Mathomathis would like to present an article on: A genuine approach on Ancient Indian Science  by author Prof. K.D.Abhyankar, F.N.A,F.A.Sc, F.N.A.Sc,A.R.A.S | Fellow , Indian National Science Academy (INSA), Hyderabad


There are two opposite views about ancient Indian science. According to one conservative Indian view all knowledge is contained in the Vedas and one has to discover it by proper decoding of its contents. On the other hand western oriented people say that Indians were ignorant of science before they came into contact with the foreigners. Both these views are extreme and wrong. Knowledge grows exponentially with time like a nyagrodha i.e. banyan tree. The father learns something by experience. He transmits his knowledge to his son. The son in turn adds to it his mew experience and conveys it to the grandson, and so on. The present day knowledge is the result of such accumulation over thousands of generations. So it is not correct to say that every thing was known in the beginning itself. But surely there was an earlier simpler beginning and it should be our aim to discover the seed of nyagrodha tree of knowledge, which was sown in ancient times. The ancient knowledge need not be as complex as modern one. Same thing applies to technology. It would certainly take a long time to graduate from a potter’s wheel to an aeroplane. Hence one need not claim that the ancients were familiar with radio, television, air travel, theory of relativity and atom bombs. Of course they were intelligent enough like us to speculate about such things. In astronomy also we have to remember that there were no telescopes at that time. So there was no knowledge about galaxies and the expansion of the universe. However the ancients made good use of their eyes and simple devices like shanku (gnomon) and ghatikapatra (water clock) for discovering some basic facts about the heavens. And we endeavor to search them.

Sense of History:- Secondly one has to have a proper historical perspective about Indian history. Here also there are two extreme views. According to one school Aryans, who spoke Sanskrit and produced the Vedic literature, came into India from outside around 1500 BC. So they would compress Vedic knowledge within this period. On the other hand traditionalists will vouch for several mahayugas of Indian history. Let us first look at the Aryan influx theory. It is based on two premises. One is the close affinity between Sanskrit and European languages. The other id the existence of 500 years old Indus valley civilization which is said to have been destroyed by the incoming Aryans, who were nomads. So Vedic knowledge cannot to be older then 1500 BC. However Malti Shndge of Pune has shown that there is a closer affinity of Sanskrit with the Sumerian and Akkadian languages of Mesopotamia. So it is more likely that these and European languages are offshoots of Sanskrit which is definitely Indian origin. Further Vedas do not talk about an earlier home of Aryans like Arianavayo of Parsis. In fact they praise the mighty Saraswati river of India with fondness and reverence. In older times saraswati was joined by yamuna in the east and Satadru (satlaj) in the west. Due to technonic movements of the earth they were diverted to Ganga and Sindhu, respectively and saraswati dried around 200 BC. Satellite photographs clearly show the dry bed of saraswati river in Rajastan. So Vedic people were living in India before that time and the so called Indus valley civilization. Most archeological sites of that civilization are found near the banks of old Saraswati. Now how far back can we go in time. It is now known that before 1000 BC the earth was passing through an ice age for a long time. Large parts of the earth were covered with the thick ice and people had to live in caves. The ice melted around 1000 BC and it was possible for men to inhabit land in river basins and take up agriculture. So one cannot go beyond 1000 BC. Our study of Vedic calendar takes us back to 7000 BC.

Evolution of Vedic calendar:- Our present calendar i.e. Panchanga, is developed during the Siddhantic period of Indian astronomy starting from the beginning of Saka/Samvat eras. It is advanced by many famous astronomers from Arybhatta of 5th century to Samant Chandarashekhar of 20th century. Siddhantic astronomy makes use of the Greek methods of deferent’s and epicycles for computing the position of the sun, moon and taragrahas. So it is claimed that Indians borrowed all astronomical knowledge from them. It is even asserted that Vedanga Jyotish was borrowed from the Babylonians, although it is quite clear that Vedanga Jyotish belongs to 1400 BC while Babylonian astronomy thrived in 5th century BC. They forget that the concepts of tithis and nakshatras, which form an important element in our panchangas, were clearly defined in Vedangas Jyotish and represent the link between Siddhantic and earlier Vedic astronomy. As Siddhantic astronomy has already been studied extensively by many scholars we have concentrated on the study of Vedic astronomy with our genuine approach outlined here. India has a hoary astronomical tradition, but it is difficult to trace its development from the earliest epoch due to the lack of any systematic historical records. So one has to interpret the stray astronomical references in the Vedic literature, which covers a long period of time (700 BC to 500 BC) by logical reasoning.

