IF there is one knowledge tradition that has come to practically define the modern age in all corners of the world, it is modern science. While Arabic, Indian and Chinese civilisations undoubtedly contributed to the enterprise of science, no one can deny that the radical transformations in world view and methods that culminated in the birth of modern science took place in the West through the 16th and 17th centuries. From its European home, the universally applicable methods and theories of modern science spread around the world, often riding on the coat-tails of colonial powers.
These two facts—that modern science was born in the West and came to the rest of the world through Western exploits—have been a source of deep angst verging on ressentiment for all proud and ancient civilisations in the East. But nowhere in the postcolonial world is this angst more deeply felt than in India, the land that bore the brunt of British colonialism for the longest duration.
The problem is this: We can neither live without modern science and the technologies it has spawned, nor can we make peace with the fact that this most fertile and powerful of all knowledge traditions is, after all, a melechha tradition. It rankles with us that these impure, beef-eating “materialists”, a people lacking in our spiritual refinements, a people whose very claim to civilisation we delight in mocking, managed to beat the best of us when it came to nature-knowledge. So, while we hanker after science and pour enormous resources into becoming a “science superpower”, we simultaneously devalue its historical and cultural significance and decry its “materialism”, its “reductionism” and its “Eurocentrism”. We want the science of the materialist upstarts from the West but cannot let go of our sense of spiritual superiority which makes us think that we are entitled to the status of jagatguru.
This lethal mixture of desire, envy and a sense of innate “Aryan” superiority has characterised India’s encounter with modern science and technology from the very start. Read any of the great works of the Hindu Renaissance—from Bankimchandra Chattopadhyaya, Vivekananda, Dayananda Saraswati, Annie Besant (and fellow Theosophists), Sarvepalli Radhakrishanan, M.S. Golwalkar and countless other gurus, philosophers and propagandists—and you encounter this simmering science envy and wounded pride at work. The current crop of Hindu nationalists and their intellectual enablers are the progeny of these thinkers and display similar traits.
Vedas as the mother of science The most recent formulation of this ressentiment is to be found in Rajiv Malhotra’s exhortation to Hindus to assert the “difference” (read “superiority”) of their dharmic traditions by “fitting modern science into the Vedic framework”. How is this feat to be accomplished? Malhotra proposes that we treat modern science as smriti —a human construct based on sensory knowledge and reasoning—of the Vedic shruti , the “eternal, absolute truth unfiltered by the human mind or context” received by our ancient seers in their “rishi state”. In practical terms, this would involve translating modern scientific concepts as mere subsets of Vedic categories: thus for example, physicists’ concept of energy—a precise and quantifiable capacity of a system to perform work—will have to be interpreted as a gross-level subtype of shakti , or “intelligent energy”, known to our yogic adepts; the entire field of physics, because it deals with causation, will become an “empirical” species of the karma theory; the Darwinian theory is merely a lower-level, materialistic rendering of the spiritual evolution taught in the Yoga Sutras , etc., etc. This way, we can have modern science and bask in our blessed rishi state too. Not just that, once we make the rivers of scientific knowledge flow into the ocean of the Vedas, the fondest dream of all Hindu nationalists will be fulfilled and India will achieve the status of World Guru.
Indeed, to claim an organic unity between the Vedic world view and modern science has been the agenda of Hindu nationalists from the very start. It is indeed an ingenious solution to our science envy: if modern science is nothing more than a minor tributary flowing into the ocean of Vedic spiritual science always-and-already known to our rishis, it is the West that should feel Veda envy. Not only is this balm for our wounded civilisational pride, this strategy of retrofitting science into the Vedas gives the latter a scientific sheen. Yet, in the end, Vedas-as-the-mother-of-science is a “magnificent dead end” (to borrow a phrase from Floris Cohen, a historian of science) as it has no potential whatsoever for asking new questions or providing new answers using methods that are accessible to non-rishis.
Distortion of the history of science What has aided this project of turning modern science into a smriti is a massive, and repeated, distortion of the history of science. The distortion works at levels of fact and of interpretation. Facts are distorted when priority claims are made for ancient India in complete disregard of evidence from sister civilisations, or when myths are interpreted literally. The more insidious distortion happens when modern-day science—quantum physics, computer science, genetics, neurosciences, and so on—are read back into the speculative musings of seers and philosophers from our hoary past. The edifice of “Vedic science” is built on such distortions.
