Sunday 9 April 2023

Varahamihira's Gravity and Sphericity

In the Vedic era preceding the Era of the 18 Siddhantas, the earth was thought to be flat. The Puranas and Smritis mention a mountain Meru, sacred and gigantic, in the middle of the earth. Deva Loka was on top of this mountain, the Devas lived on it. Asuras lived beneath our world, in Naraka Loka or Paatala Loka, also called Vadavaamukha. Meru was surrounded by four continents, Kuru to the north, Bhadrashva to the east, Bharata to the south and Ketumala to the west.

Not only Hindus, but Buddhists and Jains also seem to have accepted this concept. In their religions also, Indra, Brahma etc are significant divine beings, who live on Meru, which is an immense sacred mountain.

Meru and continents

The belief is also captured in a beautiful verse in the Tamil epic, Silappadikaaram:

ஞாயிறு போற்றுதும் ஞாயிறு போற்றுதும்
காவிரி நாடன் திகிரிபோல்
பொன்கோட்டு மேரு வலம் வருதலான்.
 “nyaayiRu poTruthum, nyaayiRu poTrudum,
kaaviri naaDan tigiripol pon koTTu meru valam varudalaan.” 

Translation Salutations (potrudhum) to the Sun (nyaayiRu); who goes around (valam varudalaan) golden mountain (pon koTu) Meru, like the wheel (tigiri) of the Chola (“kaaviri naaDan”, Lord of Kaveri country).

Gola - Earth as Sphere

At some unknown time, astronomers across the world realized that the earth was a sphere. They also realized that the sky was different from the space beyond it, and sky and space were also spheres. Perhaps an individual proposed it; perhaps a group of people discovered it and discussed the idea and it spread. What literature survives doesn’t mention this historical discovery or its acceptance. The astronomical texts referred to earth as BhuGola (Bhu is Earth; Gola means sphere). The sky (kha) was thence called KhaGola; and the realm of stars (Bha) beyond it, BhaGola.

The astronomers of this period seemed to not bothered to refute the earlier flat-earth model, but simply remapped some aspects to their new understanding. So they called or redefined Meru as the North pole of  the spherical earth (still considered DevaLoka, Abode of the Devas) and Vadavamukha as South pole (abode of the Asuras).

The spherical earth presented a new conceptual challenge. What did the earth stand on? If the earth were a sphere, how did people not fall off the sides of the sphere? How did people or animals stay put on the lower half? Would they be upside down? A similar ideological challenge must have affected Greek and Chinese astronomers. Not until Newton in the 17th century, was the concept of gravity proposed to explain planetary motion. This gravity was explained as a property of mass, though why it was so, could not be explained even by Newton. A generation before Newton, the French philosopher Rene Descartes proposed a vortex based theory of gravity. Newton’s theory became the accepted one, until Einstein’s relativistic theory of gravity overturned it.

Indian astronomers explained this away with metaphors.

Aryabhata compared the spherical earth with a kadama flower, which has a spherical centre. The buds, of a kadamba flower point outwards and their stalks point inwards; similarly explained Aryabhata, the legs of men and land animals and sea creatures point inward (toward the centre of the earth) and their heads point outward (towards the sky).

kadamba pushpa

Varahamihira used two better metaphors. The spherical earth is surrounded by a cage of stars, he said, inspiring a vision of a bird in a spherical metal cage. The earth is able to float in space, like an iron (loha) ball between two magnets (kantha), he continued. This is a scientific explanation with metaphors using common objects of his time.

पञ्च महाभूतमयस् तारागण पञ्चरे मही गोलः
खेऽयस् कान्तान्तः स्थो लोह इवा वस्थितो वृत्तः १३
Panchamahaa bhutam ayas taaragaNa panchare mahee golaH
Khe ayas kaanta-antaH stho loha ivaa vastitho vruttaH

Translation Composed of five elements(pancha mahaa bhutam), among the cage (panchara) of stars(taara), stands (stoh) the earth(mahee), as a globe(golaH), like (iva) a ball of iron (loha) between magnets (kaanta-antaH)

Cage of Stars - Taara gana panchara

Varahamihira added that like a lamp’s flame always points skywards, and any object thrown upwards falls to earth, people also walk about on earth with their heads skywards and feet on the ground.

