Boundaries of a Complex World

372 Pages·2018·12.848 MB·English

by  Andrei Ludu

Springer Series in Synergetics
Andrei Ludu
Boundaries
of a Complex
World
Second Edition
Springer Series in Synergetics
Series Editors
Henry D.I. Abarbanel, Institute for Nonlinear Science, University of California,
San Diego, CA, USA
Dan Braha, New England Complex Systems Institute, Cambridge, MA, USA
Péter Érdi, Center for Complex Systems Studies, Kalamazoo College, USA
Hungarian Academy of Sciences, Budapest, Hungary
Karl J Friston, Institute of Cognitive Neuroscience, University College London,
London, UK
Hermann Haken, Center of Synergetics, University of Stuttgart, Stuttgart, Germany
Viktor Jirsa, Centre National de la Recherche Scientifique (CNRS), Université de la
Méditerranée, Marseille, France
Janusz Kacprzyk, Systems Research, Polish Academy of Sciences, Warsaw, Poland
Kunihiko Kaneko, Research Center for Complex Systems Biology, The University
of Tokyo, Tokyo, Japan
Scott Kelso, Center for Complex Systems and Brain Sciences, Florida Atlantic
University, Boca Raton, FL, USA
Jürgen Kurths, Nonlinear Dynamics Group, University of Potsdam, Potsdam,
Germany
Ronaldo Menezes, Computer Science Department, University of Exeter, Exeter,
UK
Andrzej Nowak, Department of Psychology, Warsaw University, Warsaw, Poland
Hassan Qudrat-Ullah, Decision Sciences, York University, Toronto, ON, Canada
Linda Reichl, Center for Complex Quantum Systems, University of Texas, Austin,
TX, USA
Frank Schweitzer, System Design, ETH Zurich, Zurich, Switzerland
Didier Sornette, Entrepreneurial Risk, ETH Zurich, Zurich, Switzerland
Stefan Thurner, Section for Science of Complex Systems, Medical University of
Vienna, Vienna, Austria
Editor-in-Chief
Peter Schuster, Theoretical Chemistry and Structural Biology, University of
Vienna, Vienna, Austria
Springer Series in Synergetics
Founding Editor: H. Haken
The Springer Series in Synergetics was founded by Herman Haken in 1977. Since
then, the series has evolved into a substantial reference library for the quantitative,
theoretical and methodological foundations of the science of complex systems.
Through many enduring classic texts, such as Haken’s Synergetics and Informa-
tion and Self-Organization, Gardiner’s Handbook of Stochastic Methods, Risken’s
The Fokker Planck-Equation or Haake’s Quantum Signatures of Chaos, the series
has made, and continues to make, important contributions to shaping the foundations
of the field.
The series publishes monographs and graduate-level textbooks of broad and
general interest, with a pronounced emphasis on the physico-mathematical approach.
Andrei Ludu
Boundaries of a Complex
World
Second Edition
Andrei Ludu
Department of Mathematics
Embry-Riddle Aeronautical University
Daytona Beach, FL, USA
ISSN 0172-7389 ISSN 2198-333X (electronic)
Springer Series in Synergetics
ISBN 978-3-031-07360-1 ISBN 978-3-031-07361-8 (eBook)
https://doi.org/10.1007/978-3-031-07361-8
1st edition: © Springer-Verlag Berlin Heidelberg 2016
2nd edition: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer
Nature Switzerland AG 2022
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
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of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and
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The use of general descriptive names, registered names, trademarks, service marks, 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.
The publisher, the authors, and the editors are safe to assume that the advice and information in this book
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the editors give a warranty, expressed or implied, with respect to the material contained herein or for any
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This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
I dedicate this book to my family: Maria,
Delia, and Tim.
Preface to the Second Edition
Since the first publication of this work 6 years ago, I have been pleased with the
reception that it has received. Care has been taken in the preparation of the second
edition to make it as accurate and useful as possible, for the analysis of failures is
a critical process. Unfortunately, it is very difficult to bundle together in the same
manuscript art essays with social systems modeling with algebraic topology and
nonlinear fluid dynamics. For this reason, the book had to be written on an eclectic
skeleton with variable degrees of abstraction in various fields of human knowledge. It
is recommended that the study of the boundary of systems in general not be limited
to this book but expanded to encompass many of the references and suggestions
for further study. After more than 44 years of studying, writing, and teaching about
applied mathematics and nonlinear science, I am still learning. And so can you.
Again, I am indebted to all of those people who have suggested improvements,
particularly Prof. Denys Dutykh and Stefan Adrian Carstea who provided relevant
comments and criticism towards the second edition. I am especially thankful to the
artist Delia Krimmel, the greatest designer I could ever work with, who helped with
this book writing with art and imagination, edited, and proofread the manuscript. I am
most grateful to Prof. Maria Ludu, for her original ideas and continuous support and
confidence in my work, and for the incredible, elegant, and effective solutions she
always offered to all my problems. I am very thankful to the Hunt Library of Embry-
Riddle Aeronautical University, and especially to the Interlibrary Loan Department
which offered me the opportunity to obtain all the necessary references.
It was not an easy task to gather in one monograph such different perspectives
about the boundary, from an artistic perspective to physical descriptions, to social
behavior, and to differential geometry calculations. Because of this ambitious goal,
the book has a complicated and, in many places, discontinuous structure. In order to
