Phase-I (Discovery and Euphoria) – continued
In the previous article we read about Europe’s discovery of Indian Astronomy in 1691, via the Siamese Manuscript, and the great curiosity and awe that it aroused among European scholars of those times – somewhat like having discovered an advanced alien civilization.
At the end of the 17th century, Europe was still in the incipient stages of its meteoric rise in the modern world, and not yet the colonizing juggernaut that it would soon become. For the sea-faring nations of Europe, their primary interest in the East still lay in getting a foothold and expanding commerce, while at the same time disrupting the trade of their enemies. With intense rivalry in commerce ongoing between these countries, it is only to be expected that the state of the sciences in the eastern nations they were trading with was the least of their concerns.
And thus, it happened that nearly 80 years passed, before the next major advance occurred in Europe regarding Indian Astronomy, when the French astronomer Guillaume Le Gentil visited Pondicherry in 1768.
But it must be mentioned that these intervening 80 years were not completely devoid of any updates. There was always the evangelical side of Christian Europe, in which missionaries and Jesuit scholars travelled to far-off places, studying local religions, customs, and the state of the sciences, and funneling back that information to Europe in a steady trickle, including information on mathematics and astronomy. Researchers in the History of Science will often find a treasure trove of information in the records of these Jesuit exchanges.
We examine below a few samples of such missionary and Jesuit activities in India.
Bayer’s ‘History of the Bactrian Greek Kingdom in India’ (1738)
Theophilus Siegfried Bayer was a German scholar of Oriental studies, based at the St. Petersburg University in Russia. Though he never ventured east of Petersburg, he did develop several contacts in the East, using which he built up an impressive database on Asian History and Culture, amassing a great collection of eastern books, coins and other artifacts. He published his findings and his opinions in a book which focused primarily on the Bactrian (Greek) Kingdom in the North-West corner of India.
Primarily a sinologist, a scholar with an interest in China, he built up an extensive network of communications with Jesuits based in India, China and elsewhere. In India, his contacts were mainly in the southern Tamil province, from whom he regularly received information on Indian astronomy and Calendrics, and also copies of Almanacs that were in use in the southern province at the time.
He often wrote to these Jesuits expressing his gratitude for the information and exchange of views1. We find mentioned in these conversations the fact that the Chinese knew of the 19-year Metonic astronomical cycle long before the Greeks discovered it. Bayer also speaks of the similarities between Indian and Greek astronomies, and expresses the view that the Greeks borrowed their astronomy from India. For example, in a letter to missionaries Kogler and Pereira, he wrote: “the Greeks received much of their astronomical knowledge from India, and it would be wonderful if there was some evidence of China also being a source.”
From one C. T. Walther, a Danish missionary at Tranquebar (Tharangambadi in Tamil Nadu), Bayer received some notes on ‘The Indian Doctrine of Time’, which eventually found a place in the appendices of his book. Both Bayer and Walther admitted to not fully understanding some of the Indian computations and the numbers employed in the Tranquebar notes. Bayer eventually reached out to Euler, in the Mathematics Department at St. Petersburg, to try and resolve his difficulties, and thus it was that the greatest mathematician in the world entered the arena of Indian Astronomy.
Euler on Indian Astronomy
It has been debated whether Leonhard Euler was the greatest mathematician of all time – the other contenders being Gauss and Newton. But, greatest or not, he certainly was the most prolific mathematician ever, producing over 800 papers, articles and books. The French mathematician Pierre-Simon Laplace put his views of Euler succinctly as: “Read Euler, He is the master of us all.” Such was Euler’s reputation as a calculating machine that philosopher De Condorcet described his passing away as: “He ceased to calculate, and to live “.
India can take some pride in the fact that Euler’s interest in astronomy, and the significant output that followed, was first stoked by Indian Astronomy, when Bayer asked for his help with the Tranquebar notes.
Euler’s response to Bayer’s call for assistance appeared in the appendices of Bayer’s book as “On the Solar Year of the Indians”. In twenty-one points, he brilliantly unraveled the intricacies of the Indian computation. Some of the points he highlighted are as follows2.
- The Solar Year of the Indians is Sidereal, not Tropical.