गगनमुपैति शिखिशिखा क्षिप्तमपि क्षितिमुपैति गुरु किञ्चित्
यद्वदिह मानवानामसुराणां तद्वदेवाधः १३  Pancha Siddhantika 13-4
gaganam-upaiti shikhi-shikaa kshiptam-api kshitim-upaiti guru kincit
yadvad-iha maanavaanaam-asuraaNaam tadvadeva-adaH

Translation The flame (shikhaa) of a lamp(shikhi) points skywards (gaganam) and a heavy (guru) object (kincit) thrown (kshiptam) skywards falls back to earth (kshiti); this happens in the lands of men (maanavaanaam) and asuras (asuraaNaam)

This is as close as we get to an Indian theory of Gravity from Varahamihira – that heavy things fall to earth naturally. 

Newton’s concept gravity is much more ingenious and bold : it is not about planets but all objects: a brick exerts gravity on another brick, a tree on another tree, and of course celestial bodies on each other. But such a concept was not proposed by anyone before Newton, even Galileo or Copernicus or Kepler, leave alone the ancient Greeks like Euclid or Ptolemy.

Both Aryabhata and Varahamihira then quipped that Devas living on the north pole (Meru) and Asuras on the south pole (Vadavamukha) considered the other group as beneath them, punning on geography and social status. 

Whether the general public accepted these explanations or even heard of them is doubtful. Artists continued to depict the earth as a lady, Bhudevi in sculpture and painting, and her worship went on as usual. No one went on pilgrimages to Meru.

The Surya Siddhanta, composed unknown centuries before Aryabhata and Varahamihira, doesn’t even explain such matters. It talks about spherical earth, its longitudes and latitudes, the equator, gives the diameter of the sun and moon, explains calculations of their speed of revolution around the earth, uses geometry and trigonometry to explain their shadows and length and duration of eclipses; and gives several algorithms to calculate, predict, eclipses, star-planet conjunctions etc. Surya Siddhanta is explained as the revelation of astronomy by Surya Deva to an asura called Maya; very similar to the revelation of Vedas to the rishis during their meditations. So the spherical model was conceived, propagated and accepted among astronomers before composition of Surya Siddhanta. The other siddhantas compared by Varahamihira also don’t seem to have any explanation.

Was sphericity an idea borrowed from Greeks? It is plausible, maybe even probable. European writers assume they are, without bothering to prove so. Did the Greeks borrow the idea from the Babylonians? Again possible, but European writers don’t even mention this possibility. Can we completely rule out the possibility that Indians did not discover it on their own? No. Greek and Roman astronomers were well respected, as Varahamihira states. Romaka (name afted Rome or Roma) and Paulisa probably Paulus Alexandrinus of Alexandria, are among the 18 rishis to whom their eponymous siddhantas are attributed. But there are no books in the Greek language attributed to them. A lot of astronomy and mathematics attributed to Greeks like Ptolemy, Archimedes and Euclid are not found in Indian astronomy.

Rotation and Refutation

Aryabhata asserted that the earth rotates and the stars only seem to revolve around it. He used a metaphor for this also: just like a passenger in a boat on the Ganga feels like the trees on the shore are moving backward, rather than that the boat was moving forward, he said, so does the earth rotate from west to east, but people feel as though the sky and stars rotate westward.

This assertion, was dismissed not only by Brahmagupta and Varahamihira but even by his ardent admirers and commentators through the succeeding centuries. Perhaps because he was only a man, not a rishi – hence his composition was only a manuja grantha.

