Subject: [HM] Indian astronomy and mathematics
From: Kim Plofker (Kim_Plofker@Brown.edu)
Date: Fri Jan 28 2000 - 23:52:55 EST
> In a message dated 1/27/00, Dinesh Maheshwari refers to <<the re-dating,
> in 1990s, of the Vedas to 4300BC (based on the astronomical observations
> in the RigVeda)>>
>
> May one know more about this re-dating?
Indian "tables" of planetary parameters are lists first appearing in treatises
of the middle of the first millennium CE. The suggested re-datings of the
Vedic texts to the fourth millennium BCE or earlier, which have been
proposed in various forms over the past couple of centuries, are based on
attributing a very high degree of precision to some statements in them about
the relation of star positions to direction and seasons. An example is
Tilak's and Jacobi's famous interpretation of the _Satapathabrahmana_'s
statement that the Pleiades are "in the east" to mean that they are at
precisely the east point; owing to the earth's precession, the Pleiades'
closest approach to the intersection of ecliptic and equator took place
near the middle of the third millennium BCE. Hence this statement is
considered to imply a much earlier date for the Vedic texts than standard
Indologist chronology (which usually puts the _Satapathabrahmana_'s
composition in the early first millennium BCE) adopts. As a result,
the re-dating arguments of Elst cited by Maheshwari seem rather circular to me:
it's claimed that 1) astronomical statements in the Vedic texts are intended
as very specific indicators of position, thereby fixing the dates of the
texts in a way that would not be valid if the statements were in fact intended
as more general descriptions; 2) these positions would not have been found
by back-computation via the only systems of Indian mathematical astronomy we
have any detailed knowledge of, dating from the first millennium CE and later;
so 3) therefore, these statements must reflect actual observations at or
around these inferred dates, rather than back-computations from later dates.
If the astronomical statements were _not_ in fact intended to fix a high
degree of precision in the modern sense, this argument falls to the ground.
And in fact, more conservative historians of Indian science (whose positions
are for the most part reflected in David Pingree's "History of Mathematical
Astronomy in India" in vol. 15 of the _Dictionary of Scientific
Biography_) feel that the statements in the Vedic texts simply aren't
specific enough to imply an archeoastronomical dating that's sufficiently
secure to outweigh other evidence for a later chronology. Vedic chronology
is notoriously vague and unsatisfactory, but if the standard hypothesis
does ever turn out to be indisputably off by many centuries or more,
"Vedic astronomy" will probably not be what changes our minds.
Apart from the controversial dating, however, the large powers of ten
named in Vedic texts do indeed reflect remarkable powers of mathematical
imagination, and I'm glad to see them brought to the attention of this
list, along with mention of the interesting mathematical interpretation of
"purna", "fullness", and the Arabic adoption of the zero with the other
Indian numerals. (Whether zero can be said to "come from" the "Indian
concept of void" is carefully discussed in much more detail in R. C. Gupta's
"Who Invented the Zero?" _Ganita Bharati_ 1995.) Similarly, I am happy to
see in an earlier post of Maheshwari's a description of Pingala's intriguing
binary operations in the _Chandahsutra_, described earlier by Datta and
Singh in their _History of Hindu Mathematics_; I think, however, that
when these (_very_ terse and cryptic) sutras are interpreted so broadly as
a generalized binary number system, it somewhat obscures their historical
role as an ingenious solution of problems in "chandas" or prosody. (The
reference to a "millennium long foreign rule hostile to scholarly activities"
is unworthy of an historian, and I hope it just reflects the carelessness
of some less scholarly summarizer: in fact, the centuries after 1000 CE saw
the accomplishment of remarkable achievements in mathematical science within
India, by both Hindus (as well as Jains and others) and Muslims, both
separately and in collaboration.)
With best wishes,
Kim Plofker
Department of History of Mathematics
Brown University
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