This was a surprise to European scholars. It highlighted a significant difference between Indian and Greek astronomies. A Sidereal Year, also called Stellar Year, is the time taken by the Sun to go around the ecliptic and return to the same star. A Tropical Year, used in Greek and European astronomies, is the time taken by the Sun to go around the ecliptic and return to the Equinox point. The Sidereal Year is 20+ minutes longer than the Tropical, because the Equinox shifts by a tiny amount each year. Due to this difference, the Indian Year will fall back one day every 61 years with respect to the European Year.
- The Sidereal Year of the Indians is of 365 days, 6 hours and 12.5 minutes duration, which is about 2 minutes longer than the best European estimate at the time, of 365 days, 6 hours and 10 minutes.
Euler puts the 2-minute discrepancy down to observational error by the Indians. However, the length of the Sidereal Year is not a constant, but varies by small amounts over time, mainly due to the influence of the others planets on the Earth’s orbit. Its value has been decreasing, and therefore the Indian length of the Sidereal Year, assuming it was measured accurately, is apparently a more ancient value.
- The Indian Year can start at any time of the day or night.
Euler finds that unlike the European Year, which always begins at midnight, the Indian Year starts when the Sun arrives at a particular point on the ecliptic, which can occur at any hour of the day.
- Euler determines that the Indian Months are varied in length – summer months are longer than those of winter.
The Sun moves at varying speeds throughout the year – fastest in December and slowest in July. The length of the Indian Month, being in sync with the Sun’s motion, implies that the Indians knew of the variation in the Sun’s motion. Euler remarks that it would be interesting to know the Indian ‘Equation of the Sun’, which is a parameter that describes this variation. He has no doubt, he says, that the Indian value of the Equation will be close to the modern European value. In this, however, Euler is mistaken. The Indian Equation for the Sun is quite different from the modern value. It matches, in fact, the correct value from around 5000 BC3, showcasing the antiquity of Indian astronomy.
- The Indians use two Zodiacs, the first comprising 12 Signs, also used by western astronomy, and the second comprising 27 Signs, which is unique to Indian astronomy. Euler determines that the 27-Sign Zodiac defines a new kind of month used by the Indians – the Sidereal Month.
The Narsapur and Krishnapuram Tables
After Euler’s contribution, more than a decade passed before the next couple updates occurred in Europe’s knowledge of Indian astronomy, once again, due to the Jesuits.
In 1750, astronomer Joseph Lisle at the French Academy of Sciences received two sets of manuscripts relating to Indian astronomy.
The first was an almanac, entitled ‘Panchanga Siromani’, which was sent from India by a Father Patouillet. This was referred to as the ‘Narsapur Tables’, and was apparently from a place called Narasimhapuram.
The second set was from another Jesuit, Father Xavier Du Champ, who originally sent them to one Father Antoine Gaubil, a French Jesuit working in China. Gaubil forwarded that to Lisle at the Royal Academy of Sciences at Paris. Du Champ was said to have procured these Tables from the Brahmins of Krishnapuram.
Both these sets of Tables, from Narsapur and Krishnapuram, did not attract much attention in Europe initially. These Tables were analyzed in detail several decades later by French astronomer Jean Sylvain Bailly, which we will examine in a later article.
Tycho Brahe and Nilakantha
When Isaac Newton, in all humility, said that he was able to see farther because he stood on the shoulders of giants, he probably had Galileo and Kepler in mind. Kepler, in his turn, can doubtless give some of the credit for his ‘giant-ness’ to Tycho Brahe.
Tycho (1546-1601) was a Danish astronomer whose efforts laid the foundation for a huge leap in Europe’s astronomical knowledge. He was the most skillful and passionate (some would say fanatic) astronomical observer of the pre-telescope era. Feeling unsatisfied with the ancient Greek planetary models, he created some models of his own. But, understanding that his new planetary theories were toothless without good observational data to back them up, he made up his mind to create a vast repository of the most accurate observational data ever, and succeeded.
Tycho then hired Kepler, mainly for his mathematical skills, and asked him to use the new observational data-bank to prove the validity of his latest planetary model – the Tychonic Cosmological Model, in which the Sun and Moon orbited around the Earth while the other planets moved around the Sun. Kepler struggled for many years to fit the observational data into Tycho’s model, and failed. Tycho’s model was actually off by only a few minutes of arc, which may have been acceptable to a lesser man, but not to Kepler. He had the mathematician’s penchant for absolute accuracy. It is well-known that in the end Kepler dropped Tycho’s model, and tried a simple ellipse instead, which fit the observational data perfectly. At long last, mankind’s quest to understand the clockwork that moves the heavens had been fulfilled.
