Posts Tagged ‘culture’

Science behind Indian festivals

Posted in Blogs (Articles) on February 28th, 2009 by Rajesh Kochhar – Be the first to comment

Chief guest’s address delivered at Pushpa Gujral Science City, Kapurthala

  on National  Science Day, 28 February 2009


Science behind Indian festivals


Rajesh Kochhar

CSIR Emeritus Scientist

Indian Institute of Science Education and Research Mohali

 MG SIPA Complex,  Sector 26, Chandigarh 160019

[email protected]



The year 2009 has been declared by the United Nations as the International Year of Astronomy. The declaration is in honour of the first ever astronomical use of telescope by Galileo exactly 400 years ago. The telescope changed the human perception of their natural environment for all times to come. Telescope and microscope permitted human beings to see things   which were not part of every day experience. Astronomy today is a child of high technology. The Universe has been reduced to a mere ensemble of objects which we study with a view to discovering laws of nature and testing our theories.


 But the sky was not always like that. In the ancient past sky was viewed with awe and respect. Attempts were made to discover patterns  in it so that its wrath could be averted and its goodwill earned. Till relatively recent times, the driving force for human interest in the study of the Cosmos has been fear; first the fear of the celestial gods and then the fear of the waters. Onwards from the 15th century when European sailors took to oceanic navigation, they only had stars for company and guidance, the study of which therefore became a matter of life and death.  Curiosity- driven astronomy is thus only a few centuries old.

Our interest this evening is in that phase of human culture when propitiating the celestial gods and negotiating with them for their benevolence  were matters of the highest priority. A clear distinction was made between what was auspicious ( shubh) and what was inauspicious ( ashubh), and the  shubh times were assiduously worked out. This ritualistic sophistication was an extension of a very practical need, that is to keep track  of the passage of time. Time was cyclic; the Moon went through its phases and  seasons changed and returned.  But time passed and never returned . Understanding the complexity of time and pondering over its nature constituted the earliest philosophical and intellectual exercise undertaken by human beings.


Such a study has a contemporary significance also, because many of our extant cultural and social practices are a continuation of the times long gone by. Paradoxically while these days we are very knowledgeable about the celestial objects and the Universe as a whole, we know much less about the  tapestry of the visible sky than our ancestors did. Today when we want to know what time of the year it is, we look at the calendar. When we want to know what time of the day it is, we look at the clock. We  often forget  that  there was a time when you had to turn to the sky to  know the time.


Let us look at our watches and clocks and  construct a simple clock . This clock will have only one hand  (sui) instead of two or three. It does have a dial , but only with a single mark or digit, say at the location of 12.When the hand is in front of the digit, the counting starts. When the hand returns to the digi, we say that one unit of time has passed. ( In your real watch the time elapsed will be 12 hours.)


We have two famous natural clocks. In the first case, the Moon is the clock hand and the Sun the digit on the dial. When  the Moon is in front of the Sun, it is  New Moon ( Amavasya). When the Moon returns to the Sun , a month has passed. When the Moon is opposite the Sun , it is full Moon  , or Poornima. Since these days the word month is used independently of the Moon , we can use the term lunar month or better still lunation.  A lunation is the period from one Amavasya to the next , or what is the same thing, from one Poornima to the next. A lunation comprises about 29  and a half days.


In the second natural clock, the Sun itself acts as the clock hand. There is no obvious dial digit now. We have to create an imaginary one. The Sun appears to go around the  Earth. This path is called the ecliptic. Any point on the ecliptic can be taken to be the dial digit provided we remember  that we must  return to  the very same point. There are four important points on the ecliptic: (i)Spring equinox ( 20- 21 March)  when day and night are equal;(ii) Summer Solstice ( 20-21 June) when the day is the longest; (iii) Autumn Equinox ( 22- 23 September)  when  day and night are  again equal; and (iv) Winter Solstice ( 21-22 December)  when the night is the longest. Note that these dates are   for the  present epoch and the northern hemisphere. In the southern hemisphere dates remain the same but seasons are reversed. Spring Equinox and Winter Solstice are the two most common starting points for tracking the Sun’s apparent  orbit. The Sun takes  about 365 and a quarter days   from say one Spring Equinox to the next.


