The Number Concept: Its Origin and DevelopmentConant, Levi L. (Levi Leonard)
History
The Number Concept: Its Origin and Development
Conant, Levi L. (Levi Leonard)
Number concept
The Kamilaroi scale, given as an example of binary formation, is partly
ternary; and its word for 6, _guliba guliba_, 3-3, is purely ternary. An
occasional ternary trace is also found in number systems otherwise decimal
or quinary vigesimal; as the _dlkunoutl_, second 3, of the Haida Indians of
British Columbia. The Karens of India[196] in a system otherwise strictly
decimal, exhibit the following binary-ternary-quaternary vagary:
6. then tho = 3 x 2.
7. then tho ta = 3 x 2-1.
8. lwie tho = 4 x 2.
9. lwie tho ta = 4 x 2-1.
In the Wokka dialect,[197] found on the Burnett River, Australia, a single
ternary numeral is found, thus:
1. karboon.
2. wombura.
3. chrommunda.
4. chrommuda karboon = 3-1.
Instances of quaternary numeration are less rare than are those of ternary,
and there is reason to believe that this method of counting has been
practised more extensively than any other, except the binary and the three
natural methods, the quinary, the decimal, and the vigesimal. The number of
fingers on one hand is, excluding the thumb, four. Possibly there have been
tribes among which counting by fours arose as a legitimate, though unusual,
result of finger counting; just as there are, now and then, individuals who
count on their fingers with the forefinger as a starting-point. But no such
practice has ever been observed among savages, and such theorizing is the
merest guess-work. Still a definite tendency to count by fours is sometimes
met with, whatever be its origin. Quaternary traces are repeatedly to be
found among the Indian languages of British Columbia. In describing the
Columbians, Bancroft says: "Systems of numeration are simple, proceeding by
fours, fives, or tens, according to the different languages...."[198] The
same preference for four is said to have existed in primitive times in the
languages of Central Asia, and that this form of numeration, resulting in
scores of 16 and 64, was a development of finger counting.[199]
Public-domain text, read in full here on John Shaqi.
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