Read Does God Play Dice: The Mathematics of Chaos by Ian Stewart Free Online
Book Title: Does God Play Dice: The Mathematics of Chaos|
The author of the book: Ian Stewart
Date of issue: January 16th 1991
ISBN 13: 9781557861061
Format files: PDF
The size of the: 353 KB
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Reader ratings: 3.5
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This book is a solid, interesting and insightful introduction to Chaos theory (the relatively recent and fascinating branch of physics that deals with the study of nonlinear dynamical systems exhibiting extreme sensitivity to initial conditions, in which seemingly random complex behavior can derive from simple deterministic, innocuous-looking equations).
The material treated by the book is pretty standard for a good introduction to the subject: I think that it could actually be used as a supporting book for a non-mathematical undergraduate course in the subject. It would also be valuable reading for a course in the philosophy of science, as it contains, in a few places, fascinating discussions about the scientific method, about the contrast between the paradigm of modelling through partial differential equations and the methods of chaos theory, about the real meaning of complexity and of randomness and the challenges posed by chaotic behavior to the experimental verification of mathematical models, and other similarly interesting subjects.
Overall it is a quite enjoyable book, written with conceptual clarity, and one of the very few books about chaos theory that at least attempt to seriously get into the more subtle conceptual elements of this discipline.
However it must also be said that the subtitle “the new mathematics of chaos” is misleading - this is not a book about the mathematics of chaos, but it's more about the conceptual features of the phenomenon.
But, even if devoid of mathematics, it can be really fully appreciated only by readers who had some prior knowledge of basics of topology and of partial differential equations. From this perspective, it really leaves you wanting for a more mathematical, quantitative approach – and this is quite unsatisfactory – this book could so easily have been a real gem.
The lack of mathematical detail is occasionally frustrating (for example: Lorenz simplified mathematical model for atmospheric convection is shown, but there is no explanation of how these three differential equations are derived, nor any explanation of what the variables in the equations actually mean; another example: the concept of fractal dimension is introduced, but no mathematical detail is presented; even relatively simple examples like the driven oscillator or the double pendulum are not treated mathematically – something which the author could have at least done as a separate item in an appendix at the end of the book).
On the other hand, it is not an over-simplistic book: many fascinating features of chaos theory are addressed in a pretty rigorous, occasionally deep, but always approachable manner:
- there is an excellent introduction to the relationship between the topological features of the phase space, and the overall behavioral pattern of the dynamics of the associated system (in particular I enjoyed the part about Poincare sections and how they relate to phase portraits and attractors)
- the logistic mapping is treated beautifully, and the introduction to the concept of strange attractors is quite enjoyable, possibly one of the best I have seen
- the same applies to the concept of self-similarity and how the the enormously varied range of possible mappings gets lumped together into universality classes, where within each class the scaling ratio is always the same (for example: the famous 4.669 for the class of mappings structurally similar to the logistic mapping)
- the frustratingly complex phenomenon of turbulence is treated really well
- the relationship between strange attractors and their fractal dimension is very interesting
Overall, it is a very good introduction to chaos theory and nonlinear dynamics, recommended to readers with no prior exposure to this fascinating discipline who are interested in a serious but non-mathematical treatment of the subject.
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Read information about the authorIan Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website
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