Synopses & Reviews
This book explains why complex systems research is important in understanding the structure, function and dynamics of complex natural and social phenomena. It illuminates how complex collective behavior emerges from the parts of a system, due to the interaction between the system and its environment. You will learn the basic concepts and methods of complex system research. It is shown that very different complex phenomena of nature and society can be analyzed and understood by nonlinear dynamics since many systems of very different fields, such as physics, chemistry, biology, economics, psychology and sociology etc. have similar architecture. "Complexity Explained" is not highly technical and mathematical, but teaches and uses the basic mathematical notions of dynamical system theory making the book useful for students of science majors and graduate courses, but it should be readable for a more general audience; actually for those, who ask: What complex systems really are?
Review
REVIEW - COMPLEXITY EXPLAINED BY PETER ERDI By Karl Friston FRS, University College London This is a charming and engaging book. It treats the reader with perspectives on complexity from nearly all possible angles. This rounded approach works extremely well and highlights the connections between different formulations of complexity, both in terms of their application and historical development. The book is clearly written by someone who delights in the challenges posed by complexity research and has spent a lot of time teaching in this area. The book is written in an intuitive and accessible way; although there are mathematical expositions, they are not intimidating for the non-mathematical reader. The book is organised in a clear and purposeful way; as if it was based on a mature series of lectures. It stars from the historical fundaments of complexity theory and ends with cutting-edge research into things like evolutionary game theory. The writing style is endearingly idiosyncratic; disclosing the author's Hungarian background. Peter Erdi's ethnic and intellectual roots show themselves through the balanced references to Eastern block and Western contributions, through his Hungarian anecdotes and metaphors, through his syntax and finally through his humour. There are several nice examples of the latter; his preference for the term "player" over "agent" is not left implicit. Sometimes it is difficult to tell whether something has been lost or gained in translation, for example I had assumed that "out of ouch" meant "out of touch". However, the context in which this phrase was used (the resolution of unrequited love) made me think twice. In short, the book had great substance and made me smile a lot. The book is organised into ten chapters; the first three deal with the history of complex systems and theory. I found these chapters very illuminating. They gather together names and concepts that one has come across before and place them in useful relationship to each other. There is lots of fascinating detail about the growth of the ideas considered in later chapters. These chapters are underpinned by some excellent tutorials in relevant basics in the physical and life-sciences (e.g., Hamiltonian dynamics, statistical thermodynamics, chaotic itinerancy and so on). In areas that I am familiar with, I was impressed by the clarity and depth of this background material. This made me take the treatment of other areas equally seriously. The middle part of the book deals with the phenomenology and application domains of complexity theory; ranging from chemical kinetics to the epidemic propagation of infections and ideas. Some of the examples are a prelude to the final chapters that focus on the complexity of the brain and related models of decision making and prediction. There is diversity and coherence in these chapters, for example we move gracefully from stock-market crashes to epileptic seizures, which take us straight back to earlier chapters dealing with single-cell modelling in the brain and neuronal rhythms. As with the historical chapters, the coverage was impressive for its balance and breadth. As someone who has dealt with complex systems in a somewhat piece-meal fashion, I was impressed that nearly every relevant contribution I know about was covered in a brief but useful way. Even in areas I was familiar with, I learned a lot, particularly about the origins of some of the ideas. Most of this was scientific but sometimes it was historical (e.g., the contributions F Ventriglia to mean-field theories of statistical neurodynamics); sometimes it was personal (e.g., learning that, sadly, Esther Thelen had died). I am not sure whether this book 'explains' complexity. It certainly explains the genesis of the complexity sciences with a compelling and useful focus on the history of these ideas and the rhetoric needed to articulate them. This is a very worthwhile read for any student considering an academic career in complexity or, senior scientists who want to place their corner of enquiry in a larger context. On finishing the book, I wondered whether a better title would have been "Complexity Celebrated". From