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