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Does God Play Dice?: The New Mathematics of Chaos

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The revised and updated edition includes three completely new chapters on the prediction and control of chaotic systems. It also incorporates new information regarding the solar system and an account of complexity theory. This witty, lucid and engaging book makes the complex mathematics of chaos accessible and entertaining. Presents complex mathematics in an accessible sty The revised and updated edition includes three completely new chapters on the prediction and control of chaotic systems. It also incorporates new information regarding the solar system and an account of complexity theory. This witty, lucid and engaging book makes the complex mathematics of chaos accessible and entertaining. Presents complex mathematics in an accessible style. Includes three new chapters on prediction in chaotic systems, control of chaotic systems, and on the concept of chaos. Provides a discussion of complexity theory.


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The revised and updated edition includes three completely new chapters on the prediction and control of chaotic systems. It also incorporates new information regarding the solar system and an account of complexity theory. This witty, lucid and engaging book makes the complex mathematics of chaos accessible and entertaining. Presents complex mathematics in an accessible sty The revised and updated edition includes three completely new chapters on the prediction and control of chaotic systems. It also incorporates new information regarding the solar system and an account of complexity theory. This witty, lucid and engaging book makes the complex mathematics of chaos accessible and entertaining. Presents complex mathematics in an accessible style. Includes three new chapters on prediction in chaotic systems, control of chaotic systems, and on the concept of chaos. Provides a discussion of complexity theory.

30 review for Does God Play Dice?: The New Mathematics of Chaos

  1. 5 out of 5

    WarpDrive

    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 supporti 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.

  2. 4 out of 5

    Charbel

    Before we start with the review, let's take a moment to appreciate how good of a science communicator Ian Stewart is. Now on with the nitty gritty. When faced with accepting Quantum Mechanics, Einstein famously said: "God does not play dice with the universe", to which Stephen Hawking wittily replied: "Not only does God play, but he sometimes throws them where they cannot be seen". Quantum Mechanics, you see, cannot be handled with simple every day linear mathematics. Instead we attempt to explain Before we start with the review, let's take a moment to appreciate how good of a science communicator Ian Stewart is. Now on with the nitty gritty. When faced with accepting Quantum Mechanics, Einstein famously said: "God does not play dice with the universe", to which Stephen Hawking wittily replied: "Not only does God play, but he sometimes throws them where they cannot be seen". Quantum Mechanics, you see, cannot be handled with simple every day linear mathematics. Instead we attempt to explain it using probability. The reason behind this is chaos. Chaos may not be apparent in the overview of things, but when the smaller details add up, chaos becomes the main force behind them. It is the reason why so many behaviours seem unpredictable, or even random. To understand chaos, we cannot rely on classical linear mathematics, in fact just to glimpse it mathematicians had to become absorbed in the world of topology; a world of saddles, sinks, sources, and attractors; where a hole is not the lack of something but is in itself something (I love that!). I admit that before reading this book I underestimated topology, thinking that it could not rival calculus, statistics, and probability. But once I was asked to visualise an object in four dimensions, let alone fix or six, I understood my own ignorance. In the end, what we end up with is that chaos is not only unpredictable, but also stable; making it one of the most dazzling paradoxes around. Now enough about chaos and topology, let's talk about the book; after all that's what a review is for. Now, can you read this book without an advanced background in mathematics? Yes, I did. Will it be easy? Not particularly. The larger part of Does God Play Dice is conceptual. You have to put in an effort. If I had to compare this book to something, I'd say that it's close to an introductory course on chaos. It explains a whole lot, but it leaves you with so many questions. The best aspect of this book is that some of the most difficult things to understand are explained clearly with Ian Stewart's subtle sense of humour. And so even when I had my eyes closed trying to visualise something, like attractors, or writing down notes on the Butterfly Effect ( which is pretty useful to me), it was still fun. Challenging, but fun! Best of all, the book prepares you to read more about chaos. Because let's face it, when you finally finish this book, you're going to have one of two reactions: either "Wow, I'm so glad I read this! I need to learn more about chaos!" or "I don't even want to hear the C word again! Now where's the aspirin?". Fortunately for me, I had the former reaction. Some chapter were fantastic (chapter 16 comes to mind), others, like the pendulum chapter, could have used more "bling". So would I recommend this book? Yes, definitely. But a word of advice: take your time with it. Let the new concepts sink in first. Don't rush through it; read the sentence (or the chapter) multiple times if you have to, until you get it. Because once you do, it's worth it. If you do decide to pick it up, I hope you enjoy it. Have fun, and sorry about the long review.

