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 India’s 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 Aryabhatta’s 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 Aryabhatta’s 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. Aryabhata’s 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 Aryabhata’s predecessors had been asked about the battle’s chronology, what date would they have mentioned in answer?

DATE OF THE BHARATA BATTLE

The Puranas do not recognize Aryabhata’s date at all. They provide their own information on the subject. It is possible to calculate the Bharata battle’s 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 Pariksit’s birth (shortly after the battle) and the coronation of Mahapadma Nanda. Nanda’s 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

August 2006