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 MC gee] THE BEGINNING OF MA THEM A TICS 659

in permissive or normal conduct ; so that the exoterically binary system of thought is esoterically, or in subconscious fact, ternary. 1 The dichotomous fiducial and social structure clarifies the Australian numeral system. The abundant numerations recorded by Curr and others strongly suggest the simple binary system traced by Conant. A common form isgoona, barkoo/a, barkoola- goona, barkoola-barkoola (1, 2, 2-1, 2-2) sometimes followed by " many " or " plenty " and more rarely by barkoola-barkoola-goona (2-2-1), though usually the table does not go beyond the fourth term, which may itself be replaced by " many." Now, examina- tion of the numerous records shows (1) that none of the terms correspond with fingers ; (2) that a very few of the terms corre- spond with the word for hand, such terms being three, four, one, and two in (approximate) order of frequency; (3) that a some- what larger number of terms, chiefly three, one, and two, corre- spond with the words for man ; (4) that a considerable number of threes and ones, with a few fours and twos, suggest affinities with obscure roots used chiefly in terms for man, tribe, wild dog, I, yes, etc.; and (5) that there is a strong tendency to limit the formal numeration to three. It is particularly noticeable, too, that certain persistent number terms are used sometimes for two and sometimes for three among numerous slightly related tribes — i. e., the term is more definitely crystallized than the concept, which oscillates indiscriminately between two and three, betray- ing confusion impossible to arithmetic thought. Similarly the Tasmanian numerations are binary, and without reference to finger or hand, though five sometimes appears to connote man. These features clearly indicate that the Australasians do not count on their fingers, and are without realistic notion as to the num- ber of fingers — indeed, the Pitta-Pitta of Queensland are able to count their fingers and toes only by the aid of marks in the sand,* while the abundant Australian pictographs reveal habitual

1 Lumholtz mentions a definite "idea of the Trinity" among the southeastern Australians {Among Cannibals y 1 889, p. 129).

2 Ethnological Studies, by Walter E. Roth, op. «'/., p. 26.

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