Everything about Pingala totally explained
» For the subtle energy channel described in yoga, see Pingala_(yoga).Pingala (
पिङ्गल ) was an ancient Indian writer, famous for his work, the
Chandas Shastra (also
Chandas Sutra ), a
Sanskrit treatise on
prosody considered one of the
Vedanga. He developed advanced mathematical concepts for describing the patterns of prosody.
In Indian literary tradition, Pingala is identified as the younger brother of
Panini who according to tradition were born in
Shalatula. Panini was the great grammarian who flourished in the 4th century BC. Other traditions identify him with
Patanjali, the author of the
Mahabhashya.
Mylius (1983:68) considers the Chandas-shastra as "very late" within the Vedanga corpus. This would place it close to the beginning of the
Common Era, likely post-dating
Mauryan times (R. Hall,
Mathematics of Poetry, has "c.
200 BC").
The shastra is divided into eight chapters. It was edited by Weber (1863). It is at the transition between
Vedic meter and the classical meter of the Sanskrit epics.
The 10th century mathematician
Halayudha commented and expanded it. Pingala presents the first known description of a
binary numeral system. He described the binary numeral system in connection with the listing of Vedic meters with short and long syllables. His discussion of the combinatorics of meter, corresponds to the
binomial theorem. Halayudha' s commentary includes a presentation of the
Pascal's triangle (called
meru-prastaara). Pingala's work also contains the basic ideas of
Fibonacci number (called
maatraameru ).
Use of
zero is sometimes mistakenly ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, while Pingala used short and long syllables. Four short syllables (binary "0000") in Pingala's system, however, represented the number one, not zero. Positional use of zero dates from later centuries and would have been known to
Halayudha but not to Pingala.
Editions
- A. Weber, Indische Studien 8, Leipzig, 1863.
- Bibliotheca Indica, Calcutta 1871-1874, reprint 1987.
Further Information
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