The Influence of Indian Art Abroad
These records of ancient empires and
dynasties have an interest for the antiquarian, but they have a large interest
in the history of civilization and art. From the point of view of India they
are particularly important, for it was India that functioned there and
exhibited her vitality and genius in a variety of ways. We see her bubbling
over with energy and spreading out far and wide, carrying not only her thought
but her other ideals, her art, her trade, her language and literature, and her
methods of government. She was not stagnant, or standing aloof, or isolated and
cut off by mountain and sea. Her people crossed those high mountain barriers
and perilous seas and built up, as M.Grousset says, 'a Greater India
politically as little organized as Greater Greece, but morally equally
harmonious.' As a matter of fact even the political organization of these
Malayasian states was of a high order, though it was not part of the Indian
political structure. But M. Grousset refers to the wider areas where Indian
culture spread: 'In the high plateau of eastern Iran, in the oasis of Serindia,
in the arid wastes of Tibet, Mongolia, and Manchuria, in the ancient civilized
lands of China and Japan, in the lands of the primitive Mons and Khmers and
other tribes in Indo-China, in the countries of the Malayo-Polynesians, in
Indonesia and Malay, India left the indelible impress of her- high culture, not
only upon religion, but also upon art and literature, in a word, all the higher
things of spirit (Civilizations of the East' by Rini Grousset, Volume II, p.
276).
Indian civilization took root
especially in the countries of south-east Asia and the evidence for this can be
found all over the place to-day. There were great centres of Sanskrit learning
in Champa, Angkor, Srivijaya, Majapahit, and other places. The names of the
rulers of the various states and empires that arose are purely Indian and
Sanskrit. This does not mean that they were pure Indian, but it does mean that
they were Indianized. State ceremonies were Indian and conducted in Sanskrit.
All the officers of the state bear old Sanskrit titles and some of these titles
and designations have been continued up till now, not only in Thailand but in
the Moslem states of Malaya. The old literatures of these places in Indonesia
are full of Indian myth and legend. The famous dances of Java and Bali derive
from India. The little island of Bali has indeed largely maintained its old Indian culture down to modern
times and even Hinduism has persisted there. The art of writing went to the
Philippines from India.
In Cambodia the alphabet is derived
from South India and numerous Sanskrit words have been taken over with minor
variations. The civil and criminal law is based on the Laws of Manu, the
ancient law-giver of India, and this has been codified, with variations due to
Buddhist influence, in modern Cambodian legislation [*A. Leclire,
'Recherches sur les origines brahmaniques des lois Cambodgiennes' quoted in B.
R. Chatterji's 'Indian Cultural Influence in Cambodia' (Calcutta, 1928).These
extracts have been taken from Osbert Sitwell's'Escape with Me—An Oriental
Sketch Book' {1941)].
But above all else it is in the
magnificent art and architecture of these old Indian colonies that the Indian
influence is most marked. The original impulse was modified, adapted, and fused
with the genius of the place and out of this fusion arose the monuments and
wonderful temples of Angkor and Borobudur. At Borobudur in Java.the whole life
story of Buddha is carved in stone. At other places bas-reliefs reproduce the
legends of Vishnu and Rama and Krishna. Of Angkor, Mr. Osbert Sitwell has
written: 'Let it be said immediately that Angkor, as it stands, ranks as chief
wonder of the world to-day, one of the summits to which human genius has aspired
in stone, infinitely more impressive, lovely and, as well, romantic, than
anything that can be seen in China... .The material remains of a civilization
that flashed its wings, of the utmost brilliance, for six centuries, and then
perished so utterly that even his name has died from the lips of man.
Round the great
temple of Angkor Vat is a vast area of mighty ruins with artificial lakes and
pools, and canals and bridges over them, and a great gate dominated by 'a vast
sculptured head, a lovely, smiling but enigmatic Cambodian face, though one
raised to the power and beauty of a god.' The face with its strangely
fascinating and disturbing smile—the 'Angkor smile'—is repeated again and
again. This gate leads to the temple: 'the neighboring Bayon can be said to be
the most imaginative and singular in the world, more lovely than Angkor Vat,
because more unearthly in its conception, a temple from a city in some other
distant planet . . . . imbued with the same elusive beauty that often lives
between the lines of a great poem.
