Title
UNDERSTANDING NATURAL PHENOMENA: Self-Organization
and Emergence in Complex Systems
Author
Vinod Wadhawan
Book details
Paperback: 518 pages
Publisher: CreateSpace
Independent Publishing Platform; 2nd edition (January 17, 2018)
Language: English
ISBN-10: 1548527939
ISBN-13:
978-1548527938
Product Dimensions: 6.7 x 1.3 x 9.6 inches
Shipping Weight: 2.2 pounds
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A flower is a work of art, but there is no artist
involved. The flower evolved from lesser things which, in turn, evolved from
still lesser things, and so on, all the way down. For example, the symmetry of
a flower is the end result of a long succession of spontaneous processes and
events, as also of some simple ‘local rules’ in operation, all constrained,
even aided, by the infallible second law of thermodynamics for ‘open’ systems.
In fact, the second law is the mother of all organizing principles, leading to
the enormous amounts of cumulative self-organization, structure, symmetry, and
‘emergence’ we see in Nature.
About the book
Science is all about trying to understand natural
phenomena under the strict discipline imposed by the celebrated scientific
method. Practically all the systems we encounter in Nature are dynamical
systems, meaning that they evolve with time. Among them there are the ‘simple’
or ‘simplifiable’ systems, which can be handled by traditional, reductionistic
science; and then there are 'complex’ systems, for which nonreductionistic
approaches have to be attempted for understanding their evolution. In this book
the author makes a case that a good way to understand a large number of natural
phenomena, both simple and complex, is to focus on their self-organization and
emergence aspects. Self-organization and emergence are rampant in Nature and,
given enough time, their cumulative effects can be so mind-boggling that many
people have great difficulty believing that there is no designer involved in
the emergence of all the structure and order we see around us. But it is really
quite simple to understand how and why we get so much ‘order for free’. It all
happens because, as ordained by the infallible second law of thermodynamics,
all ‘thermodynamically open’ systems in our ever-expanding and cooling (and
therefore gradient-creating) universe constantly tend to move towards
equilibrium and stability, often ending up in ordered configurations. In other
words, order emerges because Nature tends to find efficient ways to annul
gradients of all types.
This book will help you acquire a good understanding of the essential features of many natural phenomena, via the complexity-science route. It has four parts: (1) Complexity Basics; (2) Pre-Human Evolution of Complexity; (3) Humans and the Evolution of Complexity; and (4) Appendices. The author gives centrestage to the second law of thermodynamics for ‘open’ systems, which he describes as ‘the mother of all organizing principles’. He also highlights a somewhat unconventional statement of this law: ‘Nature abhors gradients’.
The book is written at two levels, one of which hardly uses any mathematical equations; the mathematical treatment of some relevant topics has been pushed to the last part of the book, in the form of ten appendices. Therefore the book should be accessible to a large readership. It is a general-science book written in a reader-friendly language, but without any dumbing down of the narrative.
This book will help you acquire a good understanding of the essential features of many natural phenomena, via the complexity-science route. It has four parts: (1) Complexity Basics; (2) Pre-Human Evolution of Complexity; (3) Humans and the Evolution of Complexity; and (4) Appendices. The author gives centrestage to the second law of thermodynamics for ‘open’ systems, which he describes as ‘the mother of all organizing principles’. He also highlights a somewhat unconventional statement of this law: ‘Nature abhors gradients’.
The book is written at two levels, one of which hardly uses any mathematical equations; the mathematical treatment of some relevant topics has been pushed to the last part of the book, in the form of ten appendices. Therefore the book should be accessible to a large readership. It is a general-science book written in a reader-friendly language, but without any dumbing down of the narrative.
Foreword
In medieval times, our understanding of the world
around us was primarily in the realm of religion and magic. However, it was in
the 15th century that a more rational approach to the study of
nature began to appear, followed in the early 18th century by the
so-called period of enlightenment. Nonetheless, the role of religion continued
to dominate thought right through the 19th and twentieth centuries.
Yet, here we are in the 21st century, when one would have thought
that rationality would be the order of the day, we are nonetheless still
surrounded by irrationality, and partly religious magical thinking. You have
only to type the word “crystal” into Google to see page after page on the
magical healing of crystals. For we scientists, such beliefs make no sense at
all and even can be seen as an attack against the scientific method itself. No
doubt, Nature is observed to be complex and at times may seem to be mysterious,
but that does not mean that we should give up and substitute the concept of “belief”
for true scientific examination. This is why the material described in this
book is so useful and important to understand today.
Vinod Wadhawan has been a crusader for rationality
in thinking and public discourse for many years. Though this book has been
designed as a comprehensive textbook on complexity science, it serves many
other purposes as well. He explains how the known processes and understandings
of complex systems can develop from often simple beginnings. While such
happenings may often seem to the layman to be strange or even magical, they are
generally susceptible to scientific reasoning. For example, consider the
appearance in a fluid of regular hexagonal-shaped cells when the fluid is under
a large temperature gradient. This beautiful phenomenon is called Bénard convection and is fully
understood once one appreciates the underlying thermal convection currents in
the fluid. As Vinod quotes from others,
“Nature abhors gradients”.