From times immemorial the sun, moon and stars have served as directional guides to travelers on land and sea, and now even to astronauts in space. They have also helped him in the measurement of time. When man learned civilization and settled down on land he found that the groups of stars known as Nakshatras (asterisms), which are seen before sunrise or after sunset and near the full moon, changed during the course of the year. It was discovered that the seasons of spring, summer, rains etc were closely associated with the nakshatras visible at that time. He was therefore right in concluding that the association of the sun and full moon with nakshatras determined the seasons and through them the well being of the people. Thus astronomy of the sun and moon became an integral part of all ancient civilizations. We are particularly interested in the earliest Vedic astronomy and its use for forming a calendar. While a lot has been written about post- Vedic i.e. Siddhantic astronomy no one has so far constructed an evolutionary sequence of chronological development of Vedic astronomy, and this might be the first attempt.

The Earliest Vedic Calendar:- A calendar is needed for regulating the social and religious activities of people, which depend upon the seasons of the year. The periods of northward and southward movements of the sun i.e. Uttarayana (22 Dec. to 21 Jun) and Dakshinayana (22 Jun to 21 Dec) provide the most natural way of marking the seasonal vibrations during the course of the year. Even the birds make use of this phenomenon for their annual migrations. So it is not surprising that the Vedic astronomer-priests made use of it for devising a calendar of seasons i.e. Ritusamvatsara. Now, as the phases of the moon repeat after nearly 30 days and the seasons repeat after about 12 lunar months, it was simple to conceive of a calendar of 360 days made up of 12 months of 30 days each. The Vedic Rishis formulated such a calendar in the form of a yearlong sacrifice of 360 days called Gavamayanam sacrifice described in the 12th Kanda of Shathpata Brahmana. We have several passages to this effect in Vedic literature. (See Rigveda 1-164-48, 1-164-11, Tail Sumhita 7-17) Gavamayanam sacrifice was started on winter solstice day (22 Dec), which indicated the start of Uttarayana. This is clear from Aitreya Brahmana 4.3.18: i.e.

eavisha metadrupayati vishuvatam madhye samvatsarasyaitena vai
deva ekavishaadityam svarga lokaayodayachcham sa ||

The gods raised the sun to the world of heaven (maximum mid-day altitude) on Ekevinsha day, The Vishuvat in the middle of the year. Thus summer solstice (22 Jun) occurred in the middle of the year, which means the year was started on winter solstice day. Gavamayanam sacrifice lasted for 360 days. But as the sun did not start moving northward at that time the priests had to wait for 4 to 6 days before staring the next years Gavamayanam. They used this period for performing Praargya and Upasad rites of consecration (Diksha) during which they prayed to Ashivinikumars, the deities of Ashivini Nakshatra, as in those days (about 700 BC) the heliacal rising of Ashvini Nakshatra narked the winter solstice, i.e. the beginning of Uttarayana.

Pravrgya ceremony involved boiling of milk in an earthen pot, a practice which is still followed in some parts of India where people boil milk in earthen pots on Makar Sankranti, which marks the winter solstice around 300 AD, and Rathasaptami, which marks the winter solstice of Mahabharat time. In the earliest Vedic period it occurred in Vaishaka later it was found that the year contains close to 365 days i.e. 5 days in excess of 360. According to Taittiriya Samhita 7.1.8. The year was alone in the world. He desired ‘May I create seasons’. He saw this five-night rite; he grasped it and sacrificed with it. Then indeed he created seasons. The four-night sacrifice is incomplete, the six-night rite is redundant; the correct sacrifice is the five-night rite. Therefore the astronomer-priests started the practice of having a six-year in which an abhikamasa of 30 days was added at the end of six years of 360 days vide Atharvaveda 13.3.5: “ahoraatrair vimitabhi radara masam yo nirmimiite” The Shunashepa legend in Shataptha Brahmana points to this devise. According to it Harishchandra’s son Rohita, who represented the rising sun of the winter solstice avoided death by wandering for six years and he was replaced by shunashepa (adhikamasa) at the end of six years. In this calendar the year was divided into three seasons viz.

