Candravakyas

Candravakyas

Candravākyās 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 Candravākyās.[1] In Sanskrit, Candra is the Moon and vākya means a sentence. The term Candravākyās could thus be translated as Moon-sentences.[2]

Vararuci (c. 4th century CE), a legendary figure in the astronomical traditions of Kerala, is credited with the authorship of the collection of Candravākyās.[3] These were routinely made use of for computations of native almanacs and for predicting the position of the Moon.[4] The work ascribed to Vararuci is also known as Candravākyāni, or Vararucivākyāni, or Pañcāṅgavākyāni.[5]

Madhava of Sangamagrama (c. 1350 – c. 1425), the founder of the Kerala school of astronomy and mathematics, had set forth a revised set of Candravākyās, together with a method for computing them, in his work titled Venvaroha.[2]

Candravākyās were also popular in Tamil Nadu region of South India. There, the astrologers and astronomers used these vākyās to construct almanacs. These almanacs were popularly referred to as the Vākya-pañcāṅgas.[6] This is used in contrast to the modern mode computation of almanacs based on parameters derived from astronomical observations. These modern almanacs are known as Dṛk Pañcāṅgas ( or Thirukanitha Pañcāṅgas).

Contents

The Vākya tradition

The Parahita system of astronomical computations introduced by Haridatta (ca. 683 CE), though simplified the computational processes, required long tables of numbers for its effective implementation.[1] For timely use of these numbers they had to be memorised in toto and probably the system of constructing astronomical Vākyas arose as an answer to this problem. The katapayadi system provided the most convenient medium for constructing easily memorable mnemonics for the numbers in these tables. Candravākyās ascribed to Vararuci are the earliest example of such a set of mnemonics. The period of Vararuci of Kerala tradition has been determined as around fourth century CE and the year of the promulgation of the Parahita system is known to be 683 CE, Vararuci's Candravākyās should have been around at the time of the institution of the Parahita system.

Besides Vararuci's Vākyas, several other sets of Vākyas had been composed by astronomers and mathematicians of the Kerala school. While Vararuci's Vākyas contain a list of 248 numbers, another set of Vākyas relating to Moon's motion contains 3031 numbers. There is a set of 2075 Vākyas called Samudra-vākyas or Maṇḍala-vākyas or Kujādi-pañcagraha-mahāvākyas relating to the motion of the five planets Kuja (Mars), Budha (Mercury), Guru (Jupiter), Bhrigu (Venus) and Sani (Saturn). There are also lists of Vākyas encoding other mathematical tables like Madhava's sine table.[1]

Vākya-pañcāṅga

The first known text to use these Candravākyāss 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 Vākyas which has down to us is Vākya-karaṇa (karaṇa, or computations, utilising Vākyas). The authorship of this work is uncertain, but, is apocryphally assigned to Vararuci. The work is known to have been composed around 1300 CE. It has been extensively commented upon by Sundararaja (c.1500 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-pañcāṅgas.[1]

The numbers encoded in Candravākyās

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 months constitute a period of approximately 248 days. The differences in the longitudes of the Moon on the successive days of a 248-day cycle constitute the Candravākyās. Each set of Candravākyās contains a list of 248 Vākyās or sentences.[7]

See also

References

  1. ^ a b c d K.V. Sarma. A Survey of Source Materials. http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b5e_1.pdf. Retrieved 3 May 2010. 
  2. ^ a b Selin, Helaine (1997). Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Springer. ISBN 9780792340669.  (p.522)
  3. ^ Sharma, P.D. (2004). Hindu Astronomy. Global Vision Publishing House. pp. 294. ISBN 9788182200562.  (p.210 – 212)
  4. ^ Raja, C. Kunhan (1946). Candravakyas of vararuci: A practical guide for calculating the position of the sun and moon, namely, tithi and naksatra, on any day of the year. Adyar Library, Madras. 
  5. ^ Pingree, David Erwin (1994). Census of the Exact sciences in Sanskrit. American Philosophical Society. pp. 756. ISBN 9780871692139.  (p.558)
  6. ^ Karanam, Ramakumar. "Panchangam Calculations". http://www.scribd.com/doc/18006659/Panchangam-Calculations. Retrieved 5 May 2010. 
  7. ^ K. Chandra Hari (2003). "Computation of the true moon by Madhava of Sangamagrama". Indian Journal of History of Science 38 (3): 231–253. http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/2000c4df_231.pdf. Retrieved 6 May 2010. 

Further reading


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