Subject: Re: [HM] Indian astronomy and mathematics
From: Dinesh Maheshwari (dsm@cypress.com)
Date: Wed Feb 16 2000 - 03:11:14 EST
Dear HM Listmembers,
Perhaps it is already evident to you that my previous post was not a
response to Kim Plofker; I had read KP's post before posting my previous
post.
I cannot help but notice that we have come a full circle on this thread,
it started with the astronomical event dating of the Vedic texts, moved
to Indian mathematicians after 1000AD, then to "heliocentric model of
Aryabhata and now back to the "astronomical event dating".
In any case, I cab only thank Kim for giving me the opportunity, again, to
discuss the issue of dating of the Vedic texts (as it pertains to astronomy)
and the fatal flaws in the claims of the "conservative" school. I should
also thank Kim for pointing out two things in the most recent post which
I was not aware of earlier.
Let's first start by putting a framework, for logical discussion of the
issues, which is complete and sufficient for the purpose of current
discussion. (mind the brackets)
1. Principle A can be said to be derived from principle B only
1.1 if and only if B predates A temporally
1.2 and (if there is direct proof of migration of B to A
1.3 or if there is a direct proof evolution of B from A
1.4 or if there is sufficiently high degree of parallelism implying a
high degree of probability that A was derived from B and did not
develop independently)
1.5 if there is no temporal relationship that can be determined
between A and B but
1.5.1 (A and B are exactly the same
1.5.2 and the principle A has eccentricities that are only valid
in the context of B) then there is a possibility that A was
derived from B.
The corollaries to the above are :
2. Parallels between principle A and principle B are just that - parallels
and no inference as to the derivations of A from B can be made without
1.1 being true.
3. A medium of migration is again just that - a medium of migration and no
inference as to the direction of the migration can be made without 1.1
being true.
4. Arguments 1.2 or 1.3 or 1.4 can never imply 1.1
> - Its content is heavily influenced by Mesopotamian astronomical methods.
Let's discuss the above assertion logically.
> The reasons adduced for them include the following:
>
> - The Sanskrit of the _Jyotisavedanga_, post-Vedic but pre-classical,
> indicates that it's contemporary with the later Brahmanas, which
> "conservative" chronology assigns to about the middle of the first
> millennium BCE.
The above is one of the two main arguments in KP's post and it tries to date
_Jyotisavedanga_ as required by argument 1.1.
As I have already mentioned in one of the very early posts on this thread,
"conservative" chronology or "MaxMuller school" chronology, as it stands
today, is in conflict with the archaeological, geological, anthropological
and genetic (mtDNA) evidences that have been uncovered in the last decade
and a half; and is based only on the philological "speculations" of the use
of words "asva" and "ayas" in the Vedas and that too has been proven to be
not consistent across the Vedic text corpus. I have appended the relevant
portions of my previous post, dealing with the issue, to the this post.
I have also commented on the motivations behind the "conservative" chronology
by it's proponents MaxMuller et al in another post on this thread.
In ADDITION to the arguments in my previous posts, there are other evidences
for the antiquity of the Vedic literature. It is important to note that most
of the Vedic literature has interconnected chronology. For instance it is
known that the Vedas were composed in the sequence of Rg-Veda, Sam-Veda,
YajurVeda and AtharvaVeda. The Vedanga's and the Up-vedas were composed after
the Vedas, and so were the epics Mahabharata and Ramayana, the upnishads and
the puranas. Any dating mechanism has to maintain this chronologic sequence
else it can not be deemed to be a valid mechanism. The "astronomical event
dating" does produce a consistent chronologic sequence.
An interesting chronological marker is the solar-eclipse described in RgVeda
5:40:5-9. It is described as a central, non-total eclipse which took place
on the afternoon on the Kurukshetra meridian on a given day after summer
solstice. The interesting thing about this event, vis-a-vis an argument, is
that it does not involve measuring angles, there is no scope of error, and
it involves the Sun, the identification of which can not be questioned for
any reason at all by the "conservative school" . There is only one day that
satisfies that condition described - 26th July 3928BC.
