**Title**

*UNDERSTANDING NATURAL PHENOMENA: Self-Organization and Emergence in Complex Systems*

**Author**

Vinod
Wadhawan

**Book details**

**Paperback:**586 pages**Publisher:**CreateSpace Independent Publishing Platform; 1 edition (July 4, 2017)**Language:**English**ISBN-10:**1548527939**ISBN-13:**978-1548527938**Product Dimensions:**6.7 x 1.3 x 9.6 inches**Shipping Weight:**2.5 pounds

Can be ordered directly from the CreateSpace eStore also: https://www.createspace.com/7308929

**Legend for the front cover**

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.
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 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 those that are either 'simple' or 'simplifiable' and can
be handled by traditional, reductionistic science; and then there are those
that are 'complex', meaning that nonreductionistic approaches must be attempted
for understanding their evolution. In this book the author makes a case that
the best 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, the
'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 if that helps minimize the free energy. In other words, order emerges because Nature tends to
find efficient ways of annulling gradients of all types.

This book will help you acquire a good understanding of the essential features of natural phenomena, via the complex-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 centre-stage 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.

**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 can call such questions*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 remarked, ‘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, in which the gradients cannot fall any further. This is actually nothing but the infallible*second law of thermodynamics*, stated here in its most basic and general form. [Why do gradients arise at all? 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 cause of 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; 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*. 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’.__can__sometimes arise locally
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*This is called__efficiently__.*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 (i.e., more and more efficient) at absorbing and dissipating energy from the environment.
6.

*The total energy of the universe is conserved.*Since energy and mass are interconvertible, the term ‘energy’ used in this statement 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*The larger the violation of energy conservation, the smaller this duration is.__can__be violated, though only for a very small, well-specified duration.
9.

*It can be understood in terms of the second law of thermodynamics that in a system of interacting entities, entirely new (unexpected) behaviour or properties can arise sometimes 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 in a gas is governed by classical or ‘Newtonian’ mechanics, which has time-inversion 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 entropy increases. For similar reasons, even the causality principle is an emergent principle.
10.

*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, even in an environment in which there is 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 not only 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 these ten ‘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.

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 can be defined as something we associate with a complex system (described above). It is a
technical term, and is not 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 the field of complexity. 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; and 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. 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.
Biological evolution is a natural and inevitable consequence of these ongoing
processes because of the cumulative effects of

*mutations*and*natural selection*. That is why 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 proportional to the input (*x*), the proportionality factor is not independent of the input:*y*= m(*x*)*x*. 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*. The poet Thich Nhat Hanh (1991) has beautifully described the unity and interdependence of all things:*If you are a poet, you will see clearly that there is a cloud floating in this sheet of paper. Without a cloud, there will be no rain; without rain, the trees cannot grow; and without trees, we cannot make paper. The cloud is essential for the paper to exist. If the cloud is not here the sheet of paper cannot be here either. So we can say that the cloud and the paper inter-are. “Interbeing” is a word that is not in the dictionary yet, but if we combine the prefix “inter” with the verb “to be,” we have a new verb, inter-be.*

*If we look into this sheet of paper even more deeply, we can see the sunshine in it. Without sunshine, the forest cannot grow. In fact, nothing can grow without sunshine. And so, we know that the sunshine is also in this sheet of paper. The paper and the sunshine inter-are. And if we continue to look we can see the logger who cut the tree and brought it to the mill to be transformed into paper. And we see wheat. We know that the logger cannot exist without his daily bread, and therefore the wheat that became his bread is also in the sheet of paper. The logger’s father and mother are in it too. When we look in this way, we see that without all these things, this sheet of paper cannot exist.*

*Looking even more deeply, we can see ourselves in this sheet of paper too. This is not difficult to see, because when we look at a sheet of paper, it is part of our perception. Your mind is in here and mine is also. So we can see that everything is in here with this sheet of paper. We cannot point out one thing that is not here*