All these distortions were showcased in the first year of the Narendra Modi government and are running full steam ahead in any number of State-level education departments, think tanks and andolan s. By now, the famous Karna-Ganesha speech that Prime Minister Modi gave in October 2014 and the proceedings of the Indian Science Congress in Mumbai in January 2015 are well known. These high-powered events, however, are only the more visible tip of the iceberg that has never stopped growing and gaining momentum.
While these events have had their 15 seconds of infamy in the media, the actual distortions have not received a serious fact-checking by historians of science. Unless the half-truths so casually thrown about are taken apart, examined in the light of evidence from other civilisations of the antiquity, they will continue to be repeated over and over again.
In what follows, three pet claims about the Indian history of science will be examined in order to sift facts from nationalist fictions. Two of these claims have to do with mathematics: the first declares Baudhayana, the ancient Indian rope-stretcher and altar-maker, to be the real discoverer of the Pythagoras theorem; the second is our most cherished “fact” that India is the birthplace of the sunya , or zero. The third claim has to do with the science of genetics and the ancient Indian understanding of heredity. (I have examined these and related themes in my recent book, Science in Saffron: Skeptical Essays in History of Science , which can be consulted for a historical and technical background for the core of the arguments presented below.)
Pythagoras’ theorem Pythagoras, a mystic-mathematician born sometimes around 570 BCE on an island off the coast of modern-day Turkey, comes in for a lot of abuse in India. He is seen as someone who is wrongly and unfairly credited with having discovered the theorem that goes by his name, while the real discoverer was our own Baudhayana, a priest-craftsman and the composer of Baudhayana Sulvasutra s, a work dated from anywhere between 800 and 200 BCE. Since Baudhayana texts predate Pythagoras, it is assumed that Pythagoras must have travelled to India and learned the theorem (along with Hindu beliefs in reincarnation and vegetarianism) from Hindu gurus. Thus, it has been a long-standing demand of Hindu-centric historians that the theorem should be renamed “Baudhayana theorem”. Not only is Baudhayana credited with the discovery of the Pythagorean theorem, he is declared to be the first to have given a proof for the theorem, the first to have calculated “Pythagorean triples”, the first to have figured out irrational numbers, the first to calculate the square root of 2 and much else. This is the sentiment that Dr Harsh Vardhan, Minister for Science and Technology, gave voice to when he spoke at the inauguration of the Science Congress last year.
All of the above claims about Baudhayana’s priority are false. They evaporate the moment one looks beyond India to see what was going on in other major civilisations around the time when the Sulvasutra s were composed.
At least a millennium before Baudhayana was even born, Mesopotamians had figured out the relationship between the sides of a right-angle triangle described by Pythagoras’ theorem. Mesopotamians (and their neighbours, Egyptians) took to measuring land in order to affix the boundaries every time the Euphrates-Tigris and the Nile would flood and wash away the existing boundaries. While the Egyptian evidence comes much later, the evidence that Mesopotamians knew the theorem, had worked out Pythagorean triples, and learned to calculate the square root of 2 is etched in hardened clay tablets dating back 1800 BCE, a thousand-year lead over Baudhayana. Two clay tablets in particular—Plimpton 322 and YBC7289, housed in Columbia and Yale universities, respectively—were deciphered by Otto Neugebauer, the world’s foremost authority on the cuneiform script, in the 1940s. He and his colleagues established that while Plimpton was a table of what we today call Pythagorean triples, the Yale tablet shows a remarkably accurate calculation of the square root of 2. These tablets alone blow holes through much of the case for Baudhayana’s priority. Moving east from Mesopotamia, east even of India, the Chinese had not only figured out the theorem but even provided a proof around the time of Confucius (approximately 600 BCE), if not earlier. The Chinese evidence comes from a text called Chou Pei Suan Ching (which translates into “The Arithmetical Classic of the Gnomon and the Circular Path of Heavens”) dated anywhere from 1100 to 600 BCE. Later, Han dynasty (third century BCE) mathematical texts formalised the theorem and named it kou-ku (or gou-gu) theorem.
The Chinese achievement brings us to the issue of proof. The Sulvasutra s, being manuals for constructing altars, offer sophisticated and ingenious mathematical aids for all kinds of complex geometrical shapes and their transformations. But they do not set out to prove or justify these rules of geometry. Mesopotamians and Egyptians, too, have left no trace of a proof.