Gregorian calendar 

Let us now look at the  most  commonly used calendar in the world. According to it today is 28th February 2009.This calendar is so popular that on 1 January we wish one another Happy New Year as if it was THE new year. We forget that there are many other calendars in the world which start their new year  on  other days. This calendar is some times called the Christian calendar. It is however better to use a neutral term like Gregorian calendar after Pope Gregory who reformed it. This calendar has a very accurate  year length. In it the year has either 365 or 366 days. Although January, February, etc., are called months they have nothing to do with the Moon. That is why the month can have 28, 29, 30 or 31 days.


In this calendar to keep track of the passage of time we must actually count the number of days. For convenience the year is sub-divided into 12 months, but their length is arbitrary. We could have had a month of 36 days if we so wished. As far as the Gregorian calendar is concerned, the Moon is totally irrelevant. Even if the Moon did not exist the calendar would function in exactly the same way as now. Gregorian calendar is  (purely) a solar calendar. 

We can construct a solar calendar in another way, where the month is still decoupled fro the moon but now has astronomical significance. Divide the ecliptic into 12 equal parts. Each is called a zodiacal sign or rashi. Sun’s entry into a rashi is called Samkranti. The solar year would then comprise 12 Samkranti months. 

There is a good reason why a solar year has 12 months even if these months are independent of the Moon. Seasons return with the solar year ( 365 days). During this period there occur 12  lunations (  that is 12 Amavasya’s or Poornima’s)

 The problem with solar year is that the new month and therefore the new year begins Chori Chori Chupke Chupke. The fact that the word month comes from the Moon tells us that originally the Moon  was the month-maker. We can indeed  construct a calendar which dispenses with the Sun as the clock hand and instead utilizes the Moon. The Sun of course remains in the picture as the digit on the dial.


Hijri calendar


Hijri calendar is a purely lunar calendar. Muslim festivals are fixed according to it. The year  uniformly consists of 12 lunations  adding up to  354 days. The Hijri year is decoupled from the Sun. That is why Muslim festivals systematically slide through seasons.


Vikrami calendar


The Gregorian and the Hijri calendars achieve their simplicity by using  either  the Sun or  the   Moon  as the colck hand. The Vikrami calendar on the other hand insists on employing both. That is why it is complex and can be very confusing to a layperson. 

Like the Hijri calendar the Vikrami calendar also has a lunar month, which  begins with (the  ending moment of) Amavasya. But while the Hijri year consists uniformly of 12 lunations, the Vikrami calendar some times makes the year of 13 lunations. The  festivals therefore show deviation from seasons  but it will  always be less than a lunation ( 29 days). Christmas  falls on a fixed day of the Gregorian calendar ; Eid can come any time in a year  while Divali  falls within a narrow range of days.

 The  solar reference point for the Vikrami calendar is the Spring Equinox, which  currently occurs on  20-21 March. Because of wrong year length, the Vikrami calendar  at the present epoch nominally considers 14 April to be the Spring Equinox. The first month of the Vikrami year must begin before this date , on   New Moon. As already noted the year can consist of 12 or 13 lunations. There is a prescription for doing so. Also note that even when the year has 13 months there are only 12 month names. A name will therefore have to be repeated.

 Vikrami calendar is a twin-track calendar.  It keeps track of the Samkranti’s as well as   Amavasya’s and Poornima’s. Samkranti’s are the more important because they are directly related to seasons. Normally between two Samkranti’s there would occur an Amavasya. Some times it happens that  between two neighbouring  Samkranti’s  there are two  Amavasya’s instead of one.  We then count the lunar month twice; the first  one  is called Adhik Masa, pronounce Maas ( extra month). Conventionally  celebrations are reserved for the latter one, which includes a Samkranti . On very  rare occasions there will be  no Amavasya between two Samkranti’s . This month is  then  deleted as Kshaya Masa ( decayed month). A Vikrami year cannot have less than 12 months. If one month is deleted, some other must be repeated.




