Metrology

Remarkably accurate weights and measuring rules give some insight into the Harappans' numerical system. Four examples of graduated rules have been found: made of terra-cotta, ivory, copper, and shell, they came respectively from Kalibangan, Lothal, Harappa, and Mohenjo-daro. These were marked into divisions of about 1.7 millimeters, the largest unit marked on the Mohenjo-daro rule being 67.056 millimeters and others on the Lothal scale including 33.46 and 17 millimeters. The latter closely approximates the traditional unit of 17.7 millimeters known from the fourth-century BCE text Arthashastra.

The system of stone weights was similarly standardized throughout the Indus realms, and was also used overseas where it was known to the Mesopotamians as the standard of Dilmun, adopted as far away as Ebla. The weights were generally cubical, though truncated spheres also occur. The most common weight was equivalent to about 13.65 grams. Taking this as the basic unit, the Indus people also used smaller weights that were a half, a quarter, an eighth, and a sixteenth of this basic unit and larger ones that were multiples of 2, 4, 10, 12.5, 20, 40, 100, 200, 400, 500, and 800 times the basic unit.

It has been suggested that the basis for the weight system was the ratti, the weight of a seed of the gunja creeper (Abrus precatorius), equivalent to a 128th part of the Harappan basic unit, just over 0.1 grams. This is still used in India as a jeweler's weight and was the basis, among other things, for the weight

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Standards of the first Indian coins in the seventh century BCE. The use of the ratti seed as the basis for the weight system may explain the endurance of the weight system through the period after the decline of the Indus civilization, when weights themselves disappeared.

Harappan Numbers. The weight and linear measurement systems and the probable numerals in the Harappan script seem to suggest that the Harappans used both a base-8 (octonary) and a base-10 (decimal) system in counting. Aspects of both have survived in later Indian mathematics and general use. For example, in the predecimal Indian coinage, the rupee was 64 paise or 16 annas, each divided into 4 paise; and the whole system of Arabic numerals, base-10 positional notation, and the use of zero derives ultimately from India.

Asko Parpola (1994) notes that a Proto-Dravidian root *en means both "eight" and "to count," a significant pointer to an octonary system if the Harappans spoke a Dravidian language (the question of language is discussed later in this chapter).