History of Indian Science

History of Indian Science

Subhash Kak

July 31, 2002

Indian literature provides us with considerable layered evidence related

to the development of science. The chronological time frame for this history

is provided by the archaeological record which has been traced in an

unbroken tradition to about 7000 BC. Prior to this we have records of rock

paintings that are believed to be as old as 40000 BC. The earliest textual

source is the Rig Veda which is a compilation of very early material. There

are astronomical references in this and the other Vedic books which recall

events in the third or the fourth millennium BC and earlier. The recent

discovery that Sarasvati, the preeminent river of the Rig Vedic times, went

dry around 1900 BC due to tectonic upheavels implies that the Rig Veda is

to be dated prior to this epoch. According to traditional history, Rig Veda

is prior to 3100 BC.

Indian writing goes back to the beginning of the third millennium BC.

The later historical script called Brahmi evolved out of this writing. The

invention of the symbol for zero appears to have been made around 50 BC

to 50 AD.

Vedic science

Briey, the Vedic texts present a tripartite and recursive world view. The

universe is viewed as three regions of earth, space, and sky which in the

human being are mirrored in the physical body, the breath (

mind.

In the Vedic world view, the processes in the sky, on earth, and within

the mind are taken to be connected. The Vedic seers were aware that all

descriptions of the universe lead to logical paradox. The one category transcending

all oppositions was termed

consciousness was of paramount importance in this view but this did not

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mean that other sciences were ignored. Vedic ritual was a symbolic retelling

of this world view.

Knowledge was classi ed in two ways: the lower or dual; and the higher

or uni ed. The seemingly irreconciliable worlds of the material and the

conscious were taken as aspects of the same transcendental reality.

The idea of complementarity was at the basis of the systematization

of Indian philosophic traditions as well, so that complementary approaches

were paired together. We have the groups of: logic (

(

(

were formalized in the post-Vedic age, we nd the basis of these ideas in the

Vedic texts.

The Sankhya and the Yoga systems take the mind as consisting of ve

components:

lower mind which collects sense impressions. Ahankara is the sense of I-ness

that associates some perceptions to a subjective and personal experience.

Once sensory impressions have been related to I-ness by ahankara, their

evaluation and resulting decisions are arrived at by buddhi, the intellect.

Chitta is the memory bank of the mind. These memories constitute the

foundation on which the rest of the mind operates. But chitta is not merely

a passive instrument. The organization of the new impressions throws up

instinctual or primitive urges which creates di
erent emotional states. This

mental complex surrounds the innermost aspect of consciousness, which is

called

prana), andbrahman. Understanding the nature ofNyaya) and physicsVaisheshika), cosmology (Sankhya) and psychology (Yoga), and languageMimamsa) and reality (Vedanta). Although these philosophical schoolsmanas, ahankara, chitta, buddhi, and atman. Manas is theatman, the self, or brahman.

Physics and chemistry

The Vaisheshika system considers nine classes of substances, some of which

are nonatomic, some atomic, and others all-pervasive. The nonatomic ground

is provided by the three substances ether, space, and time, which are unitary

and indestructible; a further four, earth, water, re, and air are atomic

composed of indivisible, and indestructible atoms; self (

the eighth, is omnipresent and eternal; and, lastly, the ninth, is the mind

(

small.

The atoms combine to form di
erent kinds of molecules which break up

under the inuence of heat. The molecules come to have di
erent properties

based on the inuence of various potentials (

Heat and light rays are taken to consist of very small particles of high

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velocity. Being particles, their velocity is nite.

The gravitational force was perceived as a wind. The other forces were

likewise mediated by atoms of one kind or the other.

Indian chemistry developed many di
erent alkalis, acids and metallic

salts by processes of calcination and distillation, often motivated by the

need to formulate medicines. Metallurgists developed e cient techniques of

extraction of metals from ore.

atman), which ismanas), which is also eternal but of atomic dimensions, that is, in nitelytanmatras).

Geometry and mathematics

Indian geometry began very early in the Vedic period in altar problems as

in the one where the circular altar (earth) is to be made equal in area to

a square altar (heavens). Two aspects of the \Pythagoras" theorem are

described in the texts by Baudhayana and others. The geometric problems

are often presented with their algebraic counterparts. The solution to the

planetary problems also led to the development of algebraic methods.

Binary numbers

Binary numbers were known at the time of Pingala's

who lived about the fth century BC used binary numbers to classify

Vedic meters. The knowledge of binary numbers indicates a deep understanding

of arithmetic.

Chhandahshastra. Pingala,

Astronomy

Using hitherto neglected texts, an astronomy of the third millennium BC

has been discovered recently. Yajnavalkya (1800 BCE ?) knew of a 95-year

cycle to harmonize the motions of the sun and the moon and he also knew

that the sun's circuit was asymmetric.

Astronomical numbers played a central role in Vedic ritual. Part of the

ritual was to devise geometrical schemes related to the lengths of the solar

and the lunar years. The organization of the Vedic books was also according

to an astronomical code. To give just one example, the total number of verses

in all the Vedas is 20,358 which equals 261 x 78, a product of the sky and

atmosphere numbers of the Vedic ritual!

The second millennium text

the earlier calendrical astronomy to develop a theory for the mean motions

of the sun and the moon. This marked the beginnings of the application

of mathematics to the motions of the heavenly bodies. An epicycle theory

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was used to explain planetary motions. Later theories consider the motion

of the planets with respect to the sun, which in turn is seen to go around

the earth.

