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Lokavibhaga

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Lokavibhaga
Information
AuthorSiṃhasūri
LanguageSanskrit
Period458 CE

The Lokavibhāga (literally "division of the universe") is a 5th-century Sanskrit text by Rishi Simhasuri.[1] Its manuscript was first discovered in an Indian temple of Karnataka by M.R.R. Narasimhachar. The Lokavibhaga consists of 11 chapters and a total of 1737 verses (shlokas) distributed over these chapters. The text has an incomplete colophon, which states it was completed in a village named Patalika near Kanchi (Tamil Nadu) in the 22nd year of Simhavarman's rule in Banarastra. The colophon includes astronomical observations along with a samvat date and year which together indicate the surviving copy was completed on 25 August 458 CE.[2][3][4]

The Lokavibhaga is notable as the oldest known text in the world that clearly uses three principles of positional decimal arithmetic system together – graphical signs and terms as numerals, assigning a value to the same numeral depending on the position it occupies in a number, and the use of fully operational zero. This Indian system contrasted with competing ancient arithmetic systems developed independently in Babylon, ancient Rome and China.[5][6][7]

The text presents Jain cosmology. It has been claimed by the Digambara tradition of Jainism to be a Sanskrit translation of an older Prakrit-language text Loyavibhaga by Muni Sarvanandi. The Lokavibhaga mentions Sarvanandi and others, but does not mention any text called "Loyavibhaga". No manuscript copy of the claimed older Prakrit "Loyavibhaga" has been found so far.[8][9]

The Lokavibhaga presents its cosmological ideas in a form that takes its mathematical system for granted. It is not a mathematical treatise, and it does not introduce principles of positional decimal arithmetic system. The arithmetic system used in Lokavibhaga text, state Jain and Dani, must have been invented earlier by someone else in some other context. That system of expressing numbers with positional decimal arithmetic was accepted and must have been in wide use in India by mid 5th-century to appear as it does in the Lokavibhaga text.[10] The same Indian arithmetic system and operations appears in the mathematical treatise of Aryabhata published in 510 CE.[11]

The surviving manuscripts of the Lokavibhāga are listed in the New Catalogus Catalogorum.[12] The published edition of the surviving Lokvibhaga manuscript is a palm leaf copy of the original Sanskrit text, likely from 11th or 12th century.[13] The text was edited and translated in 1962 into the Hindi language by Balachandra Siddhanta-Shastri.[14][15]

References

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  1. ↑ Siddhanta-Shastri, Balachandra. Lok Vibhag (1962) Ac 6785. Digital Library Of India. pp. 25–26.
  2. ↑ Siddhanta-Shastri, Balachandra. Lok Vibhag (1962) Ac 6785. Digital Library Of India. pp. 22–25.
  3. ↑ Bailey, David H.; Borwein, Jonathan M.; Mattingly, Andrew; Wightwick, Glenn (1 August 2013). "The Computation of Previously Inaccessible Digits of π2 and Catalan's Constant" (PDF). Notices of the American Mathematical Society. 60 (6): 844. doi:10.1090/noti1015. ISSN 0002-9920.
  4. ↑ Fleet, J. R. (July 1915). "XXII. A New Gaṅga Record and the Date of aka 380". Journal of the Royal Asiatic Society. 47 (3): 471–485. doi:10.1017/S0035869X00048462.
  5. ↑ Bailey, David; Borwein, Jonathan (2010), The Greatest Mathematical Discovery?, pp. 3–5, doi:10.2172/983483, OSTI 983483
  6. ↑ Ifrah, Georges (9 October 2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Wiley. pp. 415–416. ISBN 978-0-471-39340-5.
  7. ↑ Bailey, David; Borwein, Jonathan (2010), The Greatest Mathematical Discovery?, p. 5, doi:10.2172/983483, OSTI 983483; An example of a number in the Lokavibhaga is the diameter of Nandisvaradvipa, which it states to be equal to panchabhyah khalu shunyebhyah param dve sapta chambaram ekam trini cha rupam cha yojanas = 13107200000 yojanas when the verse is read right to left
  8. ↑ Singh, Nagendra Kr (2001). Encyclopaedia of Jainism. Anmol Publications. ISBN 978-81-261-0691-2.
  9. ↑ Siddhanta-Shastri, Balachandra. Lok Vibhag (1962) Ac 6785. Digital Library Of India. pp. 25–27.
  10. ↑ Jain, Surender K.; Dani, S. G. (26 July 2022). Mathematics In Ancient Jaina Literature. World Scientific. pp. 30–31. ISBN 978-981-12-5551-9.
  11. ↑ Bailey, David; Borwein, Jonathan (2010), The Greatest Mathematical Discovery?, doi:10.2172/983483, OSTI 983483
  12. ↑ Dash, Siniruddha (2013). New catalogus catalogorum: an alphabetical register of Sanskrit and allied works and authors Vol. 26 Vol. 26. Madras: Univ. of Madras. OCLC 931470378.
  13. ↑ Aiyangar, S. Krishnaswami (1923). Some Contributions Of South India To Indian Culture.
  14. ↑ Siddhanta-Shastri, Balachandra. Lok Vibhag (1962) Ac 6785. Digital Library Of India.
  15. ↑ Gupta, R. C (1983). "Spread and Triumph of Indian Numerals". Indian Journal of History of Science Calcutta. 18 (1): 23–38.
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