Villagetalkies at 01:51, 13 January 2024

2024-01-13T01:51:51Z

New page

{{Use dmy dates|date=August 2019}}
{{Use Indian English|date=August 2019}}
'''Chandravākyas''' ({{IAST3|Candravākyas}}) are a collection of numbers, arranged in the form of a list, related to the motion of the [[Moon]] in its orbit around the [[Earth]]. These numbers are couched in the [[katapayadi system]] of representation of numbers and so apparently appear like a list of words, or phrases or short sentences written in [[Sanskrit]] and hence the terminology ''Chandravākyas''.<ref name="Sarma">{{cite journal|last=K.V. Sarma|title=A Survey of Source Materials|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b5e_1.pdf|accessdate=3 May 2010|archive-url=https://web.archive.org/web/20110111002139/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b5e_1.pdf|archive-date=11 January 2011|url-status=dead|journal = Indian Journal of history of Mathematics|volume = 20 |pages = 1-20 | year = 1985 }}</ref> In [[Sanskrit]], ''Chandra'' is the [[Moon]] and ''vākya'' means a sentence. The term ''Chandravākyas'' could thus be translated as '''Moon-sentences'''.<ref name="Selin">{{cite book|editor-last=Selin|editor-first=Helaine |editor-link=Helaine Selin|title=Encyclopaedia of the history of science, technology, and medicine in non-western cultures|publisher=[[Springer Science+Business Media|Springer]]|year=1997|isbn=978-0-7923-4066-9}} (p.522)</ref>

[[Vararuchi]] (c. 4th century [[BCE|CE]]), a legendary figure in the astronomical traditions of [[Kerala]], is credited with the authorship of the collection of ''Chandravākyas''. These were routinely made use of for computations of native almanacs and for predicting the position of the Moon.<ref>{{cite book|last=Raja|first=C. Kunhan|title=Chandravakyas of vararuci: A practical guide for calculating the position of the sun and moon, namely, tithi and naksatra, on any day of the year|publisher=Adyar Library, Madras|year=1946}}</ref> The work ascribed to Vararuchi is also known as ''Chandravākyāni'', or ''Vararucivākyāni'', or ''Pañcāṅgavākyāni''.<ref>{{cite book|last=Pingree|first=David Erwin|title=Census of the Exact sciences in Sanskrit|publisher=[[American Philosophical Society]]|year=1994|pages=756|isbn=978-0-87169-213-9}} (p.558)</ref>

[[Madhava of Sangamagrama]] (c. 1350 – c. 1425), the founder of the [[Kerala school of astronomy and mathematics]], had set forth a revised set of ''Chandravākyās'', together with a method for computing them, in his work titled [[Venvaroha]].<ref name="Selin"/>

''Chandravākyas'' were also popular in Tamil Nadu region of South India. There, the astrologers and astronomers used these ''vākyā''s to construct almanacs. These almanacs were popularly referred to as the ''Vākya-pañcāṅga''s.<ref>{{cite web|url=https://www.scribd.com/doc/18006659/Panchangam-Calculations|title=Panchangam Calculations|last=Karanam |first=Ramakumar|accessdate=5 May 2010}}</ref> This is used in contrast to the modern mode computation of almanacs based on parameters derived from astronomical observations that are known as ''Dṛk Pañcāṅgas'' ( or ''Thirukanitha Pañcāṅgas'').

==''Vākya'' tradition==

The [[Parahita]] system of astronomical computations introduced by [[Haridatta]] (ca. 683 [[BCE|CE]]), though simplified the computational processes, required long tables of numbers for its effective implementation.<ref name="Sarma"/> For timely use of these numbers they had to be memorised in toto and probably the system of constructing astronomical ''Vākya''s arose as an answer to this problem. The [[katapayadi system]] provided the most convenient medium for constructing easily memorable
[[mnemonic]]s for the numbers in these tables. ''Chandravākyās'' ascribed to [[Vararuci]] are the earliest example of such a set of [[mnemonic]]s. The period of [[Vararuci]] of [[Kerala]] tradition has been determined as around fourth century [[BCE|CE]] and the year of the promulgation of the ''Parahita'' system is known to be 683 [[BCE|CE]], Vararuci's ''Chandravākyās'' should have been around at the time of the institution of the ''Parahita'' system.