Here you will read about a mixture, or better a
fusion, of philosophical and scientific ideas, in a rather accessible language.
After all the field of physics was, and is to this day in Scotland, known as
Natural Philosophy. This soon gets us into a discussion of determinism and
whether free will exists, subjects that have before them centuries of
discussion. One of the means of rationalising the ways of nature is through the
now generally well-accepted ideas inherent in thermodynamics, especially the
Second Law for open systems. The law itself is not provable, but as with so
many examples in science, leads to conclusions that can be tested. Despite this
lack of direct proof, the laws of thermodynamics have stood the test of time
and we do not know of exceptions. Wadhawan makes considerable use of this Law
in explaining the phenomena associated with changes from simple to complex
behaviour.
An important message that suffuses the book is that
most complex systems are far too complex to be understandable in terms of the
usual reductionistic approach of conventional science. One just cannot set up
and solve a tractable number of differential equations for catching the essence
of most of the complex systems. One has to look beyond reductionism, and
attempt a holistic approach. Very often, difference equations come to the
rescue. The useful tip in this book seems to be: work with difference equations
if you cannot work with differential equations in a meaningful way for trying
to comprehend a complex system. The book gives a pride of place to the subject
of cellular automata for this reason.
So, in the first part of the book the reader is
treated to a whole range of topics from concepts of evolution, relativity,
quantum theory through the fundamental ideas of symmetry, particle physics,
chaos theory, and causes of complexity in nature. Vinod then takes us on a tour
of pre-human evolution of complexity, addressing knotty questions such as the
meaning of life (but not 42 as in the Hitchhiker’s Guide to the Galaxy!), and
the fundamental basis of the Darwinian view of the evolution of species.
Darwinian evolution is a subset of dynamical evolution. Dynamical evolution,
controlled as well as aided by the second law of thermodynamics for open
systems, is at the heart of what the science of complex systems is all about.
This fact is brought out very clearly in the book.
In the next part of the book we meet the evolution
of complexity during human existence, including the founding of various
algorithms, robotics and functions of the human brain. Many of these problems
today remain unresolved, of course, but such is the nature of the scientific
method that constant progress is actually being made in their understanding. In
this we are currently living through a remarkable period of rapid developments
of ideas. Appearance of humans on the scene has led to a rapid increase in the
rate of evolution of complexity. Even more significantly, our remarkable
progress in the field of artificial intelligence has brought up a critical
situation in which our robots are already getting better than us in more and
more aspects. As pointed out by Vinod, the self-evolution of robots can occur
exponentially rapidly, whereas we humans are hardly evolving on that time scale. There remains the question as to whether the
human brain itself can be reproduced artificially. We are now making
considerable progress in understanding how the brain works and one can argue
that surely there will come a time when science will enable a complete
artificial intelligence to be built, complete with the ability to reason, to
think and perhaps even develop a conscience. Precisely what this means is a hot
topic of current debate. Perhaps the relatively new field of quantum computing
will open this door; but, of course, prediction of the future is difficult and
likely to be wrong! What is certain though is that artificial intelligence is
advancing at such a remarkable rate that the old science fiction view of robots
is beginning to look seriously realistic. The other day I watched a small
machine running around independently mowing the lawn in a neighbour’s garden. I
saw with astonishment how it carefully manoeuvred itself around objects such as
a chair on the lawn. Look at mobile phones. My first computer had 8K store on a
magnetic drum, but today’s mobile phones are several thousand times more
powerful and are capable, for instance, of allowing photographs to be taken at
phenomenal resolution. This has been a triumph of the development of many
fields, including lens design, new materials and new software techniques, let
alone the ability to make telephone calls. Who would have thought of such phenomena outside of the world of scientific
fiction a few years ago?
Clearly the future belongs to robots. If they turn
out, for instance, to be made mainly of
inorganic materials, they will outlast all humans, and this even raises the
question as to whether humans as a species will continue to exist or even if
they need to exist. These are deep, possibly troubling, but certainly exciting
prospects to consider, both as a matter of practicality and of ethics. While we
still have some control on robots, we should apply our minds to what kind of a
future we want for ourselves. And good decisions in this regard require a basic
minimum understanding of the science of complex systems by a wide cross section
of society. We are living through a very special time. This is where this book
comes in.
It can be seen that Vinod Wadhawan has set himself a
momentous and daunting task in putting together into a single book so many
apparently diverse concepts and ideas that might at first seem to be so
disparate as to be intractable. But in fact, we see that there are common
threads, often called simply the Laws of Nature by some. These laws are rapidly
becoming ever more understood and a careful reading of this book will help us
with our observations of the world around us, so that though we may continue to
ask “why?”, sometimes we will come up with a rational explanation.
