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PRESERVESANSKRIT TO PRESERVE ANCIENT INDIAN KNOWLEDGE SYSTEMS
Howeverafter Manjul Bhargava won the Field Medal, there were a large numberof articles & debates in the Indian media asking why we don’tproduce more of such mathematicians. Well the answer is one word:Secularism.
Whenmany so-called intellectuals in the media decide to oppose thecelebration of “Sanskrit Week in Schools by Central Board ofSecondary Education”, rest assured that there is lot more behindthe obvious. Opposingteaching of Sanskrit helps to stop the progress of Indians and India. Some of you will ask how teaching Sanskrit will lead tolearning.
Inan interview to IndiaToday,Professor Manjul Bhargava said, “Growing up, I had a chance to readsome of the works of the great masters: linguists/poets such asPanini, Pingala, and Hemachandra, as well as the great mathematiciansAryabhata, Bhaskara, and of course Brahmagupta. Their workscontain incredible discoveries in mathematics, and were veryinspirational to me. The classic works of Pingala, Hemachandra, andBrahmagupta have been particularly influential in my own work.”(http://indiatoday.intoday.in/story/fields-medal-winner-manjul-bhargava-interview-3-ancient-indian-mathematicians-his-inspiration/1/377773.html)
Ancientand medieval Indian mathematical works, all composed in Sanskrit,usually consisted of a section of sutras in which a set of rules orproblems were stated with great economy in verse in order to aidmemorization by a student. This was followed by a second sectionconsisting of a prose commentary (sometimes multiple commentaries bydifferent scholars) that gave a detailed explanation of the problemalong with providing justification for the solution. In the prosesection, the form (and therefore its memorization) was not consideredso important in comparison to the ideas involved.
BhāskaraII‘streatise on mathematics,written in 1150, known as Lilavati includesa number of methods of computing numbers such as multiplications,squares, and progressions, with examples using kings and elephants,objects which a common man could understand. Here is an example:
Therule for the problem illustrated here is in verse 151,while the problem itself is in verse 152:
151: The Square of the pillar is divided by the distance between the snakeand its hole; the result is subtracted from the distance between thesnake and its hole. The place of meeting of the snake and thepeacock is separated from the hole by a number of hastas equalto half that difference.
152: There is a hole at the foot of a pillar nine hastas high,and a pet peacock standing on top of it. Seeing a snakereturning to the hole at a distance from the pillar equal to threetimes its height, the peacock descends upon it slantwise. Sayquickly, at how many hastas from the hole does the meeting oftheir two paths occur? (It is assumed here that the speed of thepeacock and the snake are equal.)
Mostof us can agree that the kids will find it more interesting to readand solve the puzzle of the snake and peacock.
Nowevery child does not have the option of getting introduced to theworks of the great mathematicians of ancient India. So opposing theteaching of Sanskrit not only deprives Indians of the knowledge oftheir forefathers but also helps to divide the society in haves andhave-nots in terms of language, knowledge and access to the same.Sadly the opposition to study Indian knowledge and knowledge systemsis quite old.
1. “Thegreatest of Greek mathematicians, Archimedes (287-212 B.C.) madeeffective use of indivisibles in geometry, but considered the idea ofinfinity as without logical foundation. Likewise, Aristotle arguedthat, since a body must have form, it must be bounded, and thereforecannot be infinite. While accepting that there were two kinds of“potential” infinities—successive addition in arithmetic(infinitely large), and successive subdivision in geometry(infinitely small)—he nevertheless polemicised against geometerswho held that a line segment is infinitely composed of many fixedinfinitesimals, or indivisibles. This denial of the infiniteconstituted a real barrier to the development of classical Greekmathematics. By contrast, the Indian mathematicians had no suchscruples and made great advances, which, via the Arabs, later enteredEurope.” (Does Mathematics Reflect Reality?, Part Four: Order OutofChaos, http://www.marxist.com/science-old/mathematicsreflectreality.html)
2.“Historians of science agree that Newton’s Latin was oftenunclear. All the formulas that are referred to as ‘Newton’sequations’ were introduced later by Euler, Daniel Bernouilli andother mathematicians. C. Truesdell wrote in 1968: ‘It is true thatwe, today, can easily read them into Newton’s words, but we do soby hindsight.’ David Park added in 1988: ‘It took a centurybefore Newton’s work was made fully intelligible and others coulddo science without being a genius.’ Formulas could trigger ascientific revolution because they were easy to understand and soonbecame intelligible to large numbers of people all over the world.But that simple hypothesis seems to have drowned in a flood ofhistorical, economical, sociological, and political explanations thatrarely touch the heart of science, which is knowledge. India providesa telling contrast: infinite power series and the trigonometricfunctions of sine, cosine, and so forth were discovered by Madhava inthe late fourteenth century, almost three centuries before they werediscovered in Europe by Gregory, Newton, and Leibniz. In Europe,infinite series were a powerful ingredient of the scientificrevolution. Indian mathematics was equally strong in this respect andstrong enough in any case to have similar consequences. But it wasformulated in a complex form of Sanskrit, more obscure than Newton’sLatin, and so nothing happened. (Artificial Languages: AsianBackgrounds or Influences? in IIAS News letter | #30 | March 2000)
Basedon such facts,it will be correct to say that in India there can be noBhargava without Sanskrit.
