Pingala

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For the subtle energy channel described in yoga, see Nadi (yoga).
Pingala
Bornunclear, 3rd or 2nd century BCE
mātrāmeru, binary numeral system
.

romanized: Piṅgalasūtrāḥ, lit. 'Pingala's Threads of Knowledge'), the earliest known treatise on Sanskrit prosody.[4]

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.[5][6] In the 10th century CE, Halayudha wrote a commentary elaborating on the Chandaḥśāstra. According to some historians Maharshi Pingala was the brother of Pāṇini, the famous Sanskrit grammarian, considered the first descriptive linguist.[7] Another think tank identifies him as Patanjali
, the 2nd century CE scholar who authored Mahabhashya.

Combinatorics

Pascal's Triangle
" as depicted in a later version of Pingala's Chandaḥśāstra

The Chandaḥśāstra presents a formula to generate systematic enumerations of

binary representation.[8] Pingala is credited with being the first to express the combinatorics of Sanskrit metre, eg.[9]

  • Create a syllable list x comprising one light (L) and heavy (G) 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
Possible combinations of Guru and Laghu syllables in a word of length n[10]
Word length (n characters) Possible combinations
1 G L
2 GG LG GL LL
3 GGG LGG GLG LLG GGL LGL GLL LLL

Because of this, Pingala is sometimes also credited with the first use of

Fibonacci numbers, called mātrāmeru.[14]

Editions

  • A. Weber, Indische Studien 8, Leipzig, 1863.
  • Janakinath Kabyatittha & brothers, ChhandaSutra-Pingala, Calcutta, 1931.[15]
  • Nirnayasagar Press, Chand Shastra, Bombay, 1938[16]

Notes

  1. ^
    ISBN 978-0-691-12067-6
    .
  2. doi:10.1016/0315-0860(85)90021-7. Archived from the original
    (PDF) on 2019-07-24. Retrieved 2018-11-29.
  3. ^ "Pingala – Timeline of Mathematics". Mathigon. Retrieved 2021-08-21.
  4. ISBN 978-81-208-0045-8
    .
  5. ^ R. Hall, Mathematics of Poetry, has "c. 200 BC"
  6. ^ Mylius (1983:68) considers the Chandas-shāstra as "very late" within the Vedānga corpus.
  7. ^ François & Ponsonnet (2013: 184).
  8. ^ Van Nooten (1993)
  9. S2CID 3637061
    . Retrieved 27 May 2022 – via JSTOR.
  10. ^ Shah, Jayant. "A HISTORY OF PIṄGALA'S COMBINATORICS" (PDF).
  11. ^ Plofker (2009), pages 54–56: "In the Chandah-sutra of Pingala, dating perhaps the third or second century BC, [...] Pingala's use of a zero symbol [śūnya] as a marker seems to be the first known explicit reference to zero. ... In the Chandah-sutra of Pingala, dating perhaps the third or second century BC, there are five questions concerning the possible meters for any value “n”. [...] The answer is (2)7 = 128, as expected, but instead of seven doublings, the process (explained by the sutra) required only three doublings and two squarings – a handy time saver where “n” is large. Pingala’s use of a zero symbol as a marker seems to be the first known explicit reference to zero."
  12. ISBN 978-981-277-582-5
    .
  13. ^ B. van Nooten, "Binary Numbers in Indian Antiquity", Journal of Indian Studies, Volume 21, 1993, pp. 31–50
  14. ISBN 978-0-253-33388-9
    . Virahanka Fibonacci.
  15. ^ Chhanda Sutra - Pingala.
  16. ^ Pingalacharya (1938). Chand Shastra.

See also

References

  • Amulya Kumar Bag, 'Binomial theorem in ancient India', Indian J. Hist. Sci. 1 (1966), 68–74.
  • George Gheverghese Joseph (2000). The Crest of the Peacock, p. 254, 355. Princeton University Press.
  • Klaus Mylius, Geschichte der altindischen Literatur, Wiesbaden (1983).
  • Van Nooten, B. (1993-03-01). "Binary numbers in Indian antiquity". Journal of Indian Philosophy. 21 (1): 31–50.
    S2CID 171039636
    .

External links
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