Symmetry And Complexity: The Spirit And Beauty Of Nonlinear Science

SYMMETRYANDCOMPLEXITY THESPIRITANDBEAUTYOFNONLINEARSCIENCE This page intentionally left blank WORLD SCIENTIFIC SERIES ON NONLINEAR SCIENCE Series A Vol. 51 Series Editor: Leon O. Chua SYMMETRY AND COMPLEXITY THE SPIRIT AND BEAUTY OF NONLINEAR SCIENCE Klaus Mainzer University of Augsburg, Germany We World Scientific NEW JERSEY · LONDON · SINGAPORE · BEIJING · SHANGHAI · HONG KONG · TAIPEI · BANGALORE Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. SYMMETRY AND COMPLEXITY The Spirit and Beauty of Nonlinear Science 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 981-256-192-7 Printed in Singapore. Preface Symmetry and complexity determine the spirit of nonlinear science. The expansion of the universe, the evolution of life and the globalization of human economies and societies lead from symmetry and simplicity to complexity and diversity. The emergence of new order and structure means symmetry breaking and transition from unstable to stable states of balance. It is explained by physical, chemical, biological, and social self-organization, according to the laws of nonlinear dynamics. Atoms and molecules, stars and clouds, organisms and brains, economies and societies are only some examples of dynamical systems. Thus, symmetry and complexity are the basic principles of a common systems science in the 21st century, overcoming traditional boundaries between natural, cognitive, and social sciences, mathematics, humanities and philosophy. This book treats the essence of my scientific work that can be described by a kind of dialectical triad. In a first step, I published a comprehensive treatise on Symmetries of Nature in 1988 (English: 1996). Early studies in geometry and space-time had inspired my interest in mathematical invariance and universal laws. As many other scientists, philosophers, and artists, I was also fascinated by the beauty of mathematical symmetries. But, physical, chemical, and biological symmetries are broken by natural processes, leading to the observed complexity and diversity of the world. Therefore, I studied the foundations of nonlinear dynamics and, as a sec