So where does the first proof of Pythagoras’ theorem come from? Whether or not Pythagoras himself offered a general proof for all right-angle triangles is not clear. The first clear proof of this theorem in the Greek tradition comes from Euclid, who lived full three centuries after Pythagoras. All evidence points to the above-mentioned Chinese text, which was written at least three centuries before Euclid, to be the first proof of Pythagoras’ theorem. Unlike Euclid’s method of logical deduction, the Chinese idea of proof was based upon producing a visual demonstration from which the general case could be inferred. The first Indian proof of this theorem comes only from Bhaskara in the 12th century, and as the eminent historian of Chinese science Joseph Needham and many others have pointed out, Bhaskara’s proof was an “exact reproduction” of the Chinese Hsuan-thu diagram from Chou Pei .
What of Pythagoras in all of this? The Greek tradition acknowledges that he learnt the theorem he is famous for from Mesopotamians and Egyptians, among whom he spent some time as a young man. The theorem was important for his school of mathematics as it led to the discovery of irrational numbers that challenged his entire world view founded on the belief that the ultimate reality of the cosmos could be understood in numbers and their ratios. Pythagoras is hugely important in history of science not because of the theorem that bears his name but because of this seminal idea that nature can be understood mathematically. It was this insight that would inspire such pioneers of modern science as Johannes Kepler and Galileo Galilei. When combined with experimentation backed by accurate, quantifiable measurements, mathematisation of nature would become an unstoppable force called modern science.
The zero and Indocentrism That India, that is, Bharat, gave zero to the world is the sacred cow of Hindu sciences. Generations of Indians have grown up believing that if it were not for us, the world would not know how to even count, higher mathematics would be all but impossible, and the information technology revolution would not have happened.
But is it really true that the numeral zero is an entirely Hindu creation? Did zero have an immaculate birth from the Hindu Mind, with no influence from anywhere else?
We can maintain this fiction only if we stick to the Indocentrism that has been the hallmark of Indian historiography of science. Like the mirror image of Eurocentrism, which holds the “Greek Miracle” to be the original source of all sciences, Indocentrism holds ancient and classical (that is, pre-Islamic) India to be the Givers and all other civilisations to be eager and grateful Receivers. If an idea can be found in India and in some other place in a comparable time frame, our Indocentric historians simply assume that it must have travelled there from India, but never to India.
It is this Indocentrism that has blinded Indian historians to the possibility of South-East Asian transmission of Chinese rod numerals—complete with decimal place value and empty spaces for null values. The possibility of the South-East Asian transmission of zero from China was argued by Needham in the third volume of his classic Science and Civilization in China . A very similar thesis has been proposed more recently by Lam Lay Yong, a well recognised historian of mathematics from Singapore National University. This rigorously argued and evidence-backed thesis is beginning to find acceptance among professionally trained historians around the world and a place in influential textbooks of the history of mathematics. In India, however, it has met with a deafening silence.
Absence of place value Conventional accounts of the Indian origins of zero gloss over two uncomfortable but well established facts, namely, the absence of place value in Indian numerals until around the sixth century of the Common Era, and secondly, that the first physical evidence of zero comes not from India but from Cambodia and other South-East Asian countries that lie between India and China. Let us look at these two facts more carefully and with an open mind. (“Place value” simply means that the value of a numeral varies with the place it occupies in a number. With this system, any number, however large, can be expressed using only nine numerals and a symbol for an empty place.) Suggestions of place value do exist in what is called the bhuta sankhya method of enumeration, which uses concrete symbols (for instance, synonyms for eyes for the number 2, agni (fire) for the number 3 as there are three ritual fires, anga (limb) for the number 6, as there are six limbs of the Vedas, and so on). As the order of the number symbols used in bhuta sankhya did determine their value, it is accepted as evidence for place value. This system was in use from as early as the third century C.E. and continued to be used by astronomers and mathematicians in the classical era, well into the 14th century. While bhuta sankhya was well suited for versification and memorisation, it was obviously not conducive to computations, which needed numerals, not symbols.
There is no sign of place value in Indian numerals for about 900 years after the first emergence of Brahmi numerals on the subcontinent. Brahmi numerals first made their appearance sometime around the time of Asoka (about 300 BCE) and gradually evolved into Devanagari numerals sometime around the end of the Gupta period (550 C.E.). None of the Brahmi inscriptions discovered so far, including the famous Nanaghat cave inscription, shows any sign of place value. Place value notations suddenly begin to appear in the late Gupta period (mostly on copper land-grant plates, many of which have been later proven to be fake), followed in quick succession by sunya bindu , or dot, to represent empty space. The first recorded evidence of zero as we know it appears only in the year 876 from a temple in Gwalior (on which more below).