For ease of calculations, a lunation is divided into 30 parts known as tithi’s. They are of unequal duration. Assigning a civil day to a festival calculated for a  tithi is based on a complicated prescription  A lunation is broken into two parts, called Paksha’s The period from Amavasya to Poornima is called Shukla ( bright) Paksha, because the Moon becomes brighter night after night. The period from Poornima to Amavasya is called Krishna ( dark) Paksha


A Vikrami new year starts with Amavasya preceding the  Spring Equinox theoretically taken to occur on 14 April. The first nine days of the first month ( strictly speaking the 9 tithi’s) , collectively known as Navaratri ( nine nights), are earmarked for piety, worship and restrained behaviour. This is in contrast to the Gregorian new year which is often ushered in with revelry and hang-over. Each of the nine tithi’s is addressed to a different deity. In particular the ninth tithi is celebrated as Ramanavami. Easter is a Christian festival still connected to the Moon. Easter falls on the Sunday that comes after the calculated Full Moon  on or after the Spring Equinox.  Since both Easter and Ramanavami are related to the Spring Equinox, they occur close together.

 Six months after the Spring Equinox comes the Autumn Equinox . The lunar month containing the Autumn Equinox again begins with Navaratri. Before  this, homage is paid to the departed ancestors in a ceremony called Shradha, pronounced Shraadh. The eighth tithi of the new month is devoted to Durga. After the Navaratri is over, the next day  Dussehra or Vijayadashmi is celebrated with great enthusiasm and fun. Note that if Dussehra were part of Navaratri, it will have to  be  a very solemn affair. About 20 days after Dussehra comes Amavasya  which is celebrated as Deepavali or Divali. The Poornima following Deepavali is celebrated as Guru Nanak Jayanti. Note that Buddha Jayanti also falls on a Poornima. Deepavali is probably the only festival associated with New Moon. 

We may now take note of two festivals towards the close of the Vikrami year. A night before Amavasya the Moon appears to be very thin. This day is devoted to Shivaratri. The  last Shivaratri of the year would of course be the one just before Navaratri.The one prior to this is celebrated as Mahashivaratri. The Poornima  after this is Holi; it is the last Poornima of the year. With the Amavasya after this begins the new year.The astronomical context of these festivals is obvious. It would be interesting to learn about the fixation of  the tithi’s of other festivals like Gansh Chaturthi, Krishnashtami,etc. 

So far we have spoken about the Sun and the Moon. In passing we may note a festival associated with Jupiter. Its entry into the Kumbha rashi ( Aquarius) is celebrated as Kumbha mela. Since  Jupiter’s orbital period is  about 12 years, the main Kumbha  celebration returns after this period.

 Finally we may make two observations. The seasonal festivals are all associated with the astronomical position of the Sun. The assumption is that Earth’s climate plays no role. This was true in the past when human beings lived in harmony with nature.. Not any more. Man made activities are now profoundly influencing the environment. 

 As  pointed above that the Vikrami calendar  has an accumulated error of  23 days. Lohri should fall on about 22 December and Baisakhi on 23 March. There is urgent need to apply corrections to the Vikrami calendar to  make it agree with the actual, observed, sky.

( Spelling of Sanskrit words employed  here does not follow any consistent pattern. An apostrophe has been added in the plurals of Sanskrit words so that the original word can be identified unambiguously. )


















Scriptures, science and mythology:Astronomy in Indian cultures

Posted in Blogs (Articles) on January 25th, 2009 by Rajesh Kochhar – 4 Comments

Invited review presented at International Astronomical Union /UNESCO Symposium 260 : The Role of Astronomy in Society and Culture, UNESCO Paris, 19-23 January 2009.



Rajesh Kochhar

CSIR Emeritus Scientist, IISER:

Indian Institute of Science Education and Research,

Sector 26, Chandigarh 160019, India

[email protected]


Indian astronomical tradition has been characterized by antiquity, continuity and interaction with the outside world. Here we focus on some selected aspects of astronomy-culture interactions;


*         How knowledge about astronomical universe was  used to regulate human conduct in the joint Indo-Iranian tradition.

*         How the religious and the ritualistic tradition influenced the astronomical pursuits.

*         How astronomical knowledge in turn modified the extant mythology.

*         We also raise an important general question : when  and how does tradition gets frozen and emerge as touch-me-not


Human beings are born astronomers. Ever since they learnt to walk upright they have looked at the sky and wondered. The sky has remained the same but not its meaning.


We can distinguish between three phases in the history of humankind’s relationship with its cosmic environment: (i) propitiatory phase; (ii) negotiatory phase; and the current (iii) expository phase (this probably needs a better name). Each of these phases leads to and coexists with the next. 

