MC gee] THE BEGINNING OF MA THEM A TICS 65 5
primitive peoples count by fingers and hands, sometimes with the addition of toes and feet, and thereby fix quinary, decimal, and vigesimal systems ; but the burden of the evidence derived from animal counting and 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 cul- ture, including the aborigines of North America. The most widespread of the mystical 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 1 ; it is crystallized in the swastika or fylfot and other cruciform sym- bols on every continent ; and it is established and perpetuated by associations with colors, social organization, and 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 inexplicable 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 en- chain 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, all-potent, of a perfection and potency far ex- ceeding that of six to the Pythagoreans and the hexagram to Paracelsus; they are unconscious or only vaguely conscious of any other numerical concept ; and many investigators fail to dis- cover the obverse of the quartered shield and trace the mystical figure to the subconscious Self which it invariably reflects. Yet careful inquiry shows that the cardinal points are never conceived apart from the Ego in the center ; that the subjectively prepotent
1 The Australian Race, op. cit, vol. I, pp. 339, 340.
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