantage of using the five fingers of the hand, or the hand as rep- 
resenting 5 as a basis would be perceived. Pebbles, sticks, or any 
other objects, would answer just as well for this purpose as the fingers 
until some reference to 5 was desirable, except that the latter were 
always convenient objects and were best adapted to use in sign 
language. When 5 was reached, and the advantage of using the hand 
became apparent, it would be used for the numbers below 5 as well as 
those above, but the inquiry here is, were the fingers considered so 
essential in counting 2 to 4, before 5 had been reached, as to bring 
evidence of the fact into the nomenclature? This can be determined 
only by obtaining the signification of the names of numbers in those 
dialects of tribes which have not reached 5 in their numeral systems.’ 
Orozco y Berra, speaking of the Mexican names for the numbers— 
ce, 13 ome, 2; yet, 3, and nahui, 4—says, ‘*no one has given a reason 
for the origin of these names.”” Chavero® contends that, although 


1Conant (Number Concept, pp. 24-25) says: ‘‘ Itseemsmost remarkable that any human beingshould 
possess the ability to count to4,and not tod. The number of fingers on one hand furnishes so obvious 
a limit to any of these rudimentary systems, that positive evidence is needed before one can accept the 
statement. A careful examination of the numerals in upwards of a hundred Australian dialects leaves 
no doubt, however, that such is the fact. The Australians in almost all cases count by pairs; and so 
pronounced is this tendency that they pay but little attention to the fingers.’’ The last sentence of 
this quotation appears to answer the author's cause of wonder expressed in the first sentence; the 
fingers were, it seems, considered by the Australians as no more essential in the process of counting 
than any other convenient objects. 
*Anales Mus. Mex., pp. 2, 34. 3 Op. cit., p. 33. 
