Everyday equations
May 25 2015
Ancient Indian mathematicians revelled in discovering efficacious algorithms for diverse problems
The word algorithm, which is commonly used for any systematic procedure of computation, has
an interesting history. It derives from the medieval word “algorism”, which referred to the process of doing arithmetic by means of Indian numerals (the so called “Hindu-Arabic numerals”) following the Indian methods of calculation based on the decimal place value system. The word algorism itself is a corruption of the name of the Central Asian mathematician al Khwarizmi (c 825) whose book on the Indian method of reckoning (Hisab al Hind) was the source from which the Indian methods of calculation reached the western world. The “algorists” in medieval Europe, who computed by algorism were at a great advantage compared to those who used the abacus or any other system of numeration such as the Roman system. The situation has been aptly described by the renowned 18th century French mathematician Pierre Simon de Laplace as follows:
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“It is India that gave us the ingenious method of expressing all numbers by means of 10 symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”
The term “mathematics” is derived from the Greek word “mathema” which means knowledge or learning. The Indian term for this discipline is “ganita” which means calculation or computation. Indian mathematics, ganita, is quintessentially a science of computation. Indian mathematical texts are not just a collection of propositions or theorems about mathematical entities, they are more in the nature of a compendia of systematic and efficient procedures for computation (with numbers, geometrical figures and algebraic symbols standing for a class of mathematical objects and so on) as applicable to diverse problems. Thus, a majority of the sutras or verses of a classical Indian mathematical text are in the form of prescriptions or rules — they are referred to by the traditional commentators as vidhi, prakriya orkarana-sutras — rules that characterise systematic procedures.
This approach is not special to mathematics alone, but common to most Indian knowledge systems — the sastras. The canonical texts of different disciplines in Indian tradition present rules which are generally called sutras or lakshanas. Most of these rules serve to characterise systematic procedures (referred to variously as vidhi, kriya or prakriya, sadhana, karmaor parikarma, karana etc.) which are designed to accomplish specific ends. In this way, the Indian sastras are always rooted in vyavahara or practical applications.
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This approach of Indian sastras allows them to have a great degree of flexibility in devising multiple approaches to the solutions of problems and not get bogged down by any dogma of inviolability of the fundamental truths posited or derived in any specific theoretical formulation employed in the discipline concerned. While the canonical texts of Indian sastras clearly assert the validity and the efficacy of the various procedures enunciated in them, they also simultaneously emphasise that these procedures are onlyupaya, or means for accomplishing specific ends, and there are no other restrictions which need to be imposed on them. The texts also declare that one is free to take recourse to any other set of systematic procedures, if they are equally efficacious in accomplishing the given ends.
It is the algorithmic approach that distinguishes the ancient Indian texts of geometry, the Sulvasutras (prior to 800 BCE), which deal with the construction of yajna-vedis (altars). While Sulvasutras do contain the earliest available statement of the so-called Pythagoras theorem — they state it in the form “the square made by the diagonal of a rectangle is equal to the sum of the squares made by its sides” — the main purpose of the Sulvasutras is to describe systematic procedures for constructing and transforming geometrical figures using a rajju (rope) and sanku (pole).
It has been remarked that the Indian scientific tradition has been profoundly influenced by the methodology of the Ashtadhyayi of Panini (prior to 500 BCE), in the same way the Greco-European tradition is said to have been influenced by the methodology of the Elements of Euclid. The Ashtadhyayi of Panini is a truly generative grammar in the modern sense that it is a collection of some 4,000 rules using which it is possible to derive every valid utterance of the Sanskrit language starting from a collection of primitive elements such as dhatus (verb-roots) and pratyayas (suffixes). Panini does not present any set of propositions or truths about language, but gives us an expert system so to say, which enables us to derive (and also analyse) all the valid utterances of Sanskrit language, an achievement which is as yet unparalleled in the grammatical tradition of any of the world languages. Many of the techniques used in Panini’s grammar — his abstract symbolism, use of the zero-morpheme (lopa), ideas of rule ordering and recursion — seem to have had significant impact on the development of Indian mathematics. They have also influenced developments in modern linguistics and computer science.
The ancient text of Sanskrit prosody, the Chandahsastra of Pingala (c 300 BCE) presents algorithms for converting a number to its binary form and vice versa. In Sanskrit prosody, any pada (line or foot) of a verse is analysed as a sequence of guru (long) and laghu (short) syllables, so that Pingala could essentially characterise it as a binary sequence. Pingala also gives an efficient algorithm for finding the n-th power of a number, which involves only around log2 (n) operations of squaring and multiplications (in contrast to the standard method which involves n multiplications), and was, therefore, adopted by all the later Indian mathematicians.
Pingala’s work also contains a cryptic sutra, which has been explained by later commentators, such as Halayudha (c 900 CE), as a rule for the computation of binomial coefficients using a tabular form, Meru, which is a version of the famous Pascal triangle. Pingala’s work set the stage for subsequent developments in combinatorics, which were initiated in texts of prosody and music and were formulated in a general mathematical setting by later mathematicians, Mahaviracharya (c 850), Bhaskaracharya II (b 1114) and especially Narayana Pandita (c 1356).
In ancient times, ganita formed an important part of the science of astronomy (jyotisha). The Aryabhatiya (c 499 CE) of Aryabhata is a great classical work which summarised the entire subject of mathematical astronomy in 121 aphoristic verses, of which the section on mathematics, Ganitapada, comprised just 32 verses. We can see that, by that time, Indian mathematicians had systematised most of the basic procedures of arithmetic (such as place value system, the standard algorithms for square-roots and cube-roots), algebra (solution of linear and quadratic equations), geometry (standard properties of planar and solid figures), commercial mathematics (rule of three, calculation of interest) and trigonometry, that are generally taught in schools today — and many more that are more advanced (such as the kuttaka method of solving linear indeterminate equations and computation of sine-tables) which are of importance in astronomy.
Several detailed commentaries (bhashyas) were written on the cryptic verses of Aryabhatiya, of which the most important ones are those of Bhaskara I (c 629 CE) and the great Kerala astronomer Nilakantha Somayaji (c 1444-1544). The commentary of Bhaskara I provides detailed explanations (along with examples) for the various results and procedures given in Aryabhatiya. The Aryabhatiya-bhashya of Nilakantha presents detailed demonstrations (upapatti, yukti). Occasionally, Nilakantha also discusses some important refinements or modifications.
We may cite, for instance, Nilakantha’s discussion of the more accurate table of sines (due to Madhava), and more importantly, his famous dictum based on the latitudinal motion of the planets Mercury and Venus, that: “The earth is not circumscribed by their orbits (the orbits of Mercury and Venus), the earth is always outside of them.” This led Nilakantha to formulate a modified planetary model according to which the five planets Mercury, Venus, Mars, Jupiter and Saturn go around the mean sun, which in turn goes around the earth. This was nearly a hundred years prior to a similar model being proposed by Tycho Brahe in Europe.
We shall not go into the contributions of the long tradition of illustrious astronomers and mathematicians who followed Aryabhata — and the tradition continued to flourish till the 19th century. We instead present some illustrations to show how the algorithmic approach of the Indian mathematicians led them to discover optimal and efficacious algorithms for diverse problems. The most famous example is, of course, the Chakravalaalgorithm for the solution of the quadratic indeterminate equation (the so called Pell’s equation): X² – DY² = 1.
Here, D is a given positive integer which is not a square and the problem is to solve for X, Y in integers. This problem (called vargaprakriti) was first explicitly posed by Brahmagupta in his Brahmasphutasiddhanta (c 628 CE), though the ancient Sulvasutras seem to have used the solution X=577, Y=408 for the case D=2, to get the rational approximation 577/408 for the square-root of 2. Brahmagupta also gave a rule of composition (calledbhavana) which allows one to obtain an infinite number of solutions once a particular solution is found.
The Chakravala method for solving the above equation has been presented in the famous textbook of algebra, Bijaganita, of Bhaskaracharya (b 1114), though it is now known that the algorithm also appears in an earlier work by Acharya Jayadeva (prior to c 1050).
Bhaskara used this method to solve the equation: X² – 61Y² = 1, and showed that the smallest solution is given by X=1766319049 and Y=226153980. What is intriguing is that the same example was posed as a challenge by the famous French mathematician, Pierre de Fermat, in February 1657 to his colleagues in France.