An interesting source of the age of the Vedic literature are the quotations
from the known mathematicians and astronomers of the first part of 1st
millennium CE. Aryabhata reports that the 60th 60 year cycle, known as the
Brhaspati cycle in the Vedic literature, ended when he was 23 years old.
This implies that the 60 year system was set rolling in 3102BC. Now to
another category of evidences -
1. rice (vrihi) is nowhere mentioned in the Rig-Veda, though it was found
in several Harappan sites (Mohenjo Daro, Lothal, Rangpur) and was of central
importance in the ritualism of the Brahmana texts. This supports the argument
for a pre-Harappan date for the Rig-Veda.
2. Like rice, cotton (karpasa) is also conspicuous by its absence in the
Rig-Veda. It is first mentioned in the Sutra literature (e.g., Gautama's
Dharma-Sutra 1.18; Baudhayana's Dharma-Sutra 16.13.10). However, cotton was
found in many Harappan sites, which again can be taken to testify to the
early age of the Rig-Veda.
3. The common building material in the Harppan valley towns was brick,
called ishtaka in Sanskrit. Significantly, even though the Rig-Veda mentions
towns (pur), which are said to belong to both Aryans and Dasyus, it does not
mention bricks anywhere. The towns are said to be made of stone (4.30.20) or
metal (4.27.1). Bricks are however, standard building material by the time
of the Brahamanas. BTW, the evidences listed above are just a sample of
evidences from different categories.
Readers can make up their own mind whether the "conservative chronology"
even holds. With the "conservative chronology" not holding ground, most of
the arguments below follow corollary 2, 3, 4.
> - The necessary avenue of transmission is provided by the Achaemenid Empire,
> extending from Mesopotamia to the Indus Valley region during this period.
The above argument corresponds to corollary 3 and by itself could very well
have served as a medium for transfer in either direction.
> - The _Jyotisavedanga_ makes reference to an instrument known from earlier
> Babylonian astronomy, the clepsydra or out-flowing water-clock.
> (D. Maheshwari is right in saying that there is a sinking-bowl
> water-clock that's Indian in origin, but there exists also an
> older instrument, the nadikayantra or water-clock with an out-flowing
> tube, similar to the Babylon clepsydra. Such a clock is described
> in, e.g., the _Arthasastra_ dating from around the turn of this era. See
> S. R. Sarma, "Astronomical Instruments in Mughal Miniatures," _Studien
> zur Indologie und Iranistik_, Band 16/17, Reinbek 1992, 235--276.)
First thanks for the information on " nadikayantra"; I was not familiar with
it's existence and I am quite excited to know that it does exist because, by
itself, it follows corollary 2 and could very well show that the Babylonian
water-clock was a derivative of the Indian water-clock and not vice-versa as
has been claimed. I am sure that Milo Gardner would also be quite interested
in the history of this instrument in India.
> - The _Jyotisavedanga_ refers to a linear zig-zag function for obtaining
> the seasonally variable amount of water to be used in the water-clock
> (verse 7 of the Rk-recension), just as Babylonian texts do. Another
> linear zig-zag function for the changing length of daylight, also
> attested in Mesopotamia, appears in verse 22.
> - The same verse 7 gives a longest/shortest day ratio of 3:2, a value very
> common in Babylonian texts from the seventh century BCE onward, but not
> applicable in most of India.
Now we come to the second most important argument in KP's post (BTW this
falls in the argument section 1.5 of the logic framework) - the linear
functions used for changing length of the daylight time. In reality the
daylight time(DT) is a sinusoid (requiring a second order ) function of the
number_of_days_from_winter_solstice(d) and not a linear function as stated
in verse 22 of VJ as follows -
DT = (d*2)/61 + 12
The interesting aspect of this function is that it gives the values in
"muhurtas" which is a Vedic unit of time such that 1 day= 30 muhurtas. As far
as I know, "muhurtas" is a Vedic concept and not a Babylonian concept. The
second interesting aspect is that it uses a prime number as a denominator.
