ARTICLE : Yuga, Mahayuga and Kalpa
Subject: ARTICLE : Yuga, Mahayuga and Kalpa
From: Prasad Gokhale <firstname.lastname@example.org>
Date: Fri, 19 Jul 1996 14:41:54 -0300
Organization: University of New Brunswick
YUGA MAHAYUGA and KALPA
By R.R. Karnik
(A/6 Woodland Flats, Ambedkar Road, Shivajinagar, Pune 411 005)
Many people including Indian astronomers such as Aryabhata, Brahmagupta
and Bhaskaracharya, as also experts outside India such as Whitney,
Burgess, Bentley, etc. believe that one Kaliyuga, is of 432,000 years,
one Mahayuga is ten times this as much (4,320,000 years) and one Kalpa
is a thousand times Kaliyuga (4,320,000,000 years). Many knowledgeable
people just do not accept these large numbers and reject such astronomy.
It appears that these numbers have a bearing on the dating of Ramayana.
According to Valmiki the period of Ramayana is at the beginning of
Tretayuga. Reckoning with these numbers some archaeologists found
volcanic ash which was 1,400,000 years old and associated it with
the period of the Ramayana. On the other hand, there are others who
assert that the Ramayana occured about 8000 years ago.
Various forms of Indian arithmetic have already found an honourable place
in the history of mathematics. It was known that complex mathematics is
available in the Surya Siddhanta, which is reputed to be very ancient.
Since these huge numbers of years for Yuga and Kalpa were to be found in
this Siddhanta, I had avoided studying it. But in my search for higher
mathematics in ancient India, I read this document in original Sanskrit,
analysing each word and its syntax. The knowledge contained in this
document is truly of a high quality. The document could not have been
written in the historical period of the fifth century A.D. with the
advent of Aryabhata and Varahamihira, as the logic for the use of these
huge number of years was not been understood by them.
In the hightech uses of computer technology there is an area called
simulation, in which time is used in two different manners. One is called
"real time" and the other, "non-real time" -- either slow motion or fast
motion. The surprising thing is that the Surya Siddhanta makes use of
this concept of time. All the arithmetics in the Surya Siddhanta is in
terms of integers for which some times "real time" is not suitable.
Some people believe that these huge number of years correspond to an
L.C.M. of the periods of revolution of the planets around the sun. There
have been attempts in Vedanga Jyotisha, where a period of five years has
been used and by Varahamihira in Romaka Siddhanta using 2,850 years.
Cicero gives 12,954 years in the thirty-fifth fragment of Hortensius by
the name of Magnun Annum. Neither of these numbers can divide 4,32,000.
In fact no number however large can give an integer multiple of the
number of years required.
The answer is simple and elementary. The least count used in Surya
Siddhanta for general computations is one Kala or minute of the arc of
which there are 21,600 in the whole circle. If one has to specify the
movememnt of planetary element to the accuracy of one Kala in a year
a period of 21,600 years will have to be taken. This is the period of a
Mahayuga and its tenth part which is 2,160 years is the period of
Kaliyuga. Dwaparyuga is twice this or 4,320 years, Tretayuga is thrice
this or 6,480 years and Krutayuga is four times this or 8,640 years,
all four totaling up to 21,600 years.
The accuracy of one Kala in a year is not adequate. To therefore obtain an
accuracy of one two-hundredth of a Kala in a year, a period that is two
hundred times 21,600 or 4,320,000 years is necessary. The first number of
21,600 years is the real time and the other number of 4,320,000 years
taken for Mahayuga is the frame time or the non-real time.
The Surya Siddhanta records in i. 10:
"Lokanam antarkt kalah kalonyah kalanatmakah
Sa dvidha sthulasuksmatvan murtas ca amurta uccyate".
Rendered in English it means:
"The time which destroys is the real time the other kind of time is
for the purpose of computations. They are of two kinds, the gross one is
used for real time use and the firm one for the purpose of computations."
For the movement of the apogee of the sun this frame time of 4,320,000
years is not adequate and a number ten times this is required which is
43,200,000 years called Kalpa. This is given in the Surya Siddhanta i.20,
"ittham yuga sehesrena bhutasanharakarkah
kaIpo brahmam ahah proktam sarvari tasya tavati"
"Such thousand yugas, of the all destroying kind, are called a day
or Kalpa of Brahma the night being of equal duration."