  3. 5 out of 5

    Natalia

    What a great introduction to chaos theory! This book is not only well-written, but it's also incredibly interesting. What a great introduction to chaos theory! This book is not only well-written, but it's also incredibly interesting.

  4. 4 out of 5

    Eleanore

    An extremely accessible history of the emergence of chaos theory and description of its fundamental elements and dynamics. Written with an eye for humor, the book is a real triumph of conceptual clarity for the non-mathematically inclined and reflects an important extension to the basic qualitative understanding of science, the ramifications of which are still working themselves out even in the hard scientific disciplines. I am, however, thoroughly looking forward to the eventual impact this new An extremely accessible history of the emergence of chaos theory and description of its fundamental elements and dynamics. Written with an eye for humor, the book is a real triumph of conceptual clarity for the non-mathematically inclined and reflects an important extension to the basic qualitative understanding of science, the ramifications of which are still working themselves out even in the hard scientific disciplines. I am, however, thoroughly looking forward to the eventual impact this new field has on the social sciences! A salutary warning to the whole range of intro-quantitative methods courses: "Linearity is a trap. The behavior of linear equations - like that of choirboys - is far from typical."

  5. 5 out of 5

    Karel Baloun

    It's stunning and intriguing review of nonlinear systems (chaos), from countless real world perspectives. Stewart's humorous and engaging writing style makes the book a pleasure. He starts from simple mathematical equations and simple physical systems such as pendulums and turbulent water, and routinely takes the idea out to cutting edge research or engineering possibilities. Now I know what math textbooks and areas of study to proceed to, and Stewart has given mea geometric ability to visualize, It's stunning and intriguing review of nonlinear systems (chaos), from countless real world perspectives. Stewart's humorous and engaging writing style makes the book a pleasure. He starts from simple mathematical equations and simple physical systems such as pendulums and turbulent water, and routinely takes the idea out to cutting edge research or engineering possibilities. Now I know what math textbooks and areas of study to proceed to, and Stewart has given mea geometric ability to visualize, necessary for success

  6. 5 out of 5

    Kerem

    At times a bit technical, this is indeed an intriguing book, a passionate account of Stewart on chaos theory and how endless applications and uses it has. I really enjoyed it, and recommend it to anyone to challenge your perspective on how things happen in world.

  7. 4 out of 5

    Alex Delogu

    This book really gets into the theoretical stuff that was missing in Gleick's book on chaos. It still doesn't go heavily into the math but I struggled with some of the more technical material. I will certainly come back to. Stewart is a gifted expositor. This book really gets into the theoretical stuff that was missing in Gleick's book on chaos. It still doesn't go heavily into the math but I struggled with some of the more technical material. I will certainly come back to. Stewart is a gifted expositor.

  8. 5 out of 5

    Koen Crolla

    Nothing particularly new, but I guess I've read enough of these now that that was pretty likely. It's a very good overview of the whats and whys of chaos theory, comparable to Gribbin's Deep Simplicity, though maybe slightly less accessible. The final chapter is marred by an ill-conceived rant at a straw man of reductionism, but nobody is perfect. Nothing particularly new, but I guess I've read enough of these now that that was pretty likely. It's a very good overview of the whats and whys of chaos theory, comparable to Gribbin's Deep Simplicity, though maybe slightly less accessible. The final chapter is marred by an ill-conceived rant at a straw man of reductionism, but nobody is perfect.

  9. 4 out of 5

    Diego Fernández

    There subjects were interesting I did not know. I learnt a lot from it. There mere interesting is I grasped on "God plays dice" - it was a referential to Einstein's quotes when he was working quantum mechanics. But yeah, it doesn't mean we refer to God popular culture. I think the law of natures has to see with chaos. Well, I have no words to say about a review of this book. Took me few days or weeks to finish due to I bought in Spanish and was quite larger. This kind of theory was new to me. I h There subjects were interesting I did not know. I learnt a lot from it. There mere interesting is I grasped on "God plays dice" - it was a referential to Einstein's quotes when he was working quantum mechanics. But yeah, it doesn't mean we refer to God popular culture. I think the law of natures has to see with chaos. Well, I have no words to say about a review of this book. Took me few days or weeks to finish due to I bought in Spanish and was quite larger. This kind of theory was new to me. I hope for this year I learn more of mathematics than I'd learnt at school or university. Well, thanks for reading my reviews, even if it was too short. :)

  10. 5 out of 5

    Pete Wung

    Please read my book review on my blog. Thank you. https://polymathtobe.blogspot.com/202... Please read my book review on my blog. Thank you. https://polymathtobe.blogspot.com/202...