He later posed this and other vargaprakriti equations (with different values of D) as a challenge to British mathematicians. To cut the story short, British mathematicians Wallace and Brouncker did come up with a method of solution, which was later systematised as an algorithm, based on the so-called regular continued fraction development of the square-root of D, by Euler and Lagrange in the 1770s.
In 1929, AA Krishnaswamy Ayyangar showed that the Chakravala algorithm corresponds to a so-called semi-regular continued fraction expansion and is also optimal in the sense that it takes much fewer steps to arrive at the solution than the Euler-Lagrange method. It is now known that on the average the Euler-Lagrange method takes about 40 per cent more number of steps than the Chakravala.
Finally, we make a brief mention of the infinite series for Pi (the ratio of the circumference to the diameter of a circle) discovered by Sangamagrama Madhava (c 1380-1460), founder of the Kerala School of Astronomy. For instance, Madhava presents the following series (the so-called Gregory-Leibniz series rediscovered in the 1670s): Pi/4 = 1 – 1/3 + 1/5 – 1/7 +...
However, Madhava is not content with merely enunciating this elegant result, as it is not of any use in actually calculating the value of Pi. Summing say 50 terms in this series does not give a value of Pi accurate even to two decimal places. The famous verses of Madhava which present the above series also go on to give a set of end-correction terms which can be used to obtain better approximations. Using only 50 terms of the above series, with the accurate end-correction term of Madhava, leads to a value of Pi accurate to 11 decimal places. Madhava also used these correction terms to transform the above series into more rapidly convergent versions. Systematic proofs of all the infinite series discovered by Madhava and their transformations may be found in the famous Malayalam work Ganitayuktibhasha (c 1530) of Jyeshthadeva.
The great astronomer Nilakantha was a third generation disciple of Madhava and the tradition of Kerala School continued (albeit at a modest level due to the greatly disturbed political situation of Kerala after the 1550s) till early 19th century. However, a century later, the algorithmic approach of Indian mathematics was in evidence again in the work of another great mathematician, Srinivasa Ramanujan (1888-1920), who seems to have been a worthy successor of Madhava in his extraordinary felicity to work with infinite series and their transformations.
(MD Srinivas is the chairman of Centre for Policy Studies, Chennai)
mdsrinivas50@gmail.com
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“It is India that gave us the ingenious method of expressing all numbers by means of 10 symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”
The term “mathematics” is derived from the Greek word “mathema” which means knowledge or learning. The Indian term for this discipline is “ganita” which means calculation or computation. Indian mathematics, ganita, is quintessentially a science of computation. Indian mathematical texts are not just a collection of propositions or theorems about mathematical entities, they are more in the nature of a compendia of systematic and efficient procedures for computation (with numbers, geometrical figures and algebraic symbols standing for a class of mathematical objects and so on) as applicable to diverse problems. Thus, a majority of the sutras or verses of a classical Indian mathematical text are in the form of prescriptions or rules — they are referred to by the traditional commentators as vidhi, prakriya orkarana-sutras — rules that characterise systematic procedures.
This approach is not special to mathematics alone, but common to most Indian knowledge systems — the sastras. The canonical texts of different disciplines in Indian tradition present rules which are generally called sutras or lakshanas. Most of these rules serve to characterise systematic procedures (referred to variously as vidhi, kriya or prakriya, sadhana, karmaor parikarma, karana etc.) which are designed to accomplish specific ends. In this way, the Indian sastras are always rooted in vyavahara or practical applications.
This approach of Indian sastras allows them to have a great degree of flexibility in devising multiple approaches to the solutions of problems and not get bogged down by any dogma of inviolability of the fundamental truths posited or derived in any specific theoretical formulation employed in the discipline concerned. While the canonical texts of Indian sastras clearly assert the validity and the efficacy of the various procedures enunciated in them, they also simultaneously emphasise that these procedures are onlyupaya, or means for accomplishing specific ends, and there are no other restrictions which need to be imposed on them. The texts also declare that one is free to take recourse to any other set of systematic procedures, if they are equally efficacious in accomplishing the given ends.
It is the algorithmic approach that distinguishes the ancient Indian texts of geometry, the Sulvasutras (prior to 800 BCE), which deal with the construction of yajna-vedis (altars). While Sulvasutras do contain the earliest available statement of the so-called Pythagoras theorem — they state it in the form “the square made by the diagonal of a rectangle is equal to the sum of the squares made by its sides” — the main purpose of the Sulvasutras is to describe systematic procedures for constructing and transforming geometrical figures using a rajju (rope) and sanku (pole).
It has been remarked that the Indian scientific tradition has been profoundly influenced by the methodology of the Ashtadhyayi of Panini (prior to 500 BCE), in the same way the Greco-European tradition is said to have been influenced by the methodology of the Elements of Euclid. The Ashtadhyayi of Panini is a truly generative grammar in the modern sense that it is a collection of some 4,000 rules using which it is possible to derive every valid utterance of the Sanskrit language starting from a collection of primitive elements such as dhatus (verb-roots) and pratyayas (suffixes). Panini does not present any set of propositions or truths about language, but gives us an expert system so to say, which enables us to derive (and also analyse) all the valid utterances of Sanskrit language, an achievement which is as yet unparalleled in the grammatical tradition of any of the world languages. Many of the techniques used in Panini’s grammar — his abstract symbolism, use of the zero-morpheme (lopa), ideas of rule ordering and recursion — seem to have had significant impact on the development of Indian mathematics. They have also influenced developments in modern linguistics and computer science.
The ancient text of Sanskrit prosody, the Chandahsastra of Pingala (c 300 BCE) presents algorithms for converting a number to its binary form and vice versa. In Sanskrit prosody, any pada (line or foot) of a verse is analysed as a sequence of guru (long) and laghu (short) syllables, so that Pingala could essentially characterise it as a binary sequence. Pingala also gives an efficient algorithm for finding the n-th power of a number, which involves only around log2 (n) operations of squaring and multiplications (in contrast to the standard method which involves n multiplications), and was, therefore, adopted by all the later Indian mathematicians.
Pingala’s work also contains a cryptic sutra, which has been explained by later commentators, such as Halayudha (c 900 CE), as a rule for the computation of binomial coefficients using a tabular form, Meru, which is a version of the famous Pascal triangle. Pingala’s work set the stage for subsequent developments in combinatorics, which were initiated in texts of prosody and music and were formulated in a general mathematical setting by later mathematicians, Mahaviracharya (c 850), Bhaskaracharya II (b 1114) and especially Narayana Pandita (c 1356).
In ancient times, ganita formed an important part of the science of astronomy (jyotisha). The Aryabhatiya (c 499 CE) of Aryabhata is a great classical work which summarised the entire subject of mathematical astronomy in 121 aphoristic verses, of which the section on mathematics, Ganitapada, comprised just 32 verses. We can see that, by that time, Indian mathematicians had systematised most of the basic procedures of arithmetic (such as place value system, the standard algorithms for square-roots and cube-roots), algebra (solution of linear and quadratic equations), geometry (standard properties of planar and solid figures), commercial mathematics (rule of three, calculation of interest) and trigonometry, that are generally taught in schools today — and many more that are more advanced (such as the kuttaka method of solving linear indeterminate equations and computation of sine-tables) which are of importance in astronomy.
Several detailed commentaries (bhashyas) were written on the cryptic verses of Aryabhatiya, of which the most important ones are those of Bhaskara I (c 629 CE) and the great Kerala astronomer Nilakantha Somayaji (c 1444-1544). The commentary of Bhaskara I provides detailed explanations (along with examples) for the various results and procedures given in Aryabhatiya. The Aryabhatiya-bhashya of Nilakantha presents detailed demonstrations (upapatti, yukti). Occasionally, Nilakantha also discusses some important refinements or modifications.
We may cite, for instance, Nilakantha’s discussion of the more accurate table of sines (due to Madhava), and more importantly, his famous dictum based on the latitudinal motion of the planets Mercury and Venus, that: “The earth is not circumscribed by their orbits (the orbits of Mercury and Venus), the earth is always outside of them.” This led Nilakantha to formulate a modified planetary model according to which the five planets Mercury, Venus, Mars, Jupiter and Saturn go around the mean sun, which in turn goes around the earth. This was nearly a hundred years prior to a similar model being proposed by Tycho Brahe in Europe.
