Tuesday, 4 July 2017


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

Vinod Wadhawan

Book details
Paperback: 514 pages
Publisher: CreateSpace Independent Publishing Platform; 2 edition (September 13, 2017)
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

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, 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.


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.

September, 2017


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
NOTE ADDED ON 13th September 2017

The second edition of this book was published today. A number of 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. Accordingly, the list of contents etc. underwent some minor changes, which have been incorporated in this blog post.