Aryabhata
I
Aryabhata
I (476-ca 550): Indian astronomer and mathematician.
Using
Hindu Brahmi (aka 'Arabic') numerals accurately calculates
pi () to 3.1416, and the solar year to 365.3586805 days.
A
thousand years before Copernicus, Aryabhata propounds a
heliocentric universe with elliptically orbiting planets
and a spherical Earth spinning on its axis, explaining the
apparent rotation of the heavens. Writes Aryabhatiya, history's
first exposition on plane and spherical trigonometry, algebra
and arithmetic.
Aryabhata
wrote Aryabhatiya , finished in 499, which is a summary
of Hindu mathematics up to that time, written in verse.
Contribution
to trigonometry The first actual appearance of the sine
of an angle appears in the work of the Hindus.
Aryabhata,
in about 500, gave tables of half chords which now really
are sine tables and used jya for our sin. Jya (India) became
Jiba then Jaib (Arabs) which then became Sinus (Romans)
which then became Sine (modern terminology).
"All
the planets whether moving in the orbits or in eccentric
circles, move anticlockwise from their apogees and clockwise
from their perigees." This law was stated before 500
C.E., over 1000 years before the first law of planetary
motion was given by Johannes Kepler in 1609 C.E.
(The
3100 B.C.E. date for the MBH War and start of Kali Yuga
is a misinterpretation of a date that astronomer Aryabhatta
used to make a fixed reference in the past which all astronomers
could use to calibrate against. 3101 or 3102 B.C.E. has
no historical meaning in Indias history as is validated
by all the Puranas as referenced against the Vedas and all
the archaeological evidence we have.)
The
blame for mixing up the Puranic and the astronomical yugas
rests squarely on the celebrated astronomer-mathematician
Aryabhatta (b. AD 476).
He
introduced two changes in the traditional yuga system.
1)
He defined a kalpa as a period of 1,008 mahayugas (instead
of 1,000). Since 1,008 is divisible by seven, each new kalpa
would begin on the same week day.
2)
He divided a mahayuga into four equal rather than unequal
parts so that each consisted of 108,000 years.
Aryabhatta
started his astronomical Kaliyuga at 6 A.M. on Friday, 18
February 3102 BC (Julian) at Lanka, which is hypothetically
placed at the intersection of the equator with the meridian
of Ujjain. In astronomical parlance, this choice of epoch
defines the Aryapaksa, the Arya school of Siddhantic
astronomy.
Aryabhatta
also propounded another system, in which the Kaliyuga began
six hours earlier, that is on the midnight of 17/18 February
3102 BC (Julian) at Ujjain. This is known as the ardha-ratri-ka-paksa
the midnight school. Since planets move, their
configuration cannot be the same at midnight and at sunrise.
In
particular, the sun and moon cannot remain aligned at two
points in time, six hours apart. It is thus clear that Aryabhattas
Kaliyuga is a theoretical artifact, and not the epoch of
an actual astronomical observation.
How
did Aryabhatta arrive at this particular date? It seems
that his starting point was the observed planetary positions
at a known epoch.
Since
he knew the orbital periods, he could calculate backwards
the epoch when all the planets could be taken to have been
aligned at the beginning of the zodiacal sign Aries (Mesa).
It is now known that planetary orbits are subject to various
kinds of perturbations, and a theory depending on the orbital
period as the sole parameter cannot give accurate results.
According
to modern numerical simulations, on 17/18 February 3102
BC the five geocentric planets were not aligned but spread
over two neighboring zodiacal signs.
This
again underlines the inference that the significance of
the date was hypothetical rather than real. Even if Aryabhatta
had chosen a slightly different epoch, it would not have
made much difference as far as the actual sky conditions
are concerned.
The
choice of 3102 BC, however, had a special significance for
Aryabhatta. Midday at Ujjain on the equinoctial day 21 March
AD 499 exactly corresponds to the beginning of the year
3600 of his Kaliyuga. Since the ardharatrikapaksa starts
its Kaliyuga six hours before the Aryapaksa, Aryabhatta
artificially made the duration of the year slightly longer
in the former case so that in both the schools the 3600th
year starts at the same time. We may recall that AD 499
is the year of the composition of Aryabhatiya.