the reviews: "In Complexity Explained, Érdi (Kalamazoo College) traces in great detail the path that complexity theory followed from classical mathematics onward. ... The list of references is extensive and may be useful for researchers. Summing Up ... Researchers/faculty." (J. A. van Reenen, CHOICE, Vol. 45 (11), July, 2008) "Érdi covers such a great deal of important data on complexity that a shorter review cannot do justice to this excellent book ... . The 581 References are one indication of his inclusive broad coverage. ... graduate students, researchers and teachers in any of the numerous sciences, technologies and humanities, as well as the general educated public are addressed. ... Any researcher planning to write a book ought to copy Érdi's styles: the English is superbly conversational, clear, uncomplicated and logically compressed ... ." (Karl H. Wolf, International Journal of General Systems, 2008) "This book has many advantages ... . It is an excellent introduction to CS for specialists in many fields. ... Summarizing, this is an excellent introduction to CS. I strongly recommend it to anyone who wants to learn CS seriously. At a more advance level, it should be followed by deeper books in individual fields e.g. CS in biology, CS in social sciences etc... I thank the author for this enjoyable and useful book." (E. Ahmed, Zentralblatt MATH, Vol. 1162, 2009) "This book is written for anyone interested in the meaning of complexity. ... the book uses mathematical notions of dynamical systems theory to show that very different complex phenomena of nature and society can be analyzed and understood by nonlinear dynamics." (IEEE Control Systems Magazine, Vol. 29, October, 2009)
Review
REVIEW - COMPLEXITY EXPLAINED BY PETER ERDI By Karl Friston FRS, University College London This is a charming and engaging book. It treats the reader with perspectives on complexity from nearly all possible angles. This rounded approach works extremely well and highlights the connections between different formulations of complexity, both in terms of their application and historical development. The book is clearly written by someone who delights in the challenges posed by complexity research and has spent a lot of time teaching in this area. The book is written in an intuitive and accessible way; although there are mathematical expositions, they are not intimidating for the non-mathematical reader. The book is organised in a clear and purposeful way; as if it was based on a mature series of lectures. It stars from the historical fundaments of complexity theory and ends with cutting-edge research into things like evolutionary game theory. The writing style is endearingly idiosyncratic; disclosing the author's Hungarian background. Peter Erdi's ethnic and intellectual roots show themselves through the balanced references to Eastern block and Western contributions, through his Hungarian anecdotes and metaphors, through his syntax and finally through his humour. There are several nice examples of the latter; his preference for the term "player" over "agent" is not left implicit. Sometimes it is difficult to tell whether something has been lost or gained in translation, for example I had assumed that "out of ouch" meant "out of touch". However, the context in which this phrase was used (the resolution of unrequited love) made me think twice. In short, the book had great substance and made me smile a lot. The book is organised into ten chapters; the first three deal with the history of complex systems and theory. I found these chapters very illuminating. They gather together names and concepts that one has come across before and place them in useful relationship to each other. There is lots of fascinating detail about the growth of the ideas considered in later chapters. These chapters are underpinned by some excellent tutorials in relevant basics in the physical and life-sciences (e.g., Hamiltonian dynamics, statistical thermodynamics, chaotic itinerancy and so on). In areas that I am familiar with, I was impressed by the clarity and depth of this background material. This made me take the treatment of other areas equally seriously. The middle part of the book deals with the phenomenology and application domains of complexity theory; ranging from chemical kinetics to the epidemic propagation of infections and ideas. Some of the examples are a prelude to the final chapters that focus on the complexity of the brain and related models of decision making and prediction. There is diversity and coherence in these chapters, for example we move gracefully from stock-market crashes to epileptic seizures, which take us straight back to earlier chapters dealing with single-cell modelling in the brain and neuronal rhythms. As with the historical chapters, the coverage was impressive for its balance and breadth. As someone who has dealt with complex systems in a somewhat piece-meal fashion, I was impressed that nearly every relevant contribution I know about was covered in a brief but useful way. Even in areas I was familiar with, I learned a lot, particularly about the origins of some of the ideas. Most of this was