Eclipses, Scriptures and the Mathematicians

Eclipses have been a part of Hindu thought and have been discussed since very early times. While the cause had been initially ascribed to mythology and recorded so in scriptures, the negative effects of eclipses were paramount and continued to be understood as detrimental to physical wellbeing. Somewhere along came the famous mathematician Aryabhata, in agreement that eclipses were important for the purposes of astrology, refined the methods of their calculations while at the same time remarking that the cause was not of mythical proportions, but one of optic origins, namely the casting of a shadow. It is quite an interesting topic to delve in, that too now, when everybody is eagerly looking forward to the next total solar eclipse in these American states on the 21st August.

To understand the importance of the stars, their positions and impact on humans, you have to go well back in time, and the understanding could be seen in even in the earliest of scriptures, namely the Rigveda. Today we can foretell weather, make forecasts, all with the help of computational methods, sensors and instruments spread around the world. But in the times long forgotten, it depended on a few people who understood the mathematics of the heavens and space beyond earth. There were always a few who gazed upwards, observed the effects of various celestial bodies on earthly beings, their own movements and codified a celestial map. Those were the early astronomers and as required in their line of work, were good mathematicians, sans calculators and computers.

The positions of stars were important and many rules were established on when to and when not to do sacrifices, rituals and poojas to propitiate a particular god. One needed to be exact with the time of the day and most of all, ensure that eclipses were taken into account, carefully. As it became complicated and a method was agreed between various mathematicians of the period, Indian astronomy, developed into the first of the sciences.

Mathematical inputs were a must due to the fact that the calendars in most regions were lunar and required an adjustment. Hindu texts used the lunar cycle for setting months and days, but used a solar cycle to figure out the whole year. This of occurs meant a mismatch between some 354 lunar days compared to 365 solar days in a year. A number of systems were developed to provide a correct almanac which was important not only for rituals, but also for cultivation, seeding and the forecast of weather patterns such as the monsoon. Interestingly, as we discussed earlier, the Malayalam Kollavarsham, the Tamil, the Bengali, the Oriya, Tripura and Assamese calendars are examples of solar calendars in India and match the Gregorian. Others had lunar or Luni solar calendars.

The Sun and the Moon as you will agree were the most visible heavenly objects, so their interaction with earth was observed keenly. Eclipses as you can imagine, rose to the fore being remarkable. As the educated upper castes and classes formulated stories to explain these in a simpler fashion for the lay person, the mathematicians ventured to understand the science and the optics behind it. The balance was precarious, and science did not refute any mythology in those days, but the records left behind by some of those great astronomers and mathematicians such as Aryabhata make it clear that their work was well grounded in reality.

Albrecht Weber (The History of Indian Literature) explains it succinctly though touching on a Greek connection. Whether the Hindus discovered the planets independently or whether the knowledge came to them from without cannot be determined, but the systematic peculiarity of the nomenclature points in the meantime to the former view. While he implies a Greek connection due to the naming of the celestial bodies, it must also be noted that some from a number of other cultures such as Chinese, Egyptians, Babylonian and Assyrians have been recording eclipses as early as 2500BC. Later on the Greeks even built a sophisticated geared machine to provide planetary and eclipse information named the Antikythera mechanism.

Let us take a look and how the understanding developed in India. As mentioned before, one can find mentions even in the earliest scripture, the Rigveda. As you would know already, any eclipse is considered to be an omen, usually bad. We also noted that it was apparent even in very early times that there were connections between the earth and the heavens, as well as its celestial bodies. Things were in synchronism most of the time, and on an inopportune day things went wrong, the sky went dark on a bright day or the moon refused to come out on a dark evening. This disturbed the public and many sought answers. Vague myths were propagated by the clergy and the powerful and sometimes wrathful rulers insisted that his resident astrologer/astronomer come up with predictions for the future considering such events. Thus were created some of the greatest people of Indian mathematics. They monitored the movements of the sun, moon and stars, kept track of various usual and unusual celestial events and used these results to refine calendars and almanacs.

One of the most important problems of ancient astronomy was the accurate prediction of eclipses. In India, as in many other countries, the occasion of an eclipse had great religious significance, and rites and sacrifices were performed. It was a matter of considerable prestige for an astronomer to demonstrate his skills by predicting an eclipse accurately. Just imagine how it would seem as he stands and imperviously in an August audience, and declares…the sky will go dark in the next few 15 nimisha and it happens, the sky goes dark in the middle of a bright day, like magic.

To start with how did the clergy, and the scriptures explain the eclipse, the most visible of these celestial misadventures to the layman? While Swarbhanu was the entity in Rig Veda devoring the sun, Rahu appeared in the Atharava Veda for the first time. This is where a new being called Rahu enters the scene and is described in great detail in the Bhagavatha Purana. I will not retell the fable, but I will requote the translated account provided by Raj Kumar Parashari.

