Mathematics Across Cultures: The History of Non-Western Mathematics

488 Pages·2000·20.64 MB·English

by  Leigh N. Wood (auth.)

MATHEMATICS ACROSS CULTURES
SCIENCE ACROSS CULTURES:
THE HISTORY OF NON-WESTERN SCIENCE
VOLUME 2
MATHEMATICS ACROSS CULTURES
Editor:
HELAINE SELIN, Hampshire College, Amherst, Massachusetts, USA
MATHEMATICS ACROSS
CULTURES
The History of Non-Western Mathematics
Editor
HELAINE SELIN
Hampshire College, Amherst, Massachusetts, USA
Advisory Editor
UBIRATAN D'AMBROSIO
State University of Campinas /I)NICAMP, Säo Paulo, Brazil (Emeritus)
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
A catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4020-0260-1 ISBN 978-94-011-4301-1 (eBook)
DOI 10.1007/978-94-011-4301-1
Printed on acid-free paper
02-0503-150 ts
All Rights Reserved
© 2000 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 2000
Softcover reprint of the hardcover 1st edition 2000
No part of the material protected by this copyright may be reproduced
or utilized in any form or by any means, electronic, mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owners.
INTRODUCTION TO THE SERIES:
SCIENCE ACROSS CULTURES: THE HISTORY OF
NON-WESTERN SCIENCE
In 1997, Kluwer Academic Publishers published the Encyclopaedia of the
History of Science, Technology, and Medicine in Non-Western Cultures. The
encyclopedia, a collection of almost 600 articles by almost 300 contributors,
covered a range of topics from Aztec science and Chinese medicine to Tibetan
astronomy and Indian ethnobotany. For some cultures, specific individuals
could be identified, and their biographies were included. Since the study of
non-Western science is not just a study of facts, but a study of culture and
philosophy, we included essays on subjects such as Colonialism and Science,
Magic and Science, the Transmission of Knowledge from East to West,
Technology and Culture, Science as a Western Phenomenon, Values and
Science, and Rationality, Objectivity, and Method.
Because the encyclopedia was received with critical acclaim, and because the
nature of an encyclopedia is such that articles must be concise and compact,
the editors at Kluwer and I felt that there was a need to expand on its success.
We thought that the breadth of the encyclopedia could be complemented by a
series of books that explored the topics in greater depth. We had an opportunity,
without such space limitations, to include more illustrations and much longer
bibliographies. We shifted the focus from the general educated audience that
the encyclopedia targeted to a more scholarly one, although we have been
careful to keep the articles readable and keep jargon to a minimum.
Before we can talk about the field of non-Western science, we have to define
both non-Western and science. The term non-Western is not a geographical
designation; it is a cultural one. We use it to describe people outside of the
Euro-American sphere, including the native cultures of the Americas. The
power of European and American colonialism is evident in the fact that the
majority of the world's population is defined by what they are not. And in fact,
for most of our recorded history the flow of knowledge, art, and power went
the other way. In this series, we hope to rectify the lack of scholarly attention
paid to most of the world's science.
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VI INTRODUCTION TO THE SERIES
As for defining science, if we wish to study science in non-Western cultures,
we need to take several intellectual steps. First, we must accept that every
culture has a science, that is, a way of defining, controlling, and predicting
events in the natural world. Then we must accept that every science is legitimate
in terms of the culture from which it grew. The transformation of the word
science as a distinct rationality valued above magic is uniquely European. It
is not common to most non-Western societies, where magic and science and
religion can easily co-exist. The empirical, scientific realm of understanding
and inquiry is not readily separable from a more abstract, religious realm.
The first two books in the series are Astronomy Across Cultures: the History
of Non-Western Astronomy, and Mathematics Across Cultures: the History of
Non-Western Mathematics. Each includes about 20 chapters. Most deal with
the topic as it is perceived by different cultures: Australian Aboriginal
Astronomy, Native American Mathematics, etc. Each book also contains a
variety of essays on related subjects, such as Astronomy and Prehistory, or
East and West. The next four in the series will cover Medicine, Nature and the