*—*

*time, space, the earth, the rain, the minerals in the soil, the sunshine, the cloud, the river, the heat. Everything co-exists with this paper. That is why I think the word inter-be should be in the dictionary. “To be” is to inter-be -- we cannot just be by ourselves alone. We have to inter-be with every other thing. This sheet of paper is, because everything else is.*

*Suppose we try to return one of the elements to its source. Suppose we return the sunshine to the sun. Do you think that this sheet of paper would be possible? No, without sunshine nothing can be. And if we return the logger to its mother, then we have no sheet of paper either. The fact is that this sheet of paper is made up only of “non-paper” elements. And if we return these non-paper elements to their sources, then there can be no paper at all. Without non-paper elements, like mind, logger, sunshine and so on, there will be no paper. As thin as this sheet of paper is, it contains everything in the universe in it.*

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 the salient features of the book:

1. It provides an 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. A proper understanding of what complexity science
has already achieved will also help discredit many of the claims of mystics,
supernaturalists, and pseudoscientists.

Bengaluru Vinod
Wadhawan

July,
2017

**Contents**

**Preface**

**I. Complexity Basics**

**1. Overview**

1.1 Preamble

1.2 A
whirlpool as an example of self-organization

1.3 Spontaneous
pattern formation: the Bénard instability

1.4 Recent
history of investigations in complexity science

1.5 Organization
of the book

**2. The Philosophical and Computational Underpinnings of**

**Complexity Science**

2.1 The
scientific method for investigating natural phenomena

2.2 Reductionism
and its inadequacy for dealing with complexity

2.3 The
Laplace demon

2.4 Holism

2.5 Emergence

2.6 Scientific
determinism, effective theories

2.7 Free
will

2.8 Actions,
reactions, interactions, causality

2.9 The
nature of reality

**3. The Second Law of Thermodynamics**

3.1 The
second law for isolated systems

3.2 Entropy

3.3 The
second law for open systems

3.4 Nucleation
and growth of a crystal

3.5 The
second law is an emergent law

3.6 Emergence,
weak and strong

3.7 Nature
abhors gradients

3.8 Systems
not in equilibrium

3.9 Thermodynamics
of small systems

**4. Dynamical Evolution**

4.1 Dynamical
systems

4.2 Phase-space
trajectories

4.3 Attractors
in phase space

4.4 Nonlinear
dynamical systems

4.5 Equilibrium, stable and unstable

4.6 Dissipative structures and processes

### 4.7 Bifurcations in phase space

4.8 Self-organization and order in
dissipative structures

**5. Relativity Theory and Quantum Mechanics**

5.1 Special
theory of relativity

5.2 General
theory of relativity

5.3 Quantum
mechanics

5.4 Summing
over multiple histories

**6. The Nature of Information**

6.1 Russell's paradox

6.2 Hilbert’s
formal axiomatic approach to mathematics

6.3 Gödel’s incompleteness theorem

6.4 Turing’s halting problem

6.5 Elementary
information theory

6.6 Entropy
means unavailable or missing information

6.7 Algorithmic
information theory

6.8 Algorithmic probability and
Ockham’s razor

6.9 Algorithmic
information content and effective complexity

6.10 Classification
of problems in terms of computational complexity

6.11 ‘Irreducible
complexity’ deconstructed

**7. Darwinian Evolution, Complex Adaptive Systems, Sociobiology**

7.1 Darwinian
evolution

7.2 Complex
adaptive systems

7.3 The inevitability of emergence of
life on Earth

### 7.4 Sociobiology, altruism, morality, group selection

**8. Symmetry is Supreme**

8.1 Of
socks and shoes

8.2 Connection between symmetry and conservation laws

8.3 Why so much symmetry?

8.4 Growth of a crystal as an ordering