We shall not go into the contributions of the long tradition of illustrious astronomers and mathematicians who followed Aryabhata — and the tradition continued to flourish till the 19th century. We instead present some illustrations to show how the algorithmic approach of the Indian mathematicians led them to discover optimal and efficacious algorithms for diverse problems. The most famous example is, of course, the Chakravalaalgorithm for the solution of the quadratic indeterminate equation (the so called Pell’s equation): X² – DY² = 1.
Here, D is a given positive integer which is not a square and the problem is to solve for X, Y in integers. This problem (called vargaprakriti) was first explicitly posed by Brahmagupta in his Brahmasphutasiddhanta (c 628 CE), though the ancient Sulvasutras seem to have used the solution X=577, Y=408 for the case D=2, to get the rational approximation 577/408 for the square-root of 2. Brahmagupta also gave a rule of composition (calledbhavana) which allows one to obtain an infinite number of solutions once a particular solution is found.
The Chakravala method for solving the above equation has been presented in the famous textbook of algebra, Bijaganita, of Bhaskaracharya (b 1114), though it is now known that the algorithm also appears in an earlier work by Acharya Jayadeva (prior to c 1050).
Bhaskara used this method to solve the equation: X² – 61Y² = 1, and showed that the smallest solution is given by X=1766319049 and Y=226153980. What is intriguing is that the same example was posed as a challenge by the famous French mathematician, Pierre de Fermat, in February 1657 to his colleagues in France.
He later posed this and other vargaprakriti equations (with different values of D) as a challenge to British mathematicians. To cut the story short, British mathematicians Wallace and Brouncker did come up with a method of solution, which was later systematised as an algorithm, based on the so-called regular continued fraction development of the square-root of D, by Euler and Lagrange in the 1770s.
In 1929, AA Krishnaswamy Ayyangar showed that the Chakravala algorithm corresponds to a so-called semi-regular continued fraction expansion and is also optimal in the sense that it takes much fewer steps to arrive at the solution than the Euler-Lagrange method. It is now known that on the average the Euler-Lagrange method takes about 40 per cent more number of steps than the Chakravala.
Finally, we make a brief mention of the infinite series for Pi (the ratio of the circumference to the diameter of a circle) discovered by Sangamagrama Madhava (c 1380-1460), founder of the Kerala School of Astronomy. For instance, Madhava presents the following series (the so-called Gregory-Leibniz series rediscovered in the 1670s): Pi/4 = 1 – 1/3 + 1/5 – 1/7 +...
However, Madhava is not content with merely enunciating this elegant result, as it is not of any use in actually calculating the value of Pi. Summing say 50 terms in this series does not give a value of Pi accurate even to two decimal places. The famous verses of Madhava which present the above series also go on to give a set of end-correction terms which can be used to obtain better approximations. Using only 50 terms of the above series, with the accurate end-correction term of Madhava, leads to a value of Pi accurate to 11 decimal places. Madhava also used these correction terms to transform the above series into more rapidly convergent versions. Systematic proofs of all the infinite series discovered by Madhava and their transformations may be found in the famous Malayalam work Ganitayuktibhasha (c 1530) of Jyeshthadeva.
The great astronomer Nilakantha was a third generation disciple of Madhava and the tradition of Kerala School continued (albeit at a modest level due to the greatly disturbed political situation of Kerala after the 1550s) till early 19th century. However, a century later, the algorithmic approach of Indian mathematics was in evidence again in the work of another great mathematician, Srinivasa Ramanujan (1888-1920), who seems to have been a worthy successor of Madhava in his extraordinary felicity to work with infinite series and their transformations.
(MD Srinivas is the chairman of Centre for Policy Studies, Chennai)
mdsrinivas50@gmail.com
Nature's basket
May 11 2015
Ancient India relied on an elaborate knowledge system to conserve and manage ecology
With every passing day, we hear more horror stories about our environment: air is
unbreathable, water undrinkable, food poisonous; piles of garbage stare at us everywhere like works of modern art. Our cities cannot survive unless pipelines bring them water from hundreds of kilometres away. We have certainly perfected the fine art of unsustainability. And while some of us may be tempted to pine for the pre-industrial age, when nature was (more or less) pristine, our deshi rationalists continue to pour contempt on ‘tree worshippers’, ‘nature worshippers’, and (shudder!) ‘cow worshippers’. Surely such primitive superstition is what is holding us back on the road to magnificent progress.
Superstition is perhaps not where we think and ancient India’s perspective of nature was anything but blind worship. It relied on an elaborate knowledge system in which mythology, symbolism, art, laws and technologies co-mingled to produce practices of nature conservation and management that, in some respects, we can only envy today.
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Nature as the divine
The tone is set in the Rig Veda, India’s most ancient text. Here, we find earth and heaven often addressed as a single being (dyavaprithivi) and honoured together; they are ‘parents of the gods’ (7.53), ‘father and mother’ but also the ‘twins’ (1.159); together, they ‘keep all creatures safe’ (1.160). This is in stark contrast with the biblical gulf between the creator and the created: here, the two are not only equal but conjoined. From this perspective, nature’s all-pervasive divinity will follow.
Vedic imagery draws heavily on nature, from mighty mountains, impetuous rivers and oceans to majestic trees and powerful animals; some hymns address their prayers not to gods but to waters or plants. In fact, the Rig Vedasees the cosmos as a thousand-branched tree (3.8.11, 9.5.10), a symbol theGita will turn upside down: the cosmic ashvattha (the pipal or holy fig tree,Ficus religiosa) has its roots above and branches below, to remind us of the real source of this manifestation. Elsewhere, the Mahabharata declares, ‘He who worships the ashvattha worships the universe.’ Hence the concept of ‘tree worship’: the tree as a cosmic symbol grants our every desire (kalpavriksha or kalpataru), which is why India’s list of sacred trees is a long one!
Later literature deve-loped the same themes, with some variations. Aditi, the mother of the gods in the Rig Veda, is ‘the divine Cow’, while the Mahabharata tells the story of the earth turning into a cow which many species come and milk, in a transparent metaphor. Indra, Surya and other gods are addressed as the ‘bull’. Even the humble dog finds its exalted representation in Sarama. Animals — birds, reptiles and mammals — act as vahanas, vehicles for major deities, occasionally lending them an elephant’s head or even their whole bodies, as with Vishnu’s first avatars, fish, tortoise and boar. The Bhagavatam evokes the child Krishna’s devotion to his cows, which they more than reciprocate: this is no pretty bucolic tale, but a recast of the Rig-Veda’s equation of earth (here, the cows) with heaven.
Indeed, hindu, buddhist or jain literature is pervaded with nature’s many charms; who has not thrilled at Kalidasa’s exquisite descriptions of forest ashrams or mountain ranges or marvelled at the boldness with which theSangam poets of Tamil Nadu made use of hills, forests, rivers and the ocean to convey their moods? For generations children, too, have been entertained by the Pañchatantra’s irresistible animal fables.
Art closely follows literature, initially at least. Seals, tablets and pottery of the Indus-Sarasvati civilisation often depict trees (especially the pipal, again); on an intriguing seal, a plant emerges from a supine woman’s womb, a clear symbol of nature’s fertility. The humped and humpless bull, the tiger, the elephant, the rhinoceros and the buffalo are often portrayed, with significances still eluding us.
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Indus seals with elephant; humped bull; tree in railing (terracotta, Harappa)
In much classical Indian art, nature provides the setting, but often with a discreet symbolic message: such is the case of the Boddhi tree, to be understood as the Buddha’s cosmic awakening. Ancient kingdoms often adopted animals for their emblems, ranging from the elephant (for the Gangas), the lion (the Kadambas) or the tiger (the Cholas) down to the humble fish (the Pandyas).
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Buddha’s bodhi tree
Protecting nature
Such lofty concepts led to actual practices of nature conservation.Manusmriti (11.64) prohibits the ‘cutting down of green trees for firewood’, while Kautilya’s Arthashastra stipulates various fines and punishments for maiming ‘fruit trees, flower trees or shady trees in the parks near a city’ and prescribes forest sanctuaries where wildlife is to be protected from slaughter (3.19). Shastras, too, proscribe the unnecessary killing of animals, while Ashoka in his edicts prohibits hunting, even ordering medical treatment to wild animals when necessary. Ashoka was perhaps the world’s first ruler to advocate vegetarianism, although he was honest enough to admit that he did not fully practise it yet!