This book is epic in the sense that it covers so
much ground that one is left somewhat dizzy. And yet, it all makes sense once
one realizes how it is possible for something that is complex, for example a
flower, to evolve via natural processes from humble beginnings. After all,
starting with single-cell creatures such as amoebae we follow a complicated but
rational evolutionary path to arrive at the most complex organizations that we
know of – ourselves. So, if you follow
the logic of this book, starting with the basic concepts of thermodynamics, symmetry,
quantum theory and so on, you will be treated to many many thought-provoking
ideas, which will likely challenge your own preconceptions and leave you
thirsting for more.
Now a few words about the author. I have personally
known Vinod for a long time, ever since he came to work for a while in my
laboratory. At the time he was working on a phenomenon known as ferrogyrotropy,
wherein certain crystals that show chiral (“handedness” if you prefer)
properties, the chiral properties can be switched by application of an external
stimulus. I think he was the only person in the world then studying this
phenomenon. After he left Oxford in 1980 we kept in constant contact, with
Vinod playing an important role as one of my regional editors with the
international journal, Phase Transitions, for which I was the general editor. I
noted that every paper sent to the journal from Indian authors had been closely
edited by Vinod beforehand, and so I knew that I could rely entirely
automatically on his personal skill and judgement. Vinod’s ability at writing
in English is commendable: he obviously has had the benefit of a classical
education. Since returning to India, he has produced several books, starting
with topics related to ferroic materials and smart structures, and eventually
moving on to the more philosophical concepts that have to do with the science
of complexity. So, we come to this his latest book, where Vinod has supplied us
with many nice examples of complexity and how it arises, and as a result the
reader will finish the book much more informed than at the beginning. That,
after all, is the purpose of a book like this.
A. M. Glazer
Emeritus Professor of
Physics and Emeritus Fellow
of Jesus College, Oxford
Former Vice President,
International Union of Crystallography
January 2018
Preface
I am a scientist and I take pride in the fact that
we humans have invented and perfected the all-important scientific method
for investigating natural phenomena. Wanting to understand natural phenomena is
an instinctive urge in all of us. In this book I make a case that taking the
complexity-science route for satisfying this urge can be a richly rewarding
experience. Complexity science enables us (fully or partially) to find answers to
even the most fundamental questions we may ask about ourselves and about our
universe. We call them the Big Questions: How did our universe
emerge out of ‘nothing’ at a certain point in time; or is it that it has been
there always? Why and how has structure arisen in our universe: galaxies,
stars, planets, life forms? How did life emerge out of nonlife? How does
intelligence emerge out of nonintelligence? These are difficult questions. But,
as Mark Twain is said to have said, ‘there is something fascinating about
science. One gets such wholesale of conjecture out of such a trifling
investment of fact’. As you will see in this book, the Big Questions, as also
many others, can be answered with a good amount of credibility by using just
the following ‘trifling investment of facts’:
1. Gradients tend to be obliterated
spontaneously. Concentration gradients, temperature gradients, pressure
gradients, etc. all tend to decrease spontaneously, till a state of equilibrium
is reached, after which the gradients cannot fall any further. This is actually
nothing but a nonstatistical-mechanical version of the second law of
thermodynamics. [Why do gradients arise at all, at a cosmic level? The
original cause of all gradients in the cosmos is the continual expansion and
cooling of our universe. At the local (terrestrial) level, the energy impinging
on our ecosphere from the Sun is the main factor creating gradients.]
2. It requires energy to prevent a gradient from
annulling itself, or to create a new gradient. A refrigerator works on this
principle, as also so many other devices.
3. Left to themselves, things go from a state of
less disorder to a state of more disorder, spontaneously. This is the more
familiar version of the second law of thermodynamics. Examples abound. Molecules
in a gas occupy a larger volume spontaneously if the larger volume is made
available to them; but there is practically no way they would occupy the
smaller volume again, on their own.
4. If a system is not left to itself, i.e., if
it is not an isolated system and can therefore exchange energy and/or matter
with its surroundings, then a state of lower disorder can sometimes
arise locally. [This is in keeping with the second law of thermodynamics,
as generalized to cover ‘thermodynamically open’ systems also.] Growth of a
crystal from a fluid is an example. A crystal has a remarkably high degree of
order and design, even though there is no designer involved. To borrow a phrase
from Stuart Kauffman, this is ‘order for free’.
5. If a sustained input of energy drives a
system far away from equilibrium, the system may develop a structure or
tendencies which enable it to dissipate energy more and more efficiently.
This is called dissipation-driven adaptive organization. England (2013)
has shown that all dynamical evolution is more likely to lead to structures and
systems which get better and better at absorbing and dissipating energy from
the environment.
6. The total energy of the universe is
conserved. This is known as the energy-conservation principle. Since energy
and mass are interconvertible, the term ‘energy’ used here really means ‘mass
plus energy’.
7. Natural phenomena are governed by the laws of
quantum mechanics. Classical mechanics, though adequate for understanding
many day-to-day or ‘macroscopic’ phenomena, is only a special, limiting, case
of quantum mechanics.
8. There is an uncertainty principle in
quantum mechanics, one version of which says that the energy-conservation
principle can be violated, though only for a very small, well-specified
duration. The larger the violation of energy conservation, the smaller this
duration is.