process

8.5 Broken symmetry

8.6 Symmetry aspects of phase transitions

8.7 Latent symmetry

8.8 Potential symmetry

8.9 The
fundamental theorem of symmetry

8.10 The
distinction between potential symmetry and latent symmetry

8.11 Emergent symmetry and complexity

8.12 Broken
symmetry and complexity

8.13 Symmetry of complex networks

**9. The Standard Model of Particle Physics**

9.1 The four fundamental interactions

9.2 Bosons and fermions

9.3 The standard model and the Higgs
mechanism

**10. Cosmology Basics**

10.1 The ultimate causes of all cosmic order
and structure

10.2 The Big Bang and its aftermath

10.3 Dark matter and dark energy

10.4 Cosmic inflation

10.5 Supersymmetry, string
theories, M-theory

10.6 Has
modern cosmology got it all wrong?

**11. Uncertainty, Complexity, and the Arrow of Time**

11.1 Irreversible processes

*can*lead to order
11.2 The arrow of time and the early
universe

11.3 When did time begin?

11.4 Uncertainty and complex adaptive
systems

**12. The Cosmic Evolution of Complexity**

12.1 Our cosmic history

12.2 We
are star stuff

**13. Why Are the Laws of Nature What They Are?**

13.1 The
laws of Nature in our universe

13.2 The anthropic principle

**14. The Universe is a Quantum Computer**

14.1 Quantum computation

14.2 Quantum
entanglement

14.3 The universe regarded as a quantum
computer

**15. Chaos, Fractals, and Complexity**

15.1 Nonlinear
dynamics

15.2 Extreme
sensitivity to initial conditions

15.3 Chaotic rhythms of population sizes

15.4 Fractal nature of the strange attractor

15.5 Chaos and complexity

**16. Cellular Automata as Models of Complexity**

16.1 Cellular automata

16.2 Conway's Game of Life

16.3 Self-reproducing
automata

16.4 The four Wolfram
classes of cellular automata

16.5 Universal cellular
automata

**17. Wolfram's 'New Kind of Science'**

17.1 Introduction

17.2 Wolfram’s
principle of computational equivalence (PCE)

17.3 The
PCE and the rampant occurrence of complexity

17.4 Why
does the universe run the way it does?

17.5 Criticism
of Wolfram’s NKS

**18. Swarm Intelligence**

18.1 Emergence of swarm intelligence in a
beehive

18.2 Ant logic

18.3 Positive and negative feedback in
complex systems

**19. Nonadaptive Complex Systems**

19.1 Composite materials

19.2 Ferroic materials

19.3 Multiferroics

19.4 Spin glasses

19.5 Relaxor ferroelectrics

19.6 Relaxor ferroelectrics as vivisystems

**20. Self-Organized Criticality**

20.1 The sandpile experiment

20.2 Power-law behaviour and complexity

20.3 Robust and nonrobust criticality

**21. Characteristics of Complex Systems**

**II. Pre-Human Evolution of Complexity**

**22. Evolution of Structure and Order in the Cosmos**

22.1 The three eras in the cosmic evolution
of complexity

22.2 Chaisson’s parameter for quantifying
the degree of complexity

22.3 Cosmic evolution of information

22.4

**Why so much terrestrial complexity?****23. The Primary and Secondary Chemical Bonds**

23.1 The
primary chemical bonds

23.2 The
secondary chemical interactions

23.3 The hydrogen bond and the hydrophobic
interaction

**24. Cell Biology Basics**

**25. Evolution of Chemical Complexity**

25.1 Of
locks and keys in the world of molecular self-assembly

25.2 Self-organization
of matter

25.3 Emergence
of autocatalytic sets of molecules

25.4 Positive feedback, pattern formation,
emergent phenomena

25.5 Pattern formation: the BZ reaction

**26. What is Life?**

26.1 Schrödinger
and life

26.2 Koshland’s
seven pillars of life

**27. Models for the Origins of Life**

27.1 The
early work

27.2 The
RNA-world model for the origin of life

27.3 Dyson's
proteins-first model for the origins of life

**28. Genetic Regulatory Networks and Cell Differentiation**

28.1 Circuits
in genetic networks

28.2 Kauffman's
work on genetic regulatory networks

