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Does God Play Dice? The New Mathematics of Chaos by Stewart, Ian (2002) Paperback
Télécharger le fichier PDF Does God Play Dice? The New Mathematics of Chaos by Stewart, Ian (2002) Paperback
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This is the second book I read from Ian Steward. I was looking for another book on the subject of chaos, and having been impressed by a book of his called "The Mathematics of Life," I decided to read this one. I wasn't disappointed.He begins with the Greeks, Eudoxus, Ptolemy, and others and moves through time to Copernicus, Kepler, and Galilei showing how the foundations of mathematics were developed. Later we learn of the works of Euler, Lagrange and his generalized coordinates, Hamilton's work on the state of dynamical systems, and Galton's contributions to the normal distribution. As the 20th century came to a close, statistical methodology took its place alongside deterministic modeling as an equal partner.By chapter six, we are into strange attractors and flows in a plane such as sinks, sources, saddles, and limit cycles. Then there is quasiperiodicity, suspensions, solenoids, and Poincaré sections which can give us interesting pictures of the dynamical behavior. Any text on chaos is, of course, going to cover logistic mapping and bifurcation diagrams, as well - so does Steward. Chapter ten introduces Mitchell Feigenbaum and the Feigenvalue - a value of 4.669 - the rate at which successive period doublings accumulate faster and faster. Chapter eleven gets into fractals, Julia sets and the infamous Mandelbrot set.I found chapter sixteen very interesting. I'll just quote Steward here, "The central thrust of the chapter is the possibility of changing the theoretical framework of quantum mechanics altogether, replacing quantum uncertainty by deterministic chaos as Einstein would have liked." As Steward delves into concepts such as quanta; wave functions; spin; eigenfunctions; decoherence; the Einstein, Podolsky, and Rosen paradox and other concepts, he exposes what he feels are some loopholes in the arguments - all very fascinating. His alternate explanation of "spooky action at a distance" or quantum entanglement eliminates the need for information to travel at speeds exceeding the speed of light. I found his argument convincing - too lengthy to describe here. In the last chapter, the discussion turns to complexity theory and how it relates to chaos.Steward presents here for us, I feel, an interesting introduction to the world of chaos - the world we live in incidentally. This is an in depth discussion of the subject, but I feel that Steward did a remarkable job of "translating" the obtuse mathematics and concepts to an understandable level for someone not expert in the field. Certainly an excellent book, and I highly recommend it.By the way, as Steward says in the Epilogue, "If God played dice ... he'd win."
This is a good book for those who are either starting to learn about chaos and nonlinear dynamics or those who would just like an overall view of what the subject is about without getting bogged down into heavy-duty math. This book has two distinct themes. One is to explain the mathematical concept of chaos, and why it is both natural and inevitable. The other is to ask the rather long question "Does the mathematical model of chaos exist in the real world, and does it help us understand some of the things that we see?".This book covers a variety of subjects that might at first seem unrelated - mathematical history, various chaotic models, weather patterns, applications - but by the end of the book everything comes together to give you a good overall view of the field. This second edition is mainly different from the first in the added three chapters on applications. These chapters cover prediction in chaotic systems, the control of chaotic systems, and then there is a speculative chapter that attempts to explain how the concept of chaos might lead to a new answer to Einstein's famous question which is also the title of this book.This book requires more imagination and an ability to visualize than a talent for mathematics, and it makes a good introduction to more technical books on the subject such as "Nonlinear Dynamics and Chaos" by Strogatz. Of course, that book requires much more in the way of mathematical maturity. This book looks more at the forest, the Strogatz book looks more at the trees.
An interesting and fun introduction to chaos. Stewart writes very well and often makes keen and insightful observations. I learned a great deal and was inspired to read other books on this fascinating topic. There were a few things I didn't like, but to be honest they are not major: 1) The deliberate avoidance of mathematical detail in this book, which does indeed present some very deep mathematical concepts, is very odd and sometimes unhelpful. Odd, for example, as when in the midst of a chapter on quantum theory Stewart takes time to painstakingly tell the reader what an absolute value is. Or, when he's describing how to perform calculations to generate chaos he stops for a paragraph to explain what it means to square a variable. Is it really possible that readers who lack such rudimentary math skills would be reading this book?? 2) For my tastes, there's way too much God talk in this book. Stewart clearly is not doing this for any religious reason - but it's odd because I have no idea why he finds it necessary to so often toss in sentences about God doing this or God thinking that, or God blah blah blah. By the end - especially at the literal end and the stupid joke in the epilogue - it really gets tiresome.
I am a college-educated, non-math major, numbers-oriented senior citizen who wanted to find out what Chaos Theory is. I got this book out of my local library to see whether I should purchase it. It reads easily, even entertainingly, so I decided to order it.However, the newest edition in paperback has very very fine print--even with reading glasses! I returned this edition, and am trying again with the older edition in hardback (same ISBN as the library book).As others have noted, this book does not go into the "deep" mathematics of Chaos. However, the material IS challenging.
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