9. It can be understood fully in terms of the
second law of thermodynamics that in a system of interacting entities, entirely
new (unexpected) behaviour or properties can arise if the interactions are
appropriate and strong enough. ‘More is different’ (Anderson 1972). The
technical term for this occurrence is emergence. Complexity science is
mostly about self-organization and emergence, and we shall encounter many
examples of them in this book. To mention a couple of them here: the emergence
of life out of nonlife; and the emergence of human intelligence in a system of
nonintelligent entities, namely the neurons. Interestingly, the second law of
thermodynamics is itself an emergent law. The motion of a molecule is governed
by classical or ‘Newtonian’ mechanics, which has time-reversal symmetry,
meaning that if you could somehow reverse the direction of time, the Newtonian
equations of motion would still hold. And yet, when you put a large number of
these molecules together, there are interactions among them and there emerges a
direction of time: Time increases in the direction in which overall
disorder increases. As I shall discuss later in the book, even the causality
principle is an emergent principle.
10. The dynamics of evolution of a complex
system of interacting entities is mostly through the operation of ‘local rules’.
Chua (1998) has introduced the important notion of cellular nonlinear networks
(CNNs), and enunciated a local-activity dogma. According to it, in order
for a ‘nonconservative’ system or model to exhibit any form of complexity, the
associated CNN parameters must be such that that either the cells or their
couplings are locally active.
11. The most adaptable are the most likely to
survive and propagate. Any species, if it is not to become extinct, must be
able to survive and propagate, in an environment in which there is always some
intra-species and/or inter-species competition because different individuals
may all have to fight for the same limited resources like food or space. The
fittest individuals or groups for this task (i.e., the most adaptable
ones) stand a greater chance of winning this game and, as a result, the
population gets better and better (more adapted) at survival and propagation in
the prevailing conditions: the more adaptable or ‘fitter’ ones are not only
more likely to survive, but also stand a greater chance to pass on their genes
to the next generation.
It is remarkable that an enormous number and
variety of natural phenomena can be understood in terms of just these few
‘commonsense’ facts, by adopting the complexity-science approach. Complexity
science helps us understand, to a small or large extent, even those natural
phenomena which fall outside the scope of conventional reductionistic science.
What is complexity science, and how is its
operational space different from that of conventional science? Let us begin by
answering the question: What does the phrase ‘system under investigation’ mean
in conventional science? Strictly speaking, since everything interacts with
everything else, the entire cosmos is one big single system. But such an
approach cannot take us very far because it is neither tractable nor useful.
So, depending on our interest, we define a subsystem which is a ‘quasi-isolated
system’. A quasi-isolated system is an imaginary construct, such that what
is outside it can be, to a good approximation, treated as an unchanging
(usually large) ‘background’, or ‘heat bath’ etc. This approach is so common in
conventional science that we just say ‘system’ when what we really mean is a
carefully identified quasi-isolated system. An example from rocket science will
illustrate the point. For predicting the initial trajectory of a rocket, we can
assume safely that a truck moving an adequate distance away from the launching
site will not affect the trajectory significantly. Conventional science
deals mostly with such ‘simple’ or ‘simplifiable’ systems. Complexity science,
by contrast, deals with systems which must be treated in their totality; for
them it is mostly not possible to identify a ‘quasi-isolated subpart’.
By definition, a complex system is one which
comprises of a large number of ‘members’, ‘elements’ or ‘agents’, which
interact substantially with one another and with the environment, and which
have the potential to generate qualitatively new collective behaviour. That is,
there can be an emergence of new (unexpected) spatial, temporal, or
functional structures or patterns. Different complex systems have different
‘degrees of complexity’, and the amount of information needed to describe the
structure and function of a system is one of the measures of that degree of
complexity (Wadhawan 2010).
‘Complexity’ is something we associate with a
complex system (defined above). It is a technical term, and does not mean
the same thing as ‘complicatedness’.
The idea of writing this book took shape when I was
working on my book Smart Structures: Blurring the Distinction between the
Living and the Nonliving (Wadhawan 2007). Naturally, there was extensive
exposure to concepts from complexity science. Like the subject of smart
structures, complexity science also cuts across various disciplines, and
highlights the basic unity of all science. The uneasy feeling grew in me that,
in spite of the fact that complexity is so pervasive and important, it is not
introduced as a well-defined subject even to science students. They are all
taught, say, thermodynamics and quantum mechanics routinely, but not complexity
science. Even among research workers, although a large number are working on
one complex system or another (and not just in physics or chemistry, but also
in biology, brain science, computational science, economics, etc.), not many have
learnt about the basics of complexity science in a coherent manner at an early
stage of their career. I have tried to write a book on complexity that takes
this subject to the classroom at a fairly introductory but comprehensive level.
There is no dumbing down of facts, even at the cost of appearing ‘too
technical’ at times.
Here are some examples of complex systems:
beehives; ant colonies; self-organized supramolecular assemblies; ecosystems;
spin-glasses and other complex materials; stock markets; economies of nations;
the world economy; the global weather pattern. The origin and evolution of life
on Earth was itself a series of emergent phenomena that occurred in highly
complex systems. Evolution of complexity is generally a one-way traffic: The new
emergent features may (in principle) be deducible from, but are not reducible
to, those operating at the next lower level of complexity. Reductionism stands
discounted.
