Back to the Vedas
Posted on 1-June-2016
In a tiny but delightful volume, The Scientific Edge, J. V. Narlikar, easily the best known Indian astrophysicist, has traced the history of science in India from the earliest times. In this he mentions the shulbh sutras in the Rig Veda which contain a solution to quadratic equations. Though these sutras show that their composers knew about quadratic equations, they do not detail the steps through which the solution is arrived at. The shulbh sutras were in the news recently when in justification for her proposal to make Sanskrit learning obligatory in Indian Institutes of Technology, India's barely literate minister of human resources development mentioned the work of an American academic who had written a paper saying that the shulbh sutras showed that its writers knew the Pythagorean theorem. Professor David Henderson of Cornell University, who had written that paper was quick to point out that he knew no Sanskrit and that he had studied the shulbh sutras in English translation as well as with the help of Sanskrit scholars. The Indian minister's piece of wisdom raises questions about the history of mathematics--history of ideas and the history of technology, generally-- and about the importance of Sanskrit.
In some of the Brahmana literature--by the time the Brahmanas were composed the earlier Vedic rituals in which real animals were sacrificed had been replaced by rituals in which sacrifice had become symbolic--there are detailed instructions not only about the shape and measurements of the altars to be constructed but also about construction and orientation of new houses, instructions which bespeak knowledge and understanding of basic geometry. That this understanding existed so long ago should itself not be a great surprise. The builders of the Great Pyramids--in an epoch long preceding the composition of Rik Samhita--possessed detailed knowledge not only of geometry but also the ability to cut enormous blocks of stone to such precision that they fitted each other so perfectly that the resulting structure of a colossal scale acquired a near perfect regular shape, and one has to look at the interior of the King's chamber in the Khufru pyramid--that is the only one I have seen--to wonder at the precision of measurements and of cutting. Not only did the ancient Hindus thus know their quadratic equations and their geometry but they also invented the concept of zero and the decimal system. When we go into antiquity we come across other equally great achievements of humans elsewhere. Pythagoras was a near contemporary of the composers of some of the shulbh sutras. Thales who lived about half a century earlier than Pythagoras is credited with another well known theorem in geometry. Archimedes, apart from making the discovery he is best known for, also tried to determine the value of the mathematical constant pi, about seven or eight hundred years before Arybhatta who also tried his hand at it but whose greatest contributions are in trigonometry.
There are many technologies the origins of which it is impossible to determine: e.g. spinning and weaving or pottery. There are others the origin of which is known to archaeologists but of the manner of their diffusion relatively little is known. It is almost certain that the earliest domestication of wheat was achieved between the eleventh and the ninth millennium BC in the fertile crescent--a development which is at the root of all that we know as civilisation. Which of the following should puff their chests about this development: Turks, Syrians, Iraqis, Jews or Palestinian Arabs? Early human knowledge, understanding and skills have spread so far and wide that they belong to all humanity. To think of them as national achievements and take national pride in them is simply inane. For people who originated them there was no nation, no state. Archimedes was a Greek born in Sicily. Thales was an Ionian born in Miletus--in modern Turkey--and Pythagoras was another Ionian born in Samos. The composers of shulbh sutras could have been Punjabis, Haryanawis or even Pakistanis. And it is not known who invented the concept of zero as a number. Aryabhatta seems to have been the first to have explicitly described the decimal system for numerical notation--some modern Biharis claim he was from Bihar. It can be said with equal force that in our days too there is no such thing as Hindu, Muslim, Christian, English, Russian, Chinese, Japanese or Indian science but only one universal science.
Let us for the moment allow present day Indian nationalists the joy of claiming that their ancestors the Vedic aryans were the greatest mathematicians of their times. It is hoped that Hindu nationalists understand that for modern mathematics, Euclidian geometry--of which the Pythagorian theorem as well as Thales' theorem are parts--,quadratic equations, the decimal system, the concept of zero and much more are part of the background noise. The ancients of whichever place had no knowledge either of the geometry of curved surfaces, or of Cartesian geometry or of irrational numbers or of integral and differential calculus or of Godel's theorem or of Turing machines or much else in the kind of advanced mathematics that a modern student of physics, chemistry, or engineering must learn. Mathematical knowledge possessed by Vedic aryans, ancient Greeks, Babylonians, Egyptians or other people could at best be themes of a background lecture or two and for which knowledge of Sanskrit is not at all necessary.
Sanskrit is one of the great classical languages of the world and its literature is no less varied, no less rich than that of classical Greek or classical Latin. There is much in the cultures and literatures of India that is derived from this rich source. There is, besides, a very close relationship between Sanskrit and all modern Indian languages of north and central India. This makes Sanskrit a ready kit bag for coining new terms for new concepts in politics, sociology or the sciences--much as European languages continue to turn to Greek for scientific terminology and to Latin for political terminology. Thirdly, study of classical languages, like study of Euclidian geometry, can be a useful tool for forming young minds. The first two of these factors are justification enough for promoting Sanskrit scholarship in Indian universities--scholarship of a modern kind and not of the kind taught in traditional seeming pretend ashrams or of the kind taught and learnt by officiant priests. Sadly, in most Indian universities, Sanskrit departments tend to be the most neglected not only when measured by resources made available or the quality of faculty but also when measured by the quality of students admitted. The third factor will justify the teaching of some basic Sanskrit in schools--Muslim students not willing to study a Hindu classical language could with great benefit learn Arabic or Persian as an alternative.