The inspiration for Angkor came from
India but it was the Khmer genius that developed it, or the two fused together
and produced this wonder. The Cambodian king who is said to have built this
great temple is named Jayavarman VII, a typical Indian name.
Dr. Quaritch Wales says that 'when the
guiding hand of India was removed, her inspiration was not forgotten, but the
Khmer genius
was released to mould from it vast new conceptions of amazing vitality
different from, and hence not properly to be compared with anything matured in
a purely Indian environment .... It is true that Khmer culture is essentially
based on the inspiration of India, without which the Khmers at best might have
produced nothing greater than the barbaric splendor of the Central American
Mayas; but it must be admitted that here, more than anywhere else in Greater
India, this inspiration fell on fertile soil [From 'Towards Angkor' by Dr.
H. G. Quaritch Wales (Harrap, 1933)].
This leads one to
think that in India itself that original inspiration gradually faded because
the mind and the soil became over-worked and undernourished for lack of fresh
currents and ideas. So long as India kept her mind open and gave of her riches
to others, and received from them what she lacked, she remained fresh and
strong and vital. But the more she withdrew into her shell, intent on
preserving herself, uncontaminated by external influences, the more she lost
that inspiration and her life became increasingly a dull round of meaningless
activities all centered in the dead past. Losing the art of creating beauty,
her children lost even the capacity to recognize it.
It is to European
scholars and archaeologists that the excavations and discoveries in Java,
Angkor and elsewhere in Greater India are due, more especially to French and
Dutch scholars. Great cities and monuments probably still lie buried there
awaiting discovery. Meanwhile it is said that important sites in Malaya
containing ancient ruins have been destroyed by mining operations or for
obtaining material for building roads. The war will no doubt add to this
destruction.
Some years ago I had
a letter from a Taai (Siamese) student who had come to Tagore's Shanti Niketan
and was returning to Thailand. He wrote: 'I always consider myself
exceptionally fortunate in being able to come to this great and ancient land of
Aryavarta and to pay my humble homage at the feet of grandmother India in whose
affectionate arms my mother country was so lovingly brought up and taught to
appreciate and love what was sublime and beautiful in culture and religion.'
This may not be typical, but it does convey some idea of the general feeling
towards India which, though vague and overladen with much else, still continues
in many of the countries of South-East Asia. Everywhere an intense and narrow
nationalism has grown, looking to itself and distrustful of others; there is
fear and hatred of European domination and yet a desire to emulate Europe and
America; there is often some contempt for India because of her dependent
condition; and yet behind all this there is a feeling of respect and friendship
for India, for old memories endure and people have not forgotten that there was
a time when India was a mother
country to these and nourished them with rich fare from her
own treasure-house. Just as Hellenism spread from Greece to the countries of the
Mediterranean and in Western Asia, India's cultural influence spread to many
countries and left its powerful impress upon them.
'From Persia to the
Chinese Sea,' writes Sylvain L6vi, 'from the icy regions of Siberia to the
islands of Java and Borneo, from Oceania to Socotra, India has propagated her
beliefs, her tales and her civilization. She has left indelible imprints on
one-fourth of the human race in the course of a long succession of centuries.
She has the right to reclaim in universal history the rank that ignorance has
refused her for a long time and to hold her place amongst the great nations summarizing
and symbolizing the spirit of Humanity [* Quoted in V. N. Ghosal's 'Progress
of Greater Indian Research, 1917-1942' {Calcutta, 1943).From Foreword to
Reginald Le May's 'Buddhist Art in Siam' {Cambridge, 1938), quoted by Ghosal in
'Progress of Greater Indian Research' {Calcutta, 1943)].
Old Indian Art
The amazing expansion
of Indian culture and art to other countries has led to some of the finest
expressions of this art being found outside India. Unfortunately many of our
old monuments and sculptures, especially in northern India, have been destroyed
in the course of ages. 'To know Indian art in India alone,' says Sir John
Marshall, 'is to know but half its story. To apprehend it to the full, we must
follow it in the wake of Buddhism, to central Asia, China, and Japan; we must
watch it assuming new forms and breaking into new beauties as it spreads over
Tibet and Burma and Siam; we must gaze in awe at the unexampled grandeur of its
creations in Cambodia and Java. In each of these countries, Indian art
encounters a different racial genius, a different local environment, and under
their modifying influence it takes on a different garb.
