The Crest of the Peacock: Non-European Roots of Mathematics - Third Edition - Softcover

Joseph, George Gheverghese

Softcover

ISBN 10: 0691135266 ISBN 13: 9780691135267

Verlag: Princeton Univers. Press, 2010

Inhaltsangabe

From the Ishango Bone of central Africa and the Inca quipu of South America to the dawn of modern mathematics, The Crest of the Peacock makes it clear that human beings everywhere have been capable of advanced and innovative mathematical thinking. George Gheverghese Joseph takes us on a breathtaking multicultural tour of the roots and shoots of non-European mathematics. He shows us the deep influence that the Egyptians and Babylonians had on the Greeks, the Arabs' major creative contributions, and the astounding range of successes of the great civilizations of India and China. The third edition emphasizes the dialogue between civilizations, and further explores how mathematical ideas were transmitted from East to West. The book's scope is now even wider, incorporating recent findings on the history of mathematics in China, India, and early Islamic civilizations as well as Egypt and Mesopotamia. With more detailed coverage of proto-mathematics and the origins of trigonometry and infinity in the East, The Crest of the Peacock further illuminates the global history of mathematics.

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Über die Autorin bzw. den Autor

George Gheverghese Joseph was born in Kerala, India, grew up in Mombasa, Kenya, and completed his degrees in England. He has worked in various occupations that have taken him to places all over the world, including East and Central Africa, India, Papua New Guinea, and South East Asia.

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The Crest of the Peacock

Non-European Roots of Mathematics By George Gheverghese Joseph

Princeton University Press

Copyright © 2011 Princeton University Press
All right reserved.
ISBN: 978-0-691-13526-7

Contents

Preface to the Third Edition................................................................xiPreface to the First Edition................................................................xxiiiChapter One The History of Mathematics: Alternative Perspectives...........................1Chapter Two Mathematics from Bones, Strings, and Standing Stones...........................30Chapter Three The Beginnings of Written Mathematics: Egypt.................................79Chapter Four The Beginnings of Written Mathematics: Mesopotamia............................125Chapter Five Egyptian and Mesopotamian Mathematics: An Assessment..........................177Chapter Six Ancient Chinese Mathematics....................................................188Chapter Seven Special Topics in Chinese Mathematics........................................246Chapter Eight Ancient Indian Mathematics...................................................311Chapter Nine Indian Mathematics: The Classical Period and After............................372Chapter Ten A Passage to Infinity: The Kerala Episode......................................418Chapter Eleven Prelude to Modern Mathematics: The Islamic Contribution.....................450References..................................................................................521Name Index..................................................................................543Subject Index...............................................................................549

Chapter One

The History of Mathematics: Alternative Perspectives

A Justification for This Book

An interest in history marks us for life. How we see ourselves and others is shaped by the history we absorb, not only in the classroom but also from the Internet, films, newspapers, television programs, novels, and even strip cartoons. From the time we first become aware of the past, it can fire our imagination and excite our curiosity: we ask questions and then seek answers from history. As our knowledge develops, differences in historical perspectives emerge. And, to the extent that different views of the past affect our perception of ourselves and of the outside world, history becomes an important point of reference in understanding the clash of cultures and of ideas. Not surprisingly, rulers throughout history have recognized that to control the past is to master the present and thereby consolidate their power.

During the last four hundred years, Europe and its cultural dependencies have played a dominant role in world affairs. This is all too often reflected in the character of some of the historical writing produced by Europeans in the past. Where other people appear, they do so in a transitory fashion whenever Europe has chanced in their direction. Thus the history of the Africans or the indigenous peoples of the Americas often appears to begin only after their encounter with Europe.

An important aspect of this Eurocentric approach to history is the manner in which the history and potentialities of non-European societies were represented, particularly with respect to their creation and development of science and technology. The progress of Europe during the last four hundred years is often inextricably—or even causally—linked with the rapid growth of science and technology during the period. In the minds of some, scientific progress becomes a uniquely European phenomenon, which can be emulated by other nations only if they follow a specifically European path of scientific and social development.

Such a representation of societies outside the European cultural milieu raises a number of issues that are worth exploring, however briefly. First, these societies, many of them still in the grip of an intellectual dependence that is the legacy of European political domination, should ask themselves some questions. Was their indigenous scientific and technological base innovative and self-sufficient during their precolonial period? Case studies of India, China, and parts of Africa, contained, for example, in the work of Dharampal (1971), Needham (1954), and Van Sertima (1983) and summarized by Teresi (2002), seem to indicate the existence of scientific creativity and technological achievements long before the incursions of Europe into these areas. If this is so, we need to understand the dynamics of precolonial science and technology in these and other societies and to identify the material conditions that gave rise to these developments. This is essential if we are to see why modern science did not develop in these societies, only in Europe, and to find meaningful ways of adapting to present-day requirements the indigenous and technological forms that still remain.

Second, there is the wider issue of who "makes" science and technology. In a material and nonelitist sense, each society, impelled by the pressures and demands of its environment, has found it necessary to create a scientific base to cater to its material requirements. Perceptions of what constitute the particular requirements of a society would vary according to time and place, but it would be wrong to argue that the capacity to "make" science and technology is a prerogative of one culture alone.

Third, if one attributes all significant historical developments in science and technology to Europe, then the rest of the world can impinge only marginally, either as an unchanging residual experience to be contrasted with the dynamism and creativity of Europe, or as a rationale for the creation of academic disciplines congealed in subjects such as development studies, anthropology, and oriental studies. These subjects in turn served as the basis from which more elaborate Eurocentric theories of social development and history were developed and tested.

One of the more heartening aspects of academic research in the last four or five decades is that the shaky foundations of these "adjunct" disciplines are being increasingly exposed by scholars, a number of whom originate from countries that provide the subject matter of these disciplines. "Subversive" analyses aimed at nothing less than the unpackaging of prevailing Eurocentric paradigms became the major preoccupation of many of these scholars. Syed Husain Alatas (1976) studied intellectual dependence and imitative thinking among social scientists in developing countries. The growing movement toward promoting a form of indigenous anthropology that sees its primary task as questioning, redefining, and if necessary rejecting particular concepts that grew out of colonial experience in Western anthropology is thoroughly examined by Fahim (1982). Edward Said (1978) has brilliantly described the motives and methods of the so-called orientalists who set out to construct a fictitious entity called "the Orient" and then ascribe to it qualities that are a mixture of the exotic, the mysterious, and the otherworldly. The rationale for such constructs is being examined in terms of the recent history of Europe's relations with the rest of the world.

In a similar vein, and in the earlier editions of this book, it was the intention to show that the standard treatment of the history of non-European mathematics exhibited a deep-rooted historiographical bias in the selection and interpretation of facts, and that mathematical activity outside Europe has as a consequence been...

Details zur Ausgabe

• Verlag: Princeton Univers. Press
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 0691135266
• ISBN 13: 9780691135267
• Einband: Taschenbuch
• Auflage: 3
• Anzahl der Seiten: 592
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: GPSR Kontakt; gpsr@libri.de; ; Europaallee 1; Bad Hersfeld; 36244; Deutschland