2019-07-02 17:32:52 UTC
The Hijacking of Indian Astronomy- II
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.
Indology | 01-07-2019
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
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
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
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
◾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
Item Al-Shatir Copernicus
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
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
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.
1.Weston, David, The Bayer Collection, University of Glasgow, 2018.
2.Plofker, Kim, Leonhard Euler, On the Solar Astronomical Year of the
Indians, translated from the Latin, July 2002.
3.Narayanan, Anil, The Pulsating Indian Epicycle of the Sun, Indian
Journal of History of Science, 46.3 (2011).
4.Narayanan, Anil, The Lunar Model in Ancient Indian Astronomy, Indian
Journal of History of Science, 48.3 (2013).
Featured Image: Nature
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