Indian art is so
intimately associated with Indian religion and philosophy that it is difficult
to appreciate it fully unless one has some knowledge of the ideals that
governed the Indian mind. In art, as in music, there is a gulf which separates
eastern from western conceptions. Probably the great artists and builders of
the middle ages in Europe would have felt more in tune with Indian art and
sculpture than modern European artists who derive part of their inspiration at
least from the Renaissance period and after. For in Indian art there is always
a religious urge, a looking beyond, such as probably inspired the builders of
the great cathedrals of Europe. Beauty is conceived as subjective, not
objective; it is a thing of the spirit, though it may also take lovely shape in
form or matter. The Greeks loved beauty for its own sake and found not only joy
but truth in it; the ancient Indians loved beauty also but always they sought
to put some deeper significance in their work, some vision of the inner truth
as they saw it. In the supreme examples of their creative work they extort
admiration, even though one may not understand what they were aiming at or the
ideas that governed them. In lesser example::, this lack of understanding, of
not being in tune with the artist's mind, becomes a bar to appreciation. There
is a vague feeling of discomfort, even of irritation, at something one cannot
grasp, and this leads to the conclusion that the artist did not know his job
and has failed. Sometimes there is even a feeling of repulsion.
I know nothing about
art, eastern or western, and am not competent to say anything about it. I react
to it as any untutored layman might do. Some painting or sculpture or building
fills me with delight, or moves me and makes me feel a strange emotion; or it
just pleases me a little; or it does not affect me at all and I pass it by
almost unnoticed; or it repels me. I cannot explain these reactions or speak
learnedly about the merits or demerits of works of art. The Buddha statue at
Anuradhapura in Ceylon moved me greatly and a picture of it has been my
companion for many years. On the other hand some famous temples in South India,
heavy with carving and detail, disturb me and fill me with unease.
Europeans, trained in
the Greek tradition, at first examined Indian art from the Grecian point of
view. They recognized something they knew in the Graeco-Buddhist art of
Gandhara and the Frontier and considered other forms in India as degraded types
of this. Gradually a new approach was made and it was pointed out that Indian
art was something original and vital and in no way derived from this
Graeco-Buddhist art, which was a pale reflection of it. This new approach came
more from the Continent of Europe than from England. It is curious that Indian
art, and this applies to Sanskrit literature also, has been more appreciated on
the Continent than in England. I have often wondered how far this has been
conditioned by the unfortunate political relation-ship existing between India
and England. Probably there is something in that, though there must be other
and more basic causes of difference also. There are of course many Englishmen,
artists and scholars and others, who have come near to the spirit and outlook
of India and helped to discover our old treasures and interpret them to the
world. There are many also to whom India is grateful for their warm friendship
and service. Yet the fact remains that there is a gulf, and an ever-widening
gulf, between Indians and Englishmen. On the Indian side this is easier to
understand, at any rate for me, for a great deal has happened in recent years
that has cut deep into our souls. On the other side perhaps some similar
reactions have taken place for different reasons; among them, anger at being
put in the wrong before the world when, according to them, the fault was not
theirs. But the feeling is deeper than politics and it comes out unawares, and
most of all it seems to affect English intellectuals. The Indian, to them,
appears to be a special manifestation of original sin and all his works bear
this mark. A popular English author, though hardly representative of English
thought or intelligence, has recently written a book which is full of a
malicious hatred and disgust for almost everything Indian. A more eminent and
representative English author, Mr. Osbert Sitwell says in his book 'Escape With
Me' (1941) that 'the idea of India, despite its manifold and diverse marvels,
continued to be repellent.' He refers also to 'that repulsive, greasy quality
that so often mars Hindu works of art.'
Mr. Sitwell is
perfectly justified in holding those opinions about Indian art or India
generally. I am sure he feels that way. I am myself repelled by much in India
but I do not feel that way about India as a whole. Naturally, for I am an
Indian and I cannot easily hate myself, however unworthy I may be. But it is
not a question of opinions or views on art; it is much more a conscious and
subconscious dislike and unfriendliness to a whole people. Is it true that
those whom we have injured, we dislike and hate?