As I said earlier, emergent behaviour is a hallmark
of complex systems. Human intelligence is also an emergent property: Thoughts,
feelings, and purpose result from the interactions among the neurons.
Similarly, even memories are emergent phenomena, arising out of the
interactions among the large number of ‘unmemory-like’ fragments of information
stored in the brain.
What goes on in a complex system is essentially as
follows: There is a large number of interacting agents, which may be viewed as
forming a network. In the network-theory jargon, the agents are the
‘nodes’ of the network, and a line joining any two nodes (i.e., an ‘edge’)
represents the interaction between that pair of agents. Any interaction amounts
to communication or exchange of information. The action or behaviour of each
agent is determined by what it ‘sees’ others doing, and its actions, in turn,
determine what the other agents may do. Further, the term game-playing
is used for this mutual interaction in the case of those complex systems in
which the agents are ‘thinking’ organisms (particularly humans). Therefore a
partial list of topics covered in this book is: information theory; network
theory; cellular automata; game theory.
Exchange of information in complex systems,
controlled like other macroscopic phenomena by the second law of
thermodynamics, leads to self-organization and emergence. In particular,
biological evolution is a natural and inevitable consequence of such ongoing
processes, an additional factor for them being the cumulative effects of mutations
and natural selection. This book has chapters on evolution of complexity
of all types: cosmic, chemical, biological, artificial, cultural.
Networked or ‘webbed’ systems have the
all-important nonlinearity feature. In fact, nonlinear response, in
conjunction with substantial departure from equilibrium, is the crux of complex
behaviour. There are many types of nonlinear systems. The most important for
our purposes in this book are those in which, although the output (y) is
indeed proportional to the input (x), the proportionality factor (m)
is not independent of the input; i.e., m is not a constant factor, but
rather varies with what x is. For a linear system we have y = m x,
with m having a fixed value, not varying with x. But for a nonlinear
system, the equation becomes y = m(x) x;
now m is not a constant. This has far-reaching consequences for
the (always networked) complex system. In particular, its future progression of
events is very sensitive to conditions at any particular point of time (the
so-called ‘initial conditions’). This sensitivity to initial conditions is also
the hallmark of chaotic systems. In fact, there is a well-justified
viewpoint that it is impossible to discuss several types of complex systems
without bringing in concepts from chaos theory. And, what is more, complex
systems tend to evolve to a configuration wherein they can operate near the
so-called edge of chaos (neither too much order, nor too much
chaos). There is a chapter on chaos which elaborates on these things.
Inanimate systems can also be complex. Whirlpools
and whirlwinds are familiar examples of dynamic nonbiological complex systems.
Even static physical systems like some nanocomposites may exhibit properties
that cannot always be deduced from those of the constituents of the composite.
A particularly fascinating class of complex materials are the so-called multiferroics.
A multiferroic is actually a ferroic crystalline material (a ‘natural’
composite) which just refuses to be homogeneous over macroscopic length scales,
so that the same crystal may be, say, ferroelectric in some part, and
ferromagnetic in another. In a multiferroic, two or all three of the electric,
magnetic and elastic interactions compete in a delicately balanced manner, and
even a very minor local factor can tilt the balance in favour of one or the
other. This class of materials offers great scope for basic research and for
device applications, particularly in smart structures.
The current concern about ecological conservation
and global warming points to the need for a good understanding of complex
systems, particularly their holistic nature. Mother Earth is a single, highly
complex, system, now increasingly referred to as the System Earth.
A better understanding of complexity may well
become a matter of life and death for the human race. And the subject of complexity
science is still at the periphery of science. It has not yet become mainstream,
in the sense that it is not taught routinely even at the college level. That
cannot go on.
There are already a substantial number of great
books on complexity science, and I have drawn on them. But I believe that this
book is student-friendly and teacher-friendly, and it brings home the
all-pervasive nature of the subject. Here are its salient features:
1. It provides a comprehensive update on the
subject.
2. It can serve as introductory or supplementary
reading for an undergraduate or graduate course on any branch of complexity
science.
3. Practically all the mathematical treatment of
the subject has been pushed to the appendices at the end of the book, so the
main text can be comprehended even by those who are not too comfortable with
equations. This is important because a large fraction of the educated public
must get the hang of the nature of complexity, so that we can successfully meet
the challenges posed to our very survival as a species.
4. Both among scientists and nonscientists there is
a large proportion of people who are insufficiently trained about the
explaining power of complexity science when it comes to some of the deepest
puzzles of Nature and, hopefully, this book would help remedy the situation to
some extent.
5. The book has a certain all-under-one-roof
character. The topics covered are so many and so diverse that it would be
well-nigh impossible for a reader, specializing in a particular branch of
complexity science, not to get exposed to what is going on in the rest of
complexity science! This is important, because using the insights gained in one
complex system for trying to understand another complex system is the hallmark
of complexity science.
