A date with history
BY PRAMOD K NAYAR
Sunday, March 7, 1999
Ugadi, March 18, 1999, is special, even as India
marches into the 52nd century of the grand old era of Kaliyuga. However, it also happens
to be the anniversary of Aryabhatta`s discovery of 'pi` and the length of a solar year.
PRAMOD K NAYAR
looks back with interest at that point of history, centuries ago, when the early
astronomers did some star-gazing.
IS the rest of the world behind time? Or is India ahead of its time? Whose
time is it anyway? These questions are not, as they
first appear, frivolous.
They arise out of a very unusual situation that occurs on the Ugadi day of March 18, 1999.
For, on this day, India marches not
into the 21st century but into the 52nd. Puzzled? Then read on.
This Ugadi we step into the 52nd century of Kaliyuga, which is calculated to have
commenced with the Krishna Avatar, 5,100
years ago. On such a historical occasion, this article also celebrates another momentous
year in India`s history: the anniversary of Aryabhatta`s 499 AD computation of pi as
3.1416 and the length of a solar year as 365.358 days.
The Arya Siddhanta of 499 AD is st ill in use! This Ugadi is therefore a significant date:
the Hindu Nirayan calendar`s 52nd
century and Aryabhatta`s way-ahead-of- his-times discovery.
As a paean to the world`s most ancient calendar, this piece looks at certain remarkable
features of this calender system.
Numerous thinkers and works contributed to making astronomy and the related sciences of
astrology and cosmogony a
near-accurate system. Among these figures are Varahamihira (490 AD) who set out the
Bijakarana, and wrote the Pancha
Siddhanta and Brihatsamita. Brahmagupta compiled the Sayan Meshasankramana. Munjala
invented the 'Ayana`
movement and determined one year as a 'kala`. Shatananda authored Bhasvatikarana and
calculated the positions of the sun
and the moon according to the constellations. Bhaskara (1114 AD) wrote the
Ganeshdaivajna (1478 AD)
compiled the Grihalagnava Garga.
However, it must be accepted that none of these developments occurred in hermetically
sealed conditions. Indian astronomers
were deeply influenced by thinkers from other civilisations, especially the Mesopotamian
and the Yavana (Greek).
The earliest sources of the Hindu calendar system are texts dating from about
This divided a solar year of 360 days into 12 lunar months of 27 (according to the
Taittiriya Samhita) or 28 (according to the Atharvaved, the fourth Veda).
The Jyotish Vedanga of 500 BC provided rules for calculating positions of the new and full
moons amongst the 27 nakshatras
and of the 'ayanas` which fall in cycles of five years, each of 366 days. In five solar
years, there were 67 lunar months.
A year of 12 months would be retained, if the 31st and 62nd months were omitted from each
cycle. This system was widely used in ancient India.
Examples are also found in the Jaina literature dating from this period. The
Taittiriya Samhita constitutes the statements of nakshatras. These nakshatras each measure an area of 13 degrees 20`` of the ecliptic
circle. The position of the sun at
midnight was calculated from the nakshatra that culminated on the meridian at that time.
The year was divided into three-thirds
of four months, each heralded by a special religious rite - the 'chaturmasa`. Each of
these periods was further divided into two
Another interesting feature of the old system was the division of the two-year moieties:
the 'uttarayana`, (northern course)
when the sun rises further North every morning and the 'dakshinayana` (southern course)
when it rises progressively further
After the influence of Greek and Mesopotamian astronomy, the nakshatras and a quarter of
one made up one zodiac period
or sign (30 degrees).
The names of the nakshatras are derived from the constellations on the horizon since those
times have remained unchanged (Chaitra, Vaisakha, etc).
Eight types of planetary movements (describing their speeds of rotation) are
also detailed in these works. It is amazing that in the absence of sophisticated
instruments, our thinkers developed such advanced theoretical formulations.
Unlike contemporary science where 'simulation` of situations is available to
validate a hypothesis, these ancient astronomers had only the crudest of implements (the
water clock, circle and quadrant were extant in those times). This context of their
epistemology is what makes their achievement so remarkable.
Later the revolution of the planet Jupiter was also used in Hindu astronomy.