Among the Englishmen
who have appreciated Indian art and applied new standards of judgment to it
have been Lawrence Binyon and E. B. Havell. Havell is particularly enthusiastic
about the ideals of Indian art and the spirit underlying them. He emphasizes
that a great national art affords an intimate revelation of national thought
and character, but it is only to be appreciated if the ideals behind it are
understood. An alien governing race misapprehending and depreciating those
ideals sows the seeds of intellectual antipathy. Indian art, he says, was not
addressed to a narrow coterie of literati. Its intention was to make the
central ideas of religion and philosophy intelligible to the masses. 'That
Hindu art was successful in its educational purpose may be inferred from the
fact, known to all who have intimate acquaintance with Indian life, that the
Indian peasantry, though illiterate in the western sense, are among the most
cultured of their class anywhere in the world [£. B. Havell: 'The Ideals of
Indian Art' {1920), p. xix] .
In
art, as in Sanskrit poetry and Indian music, the artist was supposed to
identify himself with nature in all her moods, to express the essential harmony
.of man with nature and the uni-verse. That has been the keynote of all Asiatic
art and it is because of this that there is a certain unity about the art of
Asia, in spite of its great variety and the national differences that are so
evi-dent. There is not much of old painting in India, except for the
lovely frescoes of
Ajanta. Perhaps much of it has perished. It was in her sculpture and
architecture that India stood out, just as China and Japan excelled in
painting.
Indian music, which
is so different from European music, was highly developed in its own way and
India stood out in this respect and influenced Asiatic music considerably,
except for China and the Far East. Music thus became another link with Persia,
Afghanistan, Arabia,Turkestan and, to some extent, in other areas where Arab
civilization flourished, for instance, North Africa. Indian classical music
will probably be appreciated in all these countries.
An important
influence in the development of art in India, as elsewhere in Asia, was the
religious prejudice against graven images. The Vedas were against image worship
and it was only at a comparatively late period in Buddhism that Buddha's person
was represented in sculpture and painting. In the Mathura museum there is a
huge stone figure of the Bodhisattva which is full of strength and power. This
belongs to the Kushan period about the beginning of the Christian era.
The early period of
Indian art is full of a naturalism which may partly be due to Chinese
influences. Chinese influence is visible at various stages of Indian art
history, chiefly in the development of this naturalism, just as Indian idealism
went to China and Japan and powerfully influenced them during some of their
great periods.
During the Gupta
period, fourth to sixth centuries A.C., the Golden Age of India as it is
called, the caves of Ajanta were dug out and the frescoes painted. Bagh and
Badami are also of this period. The Ajanta frescoes, very beautiful though they
are, have, ever since their discovery, exercised a powerful influence on our
present-day artists, who have turned away from life and sought to model their
style on that of Ajanta, with unhappy results.
Ajanta
takes one back into some distant dream-like and yet very real world. These
frescoes were painted by the Buddhist monks. Keep away from women, do not even
look at them, for they are dangerous, has said their Master long ago. And yet
we have here women in plenty, beautiful women, princesses, singers, dancers,
seated and standing, beautifying themselves, or in procession. The women of
Ajanta had become famous. How well those painter-monks must have known the
world and the moving drama of life, how lovingly they have painted it, just as
they have painted the Boddhisattva in his calm and other-worldly majesty.
In the seventh and
eighth centuries the mighty caves of Ellora were carved out of solid rock with
the stupendous Kailasa temple in the centre; it is difficult to imagine how
human beings conceived this or, having conceived it, gave body and shape to
their conception. The caves of Elephanta, with the powerful and subtle
Trimurti, date also from this period. Also the group of monuments at Mallapuram
in South India.
In the Elephanta
caves there is a broken statue of Shiva Nataraja, Shiva dancing. Even in its
mutilated condition, Havell says that it is a majestic conception and an
embodiment of titanic power. 'Though the rock itself seems to vibrate with the
rhythmic movement of the dance, the noble head bears the same look of serene
calm and dispassion which illuminate the face of the Buddha.'
