Date:         Sat, 21 Oct 2000 12:36:06 -0400
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From:         Michael Witzel <[log in to unmask]>
Subject:      Re: Kak review, part II
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> important review by Kim Plofker
>of Kak's Rgvedic Astronomical Code book:
  _Centaurus_ 38 (1996), 362--364.
----------

PART II


Dr. Kak goes very much further than this, however, in assuming that the
mere presence in (or association with) the text of any number
possessing possible astronomical significance implies that the number was
deliberately chosen, in accordance with the ``\*Rgvedic code,'' by authors
fully
aware of that significance. Furthermore, for the sake of this code he is
willing to postulate scientific activity on the part of the Vedic Indians
involving
procedures and quantities not attested in this or any other phase of Indian
astronomy.

Thus, a succession of 95 increments in the area of a fire-altar is  taken
to imply the use of a 95-year intercalation cycle in the calendar (pp.
84--85, 118). Likewise, the presence of the number 108 (e.g., in the number
10,800,000 enumerating the muh\=urtas in 1000 ideal years) is ascribed to
the realization that ``108 is roughly the average distance that the sun is
in terms
of its own diameter from the earth'' (p. 99); and the combined number of
s\=uktas or hymns in the fourth, sixth, eighth, and ninth ma\*n\*dalas of
the {\it
\*Rgveda}\/ was allegedly chosen to be 339 because that number is roughly
equivalent to ``the number of disks of the sun or the moon to measure the
path across the sky...[or] sun-steps'' (p. 100).

The fact that the total number of hymns in all ten ma\*n\*dalas is 1017 ($=
339 \times 3$), while the
number of (somewhat arbitrary) subdivisions of the ma\*n\*dalas (p. 90)
into various categories is 216 ($= 108 \times 2$), is therefore supposed to
confirm that ``[t]he \*Rgvedic code then expresses a fundamental connection
between the numbers 339 and 108'' (p. 99).

Dr. Kak offers several more
deductions of this type, culminating in his reconstruction (pp. 103--107)
of the alleged ``\*Rgvedic code.'' It is asserted that because the set of
integers
yielded by all possible additive combinations of the numbers of hymns in
each ma\*n\*dala includes numbers very close to the (modern) periods of
revolution in days and in tithis for the five star-planets, it must follow
that the Indians of the Vedic period, using observational data necessarily
accumulated over centuries, had correctly established these periods and
encoded them in the selection of the hymns.

In the complete absence of any real
textual evidence that the culture of the Vedic period was concerned to the
slightest degree with such endeavours, or that notions such as the
``sun-step''
have any historical place in Indian astronomy, it is incumbent upon Dr. Kak
to provide thoroughly convincing internal evidence to support his position;
and he has not accomplished this. The ``evidence,'' in fact, does not go
much beyond a single attempt, in the very brief section entitled
``Probabilistic
Validation'' (pp. 106--107), to argue from statistical data that the
presence of planetary period numbers in the \*Rgvedic hymn number
combinations
cannot be coincidental. The reasoning, however, is flawed; for the sake of
the non-technical reader who may be intimidated by mathematical jargon, it
is
worth while to explain why.

Briefly, Dr. Kak's claim is as follows: The set of numbers generated by the
additive combinations of the ten numbers  enumerating the hymns in each of
the ten books contains 461 distinct integers ranging from 43 to 1017.
Assuming that these 461 numbers are random
values uniformly distributed over this interval, the probability of finding
any given positive integer less than 1017 among them is somewhat less than
$1/2$. Thus only about half of Dr. Kak's selected astronomical constants
should appear in this set; the fact that not half but all of them are found
is
therefore considered to prove that the hymn numbers were designedly
selected to encode these values, since the probability that all of them
might appear
purely at random is ``so small that the claim that the Book numbers were
deliberately chosen may be taken to be confirmed.''

This argument, however, is
completely invalidated by the simple fact that the set of values generated
from sums of a given set of numbers is generally {\it not}\/ uniformly
distributed
over the interval it spans; as a rule, there will be a few very small sums
and a few very large ones, but most will cluster about the middle of the
interval. In
this example, out of the 461 hymn combination numbers, no fewer than 320
fall within the range 301--800 containing most of the planetary period
constants.

This, combined with the fact that Dr. Kak (by his own account; p. 105)
permits errors of at least $\pm 1$ in his matching of numbers, means
that the high proportion of matches has no statistical significance
whatever. Thus it cannot conscientiously be claimed that the mathematical
evidence is
any less dubious than the historical evidence in favor of the existence of
an ``astronomical code'' in these texts.

Such objections as these should suffice to
show that Dr. Kak has, at best, seriously overinterpreted his data, and
founded his sweeping chronological conjectures upon a few interesting
numerical
coincidences, without sufficient regard for either the historical or the
mathematical counterarguments. Dr. Kak's own confidence in this approach,
however, is profound: he suggests (p. 107) that

``[c]orroboration for the conclusion that the Vedic world knew the
planetary periods may be sought in the
artifacts and astronomical designs from the Harappan ruins...It also
becomes reasonable to reexamine the Vedic literature for further knowledge
about the
planet motions.'' Indeed, should Dr. Kak go on to seek such
``corroboration'' by similar means from the archaeological or textual
sources, it seems quite
likely that he will manage to find it. \end

-------------

Tomorrow, my quota being exhausted, my own notes.

========================================================
Michael Witzel
Department of Sanskrit & Indian Studies, Harvard University
2 Divinity Avenue, Cambridge MA 02138, USA

ph. 1- 617-496 2990 (also messages)
home page:  http://www.fas.harvard.edu/~witzel/mwpage.htm

Elect. Journ. of Vedic Studies:  http://www1.shore.net/~india/ejvs