Returning back to our story on Jesuit activity in India, the Tychonic Cosmological Model, now an uninteresting historical relic, suddenly becomes fascinating and thought-provoking, when we note that it is EXACTLY the same model as proposed a century earlier by Nilakantha Somayaji, an Indian astronomer of the Kerala School.
Was there a Jesuit connection here? Did Tycho somehow get access to Nilakantha’s work? Christian missionaries were certainly very active in the southern coastal states of Kerala and Tamil Nadu. But so far, no documentary evidence has been unearthed to support that hypothesis. But before you make up your mind, please read on to the next section.
Copernicus, Nilakantha, Al-Tusi and Al-Shatir
Everyone knows that it was Nicolaus Copernicus who first proposed a heliocentric model for the Solar system. But not many know that only a few years earlier, the Indian astronomer Nilakantha Somayaji had proposed a very similar system, known as the semi-heliocentric model.
Was Copernicus influenced by Nilakantha? The dates of the two, Nilakantha (1444-1544) and Copernicus (1473-1543), are certainly close enough to stir the imagination. Nilakantha completed his astronomical work (The Tantrasangraha) in the year 1500, while Copernicus is known to have first mentioned the heliocentric idea in a letter to a friend in 1514, though it took him another 30 years to publish his revolutionary book.
A stronger evidence of Copernicus benefitting from foreign transmission is found in the close resemblance of his planetary models with those of Islamic astronomers Al-Tusi and Al-Shatir.
Ibn Al-Tusi (1201-1274) was a Persian astronomer who studied the Greek planetary models and found them wanting. He improved the Greek models by created a geometrical technique called the Tusi-Couple to replace some problematic features in the Greek system. The Tusi-Couple somehow found its way into Copernicus’s heliocentric model.
Ibn Al-Shatir (1304–1375) was a Syrian astronomer who worked as timekeeper at the Umayyad Mosque in Damascus. After detailed observation of several eclipses, he concluded that the angular diameters of the Sun and the Moon did not agree with Greek predictions. He soon set about making major reforms to the Greek system using the Tusi-Couple. Two centuries later, Al-Shatir’s models were found duplicated, almost EXACTLY, in the works of Copernicus. For example, the Table below shows the Lunar Model parameters in the Al-Shatir and Copernicus models of the Moon4:
|First epicycle radius to deferent ratio||0.109722||0.1097|
|First epicycle motion (°/day)||13.06493657||13.06498372|
|Second epicycle radius to deferent ratio||0.023611||0.0237|
|Second epicycle motion (°/day)||24.38149538||24.381612|
|Mean Sun motion (°/day)||0.985601218||0.98558966|
|Mean Moon motion (°/day)||13.17639452||13.17639452|
Did Copernicus have access to Al-Shatir’s work? It does appear highly likely. In fact, it becomes conclusive, when we note that a mistake Al-Shatir made in his model for Mercury was also found duplicated in Copernicus’s model for that planet.
The Kerala School of Mathematics and Astronomy
On a hot Saturday afternoon, sometime in the early 90s, I walked into the Theosophical Society Building in Adyar, Chennai, out of curiosity. I had often passed the Society Campus, which is a 10-minute bicycle ride from IIT Chennai, where I was a research scholar. As I wandered into the Library room, I saw an elderly man seated at a table studying and copying some crumbling and decrepit-looking manuscripts. He saw me and cordially asked me to sit beside him on the long bench and enquired why I had come. We spoke for a few minutes after which I left. There are two things I recall about that meeting. Firstly, he said he was retired, and was volunteering his spare time in copying out ancient manuscripts for the archeological department. Secondly, it struck me odd that though he spoke English with a distinctive South-Indian-Malayali accent, he pronounced his name with a North-Indian inflection as ‘Sharma’.
Looking back, many years later, I realized that the chance meeting had brought me face-to-face with K. V. Sarma, the greatest authority on the Kerala School of Mathematics and Astronomy, and author of over 200 books and research papers.
It had long been held that Indian astronomy had gone into limbo after Bhaskara-II (AD 1114). Professor Sarma has been responsible, almost singlehandedly, for turning that view on its head. His diligent research, over several decades, unearthed not just a few, but several hundreds of ancient documents and manuscripts, highlighting the works of dozens of astronomers and mathematicians of medieval Kerala. There is probably enough material there for scholars to explore for the next 100 years.