The
acceptance of the new date must have become universal by
634 C.E. for in that year we have the public use of it in
the Aihole Inscription of King Pulakesin II dating itself
in the Kaliyuga Era side by side with the Saka Era and referring
to the Bharata War.
Unfortunately,
while talking of the passage of time, Aryabhatta did not
explicitly say before the Kailyuga. Instead,
he used the term Bharatat Purvam, that is before [the]
Bharata [battle], obviously alluding to the Puranic
yuga system. This is what gave currency to 3102 BC as the
date of the battle. The use of Aryabhattas epoch in
the Puranic context is ironical in the light of the fact
that he was severely castigated by his student critic Brahmagupta
(b. AD 598) for deviating from smrti (tradition)
while formulating his own yuga system.
The
date 3102 BC for the Puranic Kaliyuga is not tenable. First,
the Puranic and astronomical yugas are widely different
in length. The Puranas divide 94 generations from Manu to
the Bharata battle into three yugas, so that each yuga is
approximately 31 generations or say 600 years. Aryabhatas
yugas, on the other hand, run into hundreds of thousands
of years.
Secondly,
an astronomical epoch begins at a precise moment which is
chosen by the astronomer. In contrast to the astronomical
Kaliyuga, the beginning of the Puranic Kaliyuga is not precise
at all. According to Mahabharata Adiparvan (2.13), the battle
occurred at the junction of Kali and Dvapara.
The
Bhagavata Purana, on the other hand, gives two versions
of the epoch. In one version (1.15.36), Kaliyuga started
the day Krsna died, while the second version (12.2.33) starts
Kaliyuga at the very moment Krsna died. One can see the
feeling of discomfort here. It did not look quite the right
thing to have Krsna live into the Kaliyuga. (According to
the chronology of the Mahabharata, Krsna dies some 20 years
after the battle. This was the time when Yudhisthira abdicated
in favour of his grand-nephew Parikshit.)
We
thus see that the Puranic Kaliyuga is a manner of speaking
rather than a carefully chosen point of time as in astronomy.
Finally,
if the Bharata battle indeed took place in 3102 BC, how
was the epoch recorded? (It could not have been in terms
of eras that began later.) How and by who was the date kept
alive for 3,600 years? How did Aryabhata come across this
date? If Aryabhatas predecessors had been asked about
the battles chronology, what date would they have
mentioned in answer?
DATE
OF THE BHARATA BATTLE
The
Puranas do not recognize Aryabhatas date at all. They
provide their own information on the subject. It is possible
to calculate the Bharata battles date from statements
within the Puranas. Unfortunately, one can derive not one
but many dates. The Puranas contain a bland statement that
1,015 (or 1,050) years elapsed between Pariksits birth
(shortly after the battle) and the coronation of Mahapadma
Nanda. Nandas coronation was a singular event from
the Puranic point of view because he was a son of a Sudra
mother, and exterminated all blue-blooded Ksatriyas.
The
Jain Parisistaparvan calls Nanda the son of a courtesan
by a barber. The Greek historian Quintas Curtius also says
that Nanda was a barber who being handsome gained the affection
of the queen. Through her influence he obtained a position
of royal confidence which he treacherously used to murder
the king.
The
Matsya Purana assigns 88 years to the reign of the first
Nanda. The figure is unreasonably high; 88 (astasiti) appears
to be a mistake for 28 (astavimsati), which the Vayu Purana
quotes. The first Nanda was succeeded by his eight sons
who, all Puranas agree, ruled for 12 years, giving a total
of 40 years for the Nanda rule. (Ancient Sri Lankan chronicles
reduce the figure to 22 years).
A
hoard of coins discovered from the Bhir mound at Taxila
in 1924 contains 1,059 punch-marked coins from Magadha.
These coins belong to three successive dynasties: Sisunaga,
Nanda and the Maurya. Significantly, while one can distinguish
between coins issued by different kings in the case of the
Sisunagas and the Mauryas, the Nanda coins all belong to
a single ruler. This is consistent with the brevity of the
Nanda rule.
The
Nandas were dethroned by Candragupta Maurya whose date of
coronation is known from independent sources to be about
320 BC. Thus the Puranas themselves suggest about 1400 BC
for the Bharata battle.
Niraj
Mohanka
Indologist