If the present Hindu nationalist government of India really wished to promote and preserve the language of their aryan ancestors, the authors of the Vedas,--the language of the gods as some tiresomely call it-- they should start by strengthening Sanskrit departments in universities and colleges and by offering incentives to students to seek admission into these departments and if they were capable of curing the fundamental ailments of primary and secondary education in the country then at some stage they might introduce three or four years of Sanskrit in schools. Another important area of work relates to cataloguing, preservation and digitisation of as many as possible of Sanskrit manuscripts scattered all across the country. This would be an indispensible aid to Sanskrit scholars. Instead of doing any of this the government is devoting its energy and resources on meaningless tokens. The inanity uttered by the minister of human resource development about teaching Sanskrit in the Indian Institutes of Technology is one example. Another is on Doordarshan, the government owned television channel. For a long time Doordarshan has been telecasting five minute news bulletins in Sanskrit every morning. The present government has started telecasting Sanskrit magazines every week and has been organising competitions for translating popular Hindi film songs into Sanskrit, presumably in a doomed effort to increase its popular appeal. Adherents of this latter day Hindu nationalism may themselves be in need of a lesson or two about the nature of Sanskrit language itself. First of all, apart perhaps from the time of the relatively small bands of people who composed the verses of Rik Samhita who streamed into India, Sanskrit was never a language of the masses all of whom in north India spoke one prakrit or another. Sanskrit in all probabilty was rooted in one of these prakrits that was adopted by an elite for the purposes of religion, philosophical discourse and lay poetry and drama, much as among the various speeches prevalent in Italy, the speech of the district of Latium was adopted by the elite of Republican Rome for literary and political discourse and became classical Latin and the speech of the Home Counties in England with an enormous infusion of French words after the Norman conquest, became standard literary English. Returning to India, already in the fifth century BC Gautama chose Pali, the prakrit prevalent in Magadha, for speaking to his disciples. If Sanskrit was not the language of the masses in the days of Gautama or, about one thousand years later, in the days of Kalidasa, it is unlikely to be embraced by even a fraction of literate India in 21st century AD, all the bombast of the Bharatiya Janata Party, the Rashtriya Svayam Sevak Sangh or the Vishva Hindu Parishad notwithstanding. There is something else the votaries of Hindutva need to understand: the difference between the language of the Vedas and classical Sanskrit is so great that for the purposes of pedagogy they might be treated as two different languages.
Going back to the Vedas to absorb the great wisdom contained in them and to understand the immutable truths expounded by the sages who composed them--or were they revealed by a divine agent?--is a call with an ancestry. Dayanand in the nineteenth century said that the true spirit of India resided in them. Some others who preceded him harked back to the Upanishads--a body of literature also known as Vedanta, or the end of the Vedas-- as a kind of escape from the superstitions and the unacceptable social practices prevalent in the Hindu society of their times. The Vedas certainly are unique literature in many ways. They contain some sublime poetry and some very interesting thought. There is a very fine, stimulating section for example about the question of what preceded the creation of the world; the Vedanta is nothing but speculation about the nature of reality. Vedic literature is peopled not only by various nature gods--Varuna, Indra, Usha, Agni and Surya--but also by divine female beings, the Apsaras--one of the most famous ones, Urvashi fell in love with a human king, Pururava and in the process wrecked his life, so to speak. What is true of the world of Vedic aryans is likewise true of other ancient and equally literate societies: the Mycenian Greeks and the Chinese of early first millennium BC. Ancient India produced many wise sages; so did ancient China and ancient Greece. Yet in spite of that, the fact remains that in the last three millennia since the time of the Upanishads, Gautama, Confucius, Mencius, Socrates and Plato, human knowledge and human technology have made such advances that not only the content but the very nature of human awareness of the world has changed, even though the ancestors of modern humans of say 100,000 years ago had the same mental equipment as them. Were a Vedic aryan to be transported to our times he would be bewildered not only by our houses, telephones, electricity, motor cars, aircraft and satellites but by our understanding of the world, our acceptance of a Copernican solar system, our knowledge that the Sun is not a divine being but an average size thermo-nuclear ball of fire, our non-belief in a world peopled by divine and semi-divine creatures, or our discourses about democracy, elections and climate change; and he would be altogether shocked by the large numbers of people all around. Conversely, if a modern human, even the most ardent Hindu believer in the sanctity of the Vedas, arrived in the world of the Rik Samhita, he would not only find the physical living conditions thoroughly primitive but also find the world of the apsaras and the devas, the world where right action meant above all correct performance of rituals, the world of large yajnas involving at times large scale animal sacrifices--the modern urban Hindu knows only the tinsel versions of yajnas presented on television or in cinema--so totally incomprehensible, even suffocating, that he would soon be looking for an exit.
Vedic texts must be studied by those who are interested in ancient societies, those interested in the history of ideas or those interested in the study of Indo-European languages. One of the marvels of the Vedas is that these texts have been transmitted not only verbatim but also almost exactly with the original intonations from generation to generation for the last three or three and a half millennia. It is to be hoped that these incantations are being preserved on digitised audio records as an assurance against the possible dying out of those who still recite them with perfect intonation. But, an engineer who has to design a modern aircraft or to calculate the trajectory of a rocket will not find any useful knowledge either in the Vedas or in any old Sanskrit text. Nor can the Vedas offer any useful solutions to the social, political or economic problems of modern societies the complexity of which is several orders of magnitude greater than that of the society that existed in India in the first millennium BC. In the final analysis, "Back to the Vedas" is a meaningless slogan capable of creating no more than passing distractions from the many real problems of life that beset modern India. Or is it one of the snake oils the votaries of Hindutva busy themselves trying to sell?