Thinking in Complexity (PDF)

The theory of nonlinear, complex systems has become by now a proven problem-solving approach in the natural sciences. It is also recognized that many, if not most, of our social, ecological, economical and political problems are essentially of a global, complex and nonlinear nature. And it is now further accepted than any holistic perspective of the human mind and brain can hardly be achieved by any other approach. In this wide-ranging, scholarly but very concise treatment, Klaus Mainzer (physicist, computer scientist and philosopher) discusses, in essentially nontechnical language, the common framework behind these ideas and challenges. Emphasis is given to the evolution of new structures in natural and cultural systems, and we are lead to see clearly how the new integrative approach can give insights not available from traditional reductionistic methods. The fifth edition enlarges and revises almost all sections and include an entirely new chapter on the complexity of economic systems.

From the reviews of the fourth edition:

"... this highly recommended book is a wonderful resource for intuitive basic ideas in the need of rigorous formulation." (Albert A. Mullin, Zentralblatt MATH)

"This book is ambitious, incredibly erudite with 22 pages of references, and is indisputably clearly and beautifully written and illustrated. It is perfectly suited to a first course on the science of complexity. Even beginners and young graduate students will have something to learn from this book." (André Hautot, Physicalia)

"Readers of this book will enjoy Mainzer's exposition, which is based on a tight coupling between classical and historical concepts from Plato and Aristotle to modern, mathematical and physical developments ... . takes pains to point out essential differences between classical science and the science of complexity. ... Thinking in Complexity is an outstandingly readable book." (Anutosh Moitra, The IndustrialPhysicist)