Environment, Chemistry and Alchemy, and Physics and Optics.
We hope the series will be used to provide bqth factual information about
the practices and practitioners of the sciences as well as insights into the world
views and philosophies of the cultures that produced them. We hope that
readers will achieve a new respect for the accomplishments of ancient civiliza
tions and a deeper understanding of the relationship between science and
culture.
TABLE OF CONTENTS
Acknowledgments ix
About the Contributors Xl
Introduction xvii
Communicating Mathematics across Culture and Time
Leigh N. Wood 1
Anthropological Perspectives on Ethnomathematics
Ron Eglash 13
East and West
Edwin J. Van Kley 23
Rationality and the Disunity of the Sciences
David Turnbull 37
Logics and Mathematics: Challenges Arising in Working
across Cultures
Helen Verran 55
A Historiographical Proposal for Non-Western Mathematics
Ubiratan D'Ambrosio 79
The Uses of Mathematics in Ancient Iraq, 6000-600 BC
Eleanor Robson 93
Egyptian Mathematics
James Ritter 115
Islamic Mathematics
Jacques Sesiano 137
The Hebrew Mathematical Tradition
Y. Tzvi Langermann and Shai Simonson 167
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viii TABLE OF CONTENTS
Inca Mathematics
Thomas E. Gilsdorf 189
Mesoamerican Mathematics
Michael P. Closs 205
The Ethnomathematics of the Sioux Tipi and Cone
Daniel Clark Orey 239
Traditional Mathematics in Pacific Cultures
Walter S. Sizer 253
Aboriginal Australian Mathematics: Disparate Mathematics of
Land Ownership
Helen Verran 289
On Mathematical Ideas in Cultural Traditions of Central and
Southern Africa
Paulus Gerdes 313
Accounting Mathematics in West Africa: Some Stories of
Yoruba Number
Helen Verran 345
Chinese Mathematical Astronomy
Jean-Claude Martzlojf 373
The Mathematical Accomplishments of Ancient Indian
Mathematicians
T. K. Puttaswamy 409
The Dawn of Wasan (Japanese Mathematics)
Jochi Shigeru 423
Development of Materials for Ethnomathematics in Korea
Kim, Soo Hwan 455
Index 467
ACKNOWLEDGMENTS
I would like to thank Maja de Keijzer and her staff at Kluwer Academic
Publishers. I never believe that Kluwer is a large company, because of all the
individual attention the staff gives me. I would also like to thank my colleagues
at Hampshire College; I am so fortunate to be able to work with them. Special
thanks go to Aaron Berman, Brian Schultz, and Gai Carpenter for recognizing
the value of my work and giving me time to do it. And mostly I offer innumer
able, unquantifiable thanks to Bob and Lisa and Tim.
IX
ABOUT THE CONTRIBUTORS
HELAINE SELIN (Editor) is the editor of the Encyclopaedia of the History of
Science, Technology, and Medicine in Non-Western Cultures (Kluwer Academic
Publishers, 1997) and Science Librarian and FacuIty Associate at Hampshire
College in Amherst, Massachusetts. In addition to editing the new series,
Science Across Cultures, she has been teaching a course on the Science and
History of Alternative and Complementary Medicine.
UBIRATAN D'AMBROSIO (Advisory Editor; A Historiographical Proposal
for Non-Western Mathematics) is Emeritus Professor of Mathematics at the
State University of Campinas/UNICAMP in Sao Paulo, Brazil. He is President
of the Brazilian Society of History of Mathematics/SBHMat, President of the
International Study Group on Ethnomathematics/ISGEm, and President of
the Institute for Future Studies/I.E.F. He is also a Visiting Professor and
graduate advisor at several universities. He was the Director of the Institute
of Mathematics, Statistics and Computer Science of UNICAMP, Brazil from
1972-80, Chief of the Unit of Curriculum of the Organization of American
States, Washington DC (1980-82), and Pro-Rector [Vice-President] for
University Development, of UNICAMP, Brazil from 1982-90. His most recent
publications include Ethnomathematics. The Art or Technique of Explaining and
Knowing and History of Mathematics in the Periphery: The Basin Metaphor
(Berlin: Max-Planck-Institute fUr Wissenschaftsgeschichte, 1999).
MICHAEL CLOSS (Mesoamerican Mathematics) is a Professor in the
Department of Mathematics and Statistics at the University of Ottawa, Ottawa,
Canada. He is editor of the volume, Native American Mathematics (University
of Texas Press, 1986, 1996). In addition to his work on mathematical develop
ment in different Native American cultures, he has written many research
articles on the mathematics, chronology, astronomy and hieroglyphic writing
of the ancient Maya.
RON EGLASH (Anthropological Perspectives on Ethnomathematics) holds
a B.S. in Cybernetics and a M.S. in Systems Engineering, both from the
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