There is another
Shiva Nataraja in the British Museum and of this Epstein has written: 'Shiva
dances, creating the world and destroying it, his large rhythms conjure up vast
aeons of time, and his movements have a relentless magical power of
incantation. A small group of the British Museum is the most tragic summing up
of the death in love motive ever seen, and it epitomises, as no other work, the
fatal element in human passion. Our European allegories are banal and pointless
by comparison with these profound works, devoid of the trappings of symbolism,
concentrating on the essential, the essentially plastic [Epstein: 'Let There
be Sculpture' (1942), p. 193. Havell:
'The Ideals of Indian Art' (1920), p. 169.]
There is a head of a
Bodhisattva from Borobudur in Java which has been taken to the Glyptotek in
Copenhagen. It is beautiful, in the sense of formal beauty, but, as Havell
says, there is some-thing deeper in it revealing, as in a mirror, the pure soul
of the Bodhisattva. 'It is a face which incarnates the stillness of the depths
of the ocean; the serenity of an azure, cloudless sky; a beatitude beyond moral
ken.'
'Indian art in Java,'
adds Havell, 'has a character of its own which distinguishes it from that of
the continent from whence it came. There runs through both the same strain of
deep serenity, but in the divine ideal of Java we lose the austere feeling
which characterises the Hindu sculpture of Elephanta and Mamallapuram. There is
more of human contentment and joy in Indo-Javanese art, an expression of that
peaceful security which the Indian colonists enjoyed in their happy island
home, after the centuries of storm and struggle which their forefathers had
experienced on the mainland.
India's Foreign Trade
Throughout
the first millennium of the Christian era, India's trade was widespread and
Indian merchants controlled many foreign
markets. It was dominant in the eastern seas and it reached out also to the
Mediterranean. Pepper and other spices went from India or via India to the
west, often on Indian and Chinese bottoms, and it is said that Alaric the Goth
took away 3,000 pounds of pepper from Rome. Roman writers bemoaned the fact
that gold flowed from Rome to India and the east in exchange for various luxury
articles.
This trade was
largely, in India as elsewhere at the time, one of give and take of materials
found and developed locally. India was a fertile land and rich in some of the
materials that other countries lacked, and the seas being open to her she sent
these materials abroad. She also obtained them from the eastern islands and
profited as a merchant carrier. But she had further advantages. She had been
manufacturing cloth from the earliest ages, long before other countries did so,
and a textile industry had developed. Indian textiles went to far countries.
Silk was also made from very early times though probably it was not nearly as
good as Chinese silk, which began to be imported as early as the fourth century
B.C. The Indian silk industry
may have developed subsequently, though it does not seem to have gone far. An
important advance was made in the dyeing of cloth and special methods were
discovered for the preparation of fast dyes. Among these was indigo, a word
derived from India through Greece. It was probably this knowledge of dyeing
that gave a great impetus to India's trade with foreign countries.
Chemistry in India in
the early centuries A.C. was
probably more advanced than in other countries. I do not know much about it but
there is a 'History of Hindu Chemistry' written by the doyen of Indian chemists
and scientists, Sir P. C. Ray, who trained several generations of Indian
scientists. Chemistry then was closely allied to alchemy and metallurgy. A
famous Indian chemist and metallurgist was named Nagarjuna, and the similarity
of the names has led some people to suggest that he was the same person as the
great philosopher of the first century A.C.
But this is very doubtful.
The tempering of
steel was known early in India, and Indian steel and iron were valued abroad,
especially for war like purposes. Many other metals were known and used and
preparations of metallic compounds were made for medicinal purposes.
Distillation and calcination were well-known. The science of medicine was
fairly well developed. Though based mainly on the old text books, considerable
experimental progress was made right up to the medieval period. Anatomy and
physiology were studied and the circulation of the blood was suggested long
before Harvey.Astronomy, oldest of sciences, was a regular subject of the university
curriculum and with it was mixed up astrology. A very accurate calendar was worked out
and this calendar is still in popular use. It is a solar calendar having lunar
months, which leads to periodical adjustments. As elsewhere, the priests, or
Brahmins, were especially concerned with this calendar and they fixed the
seasonal festivals as well as indicated the exact time of the eclipses of the
sun and moon, which were also in the nature of festivals. They took advantage
of this knowledge to encourage among the masses beliefs and observances, which
they must have known to be superstitious, and thus added to their own prestige.
