THE SELF-EVOLVING COSMOS a P Henomenologica I Approach to Nature’S Un Ity-I N- Diversity SERIES on KNOTS and EVERYTHING
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THE SELF-EVOLVING COSMOS A P henomenologica I Approach to Nature’s Un ity-i n- Diversity SERIES ON KNOTS AND EVERYTHING Editor-in-charge: Louis H. Kauffman (Univ. of Illinois, Chicago) The Series on Knots and Everything: is a book series polarized around the theory of knots. Volume 1 in the series is Louis H Kauffman’s Knots and Physics. One purpose of this series is to continue the exploration of many of the themes indicated in Volume 1. These themes reach out beyond knot theory into physics, mathematics, logic, linguistics, philosophy, biology and practical experience. All of these outreaches have relations with knot theory when knot theory is regarded as a pivot or meeting place for apparently separate ideas. Knots act as such a pivotal place. We do not fully understand why this is so. The series represents stages in the exploration of this nexus. Details of the titles in this series to date give a picture of the enterprise. Published: Vol. 1: Knots and Physics (3rd Edition) by L. H. Kauffman Vol. 2: How Surfaces Intersect in Space — An Introduction to Topology (2nd Edition) by J. S. Carter Vol. 3: Quantum Topology edited by L. H. Kauffman & R. A. Baadhio Vol. 4: Gauge Fields, Knots and Gravity by J. Baez & J. P. Muniain Vol. 5: Gems, Computers and Attractors for 3-Manifolds by S. Lins Vol. 6: Knots and Applications edited by L. H. Kauffman Vol. 7: Random Knotting and Linking edited by K. C. Millett & D. W. Sumners Vol. 8: Symmetric Bends: How to Join Two Lengths of Cord by R. E. Miles Vol. 9: Combinatorial Physics by T. Bastin & C. W. Kilmister Vol. 10: Nonstandard Logics and Nonstandard Metrics in Physics by W. M. Honig Vol. 11: History and Science of Knots edited by J. C. Turner & P. van de Griend EH - The self-volving Cosmos.pmd 2 4/21/2008, 4:43 PM Vol. 12: Relativistic Reality: A Modern View edited by J. D. Edmonds, Jr. Vol. 13: Entropic Spacetime Theory by J. Armel Vol. 14: Diamond — A Paradox Logic by N. S. Hellerstein Vol. 15: Lectures at KNOTS ’96 by S. Suzuki Vol. 16: Delta — A Paradox Logic by N. S. Hellerstein Vol. 17: Hypercomplex Iterations — Distance Estimation and Higher Dimensional Fractals by Y. Dang, L. H. Kauffman & D. Sandin Vol. 18: The Self-Evolving Cosmos: A Phenomenological Approach to Nature’s Unity-in-Diversity by S. M. Rosen Vol. 19: Ideal Knots by A. Stasiak, V. Katritch & L. H. Kauffman Vol. 20: The Mystery of Knots — Computer Programming for Knot Tabulation by C. N. Aneziris Vol. 21: LINKNOT: Knot Theory by Computer by S. Jablan & R. Sazdanovic Vol. 24: Knots in HELLAS ’98 — Proceedings of the International Conference on Knot Theory and Its Ramifications edited by C. McA Gordon, V. F. R. Jones, L. Kauffman, S. Lambropoulou & J. H. Przytycki Vol. 25: Connections — The Geometric Bridge between Art and Science (2nd Edition) by J. Kappraff Vol. 26: Functorial Knot Theory — Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants by David N. Yetter Vol. 27: Bit-String Physics: A Finite and Discrete Approach to Natural Philosophy by H. Pierre Noyes; edited by J. C. van den Berg Vol. 28: Beyond Measure: A Guided Tour Through Nature, Myth, and Number by J. Kappraff Vol. 29: Quantum Invariants — A Study of Knots, 3-Manifolds, and Their Sets by T. Ohtsuki Vol. 30: Symmetry, Ornament and Modularity by S. V. Jablan Vol. 31: Mindsteps to the Cosmos by G. S. Hawkins Vol. 32: Algebraic Invariants of Links by J. A. Hillman EH - The self-volving Cosmos.pmd 3 4/21/2008, 4:43 PM Vol. 33: Energy of Knots and Conformal Geometry by J. O'Hara Vol. 34: Woods Hole Mathematics — Perspectives in Mathematics and Physics edited by N. Tongring & R. C. Penner Vol. 35: BIOS — A Study of Creation by H. Sabelli Vol. 36: Physical and Numerical Models in Knot Theory edited by J. A. Calvo et al. Vol. 37: Geometry, Language, and Strategy by G. H. Thomas Vol. 38: Current Developments in Mathematical Biology edited by K. Mahdavi, R. Culshaw & J. Boucher Vol. 39: Topological Library Part 1: Cobordisms and Their Applications edited by S. P. Novikov and I. A. Taimanov Vol. 40: Intelligence of Low Dimensional Topology 2006 edited by J. Scott Carter et al. EH - The self-volving Cosmos.pmd 4 4/21/2008, 4:43 PM Series on Knots and Everything - Vol. 18 