[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 # Jyotihshastra: Astral and Mathematical Literature c2: Introduction Jyotiḥśāstra: Astral and Mathematical Literature c2 - **Language:** English ### Introduction ### [c2.1](https://indike.org/pramana/ins.science.pingree-1981.c2.1) Traditionally \*jyotiḥśāstra\* is divided into three \*skandhas\*: \*saṃhitā\* (omens), \*gaṇita\* (astronomy), and \*horā\* (astrology) (see BS 1, 9); and, according to the medieval \*muhūrta\* treatises, was originally promulgated by the eighteen sages Brahmācārya, Vasiṣṭha, Atri, Manu, Paulastya, Romaśa, Marīci, Aṅgiras, Vyāsa, Nārada, Śaunaka, Bhṛgu, Cyavana, Yavana, Garga, Kaśyapa, Parāśara, and Sūrya. The validity of the first tradition was maintained only by artificially including new forms of scientific writing—e.g., treatises on mathematics, on \*muhūrta\*, or on \*praśna\*—in one or another of the three \*skandhas\*, while there was never any validity to the second. In this volume an attempt has been made to establish a more accurate classification of the areas of \*jyotiḥśāstra\* actually made the subject of independent works, and to survey the literature in each area (but omitting the sectarian Jaina contributions) in order to establish a correct historical origin (often from outside of India) and development of each. To have included discussions of the technical aspects of these sciences, however, would both have duplicated much that has already been done (though in some areas it desperately needs to be done better) and have extended the length of this volume far beyond reasonable bounds. ### [c2.2](https://indike.org/pramana/ins.science.pingree-1981.c2.2) Nor has any attempt been made to deal with the literary qualities of the works discussed. The primary texts are certainly all in metrical form, but are generally written in a very crabbed and obscure style designed to stimulate the student's memory of the procedures to be followed, but frequently not even pretending to provide the full algorithm for a particular problem; that was to be found, if not in the repetitiousness of the science, in the guru's oral tradition or in the prose commentary. Thus, while cleverness and imprecision both abound in this poetry, the normal canons of \*alaṅkāra\* are simply not applicable; only rarely, as in the \*ṛtuvarṇana\* in Bhāskara's SŚB, is any poetic feeling made manifest. ### [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. ### [c2.4](https://indike.org/pramana/ins.science.pingree-1981.c2.4) The following pages will show that our knowledge of Indian \*jyotiḥśāstra\* is rather spotty. This is due both to the accidents that cause the preservation (and availability) of one text rather than another, and to the lack of reliable and accurate descriptions of the many unpublished manuscripts. The second disability is being slowly alleviated as CESS progresses; I have generally referred the reader to it, when available, for information about an author, his works, and what modern scholars may have said about them, though I have attempted in all cases to give reasonably complete listings of published editions as they are a useful guide to modern interests. Those modern interests lie overwhelmingly in \*jātaka\*, \*tājika\*, \*muhūrta\*, \*praśna\*, and various forms of divination; classical astronomy and mathematics had virtually ceased to be studied or taught by the end of the nineteenth century. A new group of Indian and foreign scholars has, however, begun to work in these areas since World War II; and, while much is still unfortunately published that is of little or no value, some progress toward an understanding of the origins and developments of these sciences has been made. I hope that this volume will stimulate more serious interest in this field. ## Linked texts (1) - [Bṛhatsaṃhitā](https://indike.org/pramana/in.astro.samhita.rsi.brhatsamhita.1.9) — Varāhamihira, Sanskrit --- Source: [https://indike.org/pramana/ins.science.pingree-1981.c2](https://indike.org/pramana/ins.science.pingree-1981.c2) · Pramāṇa