Besides Vararuci's ''Vākya''s, several other sets of ''Vākyas'' had been composed by astronomers and mathematicians of the [[Kerala school of astronomy and mathematics|Kerala school]]. While Vararuci's ''Vākya''s contain a list of 248 numbers, another set of ''Vākyas'' relating to [[Moon]]'s motion contains 3031 numbers. There is a set of 2075 ''Vākya''s called ''Samudra-vākyas'' or ''Maṇḍala-vākyas'' or ''Kujādi-pañcagraha-mahāvākyas'' relating to the motion of the five planets Kuja ([[Mars]]), Budha ([[Mercury (planet)|Mercury]]), Guru ([[Jupiter]]), Bhrigu ([[Venus]]) and Sani ([[Saturn]]). There are also lists of ''Vākya''s encoding other mathematical tables like [[Madhava's sine table]].<ref name="Sarma"/>

==''Vākya-pañcāṅga''==

The first known text to use these ''Chandravākyas''s is [[Haridatta]]'s manual on his ''Parahita'' system, known as ''Graha-cāra-nibandhana''. The next major work that makes use of the mnemonic system of the ''Vākya''s which has come down to us is ''Vākya-karaṇa'' (''karaṇa'', or computations, utilising ''Vākya''s). The authorship of this work is uncertain, but, is apocryphally assigned to [[Vararuci]]. The work is known to have been composed around 1300 [[BCE|CE]]. It has been extensively commented upon by Sundararaja (c.1500 [[BCE|CE]]) of Trichinopopy of [[Tamil Nadu]]. The almanac makers of [[Tamil Nadu]] fully make use of this ''Vākya-karaṇa'' for computing the almanacs. These almanacs are known as ''Vākya-pañcāṅga''s.<ref name="Sarma"/>

==Numbers encoded in ''Chandravākyās''==

The [[Moon]]'s orbit approximates an [[ellipse]] rather than a circle. The orientation and the shape of this [[orbit]] is not fixed. In particular, the positions of the extreme points,
the point of closest approach ([[perigee]]) and the point of farthest excursion ([[apogee]]), make a full circle in about nine years. It takes the [[Moon]] longer to return to the same position, [[perigee]] or [[apogee]], because it moved ahead during one revolution. This longer period is called the [[anomalistic month]], and has an average length of 27.554551 days (27 d 13 h 18 min 33.2 s). The apparent diameter of the Moon varies with this period. 9 [[anomalistic month]]s constitute a period of approximately 248 days. The differences in the [[longitude]]s of the Moon on the successive days of a 248-day cycle constitute the ''Chandravākyas''. Each set of ''Chandravākyas'' contains a list of 248 ''Vākyās'' or sentences.<ref>{{cite journal|last=K. Chandra Hari|year=2003|title=Computation of the true moon by Madhava of Sangamagrama|journal=Indian Journal of History of Science|volume=38|issue=3|pages=231–253|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/2000c4df_231.pdf|accessdate=6 May 2010|archive-url=https://web.archive.org/web/20120316083104/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/2000c4df_231.pdf|archive-date=16 March 2012|url-status=dead}}</ref>

==See also==
*[[Indian astronomy]]
*[[Indian mathematics]]
*[[Vākyakaraṇa]]
*[[Vākyapañcāṅga]]
*[[Vararuchi]]

==References==

{{reflist}}

==Further reading==
*For details on Madhava's method of computation of Chandravakyas see : {{cite journal|last=K. Chandra Hari|year=2003|title=Computation of the true moon by Madhava of Sangamagrama|journal=Indian Journal of History of Science|volume=38|issue=3|pages=231–253|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/2000c4df_231.pdf|accessdate=6 May 2010|archive-url=https://web.archive.org/web/20120316083104/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/2000c4df_231.pdf|archive-date=16 March 2012|url-status=dead}}
*For a discussion on the history of the 248-day schemes see : {{cite journal|last=Jones|first=Alexander |date=March 1983|title=The development and transmission of 248-day schemes for lunar motion in ancient astronomy |journal=Archive for History of Exact Sciences|publisher=Springer |location=Berlin / Heidelberg|volume=29|issue=1|pages=1–36|bibcode = 1983AHES...29....1J |doi=10.1007/bf00535977|s2cid=121595932 }}
*For a discussion of the 248-day schemes in Babylonian astronomy see: {{cite book|last=Otto Neugebauer|title=The exact sciences in antiquity|url=https://archive.org/details/exactsciencesant00neug_249|url-access=limited|publisher=[[Courier Dover Publications]]|year=1969|pages=[https://archive.org/details/exactsciencesant00neug_249/page/n269 240]|isbn=978-0-486-22332-2 }} (Chapter II)

{{Kerala School}}
{{Scientific Research in Kerala |state=collapsed}}

[[Category:Hindu astronomy]]
[[Category:Kerala school of astronomy and mathematics]]
[[Category:Indian astronomy texts]]

Chandravakyas - Revision history

Villagetalkies at 01:51, 13 January 2024