THE SELF-EVOLVING COSMOS A Phenomenological Approach to Nature's Unity-in-Diversity Steven M. Rosen City University of New York, USA 'World Scientific NEWJERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 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 Library of Congress Cataloging-in-Publication Data Rosen, Steven M. The self-evolving cosmos : a phenomenological approach to nature's unity-in-diversity / by Steven M Rosen. p. cm. -- (Series on knots and everything ; v. 18) Includes bibliographical references and index. ISBN-13: 978-981-277-173-5 (hardcover : alk. paper) ISBN-10: 981-277-173-5 (hardcover : alk. paper) 1. Physics--Philosophy. I. Title. QC6.R56955 2008 530.01--dc22 2007043868 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. The image on the cover – courtesy of NASA, ESA, and The Hubble Heritage Team (STScl/AURA)- ESA/Hubble Collaboration. Copyright © 2008 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. Printed in Singapore. EH - The self-volving Cosmos.pmd 1 4/21/2008, 4:43 PM To Marlene, light of my lifeworld This page intentionally left blank Contents List of Illustrations ix Preface xi Chapter 1. Introduction: Individuation and the Quest for Unity 1 Chapter 2. The Obstacle to Unification in Modern Physics 11 2.1 Introduction 11 2.2 Does Contemporary Mathematical Physics Actually Depart from the Classical Formulation? 15 2.2.1 Apparent concretization of mathematical physics via symmetry breaking 15 2.2.2 The implicit attempt to maintain the classical formula and its ultimate failure 20 Chapter 3. The Phenomenological Challenge to the Classical Formula 42 Chapter 4. Topological Phenomenology 63 4.1 Introduction 63 4.2 Phenomenological Intuition, Topology, and the Klein Bottle 69 4.3 The Physical Significance of the Klein Bottle 78 4.3.1 Spin 78 4.3.2 Vorticity 81 Chapter 5. The Dimensional Family of Topological Spinors 90 5.1 Generalization of Intuitive Topology 90 5.2 Topodimensional Spin Matrix 106 Chapter 6. Basic Principles of Dimensional Transformation 116 6.1 Synsymmetry and the Self-Transformation of Space 116 6.2 From Symmetry Breaking to Dimensional Generation 120 viii THE SELF-EVOLVING COSMOS 6.3 The Three Basic Stages of Dimensional Generation 123 6.4 Kleinian Topogeny 130 Chapter 7. Waves Carrying Waves: The Co-Evolution of Lifeworlds 147 Chapter 8. The Forces of Nature 162 8.1 The Phenomenon of Light 162 8.2 Phenomenological Kaluza-Klein Theory 166 8.3 Summary Comparison of Conventional and Topo- Phenomenological Approaches to Kaluza-Klein Theory 175 Chapter 9. Cosmogony, Symmetry, and Phenomenological Intuition 178 9.1 Conventional View of the Evolving Cosmos 178 9.2 The Problem of Symmetry 180 9.3 A New Kind of Clarity 186 Chapter 10. The Self-Evolving Cosmos 196 10.1 Introduction to the Cosmogonic Matrix 196 10.2 Overview of Cosmic Evolution 197 10.3 The Role of the Fermions in Dimensional Generation 207 10.4 Projective Stages of Cosmogony: Dimensional Divergence 212 10.4.1 Stage 1 212 10.4.2 Stage 2 214 10.4.3 Stages 3 and 4 220 10.5 Proprioceptive Stages of Cosmogony: Dimensional Convergence 221 10.6 Conclusion: Wider Horizons of Cosmic Evolution 226 Chapter 11. The Psychophysics of Cosmogony 229 11.1 Psychical Aspects of the Fundamental Particles 229 11.2 Toward a Reflexive Physics 237 11.3 Concretization of the Self-Evolving Cosmos 244 Bibliography 251 Index 259 Illustrations Figures Figure 2.1. Graph of the equation for a parabola 17 Figure 2.2. Schema for standard formulation of Kaluza-Klein cosmogony 21 Figure 3.1. Light cones 54 Figure 4.1. The Klein bottle 71 Figure 4.2. Parts of the Klein bottle 71 Figure 4.3. Construction of torus and Klein bottle 74 Figure 4.4. Stages in the formation of a vortex 85 Figure 5.1. Cylindrical ring and Moebius strip 90 Figure 5.2. The lemniscate 91 Figure 5.3. Schematic comparison of cylindrical and lemniscatory rotation 91 Figure 5.4. The sub-lemniscate 92 Figure 5.5. Endpoints of a line segment, lines bounding a surface area, and planes bounding a volume of space 94 Figure 5.6. Circle, cylindrical ring, and torus 99 Figure 5.7. Edgewise views of cylindrical ring and Moebius strip 101 Figure 5.8. Stationary waves 108 Figure 5.9. Train of vortices and rhythmic array of vortices 111 Figure 6.1. Dimensional wave 122 Figure 6.2. Revolution of asymmetric figure on cylindrical ring and on Moebius strip 135 Figure 6.3.