Even to this day, patches of the country’s forest cover exist thanks to the ancient tradition of ‘sacred groves’. Named kovilkadu in Tamil Nadu, kavu in Kerala, nandavana or deivavana in Karnataka and Andhra Pradesh, deoraiin Maharashtra, they can be found in many parts of India, on the outskirts of the villages that protect them from hunting and tree cutting. Some contain hero stones or a small shrine surrounded by large terracotta figures, especially of horses. In the south, those terracotta figures are often ritually broken and made anew every year, an enactment of nature’s yearly death and rebirth. Unsurprisingly, sacred groves have been vanishing; the few that remain well protected are host to a remarkable biodiversity.
Such traditions have found expression in many rural and tribal communities, which had a vested interest in protecting nature: Bishnois are well known for initiating, once at the cost of hundreds of lives, the practice of tree-hugging, taken over by the Chipko and other movements. Bhils, Warlis, Santhals and Todas have rich ethnobotanical traditions, many of them associated with rituals celebrating birth, puberty, marriage, death, or with festivals. Most temples have at least one sacred tree (sthalavriksha), and the greater its age, the more divinity it is imbued with. Nature, let us repeat, is never seen as ‘secular’, much less a dead heap of ‘natural resources’ awaiting our exploitation. It — she, rather — is a channel connecting the worshipper to the universe.
From the sacredness of plants follows the sacredness of food, food-giving and food-sharing, one of the high traditions of India running through texts as well as historical records. The recipient of Bhishma’s monumental discourse on dharma and the duties of a king, Yudhishthira asked Krishna to summarise that teaching. Krishna’s answer is unexpected: ‘The world, both animate and inanimate, is sustained by food... The giver of food is the giver of life and indeed of everything else. Therefore, one who is desirous of well-being in this world and beyond should make special endeavour to give food.’ Hence India’s traditions of annadana and hospitality.
Harnessing nature
With its monsoon-driven regime of rainfall, India soon understood the importance of water harvesting and management — very soon, in fact, judging from the 4,500-year-old Harappan city of Dholavira, in Gujarat’s forbiddingly arid Rann of Kutch, which dedicated some 20 to 30 per cent of its fortified area (48 ha) to a vast network of interconnected reservoirs, some of them cut in sheer rock; the whole system was fed by carefully harvested rainfall as well as water diverted from two seasonal streams bracketing the city, whose waters were slowed down through series of checkdams. The largest reservoir, to the east of the castle (the city’s highest and most fortified enclosure), measured 73 x 29 m and would have contained over 20,000 m3 of water when full. In addition, a small but neatly constructed stepwell dug at the bottom provided for extended access to water, should the reservoir fall empty. As a result, the city was occupied for at least seven centuries without a break.
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Eastern reservoir Dholavira, with castle in background; Rockcut stepwell at the bottom of Dholavira
Monumental waterworks continued into the early historical era. If theMahabharata promised the builder of a tank a hundred times more punyathan would get the digger of a well, it is simply because a tank restores water to the earth, while a well draws from it — simple, but even today we are far from such basic awareness, even as a severe water crisis stares in our face.Arthashastra, again, shows prescience by paying minute attention to water management and irrigation techniques. Interestingly, and unlike today, access to water through public or private waterworks was not free; it was taxed at various rates, the highest being if irrigated water were supplied by the state. Penalties were prescribed for obstructing or diverting a watercourse, causing fields to be flooded, building a well or a dam on someone else’s land, not maintaining waterworks, or for failing to cooperate in the building of an irrigation tank.
Kautilya systematically deals with different situations; for instance, he declares, ‘No one irrigating his field from a reservoir or tank shall cause danger to the ploughed or sown field of another. The water from a lower tank shall not submerge a field fed from a higher tank built earlier. A higher tank shall not prevent the filling up of a lower tank, except when the latter has not been in use for three years....’ (3.9)
Almost echoing Kautilya, Strabo, a first-century BCE Greek geographer, noted: ‘Among [the officials], the first keep the rivers improved and the land re-measured, as in Egypt, and inspect the closed canals from which the water is distributed into the conduits, in order that all may have an equal use of it.’
Such state management of water resources finds confirmation in hundreds of inscriptions recording the constructions of dams, tanks (tataka) and ponds (vapi), also their maintenance: desilting, repair of embankments, sluices, irrigation channels.... Water diviners were not left out and were mandated to pay taxes!
Water structures
An earlier article in this series, House of commons (April 28, 2015), explained how at Sringaverapura in Uttar Pradesh, a simple but effective series of interconnected reservoirs, some of them with a well dug at the bottom, was fed by a channel from the Ganges some 2,000 years ago. Later, we find across India a bewildering variety of reservoirs, stepwells, dams, water-diverting devices and canals, all the way down to the humble village pond.
Wells came in many shapes — circular, square, vertical or horizontal —and sizes, built with bricks, stone or terracotta rings. There is a long way from Dholavira’s modest stepwell to those of classical times, especially in Gujarat and Rajasthan, which are not only engineering marvels but works of sacred art. Mention must be made here of Rani Ki Vav near Patan in Gujarat, with its pillared halls, magnificently sculpted side panels depicting Hinduism’s major gods (often accompanied by lovely apsaras or water nymphs), and the well’s inner cylinder completely covered with hundreds of sculpted stone panels — whose perfect curvature is in itself a technological feat.
![]()
Sculpted panels at Rani Ki Vav
Indians experimented with various kinds of dams, the simplest being the earthen embankment designed to create a reservoir or divert a stream. Downstream of Srirangam island on the Kaveri (Cauvery) river, some 1,800 years ago King Karikala Chola built a more ambitious structure, the Kallanai or Grand Anicut, which finds a mention in the Tamil epic Shilappadikaram. Still visible today (in restored form), at 320m long and 20m wide, it is an ingenious device which stops the Kaveri from emptying itself into its own northern distributary, the faster and steeper Kollidam (or Coleroon), preserving much of the river’s water for irrigation in the Kaveri’s lower delta.
![]()
Grand Anicut
The humblest but perhaps most important water structure was the village pond or reservoir. What made it important was not just its ability to recharge ground water, but also its interconnectedness with many neighbouring ponds — sometimes in networks extending over hundreds of kilometres, as in Karnataka and Tamil Nadu. Such networks, which enabled water-rich areas to contribute to less favoured ones, were maintained by village committees, which disappeared when the colonial administration took over — and so did most of the reservoirs and channels in their care.
How does our ‘advanced’ technological age compare with all this? I will let my reader decide, but the judeo-christian approach to nature, viewing her as an adversary to be ‘conquered’ (witness the ‘conquest’ of the two poles or the Everest) and of course ‘exploited’ for her resources, does not seem to have made our planet a happier place.
(Michel Danino is guest professor at IIT Gandhinagar’s Archaeological Sciences Centre. micheldanino@gmail.com)
RELATED ARTICLES |
Superstition is perhaps not where we think and ancient India’s perspective of nature was anything but blind worship. It relied on an elaborate knowledge system in which mythology, symbolism, art, laws and technologies co-mingled to produce practices of nature conservation and management that, in some respects, we can only envy today.
Nature as the divine
The tone is set in the Rig Veda, India’s most ancient text. Here, we find earth and heaven often addressed as a single being (dyavaprithivi) and honoured together; they are ‘parents of the gods’ (7.53), ‘father and mother’ but also the ‘twins’ (1.159); together, they ‘keep all creatures safe’ (1.160). This is in stark contrast with the biblical gulf between the creator and the created: here, the two are not only equal but conjoined. From this perspective, nature’s all-pervasive divinity will follow.
Vedic imagery draws heavily on nature, from mighty mountains, impetuous rivers and oceans to majestic trees and powerful animals; some hymns address their prayers not to gods but to waters or plants. In fact, the Rig Vedasees the cosmos as a thousand-branched tree (3.8.11, 9.5.10), a symbol theGita will turn upside down: the cosmic ashvattha (the pipal or holy fig tree,Ficus religiosa) has its roots above and branches below, to remind us of the real source of this manifestation. Elsewhere, the Mahabharata declares, ‘He who worships the ashvattha worships the universe.’ Hence the concept of ‘tree worship’: the tree as a cosmic symbol grants our every desire (kalpavriksha or kalpataru), which is why India’s list of sacred trees is a long one!