And mathematicians know that if this function were derived from another then
the odds of a prime number, e.g like 61, in the denominator are extremely
low. The most important aspect is that it is inaccurate when compared with
the actual sinusoid function.
Using the above function for winter solstice we get 12 muhuratas and for the
summer solstice we get 18 muhuratas. The ratio of the two is 18/12 i.e. 3/2.
So we see that the ratio 3/2 does not appear independently but is derived
from the function described in verse 22 of VJ. We know however that this
formula is not exactly correct.
If one were to assume that the VJ formula is absolutely correct than this
ratio will be true only for the latitude 35degree N. Babylon is at 32degreeN
whereas area from Kabul to Srinagar is at 35degree N. Perhaps I should point
out to the readers that most of today's Afghanistan was in the Vedic times
part of the Vedic civilization and in fact at the centre stage of some
important events that are depicted in Mahabharata ( e.g. depicts Gandar, the
modern day Khandar).
In fact, the name Afghanistan comes from the Sanskrit Up_Gani_sthan.
It is also important to note that the Vedic civilization started in the doab
of the 7 rivers (today -5 rivers) in what is today Pakistan, Afghanistan and
Punjab areas and then later spread to central and southern India. For the
time period that the re-dating claims for VJ, the Vedic civilization would
still be confined to North-West India. It is for this reason that we find
Sanskrit derived languages in Northern India and "Dravidian" languages
in southern India.
Now if we were to account for the error due to the VJ function being a linear
function instead of being a sinusoidal function we find that every 1% of error
introduces an error of 3degrees of latitude. Thus just a 2.33% error would
account for the whole band of 35-28N latitude i.e from Kabul to New Delhi.
So what we find is that. in the best scenario for the "conservative school",
the "conservative" school is using an argument, that is proven to have an
error such that a very small percentage error can introduce a large ambiguity,
against the astronomical dating argument where there is no proof that the
constellation were considered differently in ancient times and where it is
known that it is possible to make naked eye observations with twice the
precision that is being claimed by the observations cited in VJ.
In the worst scenario for the "conservative school", the argument can backfire,
because it appears that the formula for verse 22 in VJ is a Vedic derivation
for Vedic purposes and as A. Seidenberg would say "is primary in India and
secondary in Babylonia"; implying that it travelled from India to Babylonia.
> - The "internal astronomical evidence" in favor of a much earlier dating
> is not convincing enough to outweigh the above inferences.
I have shown that the "inferences" that KP is referring to are dependent on
only two arguments:
* A1. VJ is dated to 5th century BC as per the "conservative school"
chronology for Vedic literature.
* A2. the ratio of 3/2 is used in Babylonia and India.
Argument A1 is not tenable in face of geological, archaeological, anthropological,
genetic and surprisingly even philological evidence.
Argument A2 is ambiguous at best and at worst(for the conservative school)
proves just the opposite.
The rest of the arguments, by themselves, could very well apply to just the
reverse scenario i.e. propagation from India to Babylonia.
> While verses 5 and 6 place the winter solstice at the constellation
> Dhanistha, which would indeed occur in the early second millennium BCE,
> we have no certainty that the author of the _Jyotisavedanga_ used exactly
> the same position for that constellation as is now assigned to it, nor
> that he determined the exact location of the winter solstice as precisely
> as we now expect.
Verse 6 of VJ gives the winter solstice as 23degree20' of sidereal Capricorn
and of the summer solstice as 23degree20' of sidereal Cancer. This
corresponds to around 1350BC.