(I) Agniritu (fire season) from 22 Dec to 21 Apr when we have cold season on north India
(II) Suryaritu (sun season) from 22 Apr to 22 Aug. when we experience the power of the sun first in the form of intense heat and then in the form of copious rains, and
(III) Chandramaritu (moon season) when we have the longest and most beautiful full moons between 22 Aug to 21 Dec. later on the three seasons were subdivided into six seasons viz. Shishir, Vastanta, Grishma, Varsha, Sharad and Hemant.

The practice of starting the year from winter solstice, Uttarayana day continues throughout the Vedic period by changing the year beginning with the change of winter solstice nakshatra due to the phenomenon of ayanachalan. Adjustment of the year with seasons through the devices of adhikamasa was another feature of this period. The practice of changing the month of year beginning for having the correct seasons help us in tracing the history of Vedic Calendar.

Use of the Lunar Month:- In the beginning Gavmayanam was started with the heliacal rising of Ashvini nakshatra in vaishaka around 7000 BC. But around 6000 BC the heliacal rising of Ashvini no longer served the purpose of identifying the winter solstice. At that time the nocturnal rise of Chitra nakshatra after sunset was found to coincide with winter solstice. Further it was found that quite often there was a full moon near Chitra at that instant. So the Gavamayanam sacrifice was started in Chaitri full moon (Paurnima) day vide Taittiriya Samhita 7.4.8: “chitraapurnamaase diiksheran mukham vaa etat samvatsarasya” Consequently the priests started observing the position of the full moon among the stars every month, and later its position every day. This led to the identification of the 28 nakshatras listed in Vedic literature, which define the ecliptic i.e. Varuna’s path.

Later, when it was found that the actual period of the moons round of the ecliptic (Varuna’s path) is close to 27 1/3 which is closer to 27, the nakshatras Abhijit was dropped from the list. At that time the original Abhijit was renamed Shravana and original Sharvana was renamed Dhanishta. The Jain astronomers reintroduced Abhijit and placed it at Vega. Nakshatra are used for naming the day according to the nakshatra in which the moon is found that day. They are also used for naming the month according to the nakshatra near which the moon is found on the full moon day. Only 12 nakshatras are used for this purpose, because their deities signify Agni, the god of sacrifice. While performing the annual sacrifice the priests observed the phase of the moon every day and performed special sacrifices on new moon and full moon days, known as Darsha and Purnamasa Yastis. Such observations showed that the Moons phases are repeated after 29 ½ days and not 30 days. So they defined tithi as the 30th part of a lunar month, which is divided into two halves: the bright or Shukla Paksha and the dark half or Krishna Paksha. The 15 tithis of Shukla Paksha are called Shukla Pratipada to Shukla Chatirdasi and Purnima ; they are denoted as S1 to S14 and S15. Similarly the 15 tithis of Krishna Paksha are called Krishna Pratipada to Krishan Chaturdashi and Amavasya ; they are denoted by K1, K2 to K14 and K30

Luni-Solar Calendars:- Now, as the lunar month contains 29 ½ days instead 30 days a tithi is shorter than a day by one part in 60. So 12 lunar months containing 360φ tithis were found to be 6 days shorter than 360 days. Hence after adopting the lunar month the astronomer-priests replaced the Gavamayanam sacrifice by another sacrifice of 12 lunar months covering 354 days around 5000 BC. This so called Utsarjinamayanam sacrifice is described in Taittriya Samhita 7.5 and 7.6. It was followed by 11 Atiratra days for completing the year of seasons. So these Atiratra days were called the children of seasons vide Taittiruya Samhita 7.6: It means: Seasons were desirous of offspring; they saw this eleven-night rite and got offspring. Ritus being the mother of these they are the children of seasons. Now, this method of adjusting the year length was found to be inconvenient in a lunisolar calendar, because the tithi of the year beginning would change from year to year. So around 4000 BC Ribhus decided to add 12 tithis after 12 lunar months vid Rigveda 4.33.7 “dvaadashadhyanya dagoohyasyaa tithayah” : Ribhus stayed as guests of Agohya (sun) for 12 days. In this way one can adjust the length of the year by adding 60 tithis or 2 lunar adhikamasa in a span of 5 years at appropriate places so that the year always stated on Sl. In the beginning the adhikamasa were added at the end of the 3rd and 5th year. But it was later found convenient to add one adhikamasa after end of every 30 months. This innovation was introduced when the winter solstice had shifted to Phalguna S 15 vide Shatpatha Brahmana 6.2.18: “mukhamva etat samvatsarasya yat phalgunau paurnamaasii“. The above 5-year Yuga system has 372 tithis in one year; but it was known that the year actually contains 371 tithis.

