17.5.2016, 18.15, Room 104,

Prof. Jayant Narlikar: Astronomy tradition in India

This talk will broadly divide the past into three periods: the early Vedic period, the flourishing centuries from Aryabhata to Bhaskara and the later period of the Kerala school. While describing the early astronomical tradition the talk will dwell on the reasons why the early progress did not continue on to modern times.

The Finnish Society for Natural Philosophy

Prof. Jayant NarlikarDirector, Inter-University Centre for Astronomy and Astrophysics

in Pune, India, 1988 - 2003

• B.Sc. degree in 1957, Banaras Hindu University. • Cambridge degrees in mathematics: B.A.(1960), Ph.D. (1963)• Work with Fred Hoyle in Cambridge until 1972.• Professor, Tata Institute of Fundamental Research (TIFR) 1972-

89 • In 1988, Narlikar was invited to set up the Inter-University

Centre for Astronomy and Astrophysics (IUCAA), which became an internationally acknowledged centre for excellence in teaching and research in astronomy and astrophysics.

• President of the Cosmology Commission of the International Astronomical Union from 1994 to 1997.

Astronomy Tradition in India

Vedic to pre-colonial days

Early Mathematics and Astronomy

The “early” here refers to the time when the Vedas were the main

source of knowledge…[The Vedas were passed on by oral

tradition but they were finally written down around 1500 BC]

The Vedic Era

• Mathematics and astronomy were greatly respected subjects in Vedic times…

• Vide: these subjects were called the faultless vision of the Vedas: vide

Vedasya nirmalam chakshuh Jyotihshastramanuttamam ||

Both these branches of knowledge were considered

superior to the rest!

Vide:Like the top of peacock’s head and

the precious stone carried by the cobra, mathematics and astronomy

are considered to be at the top!

Social reasons why the two went hand in hand

Special positions of heavenly bodies were occasions for religious

rites and maths was needed to calculate their timing and

locations in the sky…

Likewise, one had to be prepared for “bad days” if the stars so

predicted…

The Shulva-Sutracollection of results

mathematically derived for various rituals…

Results known at the time (well before they became known in Greece and Europe) includethePythagoras Theorem, the

Diophantine equations,…

Approximations to π

Shulva sutra writers seemed familiar with the irrationality of π.They also had approximations like:

1 + 1/3 + 1/(3×4) – 1/(3×4×34)

The Bakshali Manuscript

Found in 1881 in an archeological site about 70 km from the village of

Bakshali near Takshashila in today’s Pakistan…

The MS describes quadratic equations, square roots,

progressions, etc.

The Shad-Vedangas

These are six volumes describing the knowledge contained in the

Vedas…

Vedanga Jyotisha

The Shulva sutra is part of one of them: Vedanga Kalpa…Kalpa stands for rituals

It is the Vedanga Jyotisha that concentrates on astronomy.

Vedanga Jyotisha (contd)

This is ascribed to the sage Lagadha… How old is it?

Astronomy provides an answer!Earliest text from India…

How old is this text?

Dating by the observations of precession of equinoxes…

At the rate of one degree per approximately 72 years.

Tilak’s approach to dating MSTilak noted that in Gita, the Lord Krishna identifies himself with the

best. But he says that amongst seasons he is spring while amongst months he is Margashirsha. Why

not the month of Chaitra?

The inconsistency is resolved if we allow for precession of

equinoxes.Tilak used this technique in his book “Orion”. The method is correct but data unreliable.

Dating continued…In Lagadha’s time the winter solstice

was at the beginning of the constellation of Shravishtha (Delphini) In

Varahamihira’s time the winter solstice was at the end of first quarter of

Uttarashadha. This is a shift of angle 23 degrees twenty second. At the above rate of precession this shift occurs in 1680 years. Since Varahamihira was around 530 A.D. the time of Vedanga Jyotish comes to be around 1150 BC.

The Golden Age

Aryabhata to Bhaskara II5th to 12th Century AD

Aryabhata

Born in 476 AD and wrote his great work Aryabhatiya in 499 AD. He

knew and used spherical trigonometry for astronomical data and prepared accurate sine tables of angles in multiples of 3-45 deg.

The – denotes break up of a degree into 60 minutes.