  11. 5 out of 5

    José González

    A good introduction to chaos. It’s rewarding both as a mathematics book and a philosophical inquiry of the nature of our relation to knowledge of the natural world. This relation is established through the human language of math.

  12. 4 out of 5

    rebecca

    i haven't read every chapter of this book, but i read most. and the book is excellent. despite the tagline, the book contains minimal maths (which is quite refreshing). would recommend to anyone interested in supplementing their learning or just curious bc it's quite accessible. somehow manages to include both depth and breadth to the subject, without being much over 400 pages long. incredible. i haven't read every chapter of this book, but i read most. and the book is excellent. despite the tagline, the book contains minimal maths (which is quite refreshing). would recommend to anyone interested in supplementing their learning or just curious bc it's quite accessible. somehow manages to include both depth and breadth to the subject, without being much over 400 pages long. incredible.

  13. 5 out of 5

    Charles

    The best mathematical models for many physical events rely on chaotic formulas and the number continues to grow rapidly. It now appears that some exposure to chaos and fractals will be a necessary component of the education of all future applied mathematicians. Given the simplicity of many of the equations, it can be strongly argued that chaos should be an early component of all mathematics education. Also, programming a computer to generate the images is very simple and a lot of fun. To study ch The best mathematical models for many physical events rely on chaotic formulas and the number continues to grow rapidly. It now appears that some exposure to chaos and fractals will be a necessary component of the education of all future applied mathematicians. Given the simplicity of many of the equations, it can be strongly argued that chaos should be an early component of all mathematics education. Also, programming a computer to generate the images is very simple and a lot of fun. To study chaos, you need a place to start, and this book will point you in the right direction and give you a brisk tail wind. The author, best known for his mathematics columns in Scientific American, writes with exceptional clarity. There are very few equations, as Stewart relies extensively on the verbal explanation. While computer generation is mentioned, only one very short BASIC program is given. The material is pretty standard for introductory chaos and could serve as a textbook for a non-mathematical course in the subject. It would also be valuable reading for a course in the philosophy of science. Fairly extensive historical backgrounds are given for many of the initial discoveries. If you have heard about chaos and want to know what all the excitement is about or are looking for reading material for a class you are teaching, this book is an excellent place to explore. Published in Journal of Recreational Mathematics, reprinted with permission and this review appears on Amazon.

  14. 4 out of 5

    Mangoo

    Chaos represents the third great scientific revolution of last century, after Einstein's relativity and (among the earliest) Plank's and Nernst's quantum field theory. As the others two, chaos is endowed with a veil of mistery and fantasy and remoteness, though appealing in this case, even though its rules are by now quite known and its growing applications are very disparate. This notwithstanding, chaos remains more a curiosity or an abused metaphor among college students, not talking about you Chaos represents the third great scientific revolution of last century, after Einstein's relativity and (among the earliest) Plank's and Nernst's quantum field theory. As the others two, chaos is endowed with a veil of mistery and fantasy and remoteness, though appealing in this case, even though its rules are by now quite known and its growing applications are very disparate. This notwithstanding, chaos remains more a curiosity or an abused metaphor among college students, not talking about youngsters, while it should have all rights to belong to high school curricula even. This because it is very interesting and essentially easy to understand if well presented. And it is highly entartaining. Ian Stewart has produced more than two decades ago this good popularization, an introduction to non-linear system dynamics for laymen, naming it after a reputedly Einsteinian sentence which, truth said, was originally referred to the epistemic a-causality that quantum mechanics seemed to purport and that he did not digest (not till its very late years, that is). Stewart's is a real introduction to chaos facts and its manifold ramifications (maps, weather forecasts, maths), as compared to the more famous yet more gossipy "Chaos" by Gleick, which deals more with the epic history of the development of ideas behind chaos theory. Suggested to neophites, and to high school students, too.

  15. 5 out of 5

    Rosalind

    It's a thankless task trying to write for a general audience about a subject as rich, varied and profound as mathematics. Especially in a culture where maths is so badly taught many adults take great pride in not being any good at it (hint: there's a lot more to maths than endlessly adding and dividing fractions!) Some fail by being too superficial, but Ian Stewart can't be accused of that. Here he takes on the relatively new field of chaos, the mathematics of systems where very small changes in It's a thankless task trying to write for a general audience about a subject as rich, varied and profound as mathematics. Especially in a culture where maths is so badly taught many adults take great pride in not being any good at it (hint: there's a lot more to maths than endlessly adding and dividing fractions!) Some fail by being too superficial, but Ian Stewart can't be accused of that. Here he takes on the relatively new field of chaos, the mathematics of systems where very small changes in parameters lead to huge differences in outcome that, to the uninformed, appear random. These chaotic systems are the true building blocks of the real world rather than the neat, straightforward formulae that create smooth, regular shapes, yet generations of mathematicians and physicists have shied away from them until very recently. Stewart shows how even the most shapeless systems, when looked at from the right angle, exhibit the most exquisite patterns and symmetries. His style is informal, chatty, sometimes iconoclastic, but be warned: it's not a book for mathematical novices. Some of the concepts are mind-twisting!