scientific but sometimes it was historical (e.g., the contributions F Ventriglia to mean-field theories of statistical neurodynamics); sometimes it was personal (e.g., learning that, sadly, Esther Thelen had died). I am not sure whether this book 'explains' complexity. It certainly explains the genesis of the complexity sciences with a compelling and useful focus on the history of these ideas and the rhetoric needed to articulate them. This is a very worthwhile read for any student considering an academic career in complexity or, senior scientists who want to place their corner of enquiry in a larger context. On finishing the book, I wondered whether a better title would have been "Complexity Celebrated". From the reviews: "In Complexity Explained, Érdi (Kalamazoo College) traces in great detail the path that complexity theory followed from classical mathematics onward. ... The list of references is extensive and may be useful for researchers. Summing Up ... Researchers/faculty." (J. A. van Reenen, CHOICE, Vol. 45 (11), July, 2008) "Érdi covers such a great deal of important data on complexity that a shorter review cannot do justice to this excellent book ... . The 581 References are one indication of his inclusive broad coverage. ... graduate students, researchers and teachers in any of the numerous sciences, technologies and humanities, as well as the general educated public are addressed. ... Any researcher planning to write a book ought to copy Érdi's styles: the English is superbly conversational, clear, uncomplicated and logically compressed ... ." (Karl H. Wolf, International Journal of General Systems, 2008) "This book has many advantages ... . It is an excellent introduction to CS for specialists in many fields. ... Summarizing, this is an excellent introduction to CS. I strongly recommend it to anyone who wants to learn CS seriously. At a more advance level, it should be followed by deeper books in individual fields e.g. CS in biology, CS in social sciences etc... I thank the author for this enjoyable and useful book." (E. Ahmed, Zentralblatt MATH, Vol. 1162, 2009) "This book is written for anyone interested in the meaning of complexity. ... the book uses mathematical notions of dynamical systems theory to show that very different complex phenomena of nature and society can be analyzed and understood by nonlinear dynamics." (IEEE Control Systems Magazine, Vol. 29, October, 2009)
Synopsis
This book is, of course about complexity. The title of the book, as you may recognize was motivated (excuse me for using this very mild expression) by Daniel Dennett's Consciousness Explained 130]. Dennett's intention was to explain consciousness as the emergent product of the interaction among c- stituents having physical and neural character. The goal of this book is to explain how various types of complexity emerge due to the interaction among constituents. There are many questions to be answered, how to understand, control, decompose, manage, predict the many-faced complexity. After tea- ing thissubjectforseveralyearsIfeelthatthe time hascome toputthe whole story together. The term "complex system" is a buzzword, but we certainly don't have a single de?nition for it. There are several predominant features of compl- ity. Complex processes may show unpredictable behavior (which we still try to predict somehow), may lead to uncontrolled explosion (such in case of epilepsy, earthquake eruptions or stock market crashes). One of the char- teristic feature of simple systems is, that there is a single cause which implies a single e?ect. For large class of complex systems it is true that e?ects are fed back to modify causes. Biological cells belong to this class. Furthermore they are open to material, energetic and information ?ow by interaction with their environment, still they are organizationallyclosed units. Another aspect of complexity is the question how collective phenomena emerge by some se- organized mechanisms.
Table of Contents
1 COMPLEX SYSTEMS: THE INTELLECTUAL LANDSCAPE 1.1 The century of complexity? 1.2 Characteristics of simple and complex systems 1.2.1 System and its environment 1.2.2 Simple systems 1.2.3 Complex systems 1.3 Connecting the dots 2 HISTORY of COMPLEX SYSTEMS RESEARCH 2.1 Reductionist success stories versus the importance of organization principles 2.1.1 Reductionism and holism in quantum physics 2.1.2 Reductionism and complexity in molecular biology 2.2 Ancestors of present day complex system research 2.2.1 Systems theory 2.2.2 Cybernetics 2.2.3 Nonlinear science in action: Theory of dissipative structures, synergetics and catastrophe theory 3 FROM THE CLOCKWORK WORLD VIEW to IRREVERSIBILITY (and BACK?) 3.1 Cyclic universe versus linear time concept: the metaphysical perspective 3.1.1 Cyclic Universe 3.1.2 Linear time concepts 3.2 The Newtonian Clockwork Universe 3.2.1 The mechanical clock 3.2.2 Kepler's integral laws 3.2.3 Newton's differential laws, Hamilton equations, conservative oscillation, dissipation 3.3 Mechanics versus Thermodynamics 3.3.1 Heat conduction and irreversibility 3.3.2 Steam engine, feedback control, irreversibility 3.3.3 The first and second laws of thermodynamics 3.4 The birth of the modern theory of dynamical systems 3.5 Oscillations 3.5.1 The Lotka -Volterra Model 3.5.2 Stable oscillation: limit cycles 3.5.3 Quasiperiodic motions: A few words about the modern theory of dynamical systems 3.6 The chaos paradigm: then and now 3.6.1 Defining and detecting chaos 3.6.2 Structural and geometrical conditions of chaos: what is important and what is not? 3.6.3 The necessity of being chaotic 3.6.4 Controlling chaos: why and how? 3.6.5 Traveling to High-dimension land: Chaotic itinerancy 3.7 Direction of evolution 3.7.1 Dollo's law in retrospective 3.7.2 Is something never-decreasing during evolution? 