Chaos Theory Tamed [Hardcover]

Garnett P. Williams (Author), A Joseph Henry Press book (Author)

Book Description

Publication Date: October 8, 1997

What is this business called 'chaos'? What does it deal with? Why do people think it's important? And how did the term 'chaos' - long associated with disorder - come to signify a new paradigm in the orderly realm of mathematics? The concept of chaos is one of the most exciting and rapidly expanding research topics of recent decades. Chaos might underlie many kinds of well-known processes - the performance of the stock market, the weather, the cries of newborn babies, the dripping of a leaky faucet, and more.In "Chaos Theory Tamed", scientist Garnett P. Williams walks the reader through this exciting territory, building an understanding of chaos and its significance in our lives. "Chaos" is a mathematical subject. If you seek bodice-ripping romance, this book is not for you. But if you are a researcher working with data...a scientist, engineer, or economist who has specialized outside the field of mathematics...or an interested person with a bit of background in algebra and statistics...then "Chaos Theory Tamed" can help you understand the basic concepts of this relatively new arm of science.Williams explains the terms necessary for an understanding of chaos theory. He discusses 'sensitive dependence on initial conditions' and what that means for long-term predictions. He explores the role of the chaotic or 'strange' attractor, order within chaos, fractal structure, and the emerging concepts of self-organization and complexity. Drawing from mathematics, physics, and statistics, the book provides a toolkit for readers, including vectors, phase space, Fourier analysis, time-series analysis, and autocorrelation.Williams describes routes that systems may take from regular behavior to chaos - period doubling, intermittency, and quasiperiodicity - and discusses nonlinear equations that can give rise to chaos. Dimension is a basic ingredient of chaos, and Williams brings clarity to the many ways in which this term is used by specialists in the field. And he explains how the magnitude of chaos may be gauged by Lyapunov exponents, Kolmogorov-Sinai entropy, and mutual information - mysterious terms that 'aren't all that difficult once we pick them apart,' says Williams. "Chaos Theory Tamed" makes generous use of lists, graphs, field examples, summaries, and - perhaps most important - friendly language to help the reader learn and use the vocabulary of chaos. It will help scientists, students, and others outside mathematics to use the concepts of chaos in working with data, and it will give the interested lay reader a foothold on the fundamentals of this new realm of thought.

Editorial Reviews

Book Description

What is this business called "chaos"? What does it deal with? Why do people think it's important? And how did the term "chaos"--long associated with disorder--come to signify a new paradigm in the orderly realm of mathematics?
The concept of chaos is one of the most exciting and rapidly expanding research topics of recent decades. Chaos might underlie many kinds of well-known processes--the performance of the stock market, the weather, the cries of newborn babies, the dripping of a leaky faucet, and more.
In Chaos Theory Tamed, scientist Garnett P. Williams walks the reader through this exciting territory, building an understanding of chaos and its significance in our lives. Chaos is a mathematical subject. If you seek bodice-ripping romance, this book is not for you. But if you are a researcher working with data...a scientist, engineer, or economist who has specialized outside the field of mathematics...or an interested person with a bit of background in algebra and statistics...then Chaos Theory Tamed can help you understand the basic concepts of this relatively new arm of science.
Williams explains the terms necessary for an understanding of chaos theory. He discusses "sensitive dependence on initial conditions" and what that means for long-term predictions. He explores the role of the chaotic or "strange" attractor, order within chaos, fractal structure, and the emerging concepts of self-organization and complexity.
Drawing from mathematics, physics, and statistics, the book provides a toolkit for readers, including vectors, phase space, Fourier analysis, time-series analysis, and autocorrelation. Williams describes routes that systems may take from regular behavior to chaos--period doubling, intermittency, and quasiperiodicity--and discusses nonlinear equations that can give rise to chaos. Dimension is a basic ingredient of chaos, and Williams brings clarity to the many ways in which this term is used by specialists in the field. And he explains how the magnitude of chaos may be gauged by Lyapunov exponents, Kolmogorov-Sinai entropy, and mutual information--mysterious terms that "aren't all that difficult once we pick them apart," says Williams.
Chaos Theory Tamed makes generous use of lists, graphs, field examples, summaries, and--perhaps most important--friendly language to help the reader learn and use the vocabulary of chaos. It will help scientists, students, and others outside mathematics to use the concepts of chaos in working with data, and it will give the interested lay reader a foothold on the fundamentals of this new realm of thought.