Thus we have 15 extra tithis or one paksha enters in a period of 15 years. So one should drop one paksha at the end of every 15 years. This is the basis of the 30 years Dakshayaniya sacrificial calendar described in the 11th Kanda of shatapatha Brahmana. Here in the first half of 30 years cycle, the months are amanta (new moon ending) in the first three 5-year yugas and the Krishna paksha of the adhikamasa at the end of the 15th year is dropped as a kshaya paksha. In the second half of the 30-year cycle the months are paurnimanta (full moon ending) in the later three 5- year yugas and the Shukla pakha of the adhikamasa at the end of the 30th year is dropped as a kshaya paksha. Alternatively it was found more convenient to drop a whole month at the end of the 30th year as a kshaya masa. It can be shown that Mahashivarathri festival, which occurred near winter solstice at that time, was introduced at around 3000 BC for determining the presence of kshayamasa. The concept of kshayamasa has been carried over into the Siddhantic period of Indian astronomy. However it was found that three Dakshayaniya sacrifices fell short of 90 years by 5 tithis. So it was decided that one 5-year yuga of 1860 tithis should be introduced after third 30-year cycle. This is the basis of the 95-year Agnichayana vidhi described in the 6th Kanda of Shataptha Brahmana. It may be mentioned that the 95-year cycle contains 5 Metonic cycles of 19 tears discovered by the Babylonians around 300 BC. But it is modified 5-year cycles as explained above. The mathematical rules for the above luni-solar calendar were formulated by sage Lagadha around 1400 BC when winter solstice coincided with sun’s position in Dhanishta Nakshatra in the masha month. In his Vedanga Jyotish, Lagadha also gave the procedure for correcting the approximate calculations to arrive at the 30-year cycle. Vedanga Jyotish type calendar continued to be used by the Jain astronomers of 500 BC and is found in the Vashishta Siddhanta mentioned in Varahamihira’s Panchsiddhantica of 500 AD.

Siddhatic Panchanga:- Vedic calendar was used for performing various daily, seasonal monthly, four monthly and annual sacrifices. As the sacrificial system was frowned upon by the Buddhist Philosophers due to its ritualist corruption, Vedanga Jyotish lost its astronomical significance. So the purpose and meaning of Text became obscure and Indians had to rediscover the art of calendar making, which was influenced by foreign ideas from Babylon and Greece. It caused a break in tradition around the beginning of Christian/ Saka Eras and gave rise to Siddhantic astronomy heralded by Aryabhatta in 476 AD.

Firstly, the simple algebraic methods based on the mean motions of the sun and the moon were replaced by the geometrical methods of eccentric kakashavrittas for calculating the true positions of not only the sun and the moon but also of the planets. The system of nakshatras was supplemented by the system of Rashis and their boundaries were fixed with respect to stars. And definitions of tithi and solar month were made more precise. However the most drastic change pertained to the beginning of the year. Instead of starting the year from winter solstice it was begun with the vernal equinox (21 March) of 285 AD on a fixed basis. This made the calendar sidereal (nakshatra varsha) instead ritusamvatsara. Hence inspite of a foolproof method of introducing adhikamasa for sidereal luni-solar adjustments, the calendar was divorced from seasons by about one day in 72 years. The difference has grown to 24 days in 1700 years. Consequently the main purpose of adjusting the social functions like agriculture according to seson is slowly being eroded. For example Vasant ritu now occurs in phalguna and chitra and not in chaitra and Vaishaka. Similarly Makarasankranti no longer represents the beginning of winter solstice, it occurs on Jan 14/15 nearly 24 days after the true beginning of Uttarayana on 22 Dec. On the other hand the Grogorian calendar is a tuned to the seasons while it is discovered from stars. For example the sun enters Mesha Rashi (Aeries) on April 14/15 and not on March 22 as shown in newspapers. It is clear that both calendars are scientific in one aspect and unscientified in the other.