A sizable portion of the 35th chapter of the Bhagvata Purana is devoted to narrating a fable as to why Rahu and Ketu are responsible for all the solar and lunar eclipses. Initially, at some stage, the gods and the demons were engaged in a great war over a very long period. Lord Vishnu persuaded both the gods and demons for a temporary peace so that the ocean in its entirety could be churned and both devas and the asuras could benefit from what the sea had to offer. The gods under the leadership of Indra grabbed the tail of the king of snakes, Vasuki, who was used as a rope for churning the ocean, while the demons under the leadership of Vali held the mouth of Vasuki. The great mountain Mandara acted as the churner. As a result of this churning, the first to come out was the terrible poison, halahala. It was voluntarily sucked in by the Lord Siva, but he held it in his throat, the reason why Siva is also known as Nilakantha. Then out came Surabhi, Kaustubha, Parijata, Laksmi, the Moon, Varuni (the goddess of wine). And finally emerged Dhanvantari, the originator of medicine, with a pot of amritam, the nectar. The demons ran away with the pot. Lord Vishnu acting in the interest of the gods transformed himself into Mohini, a beautiful woman. Dazzled by her beauty, the demons offered the pot to Mohini and asked her to distribute the nectar amongst themselves as she was found to be an appropriate person. Of course, she gave all the nectar to the gods. One of the demons, Rahu, saw through the trick and sat in the line in disguise, where the nectar was being distributed. But before he could swallow the divine nectar, the Sun and the Moon detected his masquerade and reported it to Lord Visnu, who then chopped off Rahu's head with his sudarsan chakra. Because Rahu had already drunk the nectar, he remained alive in spite of his being reduced to a trunkless body. Since then Rahu has not forgiven the Sun and the Moon. And this is the reason why, as has been depicted in the style of Pauranic description, every once in a while Rahu gobbles up the Sun or the Moon and we witness the solar and the lunar eclipses. Of course, being trunkless he cannot hold either the Sun or the Moon for long, and they come out safely after a while. With time the headless trunk of the demon came to be known as Ketu, and the earlier version of Ketu gracefully turned into what is known as Dhumketu.

It is also believed that when Swarbhanu's head was cut, its blood dropped on the earth and from that garlic and onion plants emerged, thus explaining why those veggies are not quite popular with some sects.

Rahu takes the place of the erstwhile Swarbhanu (could it not be explained off as the Moon, though it is not an ogre?) an asuara. Swarbhanu in Rigveda is a deity greater than sun, who was destroyed by Indra was born the son of Simhika, daughter of Hiranyakashipu. Since then, Rahu had become acceptable as the eighth but invisible and rogue planet, and in the astrological formulations as one of the navagrahas (nine planets) and is paired with Ketu. The time of day considered to be under the influence of Rahu is called Rahu kalam and is considered inauspicious.

Sometime in the third century A.D., the era of Siddhanta was ushered in and the 5th century Surya Siddhanta of Varahamihira gives detailed methods for making ecliptic calculations. It was around this time that Rahu and Ketu were astronomically defined to be the ascending and the descending nodes of the lunar orbit, intersecting the plane of the Earth's orbit. As is explained therein, the astronomical significance of Rahu and Ketu was reduced to mere imaginary points of intersection between the lunar orbit and the plane of the ecliptic. Technically, the point where the moon’s north node cuts the earth’s axis in the zodiac and thus makes a shadow on the zodiac is called Rahu and the South node of the moon is called Ketu.

Remember now that Rahu in astrology and mythology, is not just something that comes up during eclipses, but every day. In India, it is considered inauspicious to begin any undertaking during this "Rahukaalam" and I have seen this practiced across religions, at least in Kerala. My mother was greatly influenced by astrology and would not allow us children to do anything during the rahukaalam period, the 8th of day time every day. Every day this Rahukaalam lasts for around 90 minutes, but the duration differs according to the length of the time between sunrise to sunset. One can use the mnemonic ‘Mother Saw Father Wearing the Turban Suddenly’ or ‘Edward Bought Home A Good Ford Car’ to find the timing simply, if so interested.

In summary, Saturn, Rahu and Ketu are typically sinister and have to be taken care of properly. Their influence on humans is the worst whereas Jupiter, Venus, Mercury, Earth, Mars and the Sun exert favorable influences. There are many do’s and don’t’s during eclipse periods, and the hours preceding and following it. One should take a bath before and after an eclipse and so on. Many rituals have to be followed and some should not be carried out. So much for the myths.

