ARTICLE : 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 
given by:

"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.