An Uyirêḻuttu or svara-based system of numeration used in Tamil astronomy texts

Abstract

Indian texts of astronomy and mathematics use systems of numeration where words or sequences of syllables are used to denote pure numbers or values of astronomical quantities such as the longitude etc. Three such systems, namely the bhūta-saṅkhyā system, the Āryabhaṭīya system and the kaṭapayādi system, are well known and have been widely discussed in the literature. In this article, we shall discuss a novel and ingenious vowel (uyirêḻuttu in Tamil, svara in Sanskrit) based system of numeration which has been used in the late 12th or 13th century Tamil astronomy text, Cūḍāmaṇi Uḷḷamuḍaiyān, of Tirukkoṭṭiyūr Nambi. We show that using this numeration system, Cūḍāmaṇi Uḷḷamuḍaiyān presents what is perhaps the earliest available account of the vākya system for computing the longitude of the moon. We also indicate how the same system has been employed in later Tamil texts of astronomy and in the formulation of the 248 Candravākyas in Tamil, which are referred to as the Pañcāṅgavākyas.