Thinking in Complexity: The Complex Dynamics of Matter, Mind, and Mankind

Politics & Social Sciences

Klaus Mainzer

Philosophy

Springer, Verlag

The theory of nonlinear, complex systems has become by now a proven problem-solving approach in the natural sciences. And it is now 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, physicist, computer scientist and philosopher Klaus Mainzer 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 supplements an entirely new chapter on the complexity of economic systems. From the reviews of the fourth edition: "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." (Andre Hautot, Physicalia, Vol. 57 (3), 2005) "All-in-all, this highly recommended book is a wonderful resource for intuitive basic ideas in the need of rigorous formulation." (Albert A. Mullin, Zentralblatt MATH, vol. 1046, 2004) "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 . Every chapter begins with a section designed to orient the reader to the perspective of philosophical developments through the ages pertinent to the topic at hand. The author 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 Industrial Physicist, August/September, 2004)

Thinking in Complexity: The Computational Dynamics of Matter, Mind, and Mankind

Springer

Science & Math

History & Philosophy

Numbers (Graduate Texts in Mathematics)

Max Koecher

H-.D. Ebbinghaus

H. Hermes

F. Hirzebruch

Jürgen Neukirch

A Prestel

R. Remmert

Mathematics

Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Su I (Japanese Edition)

Reinhold Remmert

Heinz-Dieter Ebbinghaus

Hans Hermes

Friedrich Hirzebruch

Alexander Prestel

In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy. 
 Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT). 
 Readership: Undergraduate and graduate students, scientists and readers who are interested in foundational, interdisciplinary, and philosophical questions of mathematics, computer science, and science in general.

DIGITAL AND THE REAL WORLD, THE: COMPUTATIONAL FOUNDATIONS OF MATHEMATICS, SCIENCE, TECHNOLOGY, AND PHILOSOPHY

Computers & Technology

Computer Science

World Scientific Publishing Co Pte Ltd

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Books by Klaus Mainzer