(SandeepSingh, writes a weekly column on “Narendra modi & CXOLeadership” onwww.swastik.net.in )
Article Title
Preserve Sanskrit to preserve ancient Indian knowledge systems
Author
Sandeep Singh
Description
Sandeep Singh explains why Sanskrit is important to boost the knowledge of Indians.
Mathematicsand mathematical thinking have been an important aspect of Indianculture for a long time. From ancient philosophical verses like“Poornasya poornamaadaaya poornamevaavashishyate” (Infinity minusinfinity can still be infinity) that reflect mathematical thinking,to the inherently mathematical structure of the alphabets andphonetics of Indian languages, to the discovery of zero and negativenumbers, trigonometry, calculus, and more – so much mathematics hasbeen discovered for ages in a way that is deeply intertwined inIndian culture.
– ManjulBhargava, The Economic Times, 18 August 2014
PrincetonUniversity Professor Manjul Bhargava, is the first mathematician ofIndian-origin to win the Fields Medal, the highest badge of honour inmathematics. Despite having grown up in Canada and the US he iswell-versed in Hindi and Sanskrit and is very attached to his Indianroots. This makes him a suitable candidate to be branded as communal.Bhargava is not the only communal mathematician that India hasproduced. There was Ramanujan who saw his solutions in a dream whenthe Goddess Nammakkal rolled out her tongue.Howeverafter Manjul Bhargava won the Field Medal, there were a large numberof articles & debates in the Indian media asking why we don’tproduce more of such mathematicians. Well the answer is one word:Secularism.
Whenmany so-called intellectuals in the media decide to oppose thecelebration of “Sanskrit Week in Schools by Central Board ofSecondary Education”, rest assured that there is lot more behindthe obvious. Opposingteaching of Sanskrit helps to stop the progress of Indians and India. Some of you will ask how teaching Sanskrit will lead tolearning.
Inan interview to IndiaToday,Professor Manjul Bhargava said, “Growing up, I had a chance to readsome of the works of the great masters: linguists/poets such asPanini, Pingala, and Hemachandra, as well as the great mathematiciansAryabhata, Bhaskara, and of course Brahmagupta. Their workscontain incredible discoveries in mathematics, and were veryinspirational to me. The classic works of Pingala, Hemachandra, andBrahmagupta have been particularly influential in my own work.”(http://indiatoday.intoday.in/story/fields-medal-winner-manjul-bhargava-interview-3-ancient-indian-mathematicians-his-inspiration/1/377773.html)
Ancientand medieval Indian mathematical works, all composed in Sanskrit,usually consisted of a section of sutras in which a set of rules orproblems were stated with great economy in verse in order to aidmemorization by a student. This was followed by a second sectionconsisting of a prose commentary (sometimes multiple commentaries bydifferent scholars) that gave a detailed explanation of the problemalong with providing justification for the solution. In the prosesection, the form (and therefore its memorization) was not consideredso important in comparison to the ideas involved.
BhāskaraII‘streatise on mathematics,written in 1150, known as Lilavati includesa number of methods of computing numbers such as multiplications,squares, and progressions, with examples using kings and elephants,objects which a common man could understand. Here is an example:
Therule for the problem illustrated here is in verse 151,while the problem itself is in verse 152:
151: The Square of the pillar is divided by the distance between the snakeand its hole; the result is subtracted from the distance between thesnake and its hole. The place of meeting of the snake and thepeacock is separated from the hole by a number of hastas equalto half that difference.
152: There is a hole at the foot of a pillar nine hastas high,and a pet peacock standing on top of it. Seeing a snakereturning to the hole at a distance from the pillar equal to threetimes its height, the peacock descends upon it slantwise. Sayquickly, at how many hastas from the hole does the meeting oftheir two paths occur? (It is assumed here that the speed of thepeacock and the snake are equal.)
Mostof us can agree that the kids will find it more interesting to readand solve the puzzle of the snake and peacock.