A knowledge of astronomy, in its practical aspects, was of great help to the
people who went on the seas. The ancient Indians were rather proud of the
advances they had made in astronomical knowledge. They had contacts with Arab
astronomy, which was largely based on Alexandria.
It is difficult to
say how far mechanical appliances had developed then, but shipbuilding was a
flourishing industry and there is frequent reference to various kinds of
'machines,' especially for purposes of war. This has led some enthusiastic and
rather credulous Indians to imagine all kinds of complicated machines. It does
seem, however, that India at that time was not behind any country in the making
and use of tools and in the knowledge of chemistry and metallurgy. It was this
that gave her an advantage in trade and enabled her for several centuries to
control a number of foreign markets.
Possibly she had one
other advantage also—the absence of slave-labour, which handicapped Greek and
other early civilizations and came in the way of their progress. The caste
system, with all its evils, which progressively increased, was infinitely
better than slavery even for those lowest in the scale. Within each caste there
was equality and a measure of freedom; each caste was occupational and applied
itself to its own particular work. This led to a high degree of specialization
and skill in handicrafts and craftsmanship.
Mathematics in
Ancient India
Highly intellectual
and given to abstract thinking as they were, one would expect the ancient
Indians to excel in mathematics. Europe got its early arithmetic and algebra
from the Arabs— hence the 'Arabic numerals'—but the Arabs themselves had
previously taken them from India. The astonishing progress that the Indians had
made in mathematics is now well known and it is recognized that the foundations
of modern arithmetic and algebra were laid long ago in India. The clumsy method
of using a counting frame and the use of Roman and such like numerals had long
retarded progress when the ten Indian numerals, including the zero sign,
liberated the human mind from these restrictions and threw a
flood of light on the behavior of numbers. These number symbols were unique and
entirely different from all other symbols that had been in use in other
countries. They are common enough to-day and we take them for granted, yet they
contained the germs of revolutionary progress in them. It took many centuries
for them to travel from India, via Baghdad, to the western world.
A hundred and fifty years ago, during Napoleon's time, La
Place wrote: 'It is India that gave us the ingenious method of expressing all
numbers by means of ten symbols, each symbol receiving a value of position, as
well as an absolute value; a pro-found and important idea which appears so
simple to us now that we ignore its true merit, but its very simplicity, the
great ease which it has lent to all computations, puts our arithmetic in the
first rank of useful inventions; and we shall appreciate the gran-deur of this
achievement when we remember that it escaped the genius of Archimedes and
Apollonius, two of the greatest men produced by antiquity [Quoted in
Hogben's 'Mathematics for the Million', (London, 1942).tG. B. Halsted: 'On the
Foundation and Technique of Arithmetic', p. 20 (Chicago, 1912), quoted in
'History of Hindu Mathematics' by B. Datta and A. TV. Singh {1935]).
The origins of geometry, arithmetic, and algebra in
India go back to remote periods. Probably to begin with there was some kind of
geometrical algebra used for making figures for Vedic altars. Mention is made
in the most ancient books of the geometrical method for the transformation of a
square into a rectangle having a given side: ax = c. Geometrical figures are
even now commonly used in Hindu ceremonies. Geometry made progress in India but
in this respect Greece and Alexandria went ahead. It was in arithmetic and algebra
that India kept the lead. The inventor or inventors of the decimal place-value
system and the zero mark are not known. The earliest use of the zero symbol, so
far discovered, is in one of the scriptural books dated about 200 B.C.