The absence of place value for about 900 years is important because without the prior existence of the place-value system of writing numbers, a numeral for zero simply could not have emerged. Only place-value notation requires a notation to indicate the absence of any number. (For example, you can use words to express the number 2004 without using a word indicating empty spaces, but you cannot write it numerically without indicating the absences between 2 and 4. Without the zeroes, 2004 would be indistinguishable from 24.)
The first decimal system with place value that is conceptually identical to the modern “Hindu-Arabic” system of notation first emerged in China nearly four centuries before the Common Era. This system evolved bottom-up—through the actual practice of computing in everyday life—and gradually spread to all sections of society, from government officials, astronomers to monks. It used counting rods—short sticks, about 14 mm in length—which were moved around on columns drawn on any flat surface, each column representing a successive power of 10 from right to left. Each numeral from 1 to 9 was assigned a specific configuration of rods, while numbers greater than 10 were represented by moving the rods to the next column on the left. The orientation of the rods alternated between vertical and horizontal to make it easier to read the numbers. What we would call sunya , or zero, was called “kong” and was represented by an empty column. Chinese mathematicians gradually began to use the rod method for solving what we would today recognise as algebraic equations. This system of computing remained in practice until it was replaced by an abacus around the 12th century.
Why the Chinese rod numerals are important to understand the evolution of zero in India will become clearer very soon. But what is important is to recognise that we have here, in a neighbouring land—with which we had extensive contacts dating as far back as the first century BCE—a complete decimal system with place value and empty spaces to represent the absence of any number. Is it beyond the realm of possibility that the relatively sudden appearance of decimal place value in Devanagari numerals after nearly 900 years of no sign of it might have had something to do with our neighbour?
Physical evidence of zero Let us now turn to the second uncomfortable fact, namely, that the first physical evidence of zero as we know it is found not in India but in Cambodia. The Cambodian evidence comes from a stone pillar bearing the inscription “the Chaka era reached year 605 on the fifth day of the waning moon” and the “0” in 605 is represented by a dot. This inscription has been dated to the year 683. (The pillar bearing the inscription was lost under the Khmer Rouge and was rediscovered in 2013 by Amir Aczel, an American-Israeli mathematician). Similar inscriptions—all sporting a dot for zero—have been found in Sumatra, Banka islands, Malaysia and Indonesia, all dating roughly to the same period as the pillar from Cambodia.
The first physical evidence of zero found in India comes from the Chatarbhuja temple, a rock temple dedicated to Vishnu near the city of Gwalior. The inscription on the wall of the temple talks about the gift of land, measuring 270 × 187 hasta s, to the temple and promises 50 garlands to the deity every day. The numbers are written in the Nagari script with small empty circles representing empty spaces. The inscription is dated to the year 876, more than two centuries after the Cambodian inscription.
The question arises, Why, if India is the birthplace of zero, should the evidence for zero show up in South-East Asia before it shows up in India? Even if we assume that the south-eastern zeros were all influenced by India, why do they predate India’s?
A plausible explanation is offered by Needham and reinforced by Lam Lay Yong. South-East Asia is where, as Needham put it, the “eastern zone of Hindu culture met the southern zone of the culture of the Chinese”. Any number of merchants, state officials, soldiers and Buddhist pilgrims and monks would have passed to and fro between India and China through this cultural contact zone. It is not unlikely that they carried the Chinese counting rods and counting boards—both eminently portable—with them. It is equally likely that the native inhabitants of this Indo-Chinese border zone would have used the numerals they were familiar with but kept the logic behind the counting rods. Once in India, the empty space of the Chinese counting boards changed from a dot to an empty circle and gradually became our familiar zero. To quote Needham: “The written symbol for nil value, emptiness, sunya, i.e., the zero, is an Indian garland thrown around the vacant space on the Han counting boards.” In other words, the conceptual framework for decimal place value and empty space originated in China, while India provided the physical symbol that we know today as zero.
This account is bound to ruffle Indian feathers as it challenges one of our most prized achievements, our most cherished claim to fame. But it is a perfectly plausible theory which can account for the gaps in the Indian evidence. It is only our Indocentrism that prevents us from taking it seriously and exploring it further.
Mixing up myth and history The third and final case of distortion of history of science comes from none other than the Prime Minister himself. It exemplifies the kind of distortion that takes place when what we know today , after centuries of scientific research, is read into texts and sciences that belong to another era altogether.