Nowevery child does not have the option of getting introduced to theworks of the great mathematicians of ancient India. So opposing theteaching of Sanskrit not only deprives Indians of the knowledge oftheir forefathers but also helps to divide the society in haves andhave-nots in terms of language, knowledge and access to the same.Sadly the opposition to study Indian knowledge and knowledge systemsis quite old.
“Ramchandraspent the decade prior to the 1850s in attempting to introducecalculus to Indian students, and in the process confronted seriouspedagogic problems related to ethno-mathematics. Ramchandra, schooledin the algorithmic tradition of the schools of mathematics in Indiawas equally at home with the mathematics ploddingly inscribed inBritish school curricula. He wrote a treatise in English, in thetradition of the textbooks of nineteenth century mathematics.However, the Treatise contained a new method and was to be a subjectof much criticism rather than discussion on its novelty. Augustus DeMorgan, then Professor at University of London, was the first arrivedmathematician to see a copy of Ramchandra’ work-and till hereceived it, Ramchandra was the butt of ridicule by his countrymen,an exotic specimen for colonial administrators. De Morgan’s owninterest in the work of Ramchandra arose from the fact that he wasclosely associated with the formulation of curricula for mathematicsteaching in Britain; which involved devising methods for instructingBritish school students in elementary notions of complex algebra andthe new discipline of calculus. Ramchandra’s teaching could, hefelt, prove useful in the latter project in Britain. The book, DeMorgan felt, could be introduced in British schools, though it waswritten for very different purposes viz. that of instructing studentsin India brought up on the theory of equations as encountered in theBija-Ganita of Bhaskaracharya, into a relatively new branch ofmathematics.” (The Structure of Scientific Exchanges in the Age ofColonialism by Dhruv Raina and S. Irfan Habib.)
Theproblem of converting ancient to modern is not a problem faced byIndia alone. Even Europe faced the same issues. But they came out ofit successfully because they didn’t have secularists in the form ofmedia and intellectuals. A contrast in Europe and India is givenbelow:1. “Thegreatest of Greek mathematicians, Archimedes (287-212 B.C.) madeeffective use of indivisibles in geometry, but considered the idea ofinfinity as without logical foundation. Likewise, Aristotle arguedthat, since a body must have form, it must be bounded, and thereforecannot be infinite. While accepting that there were two kinds of“potential” infinities—successive addition in arithmetic(infinitely large), and successive subdivision in geometry(infinitely small)—he nevertheless polemicised against geometerswho held that a line segment is infinitely composed of many fixedinfinitesimals, or indivisibles. This denial of the infiniteconstituted a real barrier to the development of classical Greekmathematics. By contrast, the Indian mathematicians had no suchscruples and made great advances, which, via the Arabs, later enteredEurope.” (Does Mathematics Reflect Reality?, Part Four: Order OutofChaos, http://www.marxist.com/science-old/mathematicsreflectreality.html)
2.“Historians of science agree that Newton’s Latin was oftenunclear. All the formulas that are referred to as ‘Newton’sequations’ were introduced later by Euler, Daniel Bernouilli andother mathematicians. C. Truesdell wrote in 1968: ‘It is true thatwe, today, can easily read them into Newton’s words, but we do soby hindsight.’ David Park added in 1988: ‘It took a centurybefore Newton’s work was made fully intelligible and others coulddo science without being a genius.’ Formulas could trigger ascientific revolution because they were easy to understand and soonbecame intelligible to large numbers of people all over the world.But that simple hypothesis seems to have drowned in a flood ofhistorical, economical, sociological, and political explanations thatrarely touch the heart of science, which is knowledge. India providesa telling contrast: infinite power series and the trigonometricfunctions of sine, cosine, and so forth were discovered by Madhava inthe late fourteenth century, almost three centuries before they werediscovered in Europe by Gregory, Newton, and Leibniz. In Europe,infinite series were a powerful ingredient of the scientificrevolution. Indian mathematics was equally strong in this respect andstrong enough in any case to have similar consequences. But it wasformulated in a complex form of Sanskrit, more obscure than Newton’sLatin, and so nothing happened. (Artificial Languages: AsianBackgrounds or Influences? in IIAS News letter | #30 | March 2000)
Basedon such facts,it will be correct to say that in India there can be noBhargava without Sanskrit.
(SandeepSingh, writes a weekly column on “Narendra modi & CXOLeadership” onwww.swastik.net.in )
Article Title
Preserve Sanskrit to preserve ancient Indian knowledge systems
Author
Sandeep Singh
Description
Sandeep Singh explains why Sanskrit is important to boost the knowledge of Indians.