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 mc gee] THE BEGINNING OF MA THEM A TICS 6$7

points must be reckoned from a common center, the three under- worlds and the three upper-worlds are reckoned from the Middle world of actuality, and the six colors (e. g., of corn, as among the Zufti according to Cushing and others) are habitually supple- mented by a central all-color; so that, in this case as in the last, the exoterically perfect number is esoterically perfected through the unity of subjective personality. 1 The six-cult is much less extensively distributed through history and throughout the world than the four-cult, but may be traced in different continents ; and it is peculiarly meaningful in establishing that marvelous pre- potency of the number-cult which, among many tribes, carried the nascent numeral system past the point at which nature strove, through obvious organic structure and algorismic order, to im- plant the quinary system — indeed if further evidence than that of bestial and savage counting were required to show that finger- numeration 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 prevailing among tribes still lower in the scale of intellectual de- velopment. 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 their binary concept of things is 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 inter-marrying groups," say Spen-

1 The perfecting of the mystical numbers four and six by the addition of unity has been recognized by many investigators, notably Powell (On Regimentation ; 15th Annual Report of the Bureau of Ethnology, i8q3-'94, 1897, p. cxvii and elsewhere), Morris (Relation of the Pentagonal Dodecahedron . . . to Shamanism ; Proceed- ings of the American Philosophical Society, vol. xxxvi, 1897, pp. 179-183), and Cushing (ibid., p. 185 and elsewhere).

AM. ANTH. N. S., I— 42

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