Pingala


Pingala was an ancient Indian poet and mathematician, and the author of the ', also called the Pingala Sutras, the earliest known treatise on Sanskrit prosody.
The ' is a work of eight chapters in the late Sūtra style, not fully comprehensible without a commentary. It has been dated to the last few centuries BCE. In the 10th century CE, Halayudha wrote a commentary elaborating on the . According to some historians Maharshi Pingala was the brother of Pāṇini, the famous Sanskrit grammarian, considered the first descriptive linguist. Others identify him as Patanjali, the 2nd century CE scholar who authored Mahabhashya.

Combinatorics

The ' presents a formula to generate systematic enumerations of metres, of all possible combinations of light and heavy syllables, for a word of n syllables, using a recursive formula, that results in a partially ordered binary representation. Pingala is credited with being the first to express the combinatorics of Sanskrit metre, e.g.:
  • Create a syllable list x comprising one light and heavy syllable
  • Repeat till list x contains only words of the desired length n
  • * Replicate list x as lists a and b
  • ** Append syllable L to each element of list a
  • ** Append syllable G to each element of list b
  • * Append lists b to list a and rename as list x
Word length Possible combinations
1G L
2GG LG GL LL
3GGG LGG GLG LLG GGL LGL GLL LLL

Because of this, Pingala is sometimes also credited with the first use of zero, as he used the Sanskrit word śūnya to explicitly refer to the number. Pingala's binary representation increases towards the right, and not to the left as modern binary numbers usually do. In Pingala's system, the numbers start from number one, and not zero. Four short syllables "0000" is the first pattern and corresponds to the value one. The numerical value is obtained by adding one to the sum of place values. Pingala's work also includes material related to the Fibonacci numbers, called '.

Editions

  • A. Weber, Indische Studien 8, Leipzig, 1863.
  • Janakinath Kabyatittha & Brothers, Pingala Chhanda Sutram, Calcutta, 1931.
  • Nirnayasagar Press, Chand Shastra, Bombay, 1938.