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 Udayantara. Ganeshdaivajna (1478 AD) compiled the Grihalagnava
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 1000
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 parts (seasons).
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 south.
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
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
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
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
(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
kalpas, 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 then, of 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.
Observations 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
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 subsequent
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.
Ugadi will see dawn of 52nd century for Hindus
The coming Ugadi on March 18,1999 is a very special day in the Nirayan Hindu calendar,
but except members of the diminishing tribe of calendar writers, hardly anybody is aware of its enormous significance.
As less than a year later the world enters the 21st century according to the Gregorian
calendar, the Nirayan calendar will enter the 52nd century of the Kaliyuga, calculated to have started 5100 years ago at the
end of the Krishna Avatar (incarnation of Lord Krishna), according to the calendar writers.
These calendar writers are also unhappy about the fact that while there is so much
of excitement about the beginning of a new millennium, in India, not a word is being said about its own traditional Nirayan
calendar, which enters into the 51st century, thus continuing with a much older and more elaborate and perhaps advanced system
According to the Nirayan calendar writers, eminent astrologers and mathematicians
like Varahamihira, Bhaskara and Aryabhatta used this calendar in their discourses.
According to the Hindu system, the smallest unit for measuring time is the truti,
which can be compared to what one gets if one second (western system) is divided into 33,750 equal parts.
Thus, the indigenous system is so advanced in calculating time that such accuracy
cannot be achieved even by nuclear clocks, they say. According to the Nirayan calendar writers, the duration of the earlier
Yugas were first, the Krutayuga, which lasted for 17,28,000 years second, the Tretayuga, for 12,96,000 years third, the Dwaparyuga
for 8,64,000 years and finally, the present Kaliyuga, which would last for 4,32,000 years.
According to this calendar, the Kaliyuga on March 18, 1999 (Shalivahana Saka 1921),
completes 5100 years and starts the 5101st.The calendar writers say the above four yugas repeat themselves 1000 times on earth,
which makes one day for Brahma (the Creator).
Brahmas total life span, according to this system, is 31,10,40,00,00,00,000 years.
Thus, the mankind has passed through half the age of its Creator while 15,55,20,00,00,00,000 years of Brahmas life remain.
Further, there is no problem like whether the month of February would have 28, 29 or 30 days during the year 2000_2001, they
say, adding it is of immense significance to be a witness to such historic events as the Hindu calendar entering its 52nd