It is considered probable that the place-value system was invented about the
beginning of the Christian era. The zero, called shunya or nothing, was originally
a dot and later it became a small circle. It was considered a number like any
other. Professor Halsted thus emphasizes the vital significance of this
invention: 'The importance of the creation of the zero mark can never be
exaggerated. This giving to airy nothing, not merely a local habitation and a
name, a picture, a symbol but helpful power, is the characteristic of the Hindu
race from whence it sprang. It is like coining the Nirvana into dynamos. No
single mathematical creation has been more potent for the general on-go of
intelligence and power. Yet another modern mathematician has grown eloquent
over this historic event. Dantzig in his 'Number' writes: 'This long period of
nearly five thousand years saw the rise and fall of many a civilization, each leaving behind it a heritage of
literature, art, philosophy, and religion. But what was the net achievement in
the field of reckoning, the earliest art practiced by man? An inflexible numeration so
crude as to make progress well nigh impossible, and a calculating device so
limited in scope that even elementary
calculations called for the services of an ex pert . . . . Man used these
devices for thousands of years without making a single worthwhile improvement
in the instrument, without contributing a single important idea to the
system.... Even when compared with the slow growth of ideas during the dark
ages, the history of reckoning presents a peculiar picture of desolate
stagnation. When viewed in this light the achievements of the unknown Hindu, who
sometime in the first centuries of our era discovered the principle of
position, assumes the importance of a world event [Quoted in L. Hogben's
'Mathematics for the Million', (London, 1942). Hogben: 'Mathematics
for the Million', (London, 1942), p. 285.*
Dantzig is puzzled at the fact that the great mathematicians
of Greece did not stumble on this discovery. 'Is it that the Greeks had such a
marked contempt for applied science, leaving even the instruction of their
children to slaves? But if so, how is it that the nation that gave us geometry
and carried this science so far did not create even a rudimentary algebra? Is
it not equally strange that algebra, that corner-stone of modern mathematics,
also originated in India, and at about the same time that positional numeration
did?'
The answer to this question is suggested by Professor
Hog-ben: 'The difficulty of understanding why it should have been the Hindus
who took this step, why it was not taken by the mathematicians of antiquity,
why it should first have been taken by practical man, is only insuperable if we
seek for the explanation of intellectual progress in the genius of a few gifted
individuals, instead of in the whole social framework of custom thought which
circumscribes the greatest individual genius. What happened in India about A.D. 100 had happened before. May be
it is happening now in Soviet Russia.... To accept it (this truth) is to
recognize that every culture contains within itself its own doom, unless it
pays as much attention to the education of the mass of mankind as to the
education of the exceptionally gifted people.
We must assume then that these momentous inventions were not
just due to the momentary illumination of an erratic genius, much in advance of
his time, but that they were essentially the product of the social milieu and
that they answered some insistent demand of the times. Genius of a high order
was certainly necessary
to find this out and fulfill the demand, but if the demand had not been there
the urge to find some way out would have been absent, and even if the invention
had been made it would have been forgotten or put aside till circumstances more
propitious for its use arose. It seems clear from the early Sanskrit works on
mathematics that the demand was there, for these books are full of problems of
trade and social relationship involving complicated calculations. There are
problems dealing with taxation, debt, and interest; problems of partnership,
barter and exchange, and the calculation of the fineness of gold. Society had
grown complex and large numbers of people were engaged in govern-mental
operations and in an extensive trade. It was impossible to carry on without
simple methods of calculation.
The adoption of zero
and the decimal place-value system in India unbarred the gates of the mind to
rapid progress in arithmetic and algebra. Fractions come in, and the
multiplication and division of fractions; the rule of three is discovered and
perfected; squares and square-roots (together with the sign of the square-root,
V ) J cubes and cube-roots; the minus sign; tables of sines; n is evaluated as
3-1416; letters of the alphabet are used in algebra to denote unknowns; simple
and quadratic equations are considered; the mathematics of zero are
investigated. Zero is defined as a — a = 0; a + 0 = a; a - 0 = a; ax0=0; a 0
becomes infinity. The conception of negative quantities also comes in, thus: 4
= ± 2.
These and other
advances in mathematics are contained in books written by a succession of
eminent mathematicians from the fifth to the twelfth century A.C. There are earlier books also
(Baudhayana, c. eighth century B.C.;
Apastamba and Katyayana, both c. fifth century B.C.) which deal with
geometrical problems, especially with triangles, rectangles, and squares. But
the earliest extant book on algebra is by the famous astronomer, Aryabhata, who
was born in A.C. 476. He wrote
this book on astronomy and mathematics when he was only twenty-three years old.
Aryabhata, who is sometimes called the inventor of algebra, must have relied,
partly at least, on the work of his predecessors. The next great name in Indian
mathematics is that of Bhaskara I (A.C.