Jupiter`s synodic period brings it into conjunction with the sun every 398 days and
88 minutes. A year can be dated as a month of a 12-year cycle of Jupiter. This is extended
to a unit of five cycles, or the 60-year cycle of Jupiter (Brihaspati chakra), and a
'century` of 60 years results.
From the 6th century AD, this new s ystem becomes evident.
These calculations reveal a ph enomenal development in ancient India cosmogony. These
developments were significantly
governed by certain principles (which, of course, varied over the ages). The 'Pitamaha`
principle computed a year as 365
days and 21 1/2 ghatikas.
The 'Surya` principle analysed the movement of planets through constellations to draw up
'nadikas` (symbolic periods in days
of the planet). On this principle, 584 4/11 days of Mercury (for instance) equalled 89
days and 2 hours. In the 'Romak` principle a year meant 365 days, 14 ghatikas and 18
palas. The ancient Indian calculation of time is easily superior to even
present nuclear time-keeping devices. The Hindu 'truth` is obtained when one divides a
second (in the western system) with 33,750 equal parts!
The Hindu 'panchanga` system (analogously derived in its etymology from the 'fine limbs`)
is any day more complicated than
western calendars. In the Hindu panchanga, there are five basic elements in time division:
The vara (weekday) is the natural solar day (savana divasa) beginning at sunrise. This
vara has numerous sub-divisions:
A sura (prativa pala) = 0.006 secs
60 prativa palas = 1 vipala = 0.4 secs
60 vipalas = 1 pala = 24 secs
60 palas = 1 ghatika = 24 min
60 ghatikas = 1 divasa
A further refinement was the division:
10 vipalas = 1 prana (4 secs)
6 pranas = 1 pala (24 secs)
The tithi is the moment of the new moon, or the point of time when the
longitudes of the sun and moon are equal - 'amavasya`
(literally 'dwelling together`).
Tithi is the time occupied by the moon in increasing its distance from the sun by 12
degrees. The length of the tithi varies
constantly. When the difference between longitudes is 180 degrees it is the 'purnima`.
Nakshatra: as we have seen above, is 13 degrees 20". The moon travels nearly one
Yoga: is the period of ti me when the joint motion in the longitude of the sun and the
moon is increased by 13 degrees 20". Karana: is half the tithi, or the time during
which the differences in longitude of the sun and moon are increased by six degrees. A
solar year is the period of the earth`s rotation. This year has a three-fold system.
(a) The sidereal year when the earth makes one revolution round
the sun. Standard length - 365 days, 6 hrs, 9 mins, 9.29 secs.
(b) The tropical year when the earth in its revolution passes from one equinox or tropic
to the same again. Standard length - 365 days, 5 hrs, 48 mins, 45.37 secs.
(c) Anomalistic year when the earth moves from the apehilion to the perihilion or vice
versa. Standard length - 365 days, 6 hrs,
13 mins, 48.61 secs.
Does the description appear too technical? It does. For what we have at hand is one of the
most refined and accurate
measurements of time.
The break-up of the day (or years) into such minute (excuse the pun) segments is truly
astonishing and is unrivalled by any other
system in the ancient world. It is perhaps a legacy of this accuracy which many explain as
the incredibly complex and technically
perfect architecture of India`s old temples.
Surely the ancient system of mathematics had provided a base upon which future technology
and engineering could be built?
From such smaller measurements of time in the Hindu system, one progresses to
its computation of cosmic time. The length of
an ideal individual human life is 100 human years. Brahma`s (the Creator) has a day of 365
days or 'kalpas`.
A kalpa is simply one day of Brahm a`s life. The life of Brahma is 100 times 365
forming a 'mahakalpa`. This makes
Brahma`s total lifespan to be 31,10,40,00,00,00,000 years! Man has now passed half the age
of the Creator.
A kalpa is made of a 1,000 times four 'yugas`, or a 1,000 great yugas which are measured
in years of gods. The great yuga is
equal to 12,000 years of gods and is divided into four yugas of unequal length
separated by twilight. Finally one lunar year is a
day and night of the gods. Therefore one year of the gods equals 365 lunar years
(Incidentally the lunar month is India`s
contribution to the calendar system.
The term 'month` is derived from 'moon-eth`). The four yugas in descending order, starting
from the present are:
Kaliyuga: Of 432,000 solar years
Dvaparayuga: Double the length of Kaliyuga, 864,000 years
Tretayuga: Triple the length of Kaliyuga, 12,96,000 years
Krutayuga: quadruple the length of Kaliyuga, 17,28,000 years.
