[Pramāṇa](https://indike.org/pramana/) › [Studies](https://indike.org/pramana/ins) › [Science, technology and education](https://indike.org/pramana/ins.science) › [Jyotihshastra: Astral and Mathematical Literature](https://indike.org/pramana/ins.science.pingree-1981) › c2.3 # Jyotihshastra: Astral and Mathematical Literature c2.3 Jyotiḥśāstra: Astral and Mathematical Literature c2.3 - **Language:** English ### [c2.3](https://indike.org/pramana/ins.science.pingree-1981.c2.3) Two of the difficulties generated by the use of a poetic form were the necessity of expressing numbers metrically, and the difficulty of maintaining a fixed technical vocabulary. The latter impediment led to the invention of many synonyms, and the use of single terms in several different, if related, senses; this, of course, increased the ambiguity and imprecision inherent in a system where the texts' purpose is to jog the memory rather than to teach the complete course. The former problem was solved in two ways: by using common objects that appear or are understood to appear in the world in fixed quantities as synonyms for those quantities (e.g., "eyes" are "two," "fires" are "three," "Vedas" are "four"), and by using \*akṣaras\* to refer to numbers. The former system, called the \*bhūtasaṅkhyā\*, already appears in the third century in Sphujidhvaja's \*Yavanajātaka\*. Sphujidhvaja also seems to be the first to use a symbol for zero (\*bindu\*) in the decimal place-value system (YJ 79, 6 and 7), though, of course, a dot or a circle had been used previously by both Babylonians and Greeks in the sexagesimal place-value system to represent a place with no other number in it. Āryabhaṭa invented a different way of expressing numerals, in which the consonants of the Sanskrit alphabet are used to indicate the numbers and the vowels their places (up to eighteen); unfortunately, the “words” formed thus were often unpronounceable and in any case had no meaning other than the numerical one. A different system was invented in South India that obviated this difficulty. The \*kaṭapayādi\* system (in which k, ṭ, p, and y equal 1 regardless of the vowel they are followed by) uses the consonants as equivalents of the numbers 1 to 9 and 0; four varieties of this system are known. A clever \*jyotiṣī\*, then, can construct verses that are superficially on one subject while each sequence of consonants can be read as a significant number; a good example of this is Parameśvara’s Haricarita. - [Previous: c2.2](https://indike.org/pramana/ins.science.pingree-1981.c2.2) - [Next: c2.4](https://indike.org/pramana/ins.science.pingree-1981.c2.4) - [Up: c2](https://indike.org/pramana/ins.science.pingree-1981.c2) --- Source: [https://indike.org/pramana/ins.science.pingree-1981.c2.3](https://indike.org/pramana/ins.science.pingree-1981.c2.3) · Pramāṇa