8384 PRIMITIVE NUMBERS [ETH. ANN.19 
habitually think numerically up to or above three, as 1s shown by the 
plurality of plurals and by other features of their speech: and the 
meagerness of their numeration no more negates numerical capacity 
than does the absence of such systems among counting crows and foxes 
and wasps. Nevertheless, the comparison is instructive. In the first 
place, it indicates roughly corresponding ability to count on the part 
of higher animals and lower men; it also defines the origin of vocal 
numeration at the bottom of the scale of human development; and it 
is especially significant in demonstrating that neither the animals nor 
the men (1) either cognize quinary and decimal systems, or (2) use 
their own external organs (toes, fingers, ete.) as mechanical adjuncts 
to nascent notation—unless the binary numeration of certain Austra- 
lian tribes is really bimanual, as W. E. Roth implies." Many primi- 
tive peoples count by fingers and hands, sometimes with the addition 
of toes and feet, and thereby fix quinary, decimal, and vigesimal sys- 
tems; but the burden of the evidence derived from animal counting 
and from the numeration of lower savagery seems to demonstrate that 
these systems are far from primeval. 
Simple number systems of mystical or symbolic character abound 
among the better-studied tribes of middle-primitive culture, including 
the aborigines of North America. The most widespread of the mys- 
tical numbers is four. It finds expression in Cults of the Quarters in 
North America, South America, Asia, and Africa, and is suggested by 
certain customs in Australia;” it is crystallized in the swastika or fylfot 
and other cruciform symbols on every continent, save perhaps Australia; 
and it is established and perpetuated by associations with colors, with 
social organization, and with various customs among numerous tribes. 
In much of primitive culture the hold of the quatern concept is so strong 
as to dominate thought and action—so strong as to seem wholly inex- 
plicable save through the interwoven mysticism and egoism of the 
lowly mind. The devotee of the Cult of the Quarters is unable to 
think or speak without habitual reference to the cardinal points; and 
when the quadrature is extended from space to time, as among the 
Papago Indians, the concept is so strong as to enthrall thought and 
enchain action beyond all realistic motives. To most of the devotees 
of the quatern concept—forming probably the majority of the middle 
primitive tribes of the earth—the mystical number four is sacred, 
perfect, and all-potent, of a perfection and potency far exceeding that 
of six to the Pythagoreans and of the hexagram to Paracelsus and his 
disciples; they are unconscious or only vaguely conscious of any other 
numerical concept; and many investigators fail to discover the reverse 
of the quartered shield and so trace the mystical figure to the subcon- 
scious self which it invariably reflects. Yet careful inquiry shows 
| Ethnological Studies among the North-West-Central Queensland Aborigines, 1897, p. 2. 
2Curr, The Australian Race, vol. 1, pp. 339, 340. 