To begin with, sky was home to divinities who were to be feared and propitiated. As time progressed, human beings felt more secure and became intellectually more alert. Earlier awe made way for curiosity.  Skies were now scanned for discovering patterns in the behaviour of the divinities. The knowledge so gained   was put to practical use and employed to establish a negotiatory relationship with the celestial bodies. 

The third phase ,  properly speaking, began exactly four centuries ago with Galileo. The cosmic environment was now be subjected to scientific scrutiny with a view to discovering and testing laws of nature. Earlier astronomy had measured angles; now it could talk of distances.  The sky now acquired depth literally as well as figuratively. 

There is an interesting correlation between the world geopolitics and our view of the cosmos, which does not seem to have been noticed before. For a very long time, the model universe had a centre. The pride of place first belonged to the earth and then to the sun. Even when galaxies were discovered our Galaxy was believed to be the largest. It is in relatively recent times, in the post- World War II era, that the universe has truly become egalitarian. Interestingly, this cosmic scheme has been mimicked on the earth as well. When the universe was centric, the earth, or parts thereof, also had a power centre, be it local or on a larger scale. 

The Copernican principle now applies, at least in principle, on  the earth as well.  Is this a coincidence?  Or is it  that our perception of the cosmos influences the scheme of things on the earth   just as this perception itself is fashioned by the situation on earth? 

My concern today is to discuss the interplay between astronomy and culture in general in the Indian context. Much of the discussion belongs to the negotiatory phase described above.  I have advisedly used culture in the plural in the title. This is not so much to describe the scope of this review as to draw attention to its limitations.


For a number of reasons, discussed in a different context elsewhere, most of the world attention on India’s past has focused on Sanskrit texts and the associated culture (Kochhar 2008a; Kochhar 2008b).

 We have no clues whatever to the astronomical knowledge prevalent during the various phases of the  vast Harappan archaeological tradition the roots of which go back to the very beginning of agriculture and animal husbandry in what is now Baluchistan (Kochhar2000). Also the astronomical knowledge residing in the fields rather than in the archives  and especially belonging to communities officially termed scheduled tribes needs to be examined in depth. New scholarship must go beyond the Sanskrit India. 

Source material

A discussion that involves ancient India must take note of the nature and limitations of the source material available. Scripts (Kharoshthi, Brahmi) were introduced into India about 3rd century BCE or some what earlier for writing Prakrit languages derived from Sanskrit.  Script for Sanskrit itself, the language of Hindu scriptures, was adopted much later.  Writing material came from plants or trees and had a short life. Paper was not introduced into India till about 8th century CE. The Vedic texts were in any case forbidden to be written.  

Ancient Indian intellectual tradition has been oral. Texts were in the custody of specialist caste groups who memorized them and transmitted them to the next generation by word of mouth. The extant texts would have been supplemented with explanatory “notes” to serve an immediate purpose. What was not considered worth preserving was lost for ever. Also, it is not possible to assign firm dates to any early event or development. It is therefore not possible to construct a connected account about any aspect of early India. 

We must cull relevant information from a variety of literary sources. Sanskrit provides texts at three levels. (i) The most important of these is the Vedic corpus, comprising priestly books composed by a large number of authors over a long period of time, which could be as much as two thousand years, say from 1700 BCE to zero CE (Kochhar 2000).The importance of the Vedic texts lies in the fact that scrupulous care was taken to preserve them in their original form. They are thus truly representative of the time of their composition even if that time is largely indeterminable.


The pride of place in the Vedic corpus goes to the oldest and the stand-alone text, Rigveda, containing about ten thousand stanzas. According to Kochhar (2000) it was composed over a period extending say from 1700BCE to 900BCE, although its earliest portions probably contain memories of still earlier time. (Some other texts, though closed later, may contain much  older matter. ) 

There are a few stray astronomical references in the Rigveda, but for our purposes the more useful is the Yajurveda which is a manual for actual performance of ritual. It contains some observational material, such as bright  stars visible on the journey of the moon ( the nakshatras)  as also reference to  the colures.


There is a solitary Vedic text, Vedanga Jyotisha, devoted exclusively to astronomy. It is the least understood of the whole corpus, partly because it was overtaken by developments. The oldest portions could be as old as 1400 BCE. Interestingly it deals only with the movements of the sun and the moon. Zodiacal signs and week days and other pre-Ptolemy elements would be introduced into India about 100 BCE, as part of interaction with the post-Alexandrian Greco-Babylonian world; see below. (Western scholarship especially during the colonial period tended to deny antiquity or originality to ancient India. As a backlash, many researchers have tended  to    unduly stretch  the chronology backwards.)

