Klaus Mainzer

Thinking in Complexity

Heinz-Dieter Ebbinghaus

Friedrich Hirzebruch

Max Koecher

Jürgen Neukirch

Reinhold Remmert

Hans Hermes

Alexander Prestel

A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number" told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.

Numbers

Ein Handbuch zur Natur- und Wissenschaftsphilosophie

Symmetrien der Natur

A Handbook for Philosophy of Nature and Science

Symmetries of Nature

This new edition also treats smart materials and artificial life. A new chapter on information and computational dynamics takes up many recent discussions in the community.

The Complex Dynamics of Matter, Mind, and Mankind

Ortwin Renn

Michael Molls

Peter A. Wilderer

Martin Grambow

Here, expert authors delineate approaches that can support both decision makers as well as their concerned populations in overcoming unwarranted fears and in elaborating policies based on scientific evidence. Four exemplary focus areas were chosen for in-depth review, namely:- The scientific basis of risk management- Risk management in the area of environmental and ecological policy- Risk management in radiation medicine- Risk management in context with digitalization and roboticsGeneral as well as specific recommendations are summarized in a memorandum. Fundamental thoughts on the topic are presented in the introductory part of the book. The idea for and contents of the book were developed at a workshop on “Sustainable Risk Management: How to manage risks in a sensible and responsible manner?” held in Feldafing at Lake Starnberg (Germany) on April 14 to 16, 2016. The book offers important information and advice for scientists, entrepreneurs, administrators and politicians.

Sustainable Risk Management

Klaus Mainzer zeigt in diesem Buch, wie es bei dem Vorhaben, die Welt zu berechnen, zu einer Revolution der Denkart kam. Während Generationen von Mathematikern, Physikern und Philosophen auf der Suche nach der Weltformel mit Gleichungen arbeiteten und in den Kategorien von Ursache und Wirkung dachten, ist die «new science» dadurch charakterisiert, dass an die Stelle mathematischer Beweise und Theorien Computerexperimente und Algorithmen treten. «Korrelation» statt «Begründung», lautet die Devise des neuen Denkens. Die Korrelationen in Big Data sollen bislang verborgene Zusammenhänge aufdecken. Nach diesem Prinzip, schreibt das US-Magazin Time, will die 2013 von Google neu gegründete Medizinfirma Calico an der Lebensverlängerung des Menschen arbeiten, indem nicht die Ursachen von Alter und Krankheit untersucht, sondern Unmengen medizinischer Daten mit Algorithmen ausgewertet werden. Eine beispiellose Erfolgsgeschichte also? Mainzer stellt in diesem Buch die faszinierende neue Art der Wissensgewinnung vor, aber er macht auch die Gegenrechnung auf. Sein Buch ist ein Plädoyer für die Besinnung auf die Grundlagen, Theorien, Gesetze und die Geschichte, die zu der Welt führen, in der wir heute leben.

Von der Weltformel zu Big Data

Die Berechnung der Welt

' Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity. Contents:Symmetry and Complexity in Early Culture and PhilosophySymmetry and Complexity in MathematicsSymmetry and Complexity in Physical SciencesSymmetry and Complexity in Chemical SciencesSymmetry and Complexity in Life SciencesSymmetry and Complexity in Economic and Social SciencesSymmetry and Complexity in Computer ScienceSymmetry and Complexity in Philosophy and Arts Readership: Upper-level undergraduates, graduate students, researchers, academics, and professionals in interdisciplinary sciences. Keywords:Symmetry;Symmetry Breaking;Complexity;Nonlinear Science;Dynamical System;Chaos;Bifurcation;Fractal;Computational System;Information Dynamics;Philosophy of Science;ArtsKey Features:Valuable insights from natural, social and computer sciencesAttractive pictures and illustrations enhancing the spirit and beauty of nonlinear scienceReviews:“This outstanding book is a general overview of the notion of symmetry and its many connections to the ideas of complexity … The book will be especially useful to the intelligent general reader as well as advanced undergraduate students looking for challenging technical problems to solve, reconfigure, or redefine.”Zentralblatt MATH '

The Spirit and Beauty of Nonlinear Science

Symmetry and Complexity

von der Urzeit zur Computerzeit

Zeit

wie das Neue in die Welt kommt

Der kreative Zufall

Complexity and nonlinearity are prominent features in the evolution of matter, life, and human society. Even our mind seems to be governed by the nonlinear dynamics of the complex networks in our brain. This book considers complex systems in the physical and biological sciences, cognitive and computer sciences, social and economic sciences, and philosophy and history of science. An in terdisciplinary methodology is introduced to explain the emergence of order in nature and mind and in the econ omy and society by common principles. These methods are sometimes said to foreshadow the new sciences of complexity characterizing the scientific deve10pment of the 21 st century. The book critically an alyzes the successes and limits of this approach, its sys tematic foundations, and its historical and philosophical background. An epilogue discusses new standards of eth ical behavior which are demanded by the complex prob lems of nature and mind, economy and society.

Everybody knows them. Smartphones that talk to us, wristwatches that record our health data, workflows that organize themselves automatically, cars, airplanes and drones that control themselves, traffic and energy systems with autonomous logistics or robots that explore distant planets are technical examples of a networked world of intelligent systems. Machine learning is dramatically changing our civilization. We rely more and more on efficient algorithms, because otherwise we will not be able to cope with the complexity of our civilizing infrastructure. But how secure are AI algorithms? This challenge is taken up in the 2nd edition: Complex neural networks are fed and trained with huge amounts of data (big data). The number of necessary parameters explodes exponentially. Nobody knows exactly what is going on in these "black boxes". In machine learning we need more explainability and accountability of causes and effects in order to be able to decide ethical and legal questions of responsibility (e.g. in autonomous driving or medicine)! Besides causal learning, we also analyze procedures of tests and verification to get certified AI-programs. Since its inception, AI research has been associated with great visions of the future of mankind. It is already a key technology that will decide the global competition of social systems. "Artificial Intelligence and Responsibility" is another central supplement to the 2nd edition: How should we secure our individual liberty rights in the AI world? This book is a plea for technology design: AI must prove itself as a service in society.

Artificial intelligence - When do machines take over?

Klaus Mainzer

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