If Aryabhata’s rotation theory were correct, countered Varahamihira, in Pancha Siddhantika, Chapter 13, how would any falcon or other bird ever return to its nest? For the earth would have moved a great distance while the bird was flying. Flags would always stream westward due to the wind produced by the very fast moving earth. If the refutation was that earth moves slowly, how would it revolve such a great distance within a day? Varahamihira stated that the earth’s circumference is 3200 yojanas, about 25,000km as a yojana is 8km.

Someshvara, an eighth century commentator of Aryabhatiyam, went much further. If the earth revolved, he said, oceans will flood all the lands, and tops of trees and castles woud be blown away by the storm of the wind caused by such a ferocious speed of rotation. So, he concluded, the earth does not rotate.

So they didn’t understand inertia, or frame of reference for motion. But given the facts and theories at their disposal, these were scientific rejections of Aryabhata’s conjecture, not superstitious or theological objections. This is only discernible to those who study all the original material; most accounts make it seem that Aryabhata’s rotation conjecture was scientific and the others stubborn and unscientific in their rejection.

Historically, this is similar to Lord Kelvin’s rejection of Darwin’s theory of Evolution, which dated life on earth to 500 million years. Kelvin, calculated that the Sun composed of Hydrogen, could have a maximum life of only 300 million years based on chemical combustion of hydrogen to produce heat. The Sun’s true age was confirmed with Einstein’s mass-energy equivalence, nuclear physics, Bohr’s atomic model and such associated phenomena in physics (nothing in biology).

Aryabhata’s rotation conjecture is untenable without a theory of intertia and Newtonian or even Cartestian gravity. Darwin’s age of earth and life predictions were untenable without a nuclear theory of the Sun’s heat generation and subsequent long age of Sun and Earth.

Further Aryabhata and all other Indian astronomers, stated that the entire celesital sphere, gruhams and nakshatram, revolve around the earth from East to West, propelled by a celestial wind called pravaha. Here Aryabhata seems to contradict himself. Either the earth rotates and therefore it appears that stars  revolve; or the stars revolve, with no need for the earth’s rotation. Can he have both?

Varahamihira’s simple metaphor seemed to suffice for Indian astronomers. I wonder if European, Arab  or Chinese astronomers  gave a similar metaphor to explain away spherical earth.

Consequences of the Spherical Model

The spherical model of the earth led to the realization that shadows of the moon and earth cause eclipses. Varahamihira gave a clear explanation of how and why this happens, with an explicit refutation of the Rahu story (see link below).

Sphericity was important, perhaps even more so, than gravity. The development of geometry and triogonometry and understanding about the regularity of planetary orbits, culminated in the ability to predict eclipses; and later star-planet conjunctions. India led the world for a thousand years in this field because of this.

This is also why Lord Napier, a governor of Madras presidency, came to India to write a history of Mathematics, because he thought India was the birthplace of mathematics. It is notable that he was the descendant of John Napier, who invented Logarithms.

They also set Ujjain as the locus of the Prime Meridian (a role now played by the Greenwich Meridian) and all Indian astronomical calculations were based on the Ujjain meridian or at the point where the Ujjain meridian crossed the Equator.

There is an inherent understanding that both the equator and Ujjain meridian would be each be zero degree – something only Indians could use, having invented the zero. Arabs borrowed this zero a few centuries after Aryabhata (around 850 AD, during the time of Abbassid Caliph al Mamun) and Europeans mainly via Leonardo Fibonacci, a Venetian businessman who learnt it from visiting Baghdad in the thirteenth century. But the Ujjain meridian precedes Aryabhata and Varahamihira, as it is a fundamental factor in the Rishi Siddhantas.

It is an atrocity that these basic scientific concepts, Indian discoveries to be proud of, are not in our school or college books, and that most Indian scientists are unaware of these. These are low hanging fruit.

Related Essays

Varahamihira’s eclipse proof

My essays on Astronomy

Tamil podcast on Varahamihira

Here is the YouTube link for my lecture Moon Rise to Masala Dosai, where I explain adoption of spherical model of earth and its consequences