6. A proper understanding of what complexity
science has already achieved will also help discredit many of the claims of
mystics, supernaturalists, and pseudoscientists.
Bengaluru
September, 2017
Preface to the Second Edition
A number of minor corrections and other improvements have been incorporated. The font size has been reduced by 10%. New information has been added, and some less relevant material has been removed.
Vinod Wadhawan
Bengaluru
September 2017
Preface to the Second Print
This print includes a Foreword by Prof. A. M. Glazer of the University of Oxford. A former Vice President of the International Union of Crystallography, he is a veteran crystallographer and a great teacher. I am grateful to him for his kind words and also for many other inputs.
Vinod Wadhawan
Bengaluru
January 2018
Contents
Foreword
Preface
I.
Complexity Basics
1. Overview 1
1.1 Preamble 3
1.2 A whirlpool as an example of self-organization
5
1.3 Spontaneous pattern formation: the Bénard
instability 6
1.4 Recent history of investigations in complexity
science 8
1.5 Organization of the book 8
2. The Philosophical and Computational
Underpinnings of Complexity Science 9
2.1 The scientific method for understanding natural
phenomena 9
2.2 Reductionism and its inadequacy for dealing
with complexity 12
2.3 The Laplace demon 13
2.4 Holism 15
2.5 Emergence 16
2.6 Scientific determinism, effective theories 17
2.7 Free will 18
2.8 Actions, reactions, interactions, causality 21
2.9 The nature of reality 23
3. The Second Law of Thermodynamics 25
3.1 The second law for isolated systems 25
3.2 Entropy 26
3.3 The second law for open systems 27
3.4 Nucleation and growth of a crystal 29
3.5 The second law is an emergent law 32
3.6 Emergence, weak and strong 33
3.7 Nature abhors gradients 33
3.8 Systems not in equilibrium 34
3.9 Thermodynamics of small systems 35
4. Dynamical Evolution 37
4.1 Dynamical systems 37
4.2 Phase-space trajectories 37
4.3 Attractors in phase space 38
4.4 Nonlinear dynamical systems 40
4.5 Equilibrium, stable and unstable 40
4.6 Dissipative structures and processes 42
4.7 Bifurcations in phase space 43
4.8 Self-organization and order in dissipative
structures 44
5.Relativity Theory and Quantum Mechanics 47
5.1.Special theory of relativity 47
5.2 General theory of relativity 49
5.3 Quantum mechanics 52
5.4 Summing over multiple histories 55
6.The Nature of Information 57
6.1 Russell’s paradox 57
6.2 Hilbert’s formal axiomatic approach to
mathematics 58
6.3 Gödel’s incompleteness theorem 59
6.4 Turing’s halting problem 60
6.5 Elementary information theory 63
6.6 Entropy means unavailable or missing
information 65
6.7 Algorithmic information theory 66
6.8 Algorithmic probability and Ockham’s razor 69
6.9 Algorithmic information content and effective
complexity 70
6.10 Classification of problems in terms of
computational complexity70
6.11 ‘Irreducible complexity’ deconstructed 71
7.Darwinian Evolution, Complex Adaptive Systems,
Sociobiology 75
7.1 Darwinian evolution 75
7.2 Complex adaptive systems 77
7.3 The inevitability of emergence of life on Earth
79
7.4 Sociobiology, altruism, morality, group
selection 81
8. Symmetry is Supreme 83
8.1 Of socks and shoes 83
8.2 Connection between symmetry and conservation
laws 83
8.3 Why so much symmetry? 84
8.4 Growth of a crystal as an ordering process 85
8.5 Broken symmetry 86
8.6 Symmetry aspects of phase transitions 88
8.7 Latent symmetry 89
8.8 Latent symmetry and the phenomenon of emergence
in complex systems 90
8.9 Broken symmetry and complexity 91
8.10 Symmetry of complex networks 92
9. The Standard Model of Particle Physics 95
9.1 The four fundamental interactions 95
9.2 Bosons and fermions 96
9.3 The standard model and the Higgs mechanism 98
10. Cosmology Basics 101
10.1 The ultimate causes of all cosmic order and
structure 101
10.2 The Big Bang and its aftermath 102
10.3 Dark matter and dark energy 105
10.4 Cosmic inflation 108
10.5 Supersymmetry, string theories, M-theory 109
10.6 Has modern cosmology got it all wrong? 111
11. Uncertainty, Complexity, and the Arrow of Time
117
11.1 Irreversible processes, and not entropy,
determine the arrow of time 117
11.2 Irreversible processes can lead to
order 117
11.3 The arrow of time and the early universe 118
11.4 When did time begin? 119
11.5 Uncertainty and complex adaptive systems 120
12. The Cosmic Evolution of Complexity 123
12.1 Our cosmic history 123
12.2 We are star stuff 124
13. Why Are the Laws of Nature What They Are? 127
13.1 The laws of Nature in our universe 127
13.2 The anthropic principle 128
14. The Universe is a Quantum Computer 131
14.1 Quantum computation 131
14.2 Quantum entanglement 132
14.3 The universe regarded as a quantum computer
133
15. Chaos, Fractals, and Complexity 135
15.1 Nonlinear dynamics 135
15.2 Extreme sensitivity to initial conditions 136
15.3 Chaotic rhythms of population sizes 137
15.4 Fractal nature of the strange attractor 139
15.5 Chaos and complexity 141
16. Cellular Automata as Models of Complex Systems
143
16.1 Cellular automata 143
16.2 Conway’s Game of Life 143
16.3 Self-reproducing automata 145
16.4 The four Wolfram classes of cellular automata
146
16.5 Universal cellular automata 147
17. Wolfram’s ‘New Kind of Science’ 149