The Kerala School was discovered by an Englishman in the early part of the 19th century. Charles Matthew Whish, having completed his law course in England, arrived in India in 1812 to take up a legal position at a district court in South Malabar in Kerala. An expert linguist, he soon mastered the local dialect, and even published a book on grammar of the native language. He was favorably disposed to the natives and struck up friendships with a few, including a famed mathematician – a younger prince of the Royal family.
During his research on how calendars were being constructed by the natives, he made some curious discoveries. The Indians appeared to have discovered, among other things, the series expansion method to determine approximations to PI (ratio of circumference to diameter of a circle), several centuries before the Europeans had made that finding.
When he discussed this with some senior colleagues of the East India Company, they dismissed it as impossible: The Hindus never invented the series; it was communicated with many others, by Europeans, to some learned natives in modern times. The pretensions of the Hindus to such knowledge of geometry is too ridiculous to deserve attention.
Whish initially accepted their opinion, but continued his studies on Indian mathematics. In course of time he came upon further material to support his thesis, at which point he felt bold enough to publish his findings in a paper: On the Hindu Quadrature of the Circle.
He wrote: The approximations to the true value of the circumference with a given diameter, exhibited in these three works, are so wonderfully correct, that European mathematicians, who seek for such proportion in the doctrine of fluxions, or in the more tedious continual bisection of an arc, will wonder by what means the Hindu has been able to extend the proportion to so great a length.
And further: Some quotations which I shall make from these three books, will show that a system of fluxions peculiar to their authors alone among Hindus, has been followed by them in establishing their quadratures of the circle; and a few more verses, which I shall hereafter treat of and explain, will prove, that by the same mode also, the sines, cosines, etc. are found with the greatest accuracy.
Whish had stated that he would soon be presenting more results in a separate paper. That, unfortunately, never came to pass, as he shortly afterwards lost his job at the Company. He was reinstated after a year, but died soon thereafter in 1833 at the young age of 38. Expectedly, given the colonial mindset of the British, nothing further was heard on the subject of the development of infinite series in India till the middle of the 20th century, when some Indian scholars came upon Whish’s papers.
Since then, thanks to the efforts of Prof. Sarma and others, the contributions of the Kerala School have made inroads into the famous names of mathematics. The Leibniz-Series is now called Madhava-Leibniz-Series after the founder of the Kerala school. Similarly, the Gregory-Series for the power series expansion of the arctangent function is now called Madhava-Gregory-Series, etc. Scholars are now actively pursuing the possibility of Calculus having been developed in India 300 years before its re-discovery in Europe. Others are looking into the likelihood of Jesuits enabling the transmission of the fundamental ideas of Calculus from India to Europe. Exciting times ahead for Indian Mathematics!
On the Astronomy side, apart from the similarities of Tycho’s and Copernicus’s models to Nilakantha’s, there is little else to go by, for now. Prof. Sarma’s treasure-trove of astronomical documents relating to the Kerala School, more than 400 of them, awaits researchers.
In this article, we touched upon how Christian missionaries and Jesuits, travelling to far-away lands, may have contributed to the development and growth of mathematics and astronomy in Europe.
In the next article, we will read about the epic saga of Monsieur Guillaume Le Gentil, and his 11-year wandering around the Indian Ocean, all for the sake of Astronomy, and how his arrival in Pondicherry led to the second major update in Europe on Indian Astronomy.
- Weston, David, The Bayer Collection, University of Glasgow, 2018.
- Plofker, Kim, Leonhard Euler, On the Solar Astronomical Year of the Indians, translated from the Latin, July 2002.
- Narayanan, Anil, The Pulsating Indian Epicycle of the Sun, Indian Journal of History of Science, 46.3 (2011).
- Narayanan, Anil, The Lunar Model in Ancient Indian Astronomy, Indian Journal of History of Science, 48.3 (2013).
Featured Image: Nature
Disclaimer: The opinions expressed within this article are the personal opinions of the author. IndiaFacts does not assume any responsibility or liability for the accuracy, completeness, suitability, or validity of any information in this article.
Anil Narayanan is former scientist at ISRO, now working as a consultant in Washington DC. His hobby is ancient astronomy to which he devotes most of his spare time. He is the author of the book ‘History of Indian Astronomy: The Siamese Manuscript’.