ARTICLE : Yuga, Mahayuga and Kalpa

[Guest guest]

http://www.hindunet.org/srh_home/1996_7/msg00172.htmlYUGA MAHAYUGA and KALPABy 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 kalanatmakahSa 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, thus, "ittham yuga sehesrena bhutasanharakarkahkaIpo 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 saptastavahnayahThe 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 KalpaThis 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 mahasurahrahasyam 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 mayamparibabrurupety atho jnanam pepracchur adarat (Xiv.26)sa tebbyah pradadau pritau grahanam caritam mahatetyadbhutatamam loke rahasyam brahmasammitam II 27 IIThis period would be at the end of Krutayuga and the beginning of the Tretayuga.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.

[Guest guest]

Thank you Sunil Nairji for bringing in this very timely article. Regards,Sunil K. Bhattacharjya--- On Sat, 7/11/09, sunil nair <astro_tellerkerala wrote:sunil nair <astro_tellerkerala ARTICLE : Yuga, Mahayuga and Kalpa Date: Saturday, July 11, 2009, 3:49 AM

 

http://www.hindunet .org/srh_ home/1996_ 7/msg00172. htmlYUGA MAHAYUGA and KALPABy 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 kalanatmakahSa 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, thus, "ittham yuga sehesrena bhutasanharakarkahkaIpo 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 saptastavahnayahThe 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 KalpaThis 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 mahasurahrahasyam 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 mayamparibabrurupety atho jnanam pepracchur adarat (Xiv.26)sa tebbyah pradadau pritau grahanam

caritam mahatetyadbhutatamam loke rahasyam brahmasammitam II 27 IIThis period would be at the end of Krutayuga and the beginning of the Tretayuga.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.

[Guest guest]

Dear Bhattacharjya ji Thanks rgrds sunil nair , Sunil Bhattacharjya <sunil_bhattacharjya wrote:>> Thank you Sunil Nairji for bringing in this very timely article. > > Regards,> > Sunil K. Bhattacharjya> > --- On Sat, 7/11/09, sunil nair astro_tellerkerala wrote:> > sunil nair astro_tellerkerala ARTICLE : Yuga, Mahayuga and Kalpa> > Saturday, July 11, 2009, 3:49 AM> > http://www.hindunet .org/srh_ home/1996_ 7/msg00172. html> > > 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, > thus, > > "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 > Tretayuga.> > 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.>