**29. Ideas on the Origins of Species: From Darwin to Margulis**

29.1 Darwinism
and neo-Darwinism

29.2 Biological
symbiosis and evolution

29.3 What
is a species

29.4 Epigenetics

**30. Coevolution of Species**

30.1 Punctuated
equilibrium in the coevolution of species

30.2 Evolutionarily
stable strategies

30.3 Of
hawks and doves in the logic of animal conflicts

30.4 Evolutionary
arms races and the life-dinner principle

**31. Niele’s Energy-Staircase of Increasing Complexity**

31.1 The
thermophilic energy regime

31.2 The
phototrophic energy regime

31.3 The
aerobic energy regime

**III. Humans and the Evolution of Complexity**

**32. The Post-Human Epoch of Niele’s Energy Staircase of Evolution**

32.1 The
pyrocultural energy regime

32.2 The
agrocultural energy regime

32.3 The carbocultural energy regime

32.4 The
green-valley approach to System Earth

32.5 The
imperial approach to System Earth

32.6 A
nucleocultural energy regime?

32.7 A
possible 'heliocultural' energy regime

**33. Computational Intelligence**

33.1 Introduction

33.2 Fuzzy
logic

33.3 Artificial
neural networks

33.4 Genetic
algorithms

33.5 Genetic
programming: Evolution of computer programs

### 33.6 Artificial life

**34. Modelling of Adaptation and Learning in Complex Adaptive Systems**

34.1 Holland’s
model for adaptation and learning

34.2 The
bucket brigade in Holland's algorithm

### 34.3 Langton’s work on adaptive computation

### 34.4 The edge-of-chaos existence of complex adaptive systems

**35. Robots**

35.1 Behaviour-based robotics

35.2 Evolutionary robotics

35.3 Evolution of computer power per unit
cost

**36. Smart Structures**

36.1 The
three main components of a smart structure

36.2 Reconfigurable computers and machines
that can evolve

**37. Machine Intelligence**

37.1 Artificial distributed intelligence

37.2 Evolution of machine intelligence

37.3 The future of intelligence

**38. Evolution of Language**

**39. Memes and Their Evolution**

**40. Evolution of the Human Brain, and the Nature of Our Neocortex**

40.1 Evolution of the brain

40.2 The human neocortex

40.3 The history of intelligence

**41. Minsky’s and Hawkins’ Models for how Our Brain Functions**

### 41.1 Marvin Minsky’s ‘Society of Mind’

### 41.2 Can we make decisions without involving emotions?

### 41.3 Hawkins’ model for intelligence and consciousness

**42. Inside the Human Brain**

42.1 Probing the human Brain

### 42.2 Peering into the human brain

**43. Kurzweil's Pattern-Recognition Theory of Mind**

**44.**

**The Knowledge Era and Complexity Science**

44.1 The wide-ranging applications of
complexity science

44.2 Econophysics

44.3 Application of complexity ideas in
management science

44.4 Cultural evolution and complexity
transitions

44.5 Complexity leadership theory

44.6 Complexity science in everyday life

**45. Epilogue**

**IV. Appendices**

**A1. Equilibrium Thermodynamics and Statistical Mechanics**

A1.1 Equilibrium thermodynamics

A1.2 Statistical mechanics

A1.3 The ergodicity hypothesis

A1.4 The partition function

A1.5 Thermodynamics of small systems

**A2. Probability Theory**

A2.1 The notion of probability

A2.2 Multivariate probabilities

A2.3 Determinism and predictability

**A3. Information and Uncertainty**

A3.1 Information theory

A3.2 Shannon’s formula for a numerical
measure of information

A3.3 Shannon entropy and thermodynamic
entropy

A3.4 Uncertainty

A3.5 Algorithmic information theory

A3.6 Entropic
uncertainty relations

**A4. Thermodynamics and Information**

A4.1 Entropy and information

A4.2 Kolmogorov-Sinai
entropy

A4.3 Mutual
information and redundancy of information

**A5. Systems Far from Equilibrium**

A5.1 Emergence of complexity in systems far
from equilibrium

A5.2 Nonequilibrium classical dynamics

A5.3 When does the Newtonian description
break down?