Later literature deve-loped the same themes, with some variations. Aditi, the mother of the gods in the Rig Veda, is ‘the divine Cow’, while the Mahabharata tells the story of the earth turning into a cow which many species come and milk, in a transparent metaphor. Indra, Surya and other gods are addressed as the ‘bull’. Even the humble dog finds its exalted representation in Sarama. Animals — birds, reptiles and mammals — act as vahanas, vehicles for major deities, occasionally lending them an elephant’s head or even their whole bodies, as with Vishnu’s first avatars, fish, tortoise and boar. The Bhagavatam evokes the child Krishna’s devotion to his cows, which they more than reciprocate: this is no pretty bucolic tale, but a recast of the Rig-Veda’s equation of earth (here, the cows) with heaven.
Indeed, hindu, buddhist or jain literature is pervaded with nature’s many charms; who has not thrilled at Kalidasa’s exquisite descriptions of forest ashrams or mountain ranges or marvelled at the boldness with which theSangam poets of Tamil Nadu made use of hills, forests, rivers and the ocean to convey their moods? For generations children, too, have been entertained by the Pañchatantra’s irresistible animal fables.
Art closely follows literature, initially at least. Seals, tablets and pottery of the Indus-Sarasvati civilisation often depict trees (especially the pipal, again); on an intriguing seal, a plant emerges from a supine woman’s womb, a clear symbol of nature’s fertility. The humped and humpless bull, the tiger, the elephant, the rhinoceros and the buffalo are often portrayed, with significances still eluding us.
Indus seals with elephant; humped bull; tree in railing (terracotta, Harappa)
In much classical Indian art, nature provides the setting, but often with a discreet symbolic message: such is the case of the Boddhi tree, to be understood as the Buddha’s cosmic awakening. Ancient kingdoms often adopted animals for their emblems, ranging from the elephant (for the Gangas), the lion (the Kadambas) or the tiger (the Cholas) down to the humble fish (the Pandyas).
Buddha’s bodhi tree
Protecting nature
Such lofty concepts led to actual practices of nature conservation.Manusmriti (11.64) prohibits the ‘cutting down of green trees for firewood’, while Kautilya’s Arthashastra stipulates various fines and punishments for maiming ‘fruit trees, flower trees or shady trees in the parks near a city’ and prescribes forest sanctuaries where wildlife is to be protected from slaughter (3.19). Shastras, too, proscribe the unnecessary killing of animals, while Ashoka in his edicts prohibits hunting, even ordering medical treatment to wild animals when necessary. Ashoka was perhaps the world’s first ruler to advocate vegetarianism, although he was honest enough to admit that he did not fully practise it yet!
Even to this day, patches of the country’s forest cover exist thanks to the ancient tradition of ‘sacred groves’. Named kovilkadu in Tamil Nadu, kavu in Kerala, nandavana or deivavana in Karnataka and Andhra Pradesh, deoraiin Maharashtra, they can be found in many parts of India, on the outskirts of the villages that protect them from hunting and tree cutting. Some contain hero stones or a small shrine surrounded by large terracotta figures, especially of horses. In the south, those terracotta figures are often ritually broken and made anew every year, an enactment of nature’s yearly death and rebirth. Unsurprisingly, sacred groves have been vanishing; the few that remain well protected are host to a remarkable biodiversity.
Such traditions have found expression in many rural and tribal communities, which had a vested interest in protecting nature: Bishnois are well known for initiating, once at the cost of hundreds of lives, the practice of tree-hugging, taken over by the Chipko and other movements. Bhils, Warlis, Santhals and Todas have rich ethnobotanical traditions, many of them associated with rituals celebrating birth, puberty, marriage, death, or with festivals. Most temples have at least one sacred tree (sthalavriksha), and the greater its age, the more divinity it is imbued with. Nature, let us repeat, is never seen as ‘secular’, much less a dead heap of ‘natural resources’ awaiting our exploitation. It — she, rather — is a channel connecting the worshipper to the universe.
From the sacredness of plants follows the sacredness of food, food-giving and food-sharing, one of the high traditions of India running through texts as well as historical records. The recipient of Bhishma’s monumental discourse on dharma and the duties of a king, Yudhishthira asked Krishna to summarise that teaching. Krishna’s answer is unexpected: ‘The world, both animate and inanimate, is sustained by food... The giver of food is the giver of life and indeed of everything else. Therefore, one who is desirous of well-being in this world and beyond should make special endeavour to give food.’ Hence India’s traditions of annadana and hospitality.
Harnessing nature
With its monsoon-driven regime of rainfall, India soon understood the importance of water harvesting and management — very soon, in fact, judging from the 4,500-year-old Harappan city of Dholavira, in Gujarat’s forbiddingly arid Rann of Kutch, which dedicated some 20 to 30 per cent of its fortified area (48 ha) to a vast network of interconnected reservoirs, some of them cut in sheer rock; the whole system was fed by carefully harvested rainfall as well as water diverted from two seasonal streams bracketing the city, whose waters were slowed down through series of checkdams. The largest reservoir, to the east of the castle (the city’s highest and most fortified enclosure), measured 73 x 29 m and would have contained over 20,000 m3 of water when full. In addition, a small but neatly constructed stepwell dug at the bottom provided for extended access to water, should the reservoir fall empty. As a result, the city was occupied for at least seven centuries without a break.
Eastern reservoir Dholavira, with castle in background; Rockcut stepwell at the bottom of Dholavira
Monumental waterworks continued into the early historical era. If theMahabharata promised the builder of a tank a hundred times more punyathan would get the digger of a well, it is simply because a tank restores water to the earth, while a well draws from it — simple, but even today we are far from such basic awareness, even as a severe water crisis stares in our face.Arthashastra, again, shows prescience by paying minute attention to water management and irrigation techniques. Interestingly, and unlike today, access to water through public or private waterworks was not free; it was taxed at various rates, the highest being if irrigated water were supplied by the state. Penalties were prescribed for obstructing or diverting a watercourse, causing fields to be flooded, building a well or a dam on someone else’s land, not maintaining waterworks, or for failing to cooperate in the building of an irrigation tank.
Kautilya systematically deals with different situations; for instance, he declares, ‘No one irrigating his field from a reservoir or tank shall cause danger to the ploughed or sown field of another. The water from a lower tank shall not submerge a field fed from a higher tank built earlier. A higher tank shall not prevent the filling up of a lower tank, except when the latter has not been in use for three years....’ (3.9)
Almost echoing Kautilya, Strabo, a first-century BCE Greek geographer, noted: ‘Among [the officials], the first keep the rivers improved and the land re-measured, as in Egypt, and inspect the closed canals from which the water is distributed into the conduits, in order that all may have an equal use of it.’
Such state management of water resources finds confirmation in hundreds of inscriptions recording the constructions of dams, tanks (tataka) and ponds (vapi), also their maintenance: desilting, repair of embankments, sluices, irrigation channels.... Water diviners were not left out and were mandated to pay taxes!
Water structures
An earlier article in this series, House of commons (April 28, 2015), explained how at Sringaverapura in Uttar Pradesh, a simple but effective series of interconnected reservoirs, some of them with a well dug at the bottom, was fed by a channel from the Ganges some 2,000 years ago. Later, we find across India a bewildering variety of reservoirs, stepwells, dams, water-diverting devices and canals, all the way down to the humble village pond.
Wells came in many shapes — circular, square, vertical or horizontal —and sizes, built with bricks, stone or terracotta rings. There is a long way from Dholavira’s modest stepwell to those of classical times, especially in Gujarat and Rajasthan, which are not only engineering marvels but works of sacred art. Mention must be made here of Rani Ki Vav near Patan in Gujarat, with its pillared halls, magnificently sculpted side panels depicting Hinduism’s major gods (often accompanied by lovely apsaras or water nymphs), and the well’s inner cylinder completely covered with hundreds of sculpted stone panels — whose perfect curvature is in itself a technological feat.
Sculpted panels at Rani Ki Vav
Indians experimented with various kinds of dams, the simplest being the earthen embankment designed to create a reservoir or divert a stream. Downstream of Srirangam island on the Kaveri (Cauvery) river, some 1,800 years ago King Karikala Chola built a more ambitious structure, the Kallanai or Grand Anicut, which finds a mention in the Tamil epic Shilappadikaram. Still visible today (in restored form), at 320m long and 20m wide, it is an ingenious device which stops the Kaveri from emptying itself into its own northern distributary, the faster and steeper Kollidam (or Coleroon), preserving much of the river’s water for irrigation in the Kaveri’s lower delta.
Grand Anicut
The humblest but perhaps most important water structure was the village pond or reservoir. What made it important was not just its ability to recharge ground water, but also its interconnectedness with many neighbouring ponds — sometimes in networks extending over hundreds of kilometres, as in Karnataka and Tamil Nadu. Such networks, which enabled water-rich areas to contribute to less favoured ones, were maintained by village committees, which disappeared when the colonial administration took over — and so did most of the reservoirs and channels in their care.
