664 AMERICAN ANTHROPOLOGIST [n. s., i, 1899
The development of the senary-septenary system out of the quaternary-quinary arrangement forcibly suggests the genesis of the latter ; for it is but the sum or product of binary-ternary systems superposed by almacabalic augmentation. This suggested genesis would seem to be established by the occasional advances to the higher plane attested by some of the Australian numerations, as well as by the vestiges of the binary-ternary system along various* culture lines, notably the Mongolian and Aryan. The pre- sumptively primeval system apparently arose spontaneously, and became fixed through habitual mental effort shaped less by pur- pose-wrought symbols than by personal and subjective associa- tions. Analogy with the higher systems (simplified to meet the dull mentation of the Blackfellows) would indicate that their number concept might be symbolized by any regular trigram uniting the perceived pair of objects to the unapperceived Ego ; but the inequality of all social pairs in the tribal organization, the ever-varying relative potency of the good and evil mysteries, the unequal rank of the two ghostly Doppel-ichen, and other facts would suggest that a better figure for the concept would be an irregular trigram. But howsoever the system be represented graphically, the law of augmentation of the two higher systems prevails, as indicated both by certain of the Australian number- terms and by Mongolian vestiges, i. e., the augmentation pro- ceeds by successive additions to a once-reckoned Middle, yielding the values, 2+1, 4+1, 6+1, 8+1.
So it seems feasible to define an archaic almacabala, including a method of using integral numbers rather as tokens of extra- natural potencies than as symbols for natural values and combin- ing them by a simple rule tending to develop into algorismic processes, and including also a method of representing the numerical combinations by mechanical devices tending to develop into geometric forms; the system being characterized by the method of reckoning from an ill-defined unity counted but once in each combination.
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