522), and he was followed by Brahmagupta (A.C. 628), who was also a famous astronomer, and who stated the
laws applying to shunya or zero and made other notable advances. There
follow a succession of mathematicians who have written on arithmetic or
algebra. The last great name is that of Bhaskara II, who was born in A.C. 1114. He wrote three
books, on astronomy, algebra, and arithmetic. His book on arithmetic is known
as 'Lilavati', which is an odd name for a treatise on mathematics, as it is the
name of a woman. There are frequent references in the book to a young girl who
is addressed as 'O Lilavati' and is then instructed on the problems stated. It
is believed, without any definite proof, that Lilavati was Bhaskara's daughter.
The style of the book is clear and simple and suitable for young persons to
understand. The book is still used, partly for its style, in Sanskrit schools.
Books on mathematics
continued to appear (Narayana 1150, Ganesha 1545), but these are mere
repetitions of what had been done. Very little original work on mathematics was
done in India after the twelfth century till we reach the modern age.
In the eighth
century, during the reign of the Khalif Al-Mansur (753-774), a number of Indian
scholars went to Baghdad, and among the books they took with them were works on
mathematics and astronomy. Probably even earlier than this, Indian numerals had
reached Baghdad, but this was the first systematic approach, and Aryabhata's
and other books were translated into Arabic. They influenced the development of
mathematics and astronomy in the Arab world, and Indian numerals were introduced.
Baghdad was then a great centre of learning and Greek and Jewish scholars had
gathered there bringing with them Greek philosophy, geometry, and science. The
cultural influence of Baghdad was felt throughout the Moslem world from central
Asia to Spain, and a knowledge of Indian mathematics in their Arabic
translations spread all over this vast area. The numerals were called by the
Arabs 'figures of Hind' (or India), and the Arabic word for a number is
'Hindsah', meaning 'from Hind'.
From
this Arab world the new mathematics travelled to European countries, probably
through the Moorish universities of Spain, and became the foundation for
European mathematics. There was opposition in Europe to the use of the new
numbers, as they were considered infidel symbols, and it took several hundred
years before they were in common use. The earliest known use is in a Sicilian
coin of 1134; in Britain the first use is in 1490.
It seems clear that
some knowledge of Indian mathematics, and especially of the place-value system
of numbers, had penetrated into western Asia even before the formal embassy
carried books to Baghdad. There is an interesting passage in a complaint made by
a Syrin scholar-monk who was hurt at the arrogance of some Greek scholars who
looked down on Syrians. Severus Sebokht was his name, and he lived in a convent
situated on the Eupharates. He writes in A.C. 662 and tries to show that the Syrians were in no way
inferior to the Greeks. By way of illustration he refers to the Indians: 'I
will omit all discussion of the science of the Hindus, a people not the same as
the Syrians; their subtle discoveries in the science of astronomy, discoveries
that are more ingenious than those of the Greeks and the Babylonians; their
computing that surpasses description. I wish only to say that this computation
is done by means of nine signs. If those who believe, because they speak Greek,
that they have reached the limits of science, should know of these things, they
would be convinced that there are also others who know something [ Quoted in 'History of Hindu
Mathematics' by B. Datta and A. JV. Singh (1933). / am indebted to this book
for much information on this subject.]
Mathematics in India
inevitably makes one think of one extra-ordinary figure of recent times. This
was Srinivasa Ramanujam. Born in a poor Brahmin family in south India, having
no opportunities for a proper education, he became a clerk in the Madras Port
Trust. But he was bubbling over with some irrepressible quality of instinctive
genius and played about with numbers and equations in his spare time.- By a
lucky chance he attracted the attention of a mathematician who sent some of his
amateur work to Cambridge in England. People there were impressed and a
scholarship was arranged for him. So he left his clerk's job and went to
Cambridge and during a very brief period there did work of profound value and
amazing originality. The Royal Society of England went rather out of their way
and made him a Fellow, but he died two years later, probably of tuberculosis,
at the age of thirty-three. Professor Julian Huxley has, I believe, referred to
him somewhere as the greatest mathematician of the century.
Ramanujam's
brief life and death are symbolic of conditions in India. Of our millions how
few get any education at all, how many live on the verge of starvation; of even
those who get some education how many have nothing to look forward to but a
clerkship in some office on a pay that is usually far less than the
unemployment dole in England. If life opened its gates to them and offered them
food and healthy conditions of living and education and opportunities of
growth, how many among these millions would be eminent scientists,
educationists, technicians, industrialists, writers and artists, helping to
build a new India and a new world?
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