Kerala Astronomy query

Mon Mar 9 10:41:01 UTC 1992

Status: RO

Dear Richard Marsden,

I would suggest that the main starting point for Keralan astronomy in
the period you mention (14th-15th centuries) is:

  K. V. Sarma, _A history of the Kerala school of Hindu Astronomy (in
  perspective)_ (Hoshiarpur: Vishveshvaranand Institute, 1972).

This is an outstanding survey of the very remarkable mathematical
achievements of the Kerala mathematicians and astronomers from
Madhava (of Sangamagrama) onwards, and is required reading in any
study of this area.  David Pingree's works too, as Ken Zysk has already
said.  Recent articles by Takao Hayashi are also of importance (especially
nos 1. and 2. below):

1. Hayashi, T. Kusuba, T. & Yano, M. "The Correction of the
    Madhava Series for the Circumference of a Circle."
    _Centaurus_ 33 (1990): pp. 149--174.

2. Hayashi, T. Kusuba, T. \& Yano M. "The Parallel Passages on
    the Correction of the Madhava Series in Sankara's Yuktidipika
    and Kriyakramakari." _Centaurus_ , 33 (1990): pp. 149--174.
    An Appendix to the Correction of the Madhava Series for the
    Circumference of a Circle.

3. Hayashi, Takao. "A New Indian Rule for the Squaring of a
    Circle: Manavasulbasutra 3.2.9--10." _Ganita-Bharati, Bull.
    Ind. Hist. Math._ 12, 3--4 (1990): pp. 75--82.

4. Hayashi, Takao. "A Note on Bhaskara I's Rational Approximation
    to Sine." _Historia Scientiarum_ , 42 (1991): pp. 45--48.

5. Hayashi, Takao. "Narayana's Rule for a Segment of a Circle."
    _Ganita-Bharate, Bull. Ind. Soc. Hist. Math._ 12, 1--2
    (1990): pp. 1--9.

See also

1. Bag, A. K. "Madhava's Sine and Cosine Series." _Indian Journal
    of History of Science_ II, 1 (May 1976): pp. 54--57.

2. Gold, David &. Pingree, David. "A Hitherto Unknown Sanskrit
    Work concerning Madhava's Derivation." _Historia Scientiarum,
    Japan_ , 42 (March 1991): pp. 49--65.

3. Rajagopal, C. T. & Rangachari, M.S. "On Medieval Kerala
    Mathematics." _Archive for History of Exact Sciences_ 35
    (1986): pp. 91--99.

4. Sarma, K. V. "Direct Lines of Astronomical Tradition in
    Kerala." _Charudeva Shastri Felicitation Volume_ (1976): pp.
    601--604.

But none of the material I have read about the Keralan astronomers has
ever dealt with such general notions as "the nature of the cosmos".
And I doubt that the project has much of a future in its present terms.

First you have to bear in mind that we only just -- by a fluke of
manuscript preservation -- know that these guys existed at all.
Remember that when Whish first published his paper on the Hindu
Quadrature of the Circle in 1830, everyone thought he was the victim of
a forger or had somehow been duped by a crafty brahmin, because the
mathematics he was presenting was so advanced no one could credit the
Indians with its development.  What has survived is very meagre, and
extremely tantalizing:  remember, these fellows were a couple of
*centuries* ahead of Newton and Leibnitz in some of their work on power
series expansions, and it would be *very* nice to know more about
them.  Oh well.

Secondly, these Keralans were apparently wholly wrapped up in their
mathematics.  They were not developing new cosmologies, but refining
the mathematical techniques that were used to predict planetary
and stellar positions and to develop tables of geometric values. As
far as we know from the surviving sources, they just didn't say
anything about cosmology per se.  It is like looking for a theory
of general linguistics in Panini.  Very disappointing.

As for "lots of relevant works (some by missionaries) translated
into English, German, and available only in the west" (I quote from
memory), I'm afraid that that sounds like a reiteration of the
old cultural theft myth.  "The Vedas are now in Germany" and so on.
The above works are mostly published in European journals, yes.  But
Bag and Sarma have made very important contributions  -- and perhaps
Sarma's are the most important -- and these sources are
available from Indian publishers.

In my view, the *real* work to be done in this area is to scour Kerala
for more manuscript material on these schools.  The MSS of works by
known authors are listed by Pingree in the volumes of his _Census of
the Exact Sciences in India_.  The K. V.  Sarma book lists many MSS,
including anonymous works, and gives clues and guidance about where to
look, etc.  He has tried very hard himself, of course, but I feel sure
there is more to be found, given patience, tact, the right connections,
and good reading skills in Malayalam script and language, Sanskrit, and
Manipravala.  It is not a trivial business, but is very worthwhile.
Since your chap is *in* Kerala, he may well have some of this equipment
already.  His best move would be to find K. V. Sarma, and apprentice
himself to him.

Best wishes,

Dominik

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Dr Dominik Wujastyk,     | Janet:                          D.Wujastyk at uk.ac.ucl
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