 The Vedic texts constitute the heritage of Hinduism. The youngest texts, like Manava Dharma Shastra, or Manu Smriti, which could be as recent as zero CE plus minus, represent transition to Hinduism proper. 

(ii) The texts associated with Hinduism as practiced are the Puranas and the two epics, Ramayana and Mahabharata. They were narrated to the public at large and used to be recast to suit the prevailing requirements of the narrators as well as the listeners.  Interestingly only additions were made, no deletions. 

(iii) In addition there are scientific corpus dealing with astronomy ( as also with health care, that is Ayurveda) which  underwent deletion as well as addition.


So far we have listed sources in Sanskrit ( the term is used loosely to include pre-Sanskrit). (iv)  In addition valuable information comes from Buddhist and Jain sources. The former include material from outside India. 


Cosmic order and human ethics 

The eternity around us has stood in sharp contrast to the short time-span of the human beings themselves. This chasm has been sought to be bridged by denying death finality. The “burial cultures” have postulated the physical rising of the dead, while the “cremation cultures” have distinguished between the body and the soul, and spoken of the indestructibility of the latter. 

There is a beautiful concept linking the divine with the human that goes back to the joint Indo-Iranian times. Called rta in the Rgveda and arta (or asa) in the Avesta, it refers to the cosmic order, not in the sense of impersonal laws of nature as ascertained from the outside, but as an example of righteous cosmic conduct which the humans should emulate. 

The sun, moon and other geocentric planets dutifully and predictably orbit around the earth. (Their predictability was a source of comfort, in contrast to the  sudden ill-omened appearance of comets, meteors, etc.) The laws regulating the behaviour of these divinities are inbuilt into the system. But similar regulation of human conduct can come only from an explicit prescription of a code of ethical conduct. Emphasis on rta / arta is far more pronounced in the Avesta than Rigveda. 

To bring the terrestrial and the celestial closer together the Vedic people assigned the attributes of one to the other. Planets return to their place in the sky; so do seasons on the earth. But human beings are born and die. In analogy with the planets, human beings should also have continuity. To achieve this, the concept of reincarnation was introduced. But in a certain sense planets are condemned to a life of incessant motion. An endless cycle of birth and death would be a punishment rather than a boon. Therefore the concept of what we may call truncated eternity was introduced, under the name moksha or nirvana, whereby a soul is liberated from the constraints of future birth. 

The cyclic time

Far more important were the human attributes assigned to the gods. The concept of age, birth and death was introduced for the cosmos as a whole, and a cosmic chronology in the form of the yuga system was constructed by suitably scaling up the human calendar. The eternity of the planetary orbits was generalized to set up an oscillating universe without beginning or end.  

For the mathematically oriented brave hearts, the technical details are explained in Appendix I. Here we may notice some important features of the scheme.  

In the Vedic period, a year was taken to comprise 12 months and 360 days. Multiply these two numbers to get 360×12=4320. Now, suffix this number with the requisite number of zeroes to produce long structured time-spans. The basic unit is a mahayuga (mega-age): 

              1   mahayuga=4.32 million years.


A still bigger time-span, Brahma’s “twelve-hour” day (or night), or a kalpa, is defined as equal to 1000 mahayugas:


1  Brahma’s day=4.32 billion years. 

Ancient Indians were probably the only people talking of such large numbers and of the endlessness of the universe. These numbers have been noticed by modern cosmologists in their textbooks as the cosmological timescales indeed turn out to be of the order of billions of years. 

A maha-yuga, in turn, is composed of four ages or yugas :  Satya or Krta;  Treta;   Dvapara; and   Kali. The scheme has some interesting attributes: 

ü                Virtue decreases down the ages in the ratio 4:3:2:1.

ü                Duration of the individual ages also decreases in the same ratio.

ü                Kaliyuga is thus the shortest.

ü                We are currently in the kaliyuga. 

The scheme must have  been found very attractive because it was used in entirely different contexts with the same terminology. These long ages were employed in astronomy. The terminology of the four yugas was also employed by the Puranas to periodize   political history going back about 100 generations. This has caused much contemporary confusion.