Now, the "conservative school" has taken the approach of throwing out all the
astronomical datings, and not just for VJ, as being either backcalculations
or that it is not a valid evidence without giving proof for their claims that
the constellations were not considered the same in ancient times. Doesn't
this remind you of the game in the court room were the lawyers, faced with
an unfavourable evidence, try to reduce the witness' credibility by smearing
the character of the person. That is to say, at best this sounds as an excuse.
Interestingly, some of the "conservative school" chronology proponents like
Rajesh Kochar, an astro -physicist, have conceded that the astronomical
dating of the VJ solstice in verse 6 is valid. Please refer to Rajesh Kochar's
recent book "The Vedic people, their history and geography, Orient Longman,
Delhi 1999".
VJ is a composition just on astronomical issues and it is difficult to accept
that the author would not be as accurate as is possible with naked eye
observations. The naked eye observations can be made easily to the precision
of 1/6 th of a degree. And as attested by French astronomer Jean-Sylvain
Bailly , the Vedic people did indeed try to be accurate. Jean-Sylvain Bailly:
"the motions of the stars calculated by the Hindus some 4500 years vary not
a single minute from the tables of Cassini and Meyer. The Indian tables give
the same annual variation of the moon as that discovered by Tycho Brahe -- a
variation unknown to the school of Alexandria and also to the Arabs."
Let me quickly cover some points about the Zodiacs. In the interest of time,
I will elaborate on them in yet another post. And yes I have made an inadvertent
mistake in including RomakaSiddhanta in my list of Vedic texts. In this context,
by using Vedic texts I mean the Vedic concepts (from Vedic period) that were
written down, albeit in a non-Vedic period. For example, the concepts of time,
yuga etc in SuryaSiddhanta that are from the Vedic period.
Solar Zodiacal constellations in RigVeda (!) -
In RV 1:164:11, the sun wheel in heaven is said to have 12 spokes and to
be subdivided into 360 pairs of "sons": the days (consisting of day and night).
The nakshatara (sidereal) divided is divided into 12 months, each month
corresponding to a combination of 2 or 3 lunar mansions or nakshtras of
13deg20' each. There is a concept of a Lunar 27 part zodiac system each
Zodiac corresponding to each nakshatra. However, there is also a concept of
Solar 12 part Zodiac system corresponding to the 12 months. The RigVeda
mentions a number of the Solar Zodiacal constellations/rashis.
Let me quote from K Elst's article "Astronomical data and Aryan question":
"a number of Zodiacal constellations (classically conceived as
combinations of 2 or 3 successive Lunar mansions or nakshatras
of 13deg20' each) are mentioned: Simha/Leo (5:83:3 and 9:89:3),
Kanya/Virgo (6:49:7), Mithuna/Gemini (3:39.3), and Vrshabha/Taurus
(6:47:5 and 8:93:1). Here again, the precession has located them
where we would expect them in about 4000 BC. The Vrshabha rashi
is said to have stabilized the heavens with a mighty prop,
apparently a reference to the Taurus equinox in the 4th millennium
BC; the same verse links the Taurus month with its opposite,
Shukra/Jyeshtha (coinciding with Scorpio, which contained the
autumnal equinox), confirming that Vrshabha, "bull", is used here
in an astronomical-calendrical sense. That the seasons are linked
with the constellation which is "heliacally rising" (i.e. rising
just before dawn) is perhaps indicated by RV 8:93:1: "Surya, than
mountest up to meet the vrshabha", the sun rises as if to meet the
constellation which is just above the horizon.
The Mithuna rashi/Gemini is said to destroy darkness and to be
basis (budhna) of heat (tapas) (RV 3:39:3). During Gemini's
heliacal rising in 4000 BC, the sun was in Cancer, then coinciding
with our month of May, in northern India the first month of
summer (May-June), a season of drought and extreme heat.
During Leo's heliacal rising, around summer solstice in 4000 BC,
the rainy season began. Therefore, verse 5:83:3 says: "Like the
charioteer driving the horse by the whip, he releases the
messengers of shower. From afar the roars of the simha declare
that the rain-god is making the sky showering." It could not be
clearer.