How does our ‘advanced’ technological age compare with all this? I will let my reader decide, but the judeo-christian approach to nature, viewing her as an adversary to be ‘conquered’ (witness the ‘conquest’ of the two poles or the Everest) and of course ‘exploited’ for her resources, does not seem to have made our planet a happier place.
(Michel Danino is guest professor at IIT Gandhinagar’s Archaeological Sciences Centre. micheldanino@gmail.com)
http://www.mydigitalfc.com/indian-knowledge-series/natures-basket-375
![Made in India]( "Made in India")
http://www.mydigitalfc.com/indian-knowledge-series/made-india-859
Made in India
Apr 20 2015
Vedic texts give us unique insights into the development of ancient Indian metallurgy
Man and metals have an age-old relationship. Different periods of early human civilisation have
been named after metals. The attributes of gold influenced the mind and heart of Indians so much so that they conferred upon the supreme spirit the designation of hirnyagarbha. It was so called, because he remains in a golden egg as an embryo. The two important sources for the history of Indian metallurgy are archaeological excavations and literary evidence.
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Although a considerable amount of information on this subject from the study of archaeological finds is available, literary evidence has not been studied to the extent it deserves. Unique information related to metals and metallurgy is available in different Sanskrit texts beginning with Vedic texts to medieval and pre-modern texts. There are both direct and indirect types of references. An attempt has been made here to give a glimpse of some such references.
The Rigveda has widely referred to hiranya, which is the oldest Sanskrit word for gold. It has also mentioned products made from gold, such as water vessel, necklace and visor. Chariots decorated with gold have also been mentioned. The Rigveda (10.75.8) mentioned that the river Sindhu (Indus) contains gold. The word hiranyayi was used for the river. Another Rigveda hymn (8.26.18), states that the path of the river Sindhu contains gold, and the word used for it is hiranyavartanih. It is interesting to note that Sayana translated this word as hiranmayobhayakula, i.e., both banks containing gold. The above hymns are some of the earliest indirect references to the alluvial placer gold deposits in India. The river Sindhu was an important source of gold in ancient times. It is interesting to note that the references for the availability of alluvial placer gold in the river Sindhu are also reported in modern times. Tucci reported in 1977 that “there were near the Indus (Sindhu) source, as there are even now, great mines of gold in the region of the Mānasarovar and in Thokjalung.” Further, in the itinerary in Khotanese Saka from Gilgit to Chilas (written between 958-972 AD) the Indus is called Ysarnijittāji — the golden river, which is not a mere poetic attribute, but a reality.
Gold obtained from the river Jambu was called jambunada and that from the river Ganga was called gangeya. These were also, alluvial placer gold. The Pali text Anguttara Nikaya narrated the process of the recovery of gold dust or particles from alluvial placer gold deposits in allegorical form.
The Mahabharata referred to pipilika gold (ants’ gold). Heaps of this type of gold was presented to the king Yudhishthira at the time of the rajasuya yagna ceremony. Pipilika gold was powdery in nature and of high purity. It was obtained by panning the auriferous soil of ant hills formed by ants or termites as a part of their nature on the land containing placer gold deposits and hence the name ants’ gold. Kautilya described a variety of gold called rasaviddha, which was naturally occurring dissolved gold in liquid form. He stated that one pala (a measure) of this solution converts one hundred palas of silver or copper into gold, which refers to the cementation of gold on the surface of metals like silver and copper. A similar type of dissolved gold known as hatakaprabhasa was mentioned in Gandavyuha sutra. Kalidas also mentioned such gold solutions and termed it kanaka rasa. It is astonishing to note how people recognised such gold solutions in the past.
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Native gold is invariably by no means a pure metal. It contains up to 20 per cent silver, copper, iron, lead, bismuth, platinum group metals and other metals, as impurities. Thus native gold would have different colours depending upon the nature and amount of impurities present. It is logical to assume that the different colours of native gold were a major driving force for the development of gold refining process. Although evidence of gold refining is available in Vedic texts in an allegory form, it was the Arthashastra of Kautilya, which presented it in detail.
Gold refining was a two-stage process. The first stage was the melting of impure gold along with lead, which removed base metal impurities, but not noble metals like silver. The second stage was to heat impure gold sheets with the soil of Sindhu state, which contained salt. The sodium chloride present in the soil reacted with silver and the resulting silver chloride absorbed in the surrounding soil. This was a solid state process, which involved diffusion of silver in impure gold and the subsequent formation of silver chloride at the gold-soil interface.
It is important to note that Kautilya stated that the starting sheet of impure gold must be thin, as this would improve the kinetics of the solid state refining. Usage of gold in granular form, as was the case at least in part in the Sardis refinery of the Lydian kingdom of Anatolia, would result in lower yield.
Another important metal referred to in Rigveda is ayas. It has a shining appearance. Ayas has different meanings in different periods. In early Vedic period, it means either copper or copper alloys. One of the important products made from ayas, as stated in the Rigveda, was the weapon of Indra called vajra. It was made by the process of sinchan (casting). In the later Vedic period ayas or karshnayas means iron. In the Atharvaveda, rajata (silver), trapu (tin) and sisa (lead) have been mentioned.
Kautilya also described the method for refining silver, which was similar to the first stage process used in gold refining. Further, Kautilya stated a very interesting qualitative test for ensuring the purity of cast silver ingots. According to it, the surface of the cast pure silver ingots should exhibit an appearance of chulika, i.e., projections similar to a cock’s comb. In other words, the top surface of the pure silver ingot has a rising appearance at certain places. In fact, this is a reference to the spitting and sprouting behaviour of silver. Oxygen dissolves readily in molten silver. Molten silver dissolves approximately 20 times its own volume of oxygen near the melting point at one atmosphere pressure of oxygen. Just below the melting point, the solid silver can dissolve oxygen only up to half its own volume under similar conditions.
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The large difference in solubility of oxygen in the liquid and solid state causes the evolution of oxygen during solidification of molten silver. Bubbles of oxygen are then given off, resulting in “spitting” at the free surface. As a result, liquid silver from the interior is ejected on the surface of the ingot and a shape similar to a cock’s comb is formed on the top surface after solidification. This author carried out the experimental replication of the formation of chulika on a small size cast pure silver (see picture). If silver contains base metals such as lead and copper, then the dissolved oxygen would combine with it to form respective oxides. In such a situation, the phenomenon of spitting would not be observed and the surface would be smooth.
In this context, it is interesting to note that the law governing the solubility of gases in metals, known as Sievert’s law, came into existence only in the early 20th century. However, ancient Indians recognised the practical aspect of Sievert’s law in judging the purity of silver.
There is a rich Sanskrit terminology for metals, from which interesting information on history of metallurgy can be derived. Only a few uncommon terms would be cited. Silver has a tendency to tarnish. It tarnishes readily when exposed to atmosphere containing sulphur, and looks blackish. Due to this characteristic, an uncommon Sanskrit name of silver is durvarna. The copper produced in Nepal was called naipalika or nepalaka, and was of high purity. Tin recovered from lead-tin alloy was called nagaja, i.e., “that obtained from naga (lead)”. Similarly, tin recovered from the impure gold containing tin was called svarnaja. India was not rich in tin metal. Our ancestors were conscious of this problem and also exploited secondary sources for tin recovery. The presence of lead adversely affects the characteristics of gold and hence it was also called as hemaghna.
The Rasaratnasamuchchaya described three types of ferrous materials, viz. munda, tiksna and kanta. When iron ore pieces are reduced by charcoal in solid state, iron blocks containing porosity results. For this reason the reduced iron blocks are also called sponge iron blocks. Any useful products can only be obtained from this material after removing the residual porosity by hot forging. The hot forged sponge iron blocks are also termed as wrought iron. Munda was wrought iron. As the name suggests tiksna has superior hardness as compared to munda. Tiksna represented crucible steel made by liquid metallurgy and also probably further carburised wrought iron. Special varieties of iron were called kanta. An exciting example of wrought iron produced in ancient India is the world famous Delhi Iron Pillar. It was erected in the present position in Delhi in the 5th century AD by king Chandra Varman. However, the engraved Sanskrit inscription suggests that it was probably brought here from elsewhere in the Gupta period. The average composition (wt%) of the wrought iron of the pillar is- Fe- 0.15 C- 0.05 Si- 0.05 Mn- 0.25 P- 0.005 S- 0.05 Ni- 0.03 Cu- 0.02 N. The most significant aspect of the pillar is that there is no sign of any corrosion, in spite of the fact that it has been exposed to the atmosphere for about 1,600 years.