A5.4 Generalization of Newtonian dynamics

A5.5 Pitchfork bifurcation

A5.6 Extension of Newton's laws

**A6. Quantum Theory and Particle Physics**

A6.1 Introduction

A6.2 The Heisenberg uncertainty principle

A6.3 The Schrödinger
equation

A6.4 The
Copenhagen interpretation

A6.5 Time
asymmetry

A6.6 Multiple
universes

A6.7 Feynman's sum-over-histories
formulation

A6.8 Quantum Darwinism

A6.9 Gell-Mann's coarse-graining
interpretation

A6.10 Poincaré resonances and quantum theory

A6.11 Model-dependent
realism, intelligence, existence

A6.12 Particle
physics

**A7. Theory of Phase Transitions and Critical Phenomena**

A7.1 A typical phase transition

A7.2 Liberal definitions of phase
transitions

A7.3 Instabilities can cause phase
transitions

A7.4 Order parameter of a phase transition

A7.5 The
response function corresponding to the order parameter

A7.6 Phase transitions near thermodynamic
equilibrium

A7.7 The Landau theory of phase transitions

A7.8 Spontaneous breaking of symmetry

A7.9 Field-induced phase transitions

A7.10 Ferroic phase transitions

A7.11 Prototype symmetry

A7.12 Critical phenomena

A7.13 Universality classes and critical
exponents

A7.14 Scaling relations

A7.15 Renormalization-group theory

**A8. Chaos Theory**

A8.1 The logistic equation

A8.2 Lyapunov
exponents

A8.3 Divergence
of neighbouring trajectories

A8.4 Chaotic attractors

**A9. Network Theory and Complexity**

A9.1 Graphs

A9.2 Networks

A9.3 The travelling salesman problem

A9.4 Random networks

A9.5 Percolation transitions in random
networks

A9.6 Small-world networks

A9.7 Scale-free networks

A9.8 Evolution of complex networks

A9.9 Emergence of symmetry in complex
networks

A9.10 Kauffman’s work on genetic regulatory
networks . .

A9.11 Chua’s
cellular nonlinear networks as a paradigm for emergence and complexity

**A10. Game Theory**

A10.1 Introduction

A10.2 Dual or two-player games

A10.3 Noncooperative games

A10.4 Nash equilibrium

A10.5 Cooperative games

**Bibliography**

**Index**

**About the Author**

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*As science turns to complexity, one must realize that complexity demands attitudes quite different from those heretofore common in physics. Up to now, physicists looked for fundamental laws true for all times and all places. But each complex system is different: apparently there are no general laws for complexity. Instead, one must reach for ‘lessons’ that might, with insight and understanding, be learned in one system and applied to another. Maybe physics studies will become more like human experience.*

**Goldenfeld and Kadanoff (1999)**

*I think the next century will be the century of complexity.*

**Stephen Hawking (2000)**

*Successful ecosystems are complex adaptive systems, as are successful cities and societies. According to the scientist James Lovelock’s Gaia concept, the Earth as a whole is a complex adaptive system. One of its long-term adaptations that should be of concern to all of us may well be to get rid of our species to protect itself. Whether that happens or not could come down to whether we are able to understand the rules that govern its complexity, and whether we have the wisdom to adapt ourselves and conform to those rules.*

**Len Fisher (2009)**