Vedanga Jyotisha of Lagadha went beyond

Cosmology

The doctrine of the three constituent qualities:

plays a very important role in the Sankhya physics and metaphysics. In its

undeveloped state, cosmic matter has these qualities in equilibrium. As the

world evolves, one or the other of these become preponderant in di
erent

objects or beings, giving speci c character to each.

The recursive Vedic world-view requires that the universe itself go through

cycles of creation and destruction. This view became a part of the astronomical

framework and ultimately very long cycles of billions of years were

assumed. Indian evolution takes the life forms to evolve into an increasingly

complex system until the end of the cycle. The categories of Sankhya operate

at the level of the individual as well. Life mirrors the entire creation

cycle and cognition mirrors a life-history.

Cosmological speculations led to the belief in a universe that goes through

cycles of creation and destruction with a period of 8.64 billion years. Related

to this was the notion that light traveled with a speed of 186,000 miles per

second. Since these numbers were not obtained throught experimentation,

the accuracy of these gures must be seen as remarkable coincidence.

sattva, rajas, and tamas,

Grammar

Panini's grammar (5th century BC) provides 4,000 rules that describe the

Sanskrit of his day completely. This grammar is acknowledged to be one

of the greatest intellectual achievements of all time. The great variety of

language mirrors, in many ways, the complexity of nature and, therefore,

success in describing a language is as impressive as a complete theory of

physics. It is remarkable that Panini set out to describe the entire grammar

in terms of a nite number of rules. Scholars have shown that the grammar

of Panini represents a universal grammatical and computing system. From

this perspective it anticipates the logical framework of modern computers.

Medicine

Ayurveda, the Indian medicine system, is a holistic approach to health that

builds upon the tripartite Vedic approach to the world. Health is maintained

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through a balance between three basic humors (

(

physicians.

Indian surgery was quite advanced. The caesarian section was known,

bone-setting reached a high degree of skill, and plastic surgery was known.

dosha) of wind (vata), repitta), and water (kapha). Charaka and Sushruta are two famous early

The Medieval Period

Astronomical texts called siddhantas begin appearing sometime in the rst

millennium BC. According to tradition there were 18 early siddhantas of

which only a few have survived. Each siddhanta is an astronomical system

with its own constants. Some of the famous astronomer-mathematicians

that arose in India's long medieval period are listed below.

Aryabhata

mathematical, planetary, and cosmic theories. The parameters of

In his book Aryabhatiyam, Aryabhata (born 476) sketched hisAryabhatiyam

have, as their origin, the date of Friday, 18th February, 3102 BC.

Aryabhata took the earth to spin on its axis; this idea appears to have been

his innovation. Aryabhata was aware of the relativity of motion as is clear

from this passage in his book,\Just as a man in a boat sees the trees on the

bank move in the opposite direction, so an observer on the equator sees the

stationary stars as moving precisely toward the west."

Brahmagupta

Born in 598 in Rajasthan, Brahmagupta wrote his masterpiece,

Brahmasphuta Siddhanta

that of Aryabhata, has been very inuential in western and northern India.

Brahmagupta's work was translated into Arabic in the eighth century

at Baghdad and it became famous in the Arabic world as

inuenced Islamic astronomy.

One of Brahmagupta's chief contributions is the solution of a certain

second order indeterminate equation which is of great signi cance in number

theory.

, in 628. His school, which was a rival toSindhind and it

Bhaskara

an outstanding mathematician and astronomer. Amongst his mathematical

contributions is the concept of di
erentials. He was the author of Siddhanta

Shiromani, a book in four parts: (i) Lilavati on arithmetic, (ii) Bijaganita

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on algebra, (iii) Ganitadhyaya, (iv) Goladhyaya on astronomy. He epicycliceccentric

theories of planetary motions are more developed than in the earlier

siddhantas.

Belonging to the Karnataka region, Bhaskara (born 1114), was

Madhava

and astronomy in Kerala which saw itself as a successor to the school

of Aryabhata. Of these, Madhava (c. 1340-1425) developed a procedure to

determine the positions of the moon every 36 minutes. He also provided

methods to estimate the motions of the planets. He gave power series expansions

for trigonometric functions, and for pi correct to eleven decimal

places.

Subsequent to Bhaskara we see a ourishing tradition of mathematics

Nilakantha Somayaji

on astronomy, Nilakantha (c. 1444-1545) found the correct formulation for

the equation of the center of the planets and his model must be considered

a true heliocentric model of the solar system. He also improved upon the

power series techniques of Madhava. The methods developed by the Kerala

mathematicians were far ahead of the European mathematics of the day.

Another noteworthy contribution was by the school of New Logic (

Nyaya

(1475-1550), this school developed a methodology for a precise semantic

analysis of language. Its formulations are equivalent to mathematical logic.

A very proli c scholar who wrote several worksNavya) of Bengal and Bihar. At its zenith during the time of Raghunatha

The Modern period

Entering its modern era with the arrival of the English, India in the last two

centuries has witnessed a renaissance of its science and a proper appreciation

of the past achievements.

Some of the most important scientists born in the 19th century who

made international mark are Jagadish Bose (1858- 1937) in electromagnetics

and plant life, Srinivas Ramanujan (1887- 1920) in mathematics, Chandrasekhar

Venkata Raman (1888- 1970) in physics, Meghnad Saha (1893-

1956) in astrophysics, and Satyendra Bose (1894- 1974) in quantum theory.

More recent contributions of Indian science are part of the story of the

contemporary world science.