Katyayana

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Kātyāyana (c. 3rd century BC) was a Sanskrit grammarian, mathematician and Vedic priest who lived in ancient India, around the time of the Greco-Bactrian Kingdom.

He is known for two works:

• The Varttika, an elaboration on Panini's grammar. Along with the Mahā-bhāsya of Patanjali, this text became a core part of the vyākarana (grammar) canon. This was one of the six Vedangas, and constituted compulsory education for Brahman students in the following twelve centuries.
• He also composed one of the later Sulba Sutras, a series of nine texts on the geometry of altar constructions, dealing with rectangles, right-sided triangles, rhombuses, etc.

Katyayana's views on the word-meaning connection tended towards naturalism. Katyayana believed, like Plato, that the word-meaning relationship was not a result of human convention. For Katyayana, word-meaning relations were siddha, given to us, eternal. Though the object a word is referring to is non-eternal, the substance of its meaning, like a lump of gold used to make different ornaments, remains undestroyed, and is therefore permanent.

Realizing that each word represented a categorization, he came up with the following conundrum (following Matilal):

If the 'basis' for the use of the word 'cow' is cowhood (a universal) what would be the 'basis' for the use of the word 'cowhood'?

Clearly, this leads to infinite regress. Katyayana's solution to this was to restrict the universal category to that of the word itself - the basis for the use of any word is to be the very same word-universal itself.

This view may have been the nucleus of the sphota doctrine enunciated by Bhartrihari in the 5th c., in which he elaborates the word-universal as the superposition of two structures - the meaning-universal or the semantic structure (artha-jāti) is superposed on the sound-universal or the phonological structure (shabda-jāti)

In the tradition of scholars like Pingala, Katyayana was also interested in mathematics. Here his text on the sulvasutras dealt with geometry, and extended the treatment of the Pythagorean theorem as first presented in 800 BC by Baudhayana.

Katyayana belonged to the Aindra school of grammarians and may have lived towards the North west of the Indian subcontinent.

[edit] See also

• Panini
• Indian mathematicians

We cannot attempt to write a biography of Katyayana since essentially nothing is known of him except that he was the author of a Sulbasutra which is much later than the Sulbasutras of Baudhayana and Apastamba. It would also be fair to say that Katyayana's Sulbasutra is the least interesting from a mathematical point of view of the three best known Sulbasutras. It adds very little to that of Apastamba written several hundreds of years earlier. We do not know Katyayana's dates accurately enough to even guess at a life span for him, which is why we have given the same approximate birth year as death year.

Katyayana was neither a mathematician in the sense that we would understand it today, nor a scribe who simply copied manuscripts like Ahmes. He would certainly have been a man of very considerable learning but probably not interested in mathematics for its own sake, merely interested in using it for religious purposes. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites and to improve and expand on the rules which had been given by his predecessors. Katyayana would have been a priest instructing the people in the ways of conducting the religious rites he describes.

Katyayana lived in a period when the religious rites that the Sulbasutras were written to support were becoming less influential. People were turning to other religions and perhaps this lack of vigour in the religion at this time partly explains why several hundreds of years after Apastamba Katyayana adds little of importance to the Sulbasutra which he wrote.

See the article Indian Sulbasutras for more information on the Sulbasutras in general and the mathematical results which they contain.

[edit] References

• O'Connor, John J..; Edmund F. Robertson "Katyayana". MacTutor History of Mathematics archive.
• Matilal, Bimal Krishna (1990/2001), The word and the world: India's contribution to the study of language, Oxford University Press, ISBN 0-19-565512-5.

[edit] External links

• Katyayana and Advaita