About the Author

by Garnett P. Williams; A Joseph Henry Press book

Product Details

• Hardcover: 520 pages
• Publisher: Joseph Henry Press; 1 edition (October 8, 1997)
• Language: English
• ISBN-10: 0309063515
• ISBN-13: 978-0309063517
• Product Dimensions: 9.4 x 6.3 x 1.3 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars  See all reviews (19 customer reviews)
• Amazon Best Sellers Rank: #390,258 in Books (See Top 100 in Books)
  • #48 in Books > Professional & Technical > Professional Science > Physics > Chaos Theory

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Customer Reviews

Most Helpful Customer Reviews

65 of 66 people found the following review helpful:

5.0 out of 5 stars Do not let this book get away, October 16, 2000

By 

Taylor Erickson (Arvada, CO USA) - See all my reviews

This review is from: Chaos Theory Tamed (Hardcover)

This is the most comprehensive, clear-cut, to the point book on Chaos theory I have read. My only regret is that I did not read it earlier. I could have avoided a lot of confusion left from reading authors who do not clearly understand Chaos theory (I have read some books that have the right equations with the wrong answers), or understand the science but lack the ability to articulate the concepts clearly. Williams succeeds in both these areas.

Williams devotes a considerable number of pages to building a foundation of understanding before jumping into particular topics. For example, he selectively covers specific (relevant) areas of geometry, trigonometry, statistics, information theory, etc. before uncovering the mysteries and ideas of Chaos Theory that rest on that foundation of knowledge. It is almost as if he wrote the book as he learned about the topic. The reader can see the evolution of ideas and how they amalgamate into a collective understanding and perspective of Chaos. However, the easy navigation, superb writing style, and diverse references make this book also applicable for the experienced Chaos practitioner.

Before reading Chaos Theory Tamed I had read over 20 books on the subject and still lacked the conceptual framework and necessary tools to begin applying the theories. This book ties it all together and makes the theory useful and applicable. I intend on writing Williams personally and thank him for his valuable contribution to this field of study.

42 of 43 people found the following review helpful:

5.0 out of 5 stars Good introduction on chaos theory, January 20, 2001

By 

Steve Uhlig (Berlin, Germany) - See all my reviews
(REAL NAME)   

This review is from: Chaos Theory Tamed (Hardcover)

Very accessible introduction on chaos theory. Style is informal and nontechnical. You're not required to have a particular background in mathematics to understand the content. Reading it is particularly easy, and it provides excellent pointers to more advanced topics on chaos theory.

If you already have some background in dynamic systems and modeling, i would recommend Morrison's book : "The Art of Modeling Dynamic Systems : Forecasting for Chaos, Randomness, and Determinism" which is somewhat more technical but certainly more helpful for getting a good idea of what chaos theory is, at an engineering point of view.

In addition, for getting a very broad view of chaos in the real world, Schroeder's "Fractals, Chaos, Power laws: Minutes from an Infinite Paradise" is incomparable ! It overwhelms you with the footprints of chaos in every possible context. A must-read ! But very technical and requires some important knowledge in physics and science engineering...

However, as an easy nontechnical introduction on chaos theory, this book really deserves its 5 stars !

21 of 21 people found the following review helpful:

5.0 out of 5 stars Excellent!, April 1, 1998

By 

Nick Wienholt ([e-mail]) (Sydney, Australia) - See all my reviews

This review is from: Chaos Theory Tamed (Hardcover)

The best science book I have ever read.
The author's style is clear, concise and informative, and his treatment of complex mathematical concepts is the best I have ever seen.
This books fills the great void between specialist mathematical texts, and popular science novels.
If you want to understand chaos theory - buy this book. If you want to see a supurb example of science writing, do the same.