Joseph P. Zbilut's Books

From Instability to Intelligence

Complexity and Predictability in Nonlinear Dynamics

By: Michail Zak,Joseph P. Zbilut,Ronald E. Meyers

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From Instability to Intelligence

Complexity and Predictability in Nonlinear Dynamics

By: Michail Zak,Joseph P. Zbilut,Ronald E. Meyers

So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi bility in thermodynamics, the phenomena of chaos and turbulence in clas sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.

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Page Count

559

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540691219

ISBN 13

9783540691211

Unstable Singularities and Randomness

Their Importance in the Complexity of Physical, Biological and Social Sciences

By: Joseph P. Zbilut

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Unstable Singularities and Randomness

Their Importance in the Complexity of Physical, Biological and Social Sciences

By: Joseph P. Zbilut

Traditionally, randomness and determinism have been viewed as being diametrically opposed, based on the idea that causality and determinism is complicated by "noise. Although recent research has suggested that noise can have a productive role, it still views noise as a separate entity. This work suggests that this not need to be so. In an informal presentation, instead, the problem is traced to traditional assumptions regarding dynamical equations and their need for unique solutions. If this requirement is relaxed, the equations admit for instability and stochasticity evolving from the dynamics itself. This allows for a decoupling from the "burden of the past and provides insights into concepts such as predictability, irreversibility, adaptability, creativity and multi-choice behaviour. This reformulation is especially relevant for biological and social sciences whose need for flexibility a propos of environmental demands is important to understand: this suggests that many system models are based on randomness and nondeterminism complicated with a little bit of determinism to ultimately achieve concurrent flexibility and stability. As a result, the statistical perception of reality is seen as being a more productive tool than classical determinism. The book addresses scientists of all disciplines, with special emphasis at making the ideas more accessible to scientists and students not traditionally involved in the formal mathematics of the physical sciences. The implications may be of interest also to specialists in the philosophy of science.·Presents the ideas in an informal language.·Provides tools for exploring data for singularities.

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Page Count

252

Publisher

Elsevier

Published Date

ISBN 10

0080474691

ISBN 13

9780080474694

The Latent Order of Complexity

By: Joseph P. Zbilut,Alessandro Giuliani

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The Latent Order of Complexity

By: Joseph P. Zbilut,Alessandro Giuliani

The scope of public ignorance concerning how things work inevitably grows explosively. It is unreasonable to expect widespread or detailed understanding even of the many major support systems that make urban life possible (clean water, electrical supply, groceries in markets at all seasons, trash and sewage disposal....). What we don't understand seems 'complex' to us, at least until, with study or practice, we may achieve an occasional 'Ah-Ha!' moment when complexity suddenly reduces to simplicity, and part of our world view changes forever. In this welcome and appealing book the authors, who have achieved stature in both experimental and theoretical sciences, address the grandest 'how things work' issue of them all, viz., the methods and limitations of science itself. They do so in a conversational style accessible to any interested reader.

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Page Count

130

Publisher

Nova Publishers

Published Date

ISBN 10

1604560266

ISBN 13

9781604560268

Book's by Joseph P. Zbilut

From Instability to Intelligence

From Instability to Intelligence

Unstable Singularities and Randomness

Unstable Singularities and Randomness

The Latent Order of Complexity

The Latent Order of Complexity

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