Another striking feature of the pillar is its manufacturing technology. It was made by successive hot forging of directly reduced sponge iron blocks produced from the solid state reduction of iron ore by charcoal, in a die. The joint lines that have not been completely removed by forging are clearly visible on the pillar. This author discussed this aspect in detail and opined that this procedure is basically very similar to current metal powder forging techniques, with a difference that the latter is not usually used to make a long product by joining pieces together (Powder Metallurgy, 1990, 33(2), 119). In both the cases, hot forging in a die is done not only to give the required shape, but also to remove the residual porosity present in the starting material.
Indian crucible steel was a celebrated material worldwide. It was usually produced by simultaneous carburisation and melting of wrought iron in closed crucibles. Valmiki referred to it by the term “refined iron”. Kautilya termed it vratta, because it was of circular shape. Dr Helenus Scott sent specimens of a variety of crucible steel, available in Mumbai area, to Sir Joseph Banks, the then president of the Royal Society, London, for experimental investigation in 1794. He referred to this steel as wootz in his letter. Recent researches by this author have revealed that the actual name of this steel was the Sanskrit utsa, which was erroneously transliterated in Roman script as wootz by Scott. James Stodart, fellow of the Royal Society, did extensive work on this steel and mastered its hot forging. Stodart was so overwhelmed with its quality that he mentioned the name utsa in Devanagari script on his trade card, along with a note that it is to be preferred over the best steel in Europe. It was named utsa because it had a characteristic of oozing out of low melting point liquid phase when heated to moderate temperatures.
Historically brass, an alloy of copper and zinc, was known to man much earlier than they were able to extract zinc from its ore on a large scale. In early period zinc was designated as sattva of zinc ore. In medieval period, it was designated as yashada in Sanskrit. Zinc oxide, known as pushpanjan, has been referred to in Charak Samhita. Rasaratnakar (second century AD) provides the earliest documentary evidence for the cementation process for brass making and reduction-distillation process for zinc extraction. Rasarnava and Rasara-tnasamuchchaya described a typical crucible, known as vrintak, having a shape similar to that of a long variety of brinjal, to be used for making the reduction-distillation chamber. The basic principle of the process resembles that of the largescale 12th century industrial process for zinc extraction uncovered at Zawar near Udaipur. It is a unique discovery and the retorts used at Zawar are similar to the vrintak crucible.
The Mahabharata and some Puranas have referred to ferrous arrowheads, which were subjected to ‘tailadhauta’ treatment. Valmiki used this terminology in the context of battle axe. Some of the commentaries of Ramayana have defined tailadhauta as the process used for hardening (of ferrous objects). Clearly, this terminology was used in the sense of oil quench-hardening of ferrous materials.
Manasollas, written in 1131 AD, gives detailed information on fine quality metal image casting by madhuchchhishta vidhan (lost wax process). Both sushira (hollow) and ghana (solid) images were cast. Although the documentary evidence is of a later period, it had been used since a very long time ago. The famous bronze dancing girl from Mohenjodaro was made by this process. Shilparatna (later part of 16th century) has mentioned the process of making fine gold powder from thin gold leaves for painting applications. The powder produced would have a flaky shape, which gives higher covering area per unit mass.
In the Indian tradition, people with expertise in technical disciplines were highly regarded. This is reflected in a hymn of Atharvaveda, in which karmar (ironsmith or metalsmith in general) has been called manishi, i.e., a wise or learned person. Further, it has been stated in the Kavyamimansa (10th century AD) that goldsmith, ironsmith and similar other people should also be invited by kings in the kavya-pariksa sabha, i.e., literary meetings organised to judge the scholarship of poets.
Metal technology, for that matter, all other technologies, are human creations shaped historically by context. The examples discussed here illustrate how ancient Indians solved metallurgical challenges, which helped in the development of Indian metallurgy and also the scientific and technological temper in the people of those times.
It is understandable that most of the metal technologies of the past are not relevant in present times. However, examples from the past can re-energise us towards encouraging local innovations and enterprise at all levels. Finally, it is clear that Vedic and classical Sanskrit texts are knowledge texts, and the study of Sanskrit has value because Sanskrit is not just a classical language, but a vehicle of discovering our knowledge inheritance and assessing its contemporary relevance.
(Prof RK Dube is former professor and head of the department of materials science and engineering at Indian Institute of Technology, Kanpur)
For Printed Version :FC Know1,FC Know2
rkd@iitk.ac.in
RELATED ARTICLES |
Although a considerable amount of information on this subject from the study of archaeological finds is available, literary evidence has not been studied to the extent it deserves. Unique information related to metals and metallurgy is available in different Sanskrit texts beginning with Vedic texts to medieval and pre-modern texts. There are both direct and indirect types of references. An attempt has been made here to give a glimpse of some such references.
The Rigveda has widely referred to hiranya, which is the oldest Sanskrit word for gold. It has also mentioned products made from gold, such as water vessel, necklace and visor. Chariots decorated with gold have also been mentioned. The Rigveda (10.75.8) mentioned that the river Sindhu (Indus) contains gold. The word hiranyayi was used for the river. Another Rigveda hymn (8.26.18), states that the path of the river Sindhu contains gold, and the word used for it is hiranyavartanih. It is interesting to note that Sayana translated this word as hiranmayobhayakula, i.e., both banks containing gold. The above hymns are some of the earliest indirect references to the alluvial placer gold deposits in India. The river Sindhu was an important source of gold in ancient times. It is interesting to note that the references for the availability of alluvial placer gold in the river Sindhu are also reported in modern times. Tucci reported in 1977 that “there were near the Indus (Sindhu) source, as there are even now, great mines of gold in the region of the Mānasarovar and in Thokjalung.” Further, in the itinerary in Khotanese Saka from Gilgit to Chilas (written between 958-972 AD) the Indus is called Ysarnijittāji — the golden river, which is not a mere poetic attribute, but a reality.
Gold obtained from the river Jambu was called jambunada and that from the river Ganga was called gangeya. These were also, alluvial placer gold. The Pali text Anguttara Nikaya narrated the process of the recovery of gold dust or particles from alluvial placer gold deposits in allegorical form.
The Mahabharata referred to pipilika gold (ants’ gold). Heaps of this type of gold was presented to the king Yudhishthira at the time of the rajasuya yagna ceremony. Pipilika gold was powdery in nature and of high purity. It was obtained by panning the auriferous soil of ant hills formed by ants or termites as a part of their nature on the land containing placer gold deposits and hence the name ants’ gold. Kautilya described a variety of gold called rasaviddha, which was naturally occurring dissolved gold in liquid form. He stated that one pala (a measure) of this solution converts one hundred palas of silver or copper into gold, which refers to the cementation of gold on the surface of metals like silver and copper. A similar type of dissolved gold known as hatakaprabhasa was mentioned in Gandavyuha sutra. Kalidas also mentioned such gold solutions and termed it kanaka rasa. It is astonishing to note how people recognised such gold solutions in the past.
Native gold is invariably by no means a pure metal. It contains up to 20 per cent silver, copper, iron, lead, bismuth, platinum group metals and other metals, as impurities. Thus native gold would have different colours depending upon the nature and amount of impurities present. It is logical to assume that the different colours of native gold were a major driving force for the development of gold refining process. Although evidence of gold refining is available in Vedic texts in an allegory form, it was the Arthashastra of Kautilya, which presented it in detail.
Gold refining was a two-stage process. The first stage was the melting of impure gold along with lead, which removed base metal impurities, but not noble metals like silver. The second stage was to heat impure gold sheets with the soil of Sindhu state, which contained salt. The sodium chloride present in the soil reacted with silver and the resulting silver chloride absorbed in the surrounding soil. This was a solid state process, which involved diffusion of silver in impure gold and the subsequent formation of silver chloride at the gold-soil interface.
It is important to note that Kautilya stated that the starting sheet of impure gold must be thin, as this would improve the kinetics of the solid state refining. Usage of gold in granular form, as was the case at least in part in the Sardis refinery of the Lydian kingdom of Anatolia, would result in lower yield.
