MCGEE] AUSTRALIAN NUMERAL SYSTEM 837 
wholly free from the persistent dualism springing from binary inter- 
pretations of nature. Yet the mystical Two is no more complete in 
itself than the mystical Four and Six of higher culture; the primary 
classes or ‘‘sides” are perfected in the tribe both in Australia and in 
America, the Iruntarinia and Arumbaringa are conjoined in and non- 
existent apart from the personality they are held to shadow, and the 
mandates and prohibitions of Australian (and indeed of most other) 
laws are perfected in permissive, or normal, conduct; in Australia 
indeed the central factor is so well developed that Lumbholtz was led 
to note a ternary concept as expressing a definite ‘‘idea of the Trin- 
ity” among the southeastern tribes;' so that the exoterically binary 
system of thought is esoterically, or in subconscious fact, ternary. 
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 is goona, barkoola, 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, examination of the numerous records shows (1) that 
none of the terms correspond with fingers; (2) that a very few of the 
terms correspond with the word for hand, such terms being three, 
four, one, and two in (approximate) order of frequency; (3) that a 
somewhat larger number of terms, chiefly three, one, and two, cor- 
respond 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 numer- 
ation to three. It is particularly noticeable, too, that certain per- 
sistent 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 indiscrimi- 
nately between two and three, betraying a 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 Australa- 
sians do not count on their fingers, and are without realistic notion 
as to the number 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 
uncertainty as to the number of fingers in the human hand (save where 
the picture is developed from a direct impression). 
Suggestively analogous in form and meaning are certain South 

1 Among Cannibals, 1889, p. 129. 
2 Ethnological Studies, by Walter E. Roth, p. 26. 
