Intimations of infinity: the mythopoeia of the Iqwaye counting system and number

204 Pages·1988·12.871 MB·English

by  Jadran Mimica

Intimations of Infinity
The Mythopoeia of the Iqwaye Counting System
and Number
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Explorations in Anthropology
A University College London Series
Series Editor: John Gredhill
Forthcoming
Tim Ingold, James Woodburn, David Riches (eds.), Hunters & Gatherers
Vol. I. History, Evolution and Social Change
Vol. II. Property, Power and Ideology
Jadran Mimica
Intimations of Infinity
The Mythopoeia of the Iqwaye Counting
System and Number
With an Afterword by
Roy Wagner
BERG
Oxford/New York/Hamburg
Distributed exclusively in the US and Canada by
St. Martin's Press, New York
First published in 1988 by
Berg Publishers Limited
77 Morrell Avenue, Oxford OX4 lNQ, UK
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© Jadran Mimica 1988
All rights reserved.
No part of this publication may be reproduced in any form
or by any process without the written permission of
Berg Publishers Limited
British Library Cataloguing in Publication Data
Mimica, Jadran
Intimations of infinity: the mythopoeia
of the lqwaye counting system and number.
1. Numeracy - f'.apua New Guinea
2. lqwaye (Papua New Guinean people)
I. Title
305.8'9912 DU740.42
ISBN 0----85496---145-3
Library of Congress Cataloging-in-Publication Data
Mimica, Jadran.
Intimations of infinity.
Bibliography: p.
Includes index.
1. Yagwoia (Papua New Guinea people)
2. Numeration. 3. Number concept. 4. Infinite.
I. Title. II. Title: Mythopoeia of the Iqwaye
counting system and number.
DU740.42.M56 1988 513' .5'0899912 87-22412
ISBN 0--85496-145--3
Pnnted m Great Britain by Billings of Worcester
Contents
Preface 1
A Note on Orthography 4
1. Introduction 5
1.1. The Theme 5
1.2. The People 8
2. The Counting System 13
2.1. The Cultural Context of Counting 13
2.2. Social Exchange, Value and the Perception of
Quantity 18
2.3. The Numerical Series 24
2.4. The Formal Structure of the Numerical Series 37
3. The Authentic Constitution of the Numerical Series 43
3.1. Deictic Space 43
3.2. The Basic Numerals 46
3.3. The Gestural Meanings and the Binary Structure of the
Numerical Series 48
3.4. The Dialectics of the Part-Whole Identity 53
3.5. Fingers and Substantial Relatedness in the Iqwaye
Culture 59
3.6. The Meaning-structure of Counting 69
4. The Counting System in the Light of the Iqwaye View of
the Cosmos 72
4.1. An Outline of the Iqwaye Cosmogony and Cosmic
Existence 74
4.2. The Ontological Meanings of the Iqwaye Kinship and
the Dialectics of One-Twoness 87
5. The Image of Cosmic Totality and the Primordial Senses
of Infinity 96
vi Contents
6. Iqwaye Counting, the Mathematical Infinite ~nd the
Problem of the Understanding of other Mathematical
Realities 101
6.1. The Being of Number in the Iqwaye Counting
System 102
6.2. An Outline of the Formation of the Concep't of Number
in Western Ma them a tics 105
6.3. Piaget on the Transfinites and the Concept of
Number 114
6.4. On Brouwer: Intuition, Time and History in the
Construction of Number 126
7. Number and the Existential Foundations of Anthropological
Understanding of Other Cultures 145
7.1. Hall pike on Piaget and Number: the Limitations of
Anthropological Understanding 145
7.2. Levi-Strauss, Mathematical Structures and the Savage
Other: the Existential Basis of Ethnographic
Understanding 155
Afterword: Some Comments on the Iqwaye Mathematic 162
Roy Wagner
Appendices 164
A. European Currency and the lqwaye Counting System 164
B. Basic Numerals: an Exploration 168
C. Some Observed Variations in Numerical Expressions 173
D. Clarification of the Formulations of 250 and 350 176
References 178
Index 185
Dedication
I dedicate this essay to all those countless youthful souls deprived of
the intrinsic beauty of mathematics because of the numerous primary
and high school maths teachers who hide their profound ignorance
behind the mystery of number.
vii

Acknowledgments
I am grateful to the following publishers for permission to reproduce
rather lei;1gthy passages from previously published works: Cambridge
University Press, Cambridge, for excerpts from 'Intuitionism and For
malism' by L.E.J. Brouwer and 'On the Infinite' by D. Hilbert, both
reprinted in P. Benacerraf and H. Putnam (eds.), Philosophy of Mathema
tics; Jonathan Cape, London, for excerpts from C. Levi-Strauss, Tristes
T;-opiques; Columbia University Press, New York, for excerpts from
J. Piaget, Genetic Epistemology; International Universities Press, Inc., for
excerpts from 'Bisexual Meaning of Foreskin', by B. Bird, Journal of the
American Psychoanalytic Association, 6:2, 1958; Oxford University Press,
Oxford, for excerpts from C. Hallpike, The Foundations of Primitive
Thou~ht.