Nonlinear Science The Challenge of Complex Systems
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrab
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Zensho Yoshida
Nonlinear Science The Challenge of Complex Systems
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Professor Zensho Yoshida University of Tokyo, Graduate School of Frontier Sciences Kashiwa, Chiba 277-8561, Japan [email protected]
ISBN 978-3-642-03405-3 e-ISBN 978-3-642-03406-0 DOI 10.1007/978-3-642-03406-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009938821 The original Japanese edition was published by Iwanami Shoten Publishers, Tokyo, 2008 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg SPIN 12258536 Printed on acid-free paper 987654321 Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Modern science has abstracted, as compensation for establishing rigorousness, the complexity of the real world, and has inclined toward oversimplified fictitious narratives; as a result, a disjunction has emerged between the wisdom of science and reality. Reflecting on this, we see the need for science to recover reality; can it reveal new avenues for thought and investigation of the complexity? The study of science is the pursuit of clarity and distinctness. Physics, after Galilei placed it in the realm of mathematics, has been trying to establish clearness by mathematical logic. While physics and mathematics, respectively, have different intellectual incentives, they have intersected in history on countless occasions and have woven a flawless system of wisdom. The core of rigorous science is always made of mathematical logic; the laws of science cannot be represented without the language of mathematics. Conversely, it is undoubtedly difficult to stimulate mathematical intellect without a reference to the interests of science that are directed to the real world. However, various criticisms have been raised against the discourses of sciences that explain the events of the real world as if they are “governed” by mathematical laws. Sciences, being combined with technologies, have permeated, in the form of technical rationalism, the domain of life, politics, and even the psychological world. The criticisms accuse seemingly logical scientific narratives of being responsible for widespread destruction and emer
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