But whatever happened to Ketu? After the head of Svarbhanu, was cut off, his head and body joined with a snake to form 'Ketu', representing the body without a head, a shadow being usually loosely associated with comets and meteors. In summary, before 6th century, Rahu and Ketu were not planets. Rahu is a demon and Ketu a comet or a meteor. It was in the 5th century that things changed, with the advent of Aryabhata. Astro-mythology changed after Aryabhata (born 476 CE) whose great work namely the ‘Aryabhatiyam’ propounded the mathematical theory of eclipses. His work defined eclipses as non-mythic events and as they could be mathematically predicted, the two lunar nodes were eventually designated as grahas. But it went a little further though with the entry of the 10th graha, namely Gulikan, an interesting subject by itself.

I will cover the development of mathematics and its detailed connections to eclipse determination some other day, but I will mentions the basics here for completeness. Aryabhata of course was the first person to come up with a relatively precise method, in India. In 499 AD, Aryabhata explained that the eclipses occur because either the moon comes between the sun and the earth or the moon goes into the shadow of the earth. He worked out geometrical arguments and based on the relative sizes of objects, he gave a relatively precise formulation for the calculation of eclipses. What made things somewhat easy was that methods to trace the lines of movements of the Sun and the moon were known and combining all these in a precise method provided a realistic prediction system for eclipses.

Finally I will mention about some studies done on the effect of an eclipse on earth and its beings. It had been observed from ancient times that animals were the first to be directly affected. Whether it was due to humidity and temperature changes or magnetic gravitational effects is not quite clear, but most animals and birds reacted strongly before any eclipse. We can see from the papers presented that studies revealed a reduction of ozone levels, the cooling of the ozone layer and a resultant increase of eclipse induced gravity waves upwards and downwards. pH levels decreased in water reservoirs (as much as 20%) and oceans. The timing of all this fell in line with Vedic recommendations which stated that the ill effects were for four praharas (an eighth of a day) before the eclipse and three praharas after. More details on exactly how gamma rays from space effect water pH can be studied in the referenced paper. This was obviously the period when water based animals also exhibited abnormal behavior and dove to the bottoms. Nevertheless, an early scripture Manusmriti mentioned - When the Head keeps the Sun or Moon in eclipse, all water on earth becomes pure and in purity like the water of the Ganges. Did he mean that acidity of water was good? I can’t say, but I thought it should be neutral for well being.

Can you imagine how Aryabhata would have been treated for coming up with his mathematically proven theory? Were his treatises destroyed by a zealous group or was he ever persecuted? We will cover all that some time in future together with his potential connections to Malabar. Chandra Hari’s paper establishing that Aryabhata lived precisely in the modern Ponnani - Chamravattom area (latitude 10N51 and longitude 75E45) in Kerala in 6th Century AD, presents interesting reading and he establishes that two values of Earth’s circumference at the equator given by Aryabhata in his treatise suggest that his latitude of observation was 10N51, where the Bharathapuzha merges with the sea and the prime meridian of Ujjaini.

Furthermore, was he excommunicated for going out into the sea to make observations and breaking the Ocean taboo? It is said that Aryabhata and his son Devarajan were excommunicated from their caste for the double sin of going to the sea and observing the eclipse. That is something quite difficult to ascertain, but it is possible that he traveled out of Malabar and up North in that case as a result of such an excommunication.

After Aryabhata’s time, his work was severely attacked by Brahmagupta as we saw earlier and his theories of rotation were rejected. Aryabhata’s commentators themselves changed the reading of his text to read otherwise.

In Alberuni’s India we find the quote from Brahmasiddhanta where Bhrahmagupta another famous mathematician, is seen refuting Aryabhata’s postulation, mainly for purposes of popularity and adherence to religious concepts - Some people think that the eclipse is not caused by the Head. This, however, is a foolish idea, for it is he in fact who eclipses, and the generality of the inhabitants of the world say that it is the Head who eclipses.The Veda, which is the word of God from the mouth of Brahman, says that the Head eclipses, likewise the bookSmriti, composed by Manu, and the Samhitd, composed by Garga the son of Brahman.  On the contrary, Varahamihira, Srishena, Aryabhata, and Vishnucandra maintain that the eclipse is not caused by the Head, but by the moon and the shadow of the earth, in direct opposition to all (to the generality of men), and from enmity against the just-mentioned dogma. For if the Head does not cause the eclipse, all the usages of the Brahmans which they practise at the moment of an eclipse, viz. their rubbing themselves with warm oil, and other works of prescribed worship, would be illusory and not be rewarded by heavenly bliss. If a man declares these things to be illusory, he stands outside of the generally acknowledged dogma, and that is not allowed. He concludes - Therefore people practise the well-known works of piety,and therefore those authors must cease to oppose the generality, for everything which is in the Veda, Smriti, and Samhitd is true.

