836 PRIMITIVE NUMBERS (ETH. ANN.19 
less extensively distributed through history and throughout the world 
than the four-cult, though it may be traced in different continents; and 
it is peculiarly meaningful in establishing that marvelous prepotency of 
the number cult which, among many tribes, carried the nascent numeral 
system past the point at which nature strove, through the obvious 
organic structure of the hand and through simple algorithmic order, 
to implant the quinary system. Indeed, if further evidence than that of 
bestial and savage counting were required to show that finger numera- 
tion and the quinary system were not primeval, it would be afforded 
by the development of the senary-septenary system in so many lands. 
The quaternary and senary cults illumine the binary systems pre- 
vailing among tribes still lower in the scale of intellectual development. 
Especially helpful is the light on the Australian aborigines, who are 
found thereby to exemplify what might be called a Cult of the Halves; 
for they are controlled by a binary concept of things expressed not 
only by their numeration, but even more clearly by their social and 
fiducial systems, which, in turn, shape their everyday conduct and 
speech. ‘*The fundamental feature in the organization of the central 
Australian, as in that of other Australian tribes, is the division of the 
tribe into two exogamous intermarrying groups,” say Spencer and 
Gillen;' and all other students of native Australian society have either 
been overwhelmed by an apparently irresolvable nebula of overlapping 
classes and subclasses and superclasses, or have been led to a related 
conclusion. Indeed the Gordian knot of entangled relationships con- 
stituting Australian society is easily cut by the student who places 
himself in the position of an individual blackfellow, and projects from 
self dichotomous class-lines occasionally uniting and bifureating in 
other individuals, after the manner of the dichotomous lines of Aris- 
totelian classification and the Tree of Porphyry; for the social classes, 
and the conduct involved in their maintenance, are fixed by a bifureate 
series of ordinances, ostensibly descended from the mystical olden time, 
and put in the form of tabus and equally mystical mandates by the 
shamans. In like manner the obscure pantheon of the Australians 
seems to be arranged in nearly symmetric pairs; and even the indi- 
vidual shade (or mystical double of the person) is conceived as bipartite, 
as among the Arunta, who designate the ghostly attendants Iruntarinia 
and Arumbaringa, respectively.* 
Although typically developed among the Australian aborigines, the 
binary philosophy is by no means confined to the Austral continent 
and primeval culture; it existed among the Tasmanians, it reappears in 
Africa, persists in China and Mongolia, and may clearly be traced in 
America, e. @., in the **sides” forming the primary basis of society 
in the Seneca and other Amerind tribes; while no fiducial system is 
1 The Native Tribes of Central Australia, by Baldwin Spencer and F. J. Gillen, 1899, p. 55 
2Op. cit., p. 613, 
