From: N. Ganesan (email@example.com)
Date: Fri Feb 17 2006 - 05:19:14 CST
Kit Peters wrote:
> Does anybody use hexadecimal, or other non-base-10,
> notation in anything besides Western characters?
The most ancient system of counting in India seems
to be to the base of 8. Then only to the base 10.
Dravidian, of which Tamil is the most ancient recorded,
has the same word eN- 'to count' and 'eight'.
Parpola, p. 169, Deciphering the Indus script
"Some cultural traits of the Indus civilization have linguistic
implications. Its standardized weights reveal that the numeral
system was a mixed one, binary or octonary plus decimal.
The smaller ratios weigh 1/2, 1/4, 1/6, 1/8 and 1/16 of the
basic unit (13.625 g), the bigger ratios 2, 4, 10, 12.5, 20, 40, 100,
200, 400, 500, 800 times the basic unit. This agrees
with the traditions of classical India, where 8 X 8 = 64,
and 10 X 10 = 100, were considered 'round numbers', not to
mention the former division of the monetary unit, the rupee,
into 16 annas. There is evidence in the numeral system of
Proto-Dravidian for both a decimal and an octonary system.
The numerals for both 'ten' (*paHtu) and 'hundred' (*nURu)
can be reconstructed for Proto-Dravidian. On the other hand,
in Proto-Dravidian the root for 'eight' (*eN) also means
'number' and 'to count', suggesting that this was the
original turning point in counting (once apparently
performed with the help of fingers but excluding the thumbs)."
1. The PDr word for '8' *eN also means to count, enumerate etc.
2. Some archaeological evidence.
2.1 Seal texts representing numbers show some peculiarities. Sri I
Mahadevan's concordance gives relative frequencies of use of long
strokes for numbers. They are as follows:
1 | 149
2 || 365
3 ||| 314
4 |||| 64
5 ||||| 22
6 |||||| 3
7 ||||||| 6
(From W A Fairservis, The Harappan Civilization and its writing, pp.
Fairservis Jr concludes with the statement that 'There is evidence
that Dravidian once had a base eight'. Here he cites KV Zvelebil
(Comparative Drav. morphology, p. 36).
In addition, Fairservis Jr also gives some specific artifactual
evidence in his Scientific American article (Sc Am, March 1983). He
refers to the calendric sticks made of ivory that he excavated in
Allahdino in Sind wherein he found that a symbol looking like a stalk
of grain stands next to 'vertical strokes that range from one to seven
in number and with five other signs.'. He then asks 'What language has
a word for grain that also means month or moon and is associated with
a base-eight numerical system?' He then adds ' Kamil V Zvelebil has
pointed out that the orginal Dravidian number system
was indeed probably to the base eight: the count to 10, used for
conformity with the base-10 number system today, goes literally (in
translation) "one", "two", "three", "four", "five", "six",
"seven", "number", "many minus one", "many" ' etc etc.
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