          The scheme was formulated in the kaliyuga itself. It is significant that the present age was postulated to be the kaliyuga. We are now in the worst of times. Things can only improve. Imagine, if we had been placed in any of the earlier yugas, things would have had to deteriorate further before they could improve. It is thus an inherently optimistic scheme. During the movement against the British rule in India, the dark kaliyuga’a making way for satyayuga was repeatedly  invoked  to enhance nationalist consciousness. 

 A pioneering name in the  systematization of the post-Vedic astronomy  was Aryabhata (b. 476 CE). Indian mathematical astronomy , which we may call Siddhantic (since the astronomical texts were called Siddhanta, proven in the end), focused on calculating geo-centric planetary orbits and especially the lunar and solar eclipses. 

From 6th century CE till Kepler’s time , Indian astronomers were probably the only ones who could calculate eclipses with any degree of accuracy. The unbroken tradition was alive till as recently as 19th century. A Tamil astronomer computed for John Warren , a French astronomer in the service of British East India Company, the lunar eclipse of 1825 May 31-June 1 with an error of +4 minutes for the beginning,-23 minutes for the middle, and -52 minutes for the end ( Neugebauer 1983:435).


An Indian astronomer adjusted his parameters and obtained satisfactory match between the calculated sky and the actual sky. This match  would  disappear in a few centuries. A brilliant astronomer then appeared on the scene ,  and reworked the mathematics. Remarkably although the physical  goal was the same different astronomers ended up setting up and solving different equations. Mathematics was a tool for planetary calculations. There are very few full-time mathematicians in the Indian tradition ( Kochhar 1993). 

Sacred texts influence science

Use of early astronomical data in the ritual profoundly influenced the later course of astronomical developments. The yuga system with its nomenclature was borrowed by the astronomers. Thus the Surya Siddhanta would say that there were 146,568 revolutions of Saturn in a mahayuga, implying an orbital period of 29.4743 years. 

Interestingly,  at places Aryabhata   chose to  deviate from the Vedic yuga scheme. He split a mahayuga into four equal parts. Also , he  set his kalpa equal to 1008 mahayugas (instead of the Vedic 1000). Since 1008 is divisible by seven, all  kalpas,  each 4.32 billion years apart   will begin on the same day of the week. Some far sight indeed ! 

Like the  (( divine) Rigveda  astronomical texts were composed in verse, so that an astronomer had to be a Sanskrit poet first. Constraints of metre forced astronomers to use synonyms and take recourse to allusions. This introduced ambiguity at places. More importantly only   conclusions were preserved  and not the arguments leading to them. Generally speaking there was a tendency to present astronomical results as revealed knowledge rather than deduced.


Aryabhata believed in the spin of the earth and said so in his work.  This however never became a part of the mainstream. He was severally criticized for this by his “adversaries”. Even later astronomers belonging to his  own school felt so embarrassed that they tried to change a  word here and there in his work to convey the impression that the great master like everybody else took the earth  to be non-spinning.  Today we give great credit to Aryabhata for his belief in earth’s spin. But it is important to keep in mind that our source of knowledge is his critics who were putting Aryabhata’s lapses on record. (As a belated compensation Aryabhata’s glorifiers now falsely credit him with belief in heliocentrism.)

 As an analogy, we may note that we know about the deeds of  revolutionaries  fighting for India’s freedom from the charge sheets filed against them by the colonial government. 

If astronomy had followed a prose tradition (as was the case with post-Vedic Upanishads) some later scholars could have revived and expanded on Aryabhata’s hypothesis. 

Indian astronomers were not aware of the precession of equinoxes. A creative astronomer would adjust his parameters so that his computed planetary orbits matched the observations. With the passage of time the  computed sky would differ from the actual. This ar necessitated the arrival of  a new mathematician – astronomer on the scene.

 Ancient India astronomical effort was society oriented rather than sky oriented. Its aim was to prepare almanacs pinpointing auspicious times for social and religious purposes. It is certain that most if not all students who learnt astronomy did so to become practising astrologers. 

The ancient astronomical texts were unambiguously attributed to their named authors. But at the same time their contents were incorporated into traditionally-named texts that were passed off as having been revealed to the chosen ones (e.g. Surya Siddhanta). This pretension to divine connection no doubt increased the astrological market value                                                                                                                                                                                                  of the texts and ensured funding of astronomical activity by the society. 