repair this situation and offer the reader a dedicated path through the ideas and exam-
ples, we indicate below three possible tracks of different mathematical difficulties
(in analogy with skiing stations):
• Track 1: no asterisk in the title. It is recommended to keep the reading away from
any mathematical complications.
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viii PrefacetotheSecondEdition
• Track 2: one asterisk in the title*. It includes Track 1 and in addition contains
several traditional applied-mathematics descriptions. The readers interested in
this approach are welcome to read all the sections without an asterisk.
• Track 3: two asterisks in the title**. It contains more difficult mathematical
language requesting prerequisites in differential geometry and topology. The
readers interested in this approach are welcome to read all the sections of the
book.
In addition, we present below recommendations for reading various chapters and
sections for each such track.
The least mathematical complications:
Chapter 2, all the sections except Sect. 2.8, Appendix
Chapter 3, Sects. 3.1, 3.2, 3.3, 3.4, and 3.8.1, 3.8.2, 3.8.4, and 3.9
Chapter 4, Sects. 4.1, 4.2.2, 4.2.3, 4.3, and 4.7.1
Chapter 5, Sects. 5.1 and 5.8
Chapter 6, all the sections
Chapter 7, Sects. 7.1, 7.2, and 7.3
Chapter 8, Sect. 8.1
Chapter 9, Sects. Introduction, 9.1, 9.8, and 9.10
Chapter 10 completely.
Regular applied-mathematics language*
Chapter 2, Sect. 2.8, Appendix.
Chapter 3, Sect. 3.5
Chapter 4, Sects. 4.1, 4.2.1, 4.2.2, 4.2.3, 4.3, 4.4, 4.7.1, 4.7.2, and 4.8
Chapter 5, Sects. 5.2, 5.3, 5.4, and 5.6
Chapter 7, Sect. 7.4
Chapter 9, Sects. 9.2, 9.3, 9.5, 9.6, 9.7, 9.9, and appendices.
Track requesting mathematical prerequisites**
Chapter 3, Sects. 3.6, 3.7, 3.8.3, and 3.8.5
Chapter 4, Sects. 4.5, 4.6, and 4.9
Chapter 5, Sects. 5.5 and 5.7
Chapter 8, Sects. 8.2 and 8.3
Chapter 9, Sect. 9.4.
Daytona Beach, FL, USA Andrei Ludu
Preface to the First Edition
Have patience with everything unresolved in your heart, and try
to love the questions themselves as if they were locked rooms or
books written in a very foreign language. Don’t search for the
answers which could not be given to you now because you
would not be able to live them. And the point is, to live
everything. Live the questions now. Perhaps then, someday far
in the future, you will gradually, without even noticing it, live
your way into the answer.
Rainer Maria Rilke
In most dictionaries the word, ‘boundary’ is defined as something that shows where
one thing ends and another begins, or something that divides something else into
two parts. In some dictionaries a boundary is also defined as the limit of a subject,
activity, or experience. More mathematical dictionaries define a boundary as the
closure of a given set, the points separating the set from its complement. Overall,
the boundary seems to be defined by divide et… separare (see the figure below). In
this book we try to discuss the many aspects of the boundary from a unifying point
of view, an interdisciplinary angle. We shall examine how important the boundary is
for the existence, dynamics, and stability of what it bounds. In other words, we shall
discuss and exemplify the extent to which the boundary dynamics is essential for the
dynamics of the interior. The book emphasises the importance of the boundary as a
glue, rather than as a separation between various interrelated topics.
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x PrefacetotheFirstEdition
Real and apparent boundaries and frames
The direction this book has taken has been strongly influenced, if not even deter-
mined, by Dr. Christian Caron, Executive Publishing Editor at Springer and my
editorial adviser, who encouraged me to approach the topic of boundaries in parallel
with the increasing importance of interdisciplinary topics, complex systems science,
and especially the booming new socio-economic theories. He also drew my attention
to several crucial papers for the contents of this book.
Another motivation derives from the mathematical claim that, ‘a boundary has no
boundary’. I first heard this affirmation when at elementary school, from an uncle,
accountant by profession and spare-time astronomer by vocation, and for many years
I was intrigued by its strange duality. Of course, when I was taught a little geometry,
I was able to prove it, but in this book I will try to express the essence of the assertion
through several different forms of expression, and not only purely mathematically.
Last but not least, another motivation for writing this book built up from many
discussions I had with vision scientists, neuroscientists, painters, and art critics on
the difference between painting on the circular (hence infinite) surface of a vase
(ancient Greek vases, for example) as opposed to painting on a regular flat surface
delimited by the rigid boundary of a frame. The question is whether the existence of a
frame has consequences for the power of creativity, and for the freedom in choosing
a subject. I do not think we found an answer, but at least we raised a question.
The importance of boundary is discussed in this book from several points of
view: artistic, sensorial, neuroscientific, social, physical scientific, epistemological,
and mathematical. Let us give a simple example of the type of argumentation we
develop throughout the book. In a series of psychological studies on delayed grati-
fication, performed in the 1960s by Walter Mischel et al. [1], studies known as the
Standford marshmallow experiment, the subjects (children) were offered a choice
between one small reward (marshmallow, cookie) provided immediately, or two such
small rewards if they waited for a short period of time. The children could eat one
marshmallow right away, but if they waited for fifteen minutes without giving in to
the temptation, they would be rewarded with a second marshmallow. The researcher
interviewed a girl from the group of children who had waited patiently for the late