A mahayuga is 10 times the length of the Kaliyuga, of 4,320,000 years.
(Heraclitus refers to a 'great year` of 10,800 years
and Berossos, the Babylonian astronomer, spoke of a 'cosmic year` of
432,000 years). The current Kaliyuga began on the
midnight of 17/18th Feb., Thursday, 3102 BC, according to these
By comparison, the western Julian period of 7,980 year-cycle began on Tuesday, Jan 1, 4713
BC. The four yugas repeat
themselves a 1,000 times on earth, which constitutes a mere one day for Brahma!
The 'Rig Veda` computes
10,800 metrical divisions of 40 syllables each, thus again giving a figure of 432,000. And
course, over time, various dynasties and kings evolved their own 'eras`. Though lacking
any universal appeal or significance,
these divisions have continued to be of importance in India. A few of these Indian eras
are: the Vikrama era, beginning 58 BC;
the Saka era beginning 78 A D; the Gupta era beginning 320 A D; and the Harsha era
beginning 606 A D. The Vikrama and
Saka eras are in use today too.
March 18, 1999, marking the start of the 52nd century, falls under the 'Shalivahana
It must be noted that the Indian cosmogonic and astronomical systems, while developing
independently of western systems,
bear remarkable affinities with the latter. For instance, the calculation of the year in
both systems are very similar. The Arya
Siddhanta and Rajamriganka systems are in use even today.
And now, a quick look at the other major calendar systems of the world. England`s
Stonehenge, dating back to 2000 BC, is
perhaps the most famous.
were made by lining up stones with a marker and watching for the appearance of the sun or
moon against that
point on the horizon that lay in the same straight line. Today more than 600 structures,
perhaps contemporaneous with
Stonehenge, have been discovered across Britain.
Hipparchus, the Rhodes astronomer of 150 BC, calculated the length of a tropical year as
365.242 days, and a lunation as
29.53058 days, both figures remarkably close to the present day calculation of 365.242199
days and 29.53059 days
The Julian system of 7,980 year cycles was designed by the French scholar, Joseph Justus
Scaliger (1540-1609). The Roman
Republican calendar is supposed to have been introduced by the fifth Roman king,
Tarquinius Priscius (616-579 BC). This
mainly lunar calendar was 10 1/4 days short of a 365 1/4- day tropical year, thus
necessitating the intercalation of a month
(termed 'Mercedonius`, derived from 'merces`, meaning wages).The Jewish calendar, a highly complex system, is
'lunisolar`, where the years are solar
and months lunar.
The calendar employs a lunar cycle of 19 years (thus paralleling the l9-year Metonic cycle
devised by the Athenian astronomer,
Meton, in 432 BC). The Jewish era today is dated from 3761 BC. The Islamic calendar is
lunar, beginning with the approximate New Moon
and dating from the emigration of Prophet Mohammed from Mecca to Madina in 622 AD.
The western Julian system, with its long history of monarchical revisions, owes much to
Sosigenes (an Alexandrian astronomer).
Pope Gregory XIII refined it with the help of Christopher Clavius in 1582. This Gregorian
calendar had a tropical year of 365.2422 days. Other
ancient and sophisticated calendars are the Athenian, the Egyptian, the Incan, the Aztec
and the Mayan. A discussion of these
alternate systems will require long essays and is therefore being omitted here.
What emerges from the above details is the indisputable fact that ancient
Indian cosmogony is extremely complex and
advanced. As historians of this calendar system, such as SB Dikshit and CPS Menon have
demonstrated, the Hindu calendar
predates any European equivalent. Its splitting of 'levels` of time into micro-units is
perhaps equalled only by nuclear clocks
(which are of very recent origin). Today as we step into our very own 52nd century, we
ought to congratulate our ancient
astronomers who devised this system, still valid - and validated - by centuries of
On Ugadi day, March 18, 1999, the anniversary of the seminal ancient text, the Arya
Siddhanta, wishing everyone a Happy
New Year, is this ancient system. This day we have literally trysted with destiny, a
tryst predicted centuries ago. Or one might
say on this Ugadi we have a ''date" with history.