17.1 Introduction 149
17.2 Wolfram’s principle of computational
equivalence (PCE) 150
17.3 The PCE and the rampant occurrence
of complexity 151
17.4 Why does the universe run the way it does? 152
17.5 Criticism of Wolfram’s NKS 153
18. Swarm Intelligence 157
18.1 Emergence of swarm intelligence in a beehive
157
18.2 Ant logic 159
18.3 Positive and negative feedback in complex
systems 160
19. Nonadaptive Complex Systems 163
19.1 Composite materials 163
19.2 Ferroic materials 163
19.3 Multiferroics 164
19.4 Spin glasses 165
19.5 Relaxor ferroelectrics 166
19.6 Relaxor ferroelectrics as vivisystems 167
20. Self-Organized Criticality, Power Laws 169
20.1 The sandpile experiment 169
20.2 Power-law behaviour and complexity 170
20.3 Robust and nonrobust criticality 173
21. Characteristics of Complex Systems 175
II.
Pre-Human Evolution of Complexity
22. Evolution of Structure and Order in the Cosmos
183
22.1 The three eras in the cosmic evolution of
complexity 183
22.2 Chaisson’s parameter for quantifying the
degree of complexity 183
22.3 Cosmic evolution of information 184
22.4 Why so much terrestrial complexity? 186
23. The Primary and Secondary Chemical Bonds 187
23.1 The primary chemical bonds 187
23.2 The secondary chemical bonds 189
23.3 The hydrogen bond and the hydrophobic
interaction 190
24. Cell Biology Basics 193
25. Evolution of Chemical Complexity 197
25.1 Of locks and keys in the world of molecular
self-assembly 197
25.2 Self-organization of matter 199
25.3 Emergence of autocatalytic sets of molecules
202
25.4 Positive feedback, pattern formation, emergent
phenomena 204
25.5 Pattern formation: the BZ reaction 205
26. What is Life? 207
26.1 Schrödinger and life 207
26.2 Koshland’s ‘seven pillars of life’ 209
27. Models for the Origins of Life 211
27.1 The early work 211
27.2 The RNA-world model for the origin of life 213
27.3 Dyson’s proteins-first model for the origins
of life 215
27.4 Why was evolution extremely fast for the
earliest life? 218
28. Genetic Regulatory Networks and Cell
Differentiation 219
28.1 Circuits in genetic networks 220
28.2 Kauffman’s work on genetic regulatory networks
221
29. Ideas on the Origins of Species: From Darwin to
Margulis 223
29.1 Darwinism and neo-Darwinism 223
29.2 Biological symbiosis and evolution 225
29.3 What is a species 227
29.4 Horizontal gene transfer in the earliest life
forms 228
29.5 Epigenetics 229
30. Coevolution of Species 231
30.1 Punctuated equilibrium in the coevolution of
species 231
30.2 Evolutionarily stable strategies 232
30.3 Of hawks and doves in the logic of animal
conflicts 234
30.4 Evolutionary arms races and the life-dinner
principle 236
31. The Various Energy Regimes in the Evolution of
Our Ecosphere 241
31.1 The thermophilic energy regime 242
31.2 The phototrophic energy regime 244
31.3 The aerobic energy regime 245
III. Humans
and the Evolution of Complexity
32. Evolution of Niele’s Energy Staircase After the
Emergence of Humans 249
32.1 The pyrocultural energy regime 249
32.2 The agrocultural energy regime 251
32.3 The carbocultural energy regime 252
32.4 The green-valley approach to System Earth 253
32.5 The imperial approach to System
Earth 254
32.6 A nucleocultural energy regime? 256
32.7 A possible ‘heliocultural’ energy regime 258
33. Computational Intelligence 261
33.1 Introduction 261
33.2 Fuzzy logic 262
33.3 Neural networks, real and artificial 263
33.4 Genetic algorithms 265
33.5 Genetic programming: Evolution of computer
programs 267
33.6 Artificial life 271
34. Adaptation and Learning in Complex Adaptive
Systems 273
34.1 Holland’s model for adaptation and learning
273
34.2 The bucket brigade in Holland’s algorithm 274
34.3 Langton’s work on adaptive computation 276
34.4 The edge-of-chaos existence of complex
adaptive systems 278
35. Smart Structures 281
35.1 The three main components of a smart structure
281
35.2 Reconfigurable computers and machines that can
evolve 283
36. Robots and Their Dependence on Computer Power
287
36.1 Behaviour-based robotics 287
36.2 Evolutionary robotics 288
36.3 Evolution of computer power per unit cost 290
37. Machine Intelligence 295
37.1 Artificial distributed intelligence 295
37.2 Evolution of machine intelligence 296
37.3 The future of intelligence and the status of
humans 298
38. Evolution of Language 303
39. Memes and Their Evolution 307
40. Evolution of the Human Brain, and the Nature of
Our Neocortex 311
40.1 Evolution of the brain 312
40.2 The human neocortex 313
40.3 The history of intelligence 315
41. Minsky’s and Hawkins’ Models for how Our Brain
Functions 319
41.1 Marvin Minsky’s ‘Society of Mind’ 319
41.2 Can we make decisions without involving
emotions? 320
41.3 Hawkins’ model for intelligence and
consciousness 323
42. Inside the Human Brain 325
42.1 Probing the human Brain 325
42.2 Peering into the human brain 327
43. Kurzweil’s Pattern-Recognition Theory of Mind
331
44. The Knowledge Era and Complexity Science 337
44.1 The wide-ranging applications of complexity
science 337
44.2 Econophysics 338
44.3 Application of complexity-science ideas in
management science 341
44.4 Cultural evolution and complexity transitions
343
44.5 Complexity leadership theory 345
44.6 Complexity science in everyday life 345
45. Epilogue 347
IV.
