This book on complexity science comprises a collection of chapters on methods and principles from a wide variety of disciplinary fields — from physics and chemistry to biology and the social sciences.In this two-part volume, the first part is a collection of chapters introducing different aspects in a coherent fashion, and providing a common basis and the founding principles of the different complexity science approaches; the next provides deeper discussions of the different methods of use in complexity science, with interesting illustrative applications.The fundamental topics deal with self-organization, pattern formation, forecasting uncertainties, synchronization and revolutionary change, self-adapting and self-correcting systems, and complex networks. Examples are taken from biology, chemistry, engineering, epidemiology, robotics, economics, sociology, and neurology.

In this very short introduction, John Holland presents an introduction to the science of complexity. Using examples from biology and economics, he shows how complexity science models the behaviour of complex systems.

Contents 11. 2. 2. Four Main Areas of Dispute 247 11. 2. 3. Summary . . . 248 11. 3. Making Sense of the Issues . . 248 11. 3. 1. Introduction . . . . 248 11. 3. 2. The Scientific Approach 248 11. 3. 3. Science and Matters of Society . 249 11. 3. 4. Summary . 251 11. 4. Tying It All Together . . . . 251 11. 4. 1. Introduction . . . . 251 11. 4. 2. A Unifying Framework 251 11. 4. 3. Critical Systems Thinking 253 11. 4. 4. Summary 254 11. 5. Conclusion 254 Questions . . . 255 REFERENCES . . . . . . . . . . . . . . . . . . . 257 INDEX . . . . . . . . . . . . . . . . . . . . . . 267 Chapter One SYSTEMS Origin and Evolution, Terms and Concepts 1. 1. INTRODUCTION We start this book with Theme A (see Figure P. I in the Preface), which aims to develop an essential and fundamental understanding of systems science. So, what is systems science? When asked to explain what systems science is all about, many systems scientists are confronted with a rather daunting task. The discipline tends to be presented and understood in a fragmented way and very few people hold an overview understanding of the subject matter, while also having sufficient in-depth competence in many and broad-ranging subject areas where the ideas are used. Indeed, it was precisely this difficulty that identified the need for a comprehensive well-documented account such as is presented here in Dealing with Complexity.

Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).

Chaos and complexity are the new buzz words in both science and contemporary society. The ideas they represent have enormous implications for the way we understand and engage with the world. Complexity Theory and the Social Sciences introduces students to the central ideas which surround the chaos/complexity theories. It discusses key concepts before using them as a way of investigating the nature of social research. By applying them to such familiar topics as urban studies, education and health, David Byrne allows readers new to the subject to appreciate the contribution which complexity theory can make to social research and to illuminating the crucial social issues of our day.

Ecosystems, the human brain, ant colonies, and economic networks are all complex systems displaying collective behaviour, or emergence, beyond the sum of their parts. Complexity science is the systematic investigation of these emergent phenomena, and stretches across disciplines, from physics and mathematics, to biological and social sciences. This introductory textbook provides detailed coverage of this rapidly growing field, accommodating readers from a variety of backgrounds, and with varying levels of mathematical skill. Part I presents the underlying principles of complexity science, to ensure students have a solid understanding of the conceptual framework. The second part introduces the key mathematical tools central to complexity science, gradually developing the mathematical formalism, with more advanced material provided in boxes. A broad range of end of chapter problems and extended projects offer opportunities for homework assignments and student research projects, with solutions available to instructors online. Key terms are highlighted in bold and listed in a glossary for easy reference, while annotated reading lists offer the option for extended reading and research.

“If you liked Chaos, you’ll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year” (The Washington Post). In a rarified world of scientific research, a revolution has been brewing. Its activists are not anarchists, but rather Nobel Laureates in physics and economics and pony-tailed graduates, mathematicians, and computer scientists from all over the world. They have formed an iconoclastic think-tank and their radical idea is to create a new science: complexity. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell—and what the origin of life some four billion years ago can tell us about the process of technological innovation today. This book is their story—the story of how they have tried to forge what they like to call the science of the twenty-first century. “Lucidly shows physicists, biologists, computer scientists and economists swapping metaphors and reveling in the sense that epochal discoveries are just around the corner . . . [Waldrop] has a special talent for relaying the exhilaration of moments of intellectual insight.” —The New York Times Book Review “Where I enjoyed the book was when it dove into the actual question of complexity, talking about complex systems in economics, biology, genetics, computer modeling, and so on. Snippets of rare beauty here and there almost took your breath away.” —Medium “[Waldrop] provides a good grounding of what may indeed be the first flowering of a new science.” —Publishers Weekly

By now, most academics have heard something about the new science of complexity. In a manner reminiscent of Einstein and the last hundred years of physics, complexity science has captured the public imagination. ® One can go to Amazon. com and purchase books on complexification (Casti 1994), emergence (Holland 1998), small worlds (Barabási 2003), the web of life (Capra 1996), fuzzy thinking (Kosko 1993), global c- plexity (Urry 2003) and the business of long-tails (Anderson 2006). Even television has incorporated the topics of complexity science. Crime shows ® ® such as 24 or CSI typically feature investigators using the latest advances in computational modeling to “simulate scenarios” or “data mine” all p- sible suspects—all of which is done before the crime takes place. The ® World Wide Web is another example. A simple search on Google. Com using the phrase “complexity science” gets close to a million hits! C- plexity science is ubiquitous. What most scholars do not realize, however, is the remarkable role sociologists are playing in this new science. C- sider the following examples. 0. 1 Sociologists in Complexity Science The first example comes from the new science of networks (Barabási 2003). By now, most readers are familiar with the phenomena known as six-degrees of separation—the idea that, because most large networks are comprised of a significant number of non-random weak-ties, the nodes (e. g. , people, companies, etc.

Available in paperback for the first time, this book describes and considers ideas and insights from complexity science, and examines their use in organizations, especially in bringing about major organizational change.

Complexity is a new interdisciplinary approach to science and society that challenges traditional academic divisions, frameworks and paradigms. This book helps the expert, student or policy practitioner have a better understanding of the enormous potential of complexity, and how it relates to their particular area of interest or expertise.