Another important metal referred to in Rigveda is ayas. It has a shining appearance. Ayas has different meanings in different periods. In early Vedic period, it means either copper or copper alloys. One of the important products made from ayas, as stated in the Rigveda, was the weapon of Indra called vajra. It was made by the process of sinchan (casting). In the later Vedic period ayas or karshnayas means iron. In the Atharvaveda, rajata (silver), trapu (tin) and sisa (lead) have been mentioned.
Kautilya also described the method for refining silver, which was similar to the first stage process used in gold refining. Further, Kautilya stated a very interesting qualitative test for ensuring the purity of cast silver ingots. According to it, the surface of the cast pure silver ingots should exhibit an appearance of chulika, i.e., projections similar to a cock’s comb. In other words, the top surface of the pure silver ingot has a rising appearance at certain places. In fact, this is a reference to the spitting and sprouting behaviour of silver. Oxygen dissolves readily in molten silver. Molten silver dissolves approximately 20 times its own volume of oxygen near the melting point at one atmosphere pressure of oxygen. Just below the melting point, the solid silver can dissolve oxygen only up to half its own volume under similar conditions.
The large difference in solubility of oxygen in the liquid and solid state causes the evolution of oxygen during solidification of molten silver. Bubbles of oxygen are then given off, resulting in “spitting” at the free surface. As a result, liquid silver from the interior is ejected on the surface of the ingot and a shape similar to a cock’s comb is formed on the top surface after solidification. This author carried out the experimental replication of the formation of chulika on a small size cast pure silver (see picture). If silver contains base metals such as lead and copper, then the dissolved oxygen would combine with it to form respective oxides. In such a situation, the phenomenon of spitting would not be observed and the surface would be smooth.
In this context, it is interesting to note that the law governing the solubility of gases in metals, known as Sievert’s law, came into existence only in the early 20th century. However, ancient Indians recognised the practical aspect of Sievert’s law in judging the purity of silver.
There is a rich Sanskrit terminology for metals, from which interesting information on history of metallurgy can be derived. Only a few uncommon terms would be cited. Silver has a tendency to tarnish. It tarnishes readily when exposed to atmosphere containing sulphur, and looks blackish. Due to this characteristic, an uncommon Sanskrit name of silver is durvarna. The copper produced in Nepal was called naipalika or nepalaka, and was of high purity. Tin recovered from lead-tin alloy was called nagaja, i.e., “that obtained from naga (lead)”. Similarly, tin recovered from the impure gold containing tin was called svarnaja. India was not rich in tin metal. Our ancestors were conscious of this problem and also exploited secondary sources for tin recovery. The presence of lead adversely affects the characteristics of gold and hence it was also called as hemaghna.
The Rasaratnasamuchchaya described three types of ferrous materials, viz. munda, tiksna and kanta. When iron ore pieces are reduced by charcoal in solid state, iron blocks containing porosity results. For this reason the reduced iron blocks are also called sponge iron blocks. Any useful products can only be obtained from this material after removing the residual porosity by hot forging. The hot forged sponge iron blocks are also termed as wrought iron. Munda was wrought iron. As the name suggests tiksna has superior hardness as compared to munda. Tiksna represented crucible steel made by liquid metallurgy and also probably further carburised wrought iron. Special varieties of iron were called kanta. An exciting example of wrought iron produced in ancient India is the world famous Delhi Iron Pillar. It was erected in the present position in Delhi in the 5th century AD by king Chandra Varman. However, the engraved Sanskrit inscription suggests that it was probably brought here from elsewhere in the Gupta period. The average composition (wt%) of the wrought iron of the pillar is- Fe- 0.15 C- 0.05 Si- 0.05 Mn- 0.25 P- 0.005 S- 0.05 Ni- 0.03 Cu- 0.02 N. The most significant aspect of the pillar is that there is no sign of any corrosion, in spite of the fact that it has been exposed to the atmosphere for about 1,600 years.
Another striking feature of the pillar is its manufacturing technology. It was made by successive hot forging of directly reduced sponge iron blocks produced from the solid state reduction of iron ore by charcoal, in a die. The joint lines that have not been completely removed by forging are clearly visible on the pillar. This author discussed this aspect in detail and opined that this procedure is basically very similar to current metal powder forging techniques, with a difference that the latter is not usually used to make a long product by joining pieces together (Powder Metallurgy, 1990, 33(2), 119). In both the cases, hot forging in a die is done not only to give the required shape, but also to remove the residual porosity present in the starting material.
Indian crucible steel was a celebrated material worldwide. It was usually produced by simultaneous carburisation and melting of wrought iron in closed crucibles. Valmiki referred to it by the term “refined iron”. Kautilya termed it vratta, because it was of circular shape. Dr Helenus Scott sent specimens of a variety of crucible steel, available in Mumbai area, to Sir Joseph Banks, the then president of the Royal Society, London, for experimental investigation in 1794. He referred to this steel as wootz in his letter. Recent researches by this author have revealed that the actual name of this steel was the Sanskrit utsa, which was erroneously transliterated in Roman script as wootz by Scott. James Stodart, fellow of the Royal Society, did extensive work on this steel and mastered its hot forging. Stodart was so overwhelmed with its quality that he mentioned the name utsa in Devanagari script on his trade card, along with a note that it is to be preferred over the best steel in Europe. It was named utsa because it had a characteristic of oozing out of low melting point liquid phase when heated to moderate temperatures.
Historically brass, an alloy of copper and zinc, was known to man much earlier than they were able to extract zinc from its ore on a large scale. In early period zinc was designated as sattva of zinc ore. In medieval period, it was designated as yashada in Sanskrit. Zinc oxide, known as pushpanjan, has been referred to in Charak Samhita. Rasaratnakar (second century AD) provides the earliest documentary evidence for the cementation process for brass making and reduction-distillation process for zinc extraction. Rasarnava and Rasara-tnasamuchchaya described a typical crucible, known as vrintak, having a shape similar to that of a long variety of brinjal, to be used for making the reduction-distillation chamber. The basic principle of the process resembles that of the largescale 12th century industrial process for zinc extraction uncovered at Zawar near Udaipur. It is a unique discovery and the retorts used at Zawar are similar to the vrintak crucible.
The Mahabharata and some Puranas have referred to ferrous arrowheads, which were subjected to ‘tailadhauta’ treatment. Valmiki used this terminology in the context of battle axe. Some of the commentaries of Ramayana have defined tailadhauta as the process used for hardening (of ferrous objects). Clearly, this terminology was used in the sense of oil quench-hardening of ferrous materials.
Manasollas, written in 1131 AD, gives detailed information on fine quality metal image casting by madhuchchhishta vidhan (lost wax process). Both sushira (hollow) and ghana (solid) images were cast. Although the documentary evidence is of a later period, it had been used since a very long time ago. The famous bronze dancing girl from Mohenjodaro was made by this process. Shilparatna (later part of 16th century) has mentioned the process of making fine gold powder from thin gold leaves for painting applications. The powder produced would have a flaky shape, which gives higher covering area per unit mass.
In the Indian tradition, people with expertise in technical disciplines were highly regarded. This is reflected in a hymn of Atharvaveda, in which karmar (ironsmith or metalsmith in general) has been called manishi, i.e., a wise or learned person. Further, it has been stated in the Kavyamimansa (10th century AD) that goldsmith, ironsmith and similar other people should also be invited by kings in the kavya-pariksa sabha, i.e., literary meetings organised to judge the scholarship of poets.
Metal technology, for that matter, all other technologies, are human creations shaped historically by context. The examples discussed here illustrate how ancient Indians solved metallurgical challenges, which helped in the development of Indian metallurgy and also the scientific and technological temper in the people of those times.
It is understandable that most of the metal technologies of the past are not relevant in present times. However, examples from the past can re-energise us towards encouraging local innovations and enterprise at all levels. Finally, it is clear that Vedic and classical Sanskrit texts are knowledge texts, and the study of Sanskrit has value because Sanskrit is not just a classical language, but a vehicle of discovering our knowledge inheritance and assessing its contemporary relevance.
(Prof RK Dube is former professor and head of the department of materials science and engineering at Indian Institute of Technology, Kanpur)
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rkd@iitk.ac.in
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Who knows for certain?
Who shall here declare it?
Whence was it born, whence came creation?
The gods are later than this world’s formation;
Who then can know the origins of the world?
None knows
Who shall here declare it?
Whence was it born, whence came creation?
The gods are later than this world’s formation;
Who then can know the origins of the world?
None knows
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