Aryabhata’s anti-geocentric statement

In his book Aryabhata states that just as an observer on a boat sees fixed objects

on the bank going in opposite directions so do stellar objects appear to go westward even though they are really fixed! Typical reactions were:

1. He never said so…others have put the statement in his book.

2. He really said something different3. Aryabhata was a fool.

Interaction with the Middle- East

Varahamihira with ancestry dating back to Persia was from the family

of Sun-worshippers. Amongst other things he classified comets according to the shapes of their

tails!

Brahmagupta

On occasions very critical of Aryabhata, Brahmagupta did

appreciate the contributions made by him. Al-Biruni the Arabic

scholar did appreciate both the Indian astronomers and translated

into Arabic their major works.

From a speech by Abdus Salam,

Almost exactly twelve hundred years ago, Abdullah Al Mansur, the second Abbasaid Caliph celebrated

the founding of his new capital, Baghdad, by inaugurating an

international scientific conference. To this conference were invited Greek, Nestorian, Byzantine,

Jewish as well as Hindu scholars.

Continued…

From this conference, the first international conference in an Arab

country, dates the systematic renaissance of science associated

with Islam. The theme of the conference was observational

astronomy. Al Mansur was interested in more accurate

astronomical tables than available then.

Continued…He wanted, and he ordered at the conference, a better determination of the circumference of the Earth. No one realized it then but there

was read at the conference a paper destined to change the whole course of mathematical thinking. This was

a paper read by the Hindu astronomer Kankah, on Hindu

numerals, then unknown to anyone outside India.

Bhaskara II

Space is inadequate to highlight the contributions of Bhaskara II an

eminent astronomer and mathematician who made several

seminal contributions to theoretical astronomy as well as to observational one. His

mathematical prowess is seen from his solution of the equation

61 X2 + 1 = Y2

Continued…where X and Y are integers.

Bhaskara had a solution of the problem using Chakrawaal method which gave the smallest numbers as

X= 22,61,53,980 and Y = 1,76,63,19,049

In 1657 the French mathematician Fermat raised this problem which was solved by Euler in 1732. Later it was realised that Bhaskara had

solved it in 1150.

Bhaskara and gravitation

The Buddhist philosophy said that a stone tossed up falls down on the

Earth because it has different speed. To this Bhaskara argued that the

effect is not because of speed difference but because the Earth

attracts the stone.However, he did not go into detail.

Bhaskara and calculusWhile working on spherical

astronomy Bhaskara used some results from differential calculus

like:dsin x= cos x;

dF=0 at maxima or minima of F.

Bhaskara’s astronomy volumeThe book by Bhaskara called the

GoladhyayaDeals with several astronomical

problems like:Retrograde motions of planets,

eclipses, sunrise and sunset, long days and nights near the poles, etc., followed by problems to be solved.

Bhaskara as a teacherIn his writings Bhaskara had

included solved problems as well as exercises. The book on

mathematics called Lilavati is supposedly directed at his daughter

of the same name and is full of delightful problems.

A problem from LilavatiThe square root of half the total

number of a swarm of bees aent to a Malati tree, followed by another eight ninth of the total. One bee was trapped inside a lotus flower, while his mate came humming in

response to his call. O Lady tell me how many bees were there in all?

Post-Bhaskara DevelopmentsThe major work on astronomy

seems to have slowed down after Bhaskara. However, some work of

advanced nature came from Kerala and it was discovered by the British

East India Company in an unexpected way.

The Kerala School (14-16) Century AD

Two officers of the Company, Benjamin Hain and Charles Whish in the first quarter of 19th Century

noticed that some local astronomers were using advanced mathematics in their data reduction. Where did

they learn it?

Follow up led to the work in Kerala

Searches revealed a chain of mathematicians from Madhava

(1340-1425)Through Nilakantha Somayaji, Jyeshthadeva, Achyut Pisharti,

Panikkar, etc.They used various trigonometric

series

Kerala School Continued…

Including the Gregory series for ‘pi’.

Recently lot of research is being done to learn about the work of the

Kerala School.

Concluding Remarks

Why did India lose momentum in astronomy and mathematics?There may be several reasons!

Why science in India slowed down?…

1. No royal patronage2. Benign living conditions

3. Lack of curiosity about nature4. Discouraged by religion