Binary fractions and a whole unit 'measure of value' in the seal-texts of the Indus civilization

Abstract

Address preprint feedback to chandra@think-sa.org Short sequences of symbols on tiny stone seals, miniature tablets and assorted media are the only evidence of writing in the Indus Civilization (flourished ca. 2600-1900 BCE). About five thousand specimens bearing such brief 'texts' have been cataloged so far, and despite nearly a hundred years of study, the texts cannot be read. This study proposes based on a consilience of evidences that a small number of symbols that occur prominently at the beginning of several texts in the corpus are pictorial expressions of binary fractions from the 'onesixteenth' to the 'half', a 'whole' unit, and an 'equivalence' indicator whose form may have emerged from the same cognitive basis as the modern mathematical symbol for 'equality'. The correspondence of the fractions to the system of tiny weights in binary ratios found in the Indus archaeological record suggests the 'fractions' were not used in a mathematical sense, but were representations of small quantities of objects of value such as precious metal that likely functioned as measures of economic 'worth'. Parallels from contemporaneous Egypt and Mesopotamia, as well as specific Indus texts investigated in this study, suggest that the texts which begin with these symbols encoded 'worth equivalences', in which the worth of commodities of trade and articles of value were expressed against a standard measure of value. The use of such standardized expressions of economic worth over a vast geographical area offers concrete evidence of a high degree of economic integration among the different regions of the Indus Civilization.ancient scripts | indus civilization | binary fractions | economy T he Indus Civilization flourished in the north-western region of the Indian subcontinent ca. 2600-1900 BCE. Spread over a million square kilometres, and nourished by the Indus river system and what survives as the Ghaggar-Hakra channel, the Indus Civilization was larger than contemporaneous Egypt and Mesopotamia. Its remains attest to a period of technological and artistic achievements, well-developed urban centers and active trade with Mesopotamia and the Persian Gulf region (1) but, unlike ancient Egypt and Mesopotamia that committed lengthy administrative texts and literary compositions to writing, the Indus Civilization does not appear to have produced any written documents. The only evidence of writing is in the form of brief 'texts', about five symbols long on an average, found mainly on tiny stone seals, and as their impressions on clay, and on assorted material like miniature terracotta and copper/bronze tablets, potsherds, tools, ivory rods, and one exceptional, monumental 'signboard'. Production of these texts ceased by about 1900 BCE, concomitant with a general decline in urban culture. Since their discovery about a hundred years ago, major and minor Indus sites have yielded about five thousand specimens bearing texts that still defy decipherment.The nature of the texts. Scholars have speculated that the Indus texts likely encoded f...