It is also interesting to see how these mathematicians presented their work in a largely oral system, for recording equations as we know today was not in vogue, those days. They used what we can loosely call scientific poetry which was easy to memorize. Though the poetry sometimes sounded nonsensical, you had to use words to match the equation. Two systems were devised to represent numbers in these verses: the Bhutasankhya system, in which common objects were associated with numbers (eye = 2, gods = 33, for example), and the katapayadi system, in which each number was assigned a set of letters so that meaningful words could be created to represent strings of numbers. As time went by, the Kerala School of Mathematics was developed and strode forward in leaps and bounds. We will tackle that interesting subject on yet another day, after I go over the concepts of the Katapayadi system, then.

Coming back to solar eclipses, it is not quite right that a total eclipse of the sun is a rare occurrence, though you can see it roughly only once in 360 years from a given location. It happens approximately once every 18 months when a total solar eclipse is visible from some place on Earth’s surface.

There are so many interesting trivia related to Solar eclipses and India - French astronomer Pierre Janssen observed the eclipse from India in 1868 and, using a spectroscope, spotted light from a new element ‘helium’ decades before it was found on earth! A solar eclipse always takes place about a fortnight before or after a lunar eclipse.

Remember also that these total eclipses are gone in a flash, in fact the longest observed total solar eclipse took place over Nepal and lasted just over 6 minutes as the moons shadow zoomed over the earth’s surface at 5000 miles per hour! Also did you know that the sun is 400 times larger than the moon but is also 400 times farther from Earth, making the two bodies appear the exact same size in the sky! Then again, the moon is sadly drifting away (The moon is receding from the Earth at the rate of about 1.5 inches a year) due to tidal friction and in about 620 million years it will appear too small to cover the sun, and you will see no more total solar eclipses. Sigh…

You know, there is a proverb in Kerala mentioning – like an earthworm coming out and lifting its head during an eclipse. What would you think it means? The significance of this is that when the mighty falls even the minions will raise their heads to show they are big.

A solar eclipse worth talking about is the one which took place in 955BC. Interestingly at Kurukshetra, it would have occurred at the right time for Lord Krishna to delay the sunset and save Arjuna. The date of 4th Oct 955BC is thus a potential (there are others) in dating the Mahabharata war. As the story goes, Abhimanyu is trapped in a chakravyuha formation and killed, as the Pandavas blame Jayadratha for the boy’s death. Arjuna vows to kill Jayadratha the next day, the 14th day of battle, by sunset or immolate himself. At the climactic moment, with the sun nearly setting and thousands of warriors still between Arjuna and Jayadratha, the solar eclipse takes place, darkening the scene (In the story, Krishna masks the sun with his Sudarshana chakra and create an illusion of sunset). The Kaurava warriors rejoice over Arjuna's defeat and look forward for his imminent suicide. Jayadratha who was hiding behind Duryodhana, comes out of the formation. Suddenly the sun was free from the eclipse and Krishna explains the eclipse to Arjuna. He then points out the location of Jayadratha, enabling Arjuna to shoot an arrow and sever his head.

So much for solar eclipses. We have our much talked about eclipse coming up on the 21st of August. Let’s see how it goes….

Influence of solar eclipse on seawater Sukumaran Santhosh Kumar, Rethinassamy Rengaiyan, Natural Science Vol.3, No.1, 69-74 (2011)
Concept and Perceptions of Eclipses in Hindu Mythology - Raj Kumar Parashari
The Crest of the Peacock - George Gheverghese Joseph
Eclipse observed by Aryabhata in Kerala – K Chandra Hari
Vedic methodology of solar eclipse and its scientific validation –Santhosh Kumar, Rengaiyan – Indian journal of traditional knowledge Oct 2014
AlBeruni’s India
Myths and legends related to eclipses – NC Rana

Note - Remember the famous Surya grahanam song from Oru Pennintekatha? Try listening to that, the lyrics are interesting and you can see that Rahu is briefly mentioned.

pics – Orbits , Eclipse path – NASA images, others form google images – uploaders acknowledged with thanks 


Brahmanyan said…
Excellent article on "Grahanam". Though lengthy
enjoyed reading. Thanks.
B Pradeep Nair said…
Never been able to understand fully the theories enveloping the sun and the moon. The overlap of science and faith is interesting though.
Maddy said…
Thanks Brahmanyan
Sorry it was too lengthy..the topic was such...
but glad that you enjoyed it.
Maddy said…
hi pradeep..

thanks - the problem is due to the 3D aspect. imagine multiple planes and differing orbits, so the prospect of getting these three objects in a straight line is tricky.
Veena Udhay said…
Wonderful Mr.M! Enjoyed the interesting details.

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