Geometries of Nature, Living Systems And Human Cognition: New Interactions of Mathematics With Natural Sciences And Humanities

444 Pages·1988·17.52 MB·English

by  Luciano Boi

Geometr ies of Nature,
Living Systems and
Human Cognit ion
New Interactions of
Mathematics with
Natural Sciences
and Humanities
edited by
Luciano Boi
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Geometr ies of Nature,
Living Systems and
Human Cognit ion
New Interactions of
Mathematics with
Natural Sciences
and Humanities
s i •
edited by
Luciano Boi
Ecole der. Hautes Etudes en Sciences Sociales,
Contra de Machematiques, and LUTH,
Qbservatoire do Paris-Meudon, France
PP
Geomet r ies of Natu re
Living Systems and
Human Cogni t ion
New Interactions of
Mathematics with
Natural Sciences
and Humanities
\jjp World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
Published by
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
GEOMETRIES OF NATURE, LIVING SYSTEMS AND HUMAN COGNITION
New Interactions of Mathematics with Natural Sciences and Humanities
Copyright © 2005 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN 981-256-474-8
Printed in Singapore by Mainland Press
To my brother
Piergiorgio Boi,
whom I honour and still love,
and
my daughter
Vega Boi
who blossomed into
a living being
but she was never born.
To my son
Aliocha Boi,
who came to life
and since then has inspired me
in thinking and writing.
I dedicate this book to him.
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"Geometry is a magic that
works"
RENE THOM
"Topology unlocks the secrets
of the universe"
HERMANN WEYL
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Contents
Foreword xi
About the Contributors xix
PART I MATHEMATICAL IDEAS AND TECHNIQUES IN
CLASSICAL AND QUANTUM PHYSICS
1. T-Duality, Functional Equation, and Nonconunutative String
Spacetime 3
M. Lapidus {University of California at Riverside)
2. On the Soliton-Particle Dualities 93
F. Helein & J. Kouneiher {University of Paris 7)
PART II KNOTS IN MATHEMATICS AND EM NATURE
3. Knots 131
L. H. Kaujfman {University of Illinois at Chicago)
4. Topological Knots Models in Physics and Biology 203
L. Boi {EHESS - CAMS, Paris)
PART III MATHEMATICAL AND LOGICAL MODELING IN
THE NATURAL SCIENCES AND LIVING SYSTEMS
5. Beyond Modeling: A Chalenge for Aplied Mathematics 281
P. T. Saunders {King's College, University of London)
6. Fondements Cognitifs de la Geometrie et Experience de L'espace 303
A. Berthoz {College de France)
1. The Reasonable Effectiveness of Mathematics and Its
Cognitive Rots 351
G. Longo {CNRS and Ecole Normale Superieure)
8. Pathways of Deductions 383
A. Carbone {University of Paris 6 and IHES)
9. Phenomenologie et Theorie des Categories 401
F. Patras {Lab. J.A. Dieudonne, CNRS-University Nice)