The Surya Siddhanta gives the rates of motions of apogees and nodes
starting from i.41. It starts with the apogee of the sun which rate is
"Braggate surya mandasya kalpe saptastavahnayah"
"The apogee (mandocca) of sun goes eastwards 387 (bhagana) in a Kalpa."
The computation of the modern value is as follows:
Mean motion of the sun (tropical) 36000.76892 degrees per 100 years
Motion of precession -1.39571 degrees per 100 years
Mean sidereal motion of the sun 35999.37321 degrees per 100 years
Motion of anomaly 35999.04975 degrees per 100 years
Motion of apogee .32346 degrees per 100 years
which is X 1200 = 388.152 bhagana in a Kalpa
This is the fineness with which the motion of the apogee of the sun has
been given in the Surya Siddhanta.
Surya Siddhanta (i.2) states:
"alpavasiste tu krte mayonama mahasurah
rahasyam paramam punyam jijnasur jnanam uttamam"
A short time (10 to 12 years according to critics) before the end of
Krutayuga, a great Asura named Maya sought to acquire this high quality
knowledge endowed with spiritual blessings."
At the end of the Surya Siddhanta there are two verses describing that
when the sages came to know that the Sun has blessed the Maha Asura Maya
with the knowledge of astronomy, they went to him with great respect,
touched his feet and prayed that this knowledge be given to them.
Maya then with great love and affection (in a thorough and complete
manner) imparted this knowledge to them. Xiv. 26-27.
"jnatva tamrsyasc atha surylabdhavaram mayam
paribabrurupety atho jnanam pepracchur adarat (Xiv.26)
sa tebbyah pradadau pritau grahanam caritam mahat
etyadbhutatamam loke rahasyam brahmasammitam II 27 II
This period would be at the end of Krutayuga and the beginning of the
The period of Ramayana is of Tretayuga. Mayasura is the father of
Mandodari the wife of Ravana. It is obvious that this knowledge was
obtained by the sages before the Great War between Rama and Ravana.
After his defeat it is said that Mayasura went home by the land route
in a westward direction to his place. There is a reference to a period of
counting of 360 days, visibility of Sagittarius in the land of Asuras
(when Aeries is visible in the land of Suras) and the sky in the land of
Asuras rotating in the clockwise direction (when it rotates in an
anti-clockwise direction in the land of Suras) in the Surya Suddhanta
suggesting a link with the South American continent for Maya and with the
Mayan culture there. It is to be noted that the fifth ice age was on at
this time and journey from Europe to the American continent would have
been possible by land route at that time. It is said that Mayasura
travelled using this route.
If a learned person like Maya has to "run away", then what can one say of
his disciples and his teachings. It also seems that this knowledge had
to be practised in a surreptitious manner, bearing the wrath of royal
displeasure. It seems that Aryabhata got this method of astronomy
official recognition, however, in the time from Maya to Aryabhatta much
knowledge was lost.
Aryabhatiya shastra has two distinct parts. One of the parts consists of
108 Aryas taken from the Surya Siddhanta and the other part contains 10
Giti -- the original compositions of Aryabhata. On this Brahmagupta
scathingly attacks Aryabhata (Brahmasputa Siddhanta ix.8)
"aryastasate pata bhramanti dasagitike sthirah pata"
[In 108 Arya the nodes rotate (but) in 10 Giti they are stationary.]
But Bhaskara tries to defend Aryabhata.
"atyanta suksmaisam gatir mahata kalena kiyate apy upaciyate
tayoh stokatvad antarasya viksepah sphuta eva laksante"
[A mere eye wash. because of the extremely slow motion even after large
periods of time the deviation is correct i.e. is negligible.]
Obviously, none of the three, Aryabhata, Bhaskara or Brahmagupta had any
knowledge of the correct number of years to be taken for the revolutions
of the apogee of the sun. After them no one has been able to decipher the
mystery of the revolutions of apogees and nodes of the planets.
Indian astronomy has been possessed by these non-real time computation of
Mahayuga and Kalpa and their influence still remains. It has become
almost impossible to view the epics of Ramayana and Mahabharata in an
objective manner due to this. The correct measure that can be seen in
the light of the mathematical contents of Surya Siddhanta for Kaliyuga,
Mahayuga and Kalpa, have been given here. This may perhaps help in
exorcising-the influence of imaginary numbers which have afflicted the
thinking in India for several centuries.