(It is noteworthy that Buddha was against astrology. As long as Buddhism held sway astronomy went in decline. It is only on resurgence of Hinduism that astronomy revived. By the time Buddhism was exported, astrology had become part of it.) 

Aryabhata’s influential and pioneering work  closes with the stanza : “This work , Aryabhatiya by name,is the same as  the ancient Swayambhuva [i.e. revealed by Swayambh] and as such it is true for all times. One who imitates it or finds fault with it shall lose his  good deeds and longevity “. It has been argued-and with justification-that a man of  Aryabhata’s   known scientific approach could not have made such a pompous and intimidating statement. While this argument exonerates Aryabhata, it does indict his                           later-day followers , and tells us about the  atmosphere in which such a statement could be made and attributed to Aryabhata himself (Kochhar 1993).


Old astronomical knowledge  has remained a living tradition even if its role is not so obvious now. Spring and autumn equinoxes as well as winter solstice ( but not the summer solstice) are still celebrated as religious festivals. (Thus  spring and autumn equinoxes are honoured by nine-day celebration each, called navaratri. Makar samkranti, the sun’s ingress into Capricorn , on about 14 January,  is nominally celebrated as northward turning of the sun . Jupiter’s 12-year orbital period is commemorated by the Kumbh festival, marking Jupiter’s computed ingress into Aquarius.) 

Traditional  almanacs in  current use still use old prescriptions. They have accumulated an error of 23 days due to precession of equinoxes, but nobody seems to mind. The reason is that phenomena like ingress into a zodiacal sign are not visible to the eye. Since eclipses can be timed now with great accuracy, their computation is  not done traditionally but    on the basis of modern algorithms. 

Much of the contemporary interest still centres on the astrological universe.( Use of high technology as represented by the computers  along with the  insecurities  introduced by globalization  seems to have  lent new legitimacy  to astrology.)  The  interest in  the  progress since, for some reason,   extends only to black holes and the origin of the universe. This is probably so because here the difference between the layperson and the expert gets blurred. All  astronomical developments in between  commonly leave the laypersons rather unenthused.


Science modifies sacred texts

We have  already seen how astronomical tradition was influenced by the Vedic. But  the traffic was two-way. Early  Vedic mythology attributed the eclipses to a demon Rahu, who is explicitly named in  Atharvaveda. Chhandogya Upanishad declares that a  soul which has  acquired pure knowledge is liberated  from the body   like the moon becoming free from Rahu. ( Kane V.1: 569) The correct mathematical theory of eclipses, which probably made its appearance in India about 100 BCE or so , points out that for an eclipse to occur the moon should be at one of its nodes, that is, at one of the two points where the lunar orbit intersects the ecliptic. The term Rahu was borrowed from the Vedic texts and applied to the lunar node, especially the ascending node (when the moon crossed the ecliptic moving northwards). The other node was termed Ketu. Maitrayani Upanishad mentions both Rahu and Ketu ( Kane  V.1:569). Incidentally this also tells us that the  Vedantic part of the  corpus was still open say about zero CE. 

At a more popular level  an elaborate  mythology was created to cut the old single demon Rahu  into two . The head retained the old name  while the  torso  was called Ketu. Subsequently the concept of Rahu and Ketu travelled outside India also. Burma knew of Rahu as Yahu ( Kochhar 1990) Interestingly,  in China while Rahu stood for the ascending node, Ketu denoted the lunar apogee, an identification not known in India.

 It is noteworthy that no religious, spiritual or revealed text or folklore has ever contradicted what the people at the time accepted as scientific knowledge. There is a basic difference between scientific tradition and the  other societal traditions. Science is inherently progressive. It continually updates itself.  There is no concept of frozenness associated with it.  On the other hand  the textual content of sacred tradition or folklore remains open for a while during which it takes note of contemporaneous scientific developments. But then it  becomes static and at times even may see later scientific developments antagonistically. (Hindu society has tended to accept modern scientific discoveries through the side door, by pretending that they were known to the ancient scriptures!) 

Appendix 1: Creation chronology 

The Rgveda uses yuga in the sense of a time-span, an age, or a generation. Vedanga Jyotisha refers to a five-year yuga. Atharvaveda  mentions in order 100 years, 1000 years, ayuta (10,000 years) and then two, three or four yugas. This suggests that a yuga here means an ayuta. The yuga-system as now commonly understood is set forth in the relatively late Vedic text Manusmrti (1.68-1.86), and expanded in the various Puranas.


