Sunday, October 11, 2009

A convention in Sanskrit literature for representing numerals

What you are referring to is a Sanskrit convention that attaches, based on Indian mythology, puranaas, and other traditional literature, certain numerals with names of deities, natural phenomena, parts of the human body etc.

Instead of writing those numbers, the associated names could be used by an author and the reader could conjecture at the underlying numbers. This was particularly of use when putting down a number in a stanza as that gave the writer the freedom to use an alternate for the number that would agree with the meter. (As you are perhaps aware, most Sanskrit writing, including works on subjects like jyotisha - a mix of astronomical calculations of position of heavenly bodies and astrological predictions - was composed in meters, perhaps to make it easy to learn by heart.)

As an example, see the following from Leelavati, a composition of Bhaskara (12th century) that deals with arithmetic, some algebra and some geometry. Here Bhaskara gives two formulas about the relation between the diameter and the circumference of a circle. In the first he proposes that the diameter be multiplied by 3927, and the product divided by 1250; the quotient will be a very precise circumference. He also states that as a broad calculation, diameter multiplied by 22 and divided by 7 gives a result for practical use. His exact verse for this is as follows: (Transliteration coded as for Itrans)

vyaase bhanandaagnihate vibhakte khabaaNasuuryaiH paridhiH susuukShmaH | dwaavi.nshatinighne vihR^ite.atha shailaiH sthuulothavaa.asyaadvyavahaarayogyaH ||

This translates as follows: When the diameter (vyaasa) is multiplied by bha nanda agni (representing respectively 27 9 3 i.e. 3927), and divided by kha baana suurya (representing 0 5 12 i.e. 1250) , it gives an accurate measure of the circumference. When the diameter is multiplied by dwaa+vi.nshati (22, the actual number) and divided by shailas, it gives a result which is a rough measure. [The number 7 is represented by shaila or mountain - the Sanskrit literary tradition counts 7 mountains as kulashailas or major mountains. These are i) Mahendra ii) Malaya iii) Sahya iv) Shuktiman v) R^ikSha vi) Vindhya vii) paariyaatra. All these are identifiable. Sahya is Sahyaadri, parallel to the western coastline, Shuktimaan is the Himalaya, R^ikSha is the Aravali, Vindhya is the Central Indian Range etc.]

To explain this further, bha is the sky or a constellation. There are 27 stellar constellations in the Hindu tradition. Nanda is the dynasty which Chandragupta Maurya, a contemporary of Alexander, overthrew to found his own empire. The number 9 is traditionally associated with the Nandas. Agni (fire) is associated with 3 as there were 3 types of agnis in the Hindu ritualistic tradition. Moving further, kha is the sky, associated with emptiness, or 0. 5 is baana or arrow. Why? The convoluted answer is that the God of Carnal Love, Madana (Indian Cupid) is armed with 5 arrows. One of his alternative names is pa~ncasaayaka - the one with five arrows. Thus the number 5 is associated with baana or arrow. 12 is associated with the Sun God.

As you must have by now realized, these words are used as shorthands or alternatives for names of numerals. There are several ways of doing this as Sanskrit traditionally has several alternative words to describe the same thing, most describing some peculiar attribute of that thing. This increases the variety of ways in which a thing can be described. The reader, who is supposed to well-armed with the knowledge of the traditional literature, can easily cut his way through this delightful confusion!

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