Research Into Indic Mathematicians

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I should do a complete review of Kim Plofkers book . It is not a bad book, and she does use the adjective brilliant towards the end of the book. but i sill have reservations about the manner in which she approaches the subject.I will give an excerpt from my book,which is relatively mild in its criticism of Plofkers ( in contrast to her guru David Pingree, who does not fare well in my book)



Plofker , p. 293 Quote: "It is not unusual to encounter in discussions of Indian mathematics such assertions as that “the concept of differentiation was understood [in India] from the time of Manjula (... in the 10th century)” [Joseph 1991, 300], or that “we may consider Mādhava to have been the founder of mathematical analysis” (Joseph 1991, 293), or that Bhāskara II may claim to be “the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus” (Bag 1979, 294). ... The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)). ... It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit (or Malayalam) and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian “discovery of the principle of the differential calculus” somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. The differential “principle” was not generalized to arbitrary functions—in fact, the explicit notion of an arbitrary function, not to mention that of its derivative or an algorithm for taking the derivative, is irrelevant here".

But Plofker’s objections to assigning credit to the Indians cannot be taken seriously , since most science is developed by observing specific instances and then in the course of time it is possible to see a pattern which permits the generalization to a broader principle , so when she says that application of a derivative to a trigonometric functions does not make a calculus, she is being disingenuous, because Indic mathematicians were already applying analysis to a large class of functions. It must be conceded that Europe steadily drew ahead after 1700, but the reasons for that have little to do with the work that Indic mathematicians did in the past.



I am appending excerpts from the Preface to the book





This is the title of the book which is Volume 5 of the Series on Distortions in Indian History. The book is being released with immediate effect for public consumption. The book deals with the effects of Colonialism and Eurocentricity. Colonialism is not merely the conquest of dominion of vast lands and exerting your will on millions of people. It is more than the act of unleashing violence, a violence not restricted to the physical realm. It subjects the colonized to an epistemic rupture of vast proportions. This is the narrative of one example of such an epistemic rupture. We tell the story ( and the history ) of such a rupture in the case of Astronomy and Mathematics in the Indian suibcontiennt



(PRWEB) September 12, 2010 -- This book is the narrative of one example of an epistemic rupture, of the theft and destruction of i the cultural heritage. We tell the story ( and the history ) of such a rupture in the case of Astronomy and Mathematics. Indic Studies Foundation is pleased to announce the release of Volume 5 of the Series on Distortions in Indian History. The book is available at http://www.lulu.com/product/hardcover/th...f/center/4



The main reason for writing this book is that the real story of the Indic contribution to Astronomy has yet to be told in the text books of the west. Few books(1,2) give a coherent account of the Indic odyssey as it unfolds from the mists of antiquity to the pioneering work of Astrophysicist Chandrasekhar on the nature of the universe. If they do mention it at all, it is merely to say that they borrowed everything from Greece or Babylon. When challenged, the mathematician in the west will quote one of the 3 or 4 Occidental historians of Mathematics (e.g. Toomer, Van der Waerden or David Pingree) as their authoritative source. Rarely will they mention a Primary source in Sanskrit, because they are not familiar with the literature in Sanskrit and they do not trust the Indics to tell the true story. They prefer to get the story from an Occidental who may not have read a single book in its Sanskrit original rather than get it from an Indic. The net result is a book filled with clichés where the content is already degraded from multiple levels of interpretation and inadvertent filtering of the original source.



Part of the reason for writing this book is to influence all the readers, regardless of their ethnicity, ideology, or geography to adopt a more global perspective on matters relating to History and philosophy of the sciences. Under such a perspective, few would feel compelled to defend or attack a viewpoint if the extent of the antiquity was the sole issue at stake. But the yearning for a competitive antiquity is not restricted to those of a particular ethnicity. It appears to be a predominant factor when a more aggressive and authoritarian civilization subjugates a people with a more advanced episteme. Time and again , this pattern of behavior has been the norm, where the aggressor has adopted the Epistemes of the subjugated people, after devoting a massive effort to absorb the knowledge, and once he is fairly confident that he has been successful in this endeavor, he will turn around and assert precisely the opposite, that in fact it is the subjugated civilization that has borrowed the episteme and the resulting knowledge.



Keep in mind that antiquity affects many factors that have a bearing on the sense of uniqueness that a people have of themselves and a sense that continuity and longevity of a civilization bestows a modicum of a sense of wellbeing. A loss of epistemic continuity that is now being experienced in the Indian subcontinent has long term consequences for the manner in which the Indics will look upon themselves. Civilization is a fragile thing, if I may paraphrase Will Durant, the great historian who compiled the monumental Story of Civilization over a thirty year period, and it does not take much to obliterate a civilization.



The Indic approach to astronomy, contrary to presuppositions in the occident was characterized by mundane motivations namely the need to determine accurately the date, time and place of the location of the main planetary bodies that he could see with the naked eye; the Sun, Moon, Venus, Mercury, Jupiter and Saturn in relation to the Earth. As we shall repeat on more than one occasion, in this endeavor he was eminently practical. Again, his motivation for the determination of these quantities was also driven by pragmatic considerations like a need for fixing the seasons when planting was necessary. He may have found it politic to cloak these mundane considerations in ritualistic garb in order to impress those in society not blessed with the analytical skills that he may have used. In summary the goal of the Ancient Indic Prayojana or raison-de-être of the stra was primarily the determination of Kalá (Time), Dik (direction or orientation), and Desha (Place)



The story of the calendar and the development of mathematics and astronomy is indeed a fascinating chapter in the intellectual history of the species. It is laced with people of superior talents, but all too often these very same gifted individuals were not able to rise above petty considerations, while they were uncovering the secrets of the skies.



It is unfortunate that the Indic role in this fascinating chapter has been largely ignored in most western descriptions of the history of astronomy and time. There hardly exists a history book in Astronomy that does justice to the fact that the ancient Indic left behind a staggering amount of literature for us to decipher. In fact the perception is just the opposite that Information about Indian math is hard to get. This is in large part a problem that the occidental has created by imposing very high standards of reliability, in many cases standards that are impossible to meet and certainly were never demanded of similar sources from Ancient Greece. As a result the bias against Indic contributions in antiquity has been institutionalized to a large degree. This is regrettable and as a result, the story within a story of how the occidental tried to ignore, minimize and even suppress the Indic contribution is equally interesting.



This book is not about the glories of a bygone era, where one bemoans the ephemeral nature of an enlightened past. It is a recounting of the irreversible nature of the changes that take place when a civilization is subjugated. Its traditions are ridiculed. Its history is rewritten, its language is driven into oblivion and any attempt to combat this assault albeit in a non-violent and scholarly manner, marks the individual as a fundamentalist. The calendar, astronomy, and the story of time combine to make a fascinating chapter in the story of the homo sapien, but it is to be hoped tha it is the larger Civilizational canvas that the reader will focus on.



What do I take away from the writing of this book? My faith in the universality of the human spirit. If there is one thing above all that I treasure from this experience is that the love of science and mathematics does not recognize man made geographies, boundaries, ethnic classifications, language, social strata or economics. It is for this reason I find that the current Eurocentrric emphasis in the Occident which persists among authors even to this day to be a anathema and to be of a particularly egregious nature with which I have little sympathy and have no tolerance whatsoever. The book can be ordered from www.lulu.com. References



1.See for instance, James Evans, The history and practice of Ancient Astronomy, Oxford University press, New York,1998 2.Hoskin, Michael, "The Cambridge Concise History of Astronomy”, Ed. By, Cambridge University Press, Cambridge, UK. 1999



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