Appendices
A1. Equilibrium Thermodynamics and Statistical
Mechanics 357
A1.1 Equilibrium thermodynamics 357
A1.2 Statistical mechanics 360
A1.3 The ergodicity hypothesis 360
A1.4 The partition function 361
A1.5 Tsallis thermodynamics of small systems 361
A2. Probability Theory 365
A2.1 The notion of probability 365
A2.2 Multivariate probabilities 365
A2.3 Determinism and predictability 367
A3. Information and Uncertainty 369
A3.1 Information theory 369
A3.2 Shannon’s formula for a numerical measure of
information 370
A3.3 Shannon entropy and thermodynamic entropy 371
A3.4 Uncertainty 372
A3.5 Algorithmic information theory 373
A4. Thermodynamics and Information 375
A4.1 Entropy and information 375
A4.2 Kolmogorov-Sinai entropy 376
A4.3 Mutual information and redundancy of
information 377
A5. Systems Far from Equilibrium 379
A5.1 Emergence of complexity in systems far from
equilibrium 379
A5.2 Nonequilibrium classical dynamics 380
A5.3 When does the Newtonian description break
down? 383
A5.4 Generalization of Newtonian
dynamics 384
A5.5 Pitchfork bifurcation 386
A5.6 Extension of Newton’s laws 386
A6. Quantum Theory and Particle Physics 389
A6.1 Introduction 389
A6.2 The Heisenberg uncertainty principle 389
A6.3 The Schrödinger equation 390
A6.4 The Copenhagen interpretation 391
A6.5 Time asymmetry 391
A6.6 Multiple universes 391
A6.7 Feynman’s sum-over-histories formulation 392
A6.8 Quantum Darwinism 393
A6.9 Gell-Mann’s coarse-graining interpretation 393
A6.10 Poincaré resonances and quantum theory 394
A6.11 Model-dependent realism, intelligence,
existence 396
A6.12 The principle of conservation of quantum
information 397
A6.13 Particle physics 398
A7. Theory of Phase Transitions and Critical
Phenomena 401
A7.1 A typical phase transition 401
A7.2 Liberal definitions of phase transitions 401
A7.3 Instabilities can cause phase transitions 402
A7.4 Order parameter of a phase transition 403
A7.5 The response function corresponding to the
order parameter 404
A7.6 Phase transitions near thermodynamic
equilibrium 404
A7.7 The Landau theory of phase transitions 405
A7.8 Spontaneous breaking of symmetry 407
A7.9 Field-induced phase transitions 407
A7.10 Ferroic phase transitions 408
A7.11 Prototype symmetry 409
A7.12 Critical phenomena 409
A7.13 Universality classes and critical exponents
410
A8. Chaos Theory 413
A8.1 The logistic equation 413
A8.2 Lyapunov exponents 416
A8.3 Divergence of neighbouring trajectories 417
A8.4 Chaotic attractors 419
A9. Network Theory and Complexity 421
A9.1 Graphs 421
A9.2 Networks 425
A9.3 The travelling-salesman problem 426
A9.4 Random networks 427
A9.5 Percolation transitions in random networks 428
A9.6 Small-world networks 429
A9.7 Scale-free networks 431
A9.8 Evolution of complex networks 432
A9.9 Emergence of symmetry in complex networks 433
A9.10 Chua’s cellular nonlinear networks as a
paradigm for emergence and complexity 435
A10. Game Theory 439
A10.1 Introduction 439
A10.2 Dual or two-player games 442
A10.3 Noncooperative games 449
A10.4 Nash equilibrium 450
A10.5 Cooperative games 450
Bibliography 453
Index 481
Acknowledgements 491
About the Author 492