3.8 Cyclic universe: revisited. . . and criticized 4 THE DYNAMIC WORLD VIEW in ACTION 4.1 Causality, teleology and about the scope and limits of the dynamical paradigm 4.1.1 Causal versus teleological description 4.1.2 Causality, networks, emergent novelty 4.2 Chemical kinetics: a prototype of nonlinear science 4.2.1 On the structure - dynamics relationship for chemical reactions 4.2.2 Chemical kinetics as a metalanguage 4.2.3 Spatiotemporal patterns in chemistry and biology 4.3 Systems biology: the half admitted renaissance of cybernetics and systems theory 4.3.1 Life itself 4.3.2 Cells as self-referential systems 4.3.3 The old-new systems biology 4.3.4 Random Boolean networks: model framework and applications for genetic networks 4.4 Population dynamic and epidemic models: biological and social 4.4.1 Connectivity, stability, diversity 4.4.2 The epidemic propagation of infections and ideas 4.4.3 Modeling social epidemics 4.5 Evolutionary dynamics 4.6 Dynamic models of war and love 4.6.1 Lanchaster's combat model and its variations 4.6.2 Is love different from war? 4.7 Social dynamics: some examples 4.7.1 Segregation dynamics 4.7.2 Opinion dynamics 4.8 Nonlinear dynamics in economics: some examples 4.8.1 Business cycles 4.8.2 Controlling chaos in economic models 4.9 Drug market: controlling chaos 5 THE SEARCH FOR LAWS: DEDUCTIVE VERSUS INDUCTIVE 5.1 Deductive versus inductive arguments 5.2 Principia Mathematica and the deductive approach: From Newton to Russell and Whitehead 5.3 Karl Popper and the problem of induction 5.4 Cybernetics: Bridge between Natural and Artificial 5.5 John von Neumann: the real pioneer of complex systems studies 5.6 Artificial Intelligence , Herbert Simon and the bounded rationality 5.7 Inductive reasoning and bounded rationality: from Herbert Simon to Brian Arthur 5.8 Minority Game 5.9 Summary and "what next?" 6 STATISTICAL LAWS: FROM SYMMETRIC TO ASYMMETRIC 6.1 Normal distribution 6.1.1 General remarks 6.1.2 Generation of normal distribution: Brownian motion 6.1.3 Liouville process, Wiener and special Wiener process, Ornstein - Uhlenbeck process 6.2 Bi- and multimodal distributions 6.3 Long tail distributions 6.3.1 Lognormal and power law distributions: phenomenology 6.3.2 Generation of lognormal and power-law distributions 7 SIMPLE AND COMPLEX STRUCTURES: BETWEEN ORDER AND RANDOMNESS 7.1 Complexity and randomness 7.2 Structural complexity 7.2.1 Structures and graphs 7.2.2 Complexity of graphs 7.2.3 Fractal structures 7.3 Noise-induced ordering: an elementary mathematical model 7.4 Networks everywhere: between order and randomness 7.4.1 Statistical approach to large networks 7.4.2 Networks in cell biology 7.4.3 Epidemics on networks 7.4.4 Citation and collaboration networks in science and Technology 8 COMPLEXITY OF THE BRAIN: STRUCTURE, FUNCTION AND DYNAMICS 8.1 Introductory remarks 8.2 Windows on the brain 8.2.1 A few words about the brain-mind problem 8.2.2 Experimental methods: a brief review 8.3 Approaches and organizational principles 8.3.1 Levels 8.3.2 Bottom up and top down 8.3.3 Organizational principles 8.4 Single cells 8.4.1 Single cells: general remarks 8.4.2 Single cell modeling: deterministic and stochastic Framework 8.5 Structure, dynamics, function 8.5.1 Structural aspects 8.5.2 Neural rhythms 8.5.3 Variations on the Hebbian learning rule: different roots 8.6 Complexity and Cybernetics: towards a unified theory of brain-mind and computer 8.6.1 Cybernetics strikes back 8.6.2 From cognitive science to embodied cognition 8.6.3 The brain as a hermeneutic device 8.6.4 From neurons to soul and back 9 FROM MODELS to DECISION MAKING 9.1 Equation-based versus agent-based model 9.1.1 Motivations 9.1.2 Artifical life 9.1.3 Artificial societies 9.1.4 Agent-based computational economics 9.2 Game theory: where we are now? 9.2.1 Classical game theory 9.2.2 Evolutionary game theory 9.3 Widening the Limits to Predictions: Earthquake, Eruptions Epileptics Seizures, and Stock Market Crashes 9.3.1 Scope and limits of predictability 9.3.2 Phenomenology 9.3.3 Statistical analysis of extreme events 9.3.4 Towards predicting seizures 9.3.5 Towards predicting market crashes: analysis of price peaks 9.3.6 Dynamical models of extreme events 10 HOW MANY CULTURES WE HAVE? 10.1 Complexity as a unifying concept 10.1.1 Systems and simulations 10.1.2 The topics of the book in retrospective: natural and human socioeconomic systems 10.2 The ingredients of complex systems 10.3 Complexity explained: In defense of (bounded) rationality References Index