Leo is followed by Virgo, indicating the second half of the rainy
season, when the water level in the rivers rises dramatically: in
life, waterstream-full". The reference to Chitra, the asterism
Spica, the most conspicuous part of the constellation Virgo, dispels
any lingering doubt that Kanya/Virgo does indeed mean the sixth
constellation of the Zodiac. This means that the Zodiac is as old as
the oldest Veda, and that the Zodiac itself helps to date the Vedas
to the age when Virgo was connected with the rainy season".
To be continued ...
Best Regards,
Dinesh
--
Dinesh Maheshwari
Advanced Design Methods
Cypress Semiconductor
San Jose, CA , USA.
PS: Excerpts from my previous post :
And now to the so-called larger evidence put forth by the "MaxMueller school" -
Max Mueller first proposed this hypothesis to fit his understanding of
the Mosaic history of the world with the biblical floods etc. And because
Buddha had by then been accepted to be born around 600BC the Vedic
literature had to be prior to it. And he conjectured RigVeda to have
been written around 1200BC, the iron age,- because RigVeda uses a term
"ayas" which he inferred to mean iron and it also uses "asva" which he
inferred to mean horse. He did not read all of the Vedas to realise that
"ayas" was used to connote any metal or ore and not necessarily iron.
And similarly that "asva" was used in an generic way where it could also
mean an ass.
BTW, the ass had a special significance in the Vedic rituals because it
has a gestation period of 365 days - closest to the then understanding
of a year. Max Mueller school also interprets parts of RigVeda to mean
that there was an Aryan race and a Dravidiian race, without reading all
of the Veda, where-in even the so-called Dravidians used the term Aryan
for the noble people amongst them. A careful analysis shows that the term
Arya was used merely to connote being noble. Later Max Mueller himself
recanted his hypothesis on the chronology of Vedas but in the heady days
of Super-Race concept the hypothesis stuck.
After the early excavations of the Indus Valley civilization in 1920,
the Max Mueller school claimed archeological evidence of having un-covered
the DRavidian civilization that the Aryans were supposed to have eliminated.
However, later excavations showed no sign of an invasion in the Indus valley
civilization sites and the most recent excavations[1990s] show that in
fact the so-called Dravidian Indus valley civilization sites flourished
without break in continuity until 300BC. Anthropologists have concluded from
the bones found on the sites that the Indus people are closely aligned with
the current day Indians with all the structural diversity seen in current
India.
Meanwhile it was also discovered by the geologists that the grandest of the
then-seven (5 today) rivers saraswati described in the RigVeda had dried up
1900BC and was only a "monsoon-season" river by 2600BC. Which meant that
the RigVeda had to be written prior to that.
The most recent mtDNA (mitochondrial DNA) [1998-99] analysis show again that
there was no Aryan invasion and interestingly it also showed that there is
a possibility that the human migrations out of Africa first happened to
India (through the "pre-flood era" exposed land bridges) and thence to every
where else.
So now the "MaxMueller school " is left with only the so-called "larger -? "
evidence - "linguistic" evidence of "ayas" and "asva" with everything else
against them. [In fact the "asva" support is fading fast because the horse
bones were discovered in the plains north of himalaya and dated to 4000BC.]
Now anyone who knows the etymology of the words like "witch" [from generic
"wit"], wife [from generic "waif"] oxygen [from the generic term for "acid
producer"], cylinder [from generic term for "roller" and many words like
these knows that there are enough instances of words in languages that evolve
from generic connotations to specific connotations. Besides linguistics -
probably the most in exact science - is a poor substitute for other evidence
from other fields.
So, in any case, the "MaxMueller school" today has a very tenuous hypothesis
that does not hold any water against the other evidence that is emerging.
But the implications of fall of Max-Mueller chronology is so large for the
Indo-European people's Urheimat that there will be some who may never bring
themselves to accept it.
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