Quick Facts
Biography
Pingala (Devanagari: पिङ्गल piṅgala) (c. 3rd/2nd century BC), is the influential ancient scholar and the author of the Chandaḥśāstra (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody.
The Chandaḥśāstra 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. The 10th century mathematician Halayudha wrote a commentary on the Chandaḥśāstra and expanded it.
Combinatorics
The Chandaḥśāstra presents the first known description of a binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables. The discussion of the combinatorics of meter corresponds to the binomial theorem. Halāyudha's commentary includes a presentation of the Pascal's triangle (called meruprastāra). Pingala's work also contains the Fibonacci numbers, called mātrāmeru.
Use of zero is sometimes ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, but Pingala used light (laghu) and heavy (guru) rather than 0 and 1 to describe syllables. As Pingala's system ranks binary patterns starting at one (four short syllables—binary "0000"—is the first pattern), the nth pattern corresponds to the binary representation of n-1 (with increasing positional values).
Pingala is credited with using binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), a notation similar to Morse code. Pingala used the Sanskrit word śūnya explicitly to refer to zero.
Editions
- A. Weber, Indische Studien 8, Leipzig, 1863.