In the Vedic times, a year comprised 12 months and 360 days. A human year was set equal to a day of the gods, so that a divine year (Dyr) would consist of 360 human years (yr).The divine year in turn was used to construct an elaborate chronology.


A mahayuga or chaturyuga (great age or four-age) was postulated as made up of four sub-ages or yugas: kaliyuga, dvaparayuga, tretayuga and krtayuga, with lengths in the ratio 1:2:3:4. The names are significant. The two middle ones obviously refer to the second and the third. The names of the two end yugas are taken from the game of dice, kali referring to one, and krta to four. The numbering is thus backwards, kaliyuga being the shortest and the latest.


It will be convenient to use mathematical notation to properly understand the formulation of the yuga system. A kaliyuga is said to contain 1200 Dyr. Let us denote the duration of a kaliyuga by the symbol k and of a mahayuga by m. dvapara, treta and krta are then 2k,3k and 4k respectively, so that




For later reference, let us denote a krtayuga (=4k) by s. Then




We now construct a still bigger time-span called kalpa, comprising 1000 mahayugas. To complicate matters, let us introduce structure into a kalpa as follows:


1 kalpa 




      = 994m+6m     


       =14 x 71m+15s   






Let us call 71m a Manvantara (Manu’s interval) so called because this span is presided over by a ruler designated Manu. (There are thus 14 Manus.) We can now describe a kalpa in words. A kalpa begins with a dawn equal to a krtayuga. This dawn is followed in succession by 14 Manvantaras, at the end of each of which there occurs a deluge (pralaya) lasting a krtayuga. This complex scheme has perplexed many modern-day commentators. Thus, Ebenezer Burgess in his famous 1860 annotated translation of the Surya Siddhanta declared: “Why the factors fourteen and seventy – one were thus used in making up the Aeon [kalpa] is not obvious” (Ebnezer 1860:11). I think this scheme was constructed working backwards from the neat round figure of 1000.


To sum up so far, a kalpa comprises 1000 mahayugas, with one mahayuga equaling in length ten kaliyugas. It now remains to give recognizable values to these numbers. A kaliyuga was set equal to 1200 divine years. Recalling that a divine year consists of 360 (human) years, we can express the yugas in human years:


      Kaliyuga   =4, 32,000 yr

      Mahayuga=4.32×106 yr

      Kalpa       =4.32×10 yr.


Kalpa becomes the basis for constructing a chronology for Brahma, the supreme creator. A kalpa is set equal to Brahma’s day or night. 360 kalpa pairs define Brahma’s year, 100 years making his life-span. Currently, we are in the midst of Brahma’s life. He has completed 50 years of his life. In the current kalpa seven out of the fourteen Manvantara are over, and so on.



Burgess, Ebenezer (1860) The Surya Siddhanta (reprint; Delhi: Motilal Banarsidass, 2005)


Kane, P.V. (1977) History of Dharmasastra, Vol. V. ( Poona : Bhandarkar Oriental Research Institute)


Kochhar, R.K. (1990) Rahu in Burmese tradition (Correspondence) ”. Quart. J. R. Astr. Soc., 31,257


Kochhar Rajesh (1993) “ Historical perspective”. In: Astronomy in India : Past, Present and Future ( eds.: Rajesh Kochhar and Jayant Narlikar) ( Pune : IUCAA)

Kochhar, Rajesh (2000) The Vedic People: Their History and Geography (Hyderabad:Orient Longman)


Kochhar, Rajesh (2008) “Cultivation of science in the 19th century Bengal”. Indian Journal of Physics, 82(8), 1003-1082. (Akshoy Datta Memorial Lecture at Indian Association for the Cultivation of  Science, Kolkata.)


     Kochhar, Rajesh (2008) “Seductive orientalism: English education and modern science in colonial India”. Social Scientist, 36:45-63. (S.C.  Mishra Lecture at 68th Indian History Congress,   Delhi.)


Mani, Vettam (1975) Puranic Encyclopaedia (Delhi: Motilal Banarasidass)


Neugebauer, Otto (1983) Astronomy and History: Selected Essays (New York: Springer)// FaceBook maxweb Twitter maxweb linkedin maxweb googleplus maxweb facebook facebook ChandigarhCity.Info facebook facebook