The contents of Narendra Modi’s Karna-Ganesha speech are familiar enough. He turned Karna from the Mahabharata into an in vitro baby which, he said, “means that genetic science was present at that time”. Ganesha’s elephant head was evidence that “there must have been some plastic surgeon at that time” who could presumably do an inter-species head transplant.
One could perhaps overlook this speech as one of the over-the-top things all politicians say sometimes. But Modi, a life-long swayamsewak, is a product of the shakha culture that respects no boundaries between myth and facts of history. The shakha interpretations are replete with anachronistic history in which the ideas, aspirations, motivations and desires of the present are read back into the past. This kind of “history” is more dangerous, as Eric Hobsbawm pointed out, than outright lies for it breeds doublethink and creates an impression of a glorious past. When applied to science, it turns the science of previous eras into a precursor, or an anticipation, of what we know today. The past is updated and ancestors turned into scientific geniuses who were ahead of their times.
Take Modi’s statement that “genetic science was present [at the time of the Mahabharata .]”. This is not just a piece of grandstanding by a politician. It belongs to a long tradition in India of legitimising caste practices in eugenic terms. Such ideological defences of the varna order were quite common among Indians (including the erudite Sarvepalli Radhakrishnan) in the early part of the 20th century before the Nazi horrors discredited the “science” of eugenics. In our own time, genetic reasoning is being advocated to defend the khap strictures on same- gotra marriages. To give the cover of “genetics” amounts to rationalisation of oppressive practices based upon religious superstitions, economic interests, caste and gender prejudices.
There was obviously no “genetics” before the discovery of the gene. The concept of a gene as a discrete unit of heredity was not known until the beginning of the 20th century when Gregor Mendel’s (1822-1884) work was rediscovered.
Even the great Charles Darwin (1809-1882) thought that traits were inherited through the blending of “gemmules”—tiny particles that were supposedly shed into the blood by all the cells of the body. It was Mendel’s tireless and patient work, confirmed later by Hugo de Vries and others, that gave birth to the idea of a non-blending, discrete unit of heredity. That these units of heredity sit on the chromosomes and that the chromosomes are made up of double-helical DNA (deoxyribonucleic acid) are all 20th century discoveries.
Strictly speaking, then, there was no “genetic science” anywhere before there was the idea of the gene. That, of course, does not mean that people did not puzzle over heredity. Like in all civilisations, ancient Indians, too, pondered over the mystery of heredity. Their most “scientific” theory—by the standards of that era—is recorded in the Charka Samhita , the foundational text of Ayurveda.
According to the Charka Samhita , the birth of any living being involves not two, but three partners: the mother, the father and the soul ( atman ) attached to a subtle body ( sukshama sharira ) looking for a new body after the death of its previous gross body ( sthula sharira ). As explained in great depth by S.N. Dasgupta, the subtle body “passes invisibly into a particular womb, on account of its karma” and that is what initiates the formation of the foetus in the womb. Biological parents are necessary but not sufficient for the birth of a child: it is the subtle body, transmigrating from a dying person, with all its past memories and samskara s intact, that is the key to heredity.
This is the “science of genetics” that existed at the time of the Mahabharata. To create an impression of equivalence and continuity between this and what we understand as the “science of genetics” today is laughable.
One cannot but suspect that there is a deeper, unstated reason beyond glorifying the ancient Hindu nation for Hindutva warriors to indulge in this kind of absurdity. They know that advances in the real science of genetics have made their transmigrating soul stuff completely irrelevant and superfluous to the explanation of the phenomenon of life—after all, we live in an age of synthetic biology where completely functional organisms can be created starting with chemicals taken off the shelf. They know that the spiritualist metaphysics of Brahmins cannot withstand a serious scientific scrutiny. To cover this obscurantist metaphysics as “science” is a desperate attempt to protect it from the critical scrutiny of real science.
Hindutva’s science envy, then, extends beyond nationalism: it is a rearguard strategy to defend the very foundations of Hindu beliefs and practices. As Sadiq al-Azm, the great Syrian philosopher, put it: “The attempt to efface the features of the struggle between religion and science is nothing but a hopeless effort to defend religion. It is resorted to every time religion is forced to concede a traditional position and every time it is forced to withdraw from a centre that it formerly held.”
This is the real source of Hindutva’s science envy.
Meera Nanda specialises in the history of modern science.