  16. 5 out of 5

    Brian Powell

    I enjoyed this book initially but felt like it kinda ran out of steam about half-way through. The author's writing style is friendly and engaging, and the material is most definitely interesting. Overall, it was light in details -- which I guess is the point of a popular-level account -- but I found it generally lacking. The title is a bit sensationalized too -- god does play dice but not through chaos. The subtitle is also misleading -- this is not a book about the mathematics of chaos per se.. I enjoyed this book initially but felt like it kinda ran out of steam about half-way through. The author's writing style is friendly and engaging, and the material is most definitely interesting. Overall, it was light in details -- which I guess is the point of a popular-level account -- but I found it generally lacking. The title is a bit sensationalized too -- god does play dice but not through chaos. The subtitle is also misleading -- this is not a book about the mathematics of chaos per se... it's more about the conceptual essence of the phenomenon.

  17. 4 out of 5

    Franck Chauvel

    Ian explains in, I think, a very accessible way the mathematics of "Chaos". I found the selected examples simple enough and yet compelling and I liked the stories about the scientists who pioneered the field. Ian also outlook various applications of chaos theory to practical issues, including spring manufacturing. A very nice introduction, which I recommend to those, like me, who run away when Greek symbols show up. I eventually did not understood whether God plays dice or not, but the I learned Ian explains in, I think, a very accessible way the mathematics of "Chaos". I found the selected examples simple enough and yet compelling and I liked the stories about the scientists who pioneered the field. Ian also outlook various applications of chaos theory to practical issues, including spring manufacturing. A very nice introduction, which I recommend to those, like me, who run away when Greek symbols show up. I eventually did not understood whether God plays dice or not, but the I learned a lot about chaotic systems on the way.

  18. 4 out of 5

    Eric Hertenstein

    More Mathy than Chaos but covering much of the same ground. An excellent introduction to the wonders of phase space, and there's a fantastic little bit about Pointcaré near the beginning. Stewart's kind of a cad, though. More Mathy than Chaos but covering much of the same ground. An excellent introduction to the wonders of phase space, and there's a fantastic little bit about Pointcaré near the beginning. Stewart's kind of a cad, though.

  19. 5 out of 5

    Josh Holland

    Lovely introduction to chaos and its discovery and applications in nonlinear dynamics. The style of writing is accessible but not patronising, and there is a nice amount of Ian Stewart's wit scattered amongst the pages. It focuses more on chaos than the quantum mechanics the titular quote refers to, but there is a chapter on QM at the end. It is a very good read for people interested in chaos and how the world really works. Lovely introduction to chaos and its discovery and applications in nonlinear dynamics. The style of writing is accessible but not patronising, and there is a nice amount of Ian Stewart's wit scattered amongst the pages. It focuses more on chaos than the quantum mechanics the titular quote refers to, but there is a chapter on QM at the end. It is a very good read for people interested in chaos and how the world really works.

  20. 4 out of 5

    Mark

    A good introduction to chaos theory, and some of the mathematics behind it, and possible applications. Topics include strange attractors, self-similarity, and fractals. The book includes some helpful illustrations. The book seems to go into a bit more mathematical detail (some actual equations) than a typical book about chaos theory for a general audience. This particular edition of the book seems to be a bit out-dated in some places (given that it was published in 1990).

  21. 4 out of 5

    T Campbell

    Entertaining and clearly the basis for a lot of modern understanding of the concept. I highly recommend it for anyone who wants to brush up their own mathematical knowledge. It's an older book with added chapters, and could stand to be updated to be a bit more contemporary in terms of the modern implications of its subjects, but that's a tough compromise to manage: get too meaty and you lose accessibility. Still, I'm picking up another Ian Stewart book now. Entertaining and clearly the basis for a lot of modern understanding of the concept. I highly recommend it for anyone who wants to brush up their own mathematical knowledge. It's an older book with added chapters, and could stand to be updated to be a bit more contemporary in terms of the modern implications of its subjects, but that's a tough compromise to manage: get too meaty and you lose accessibility. Still, I'm picking up another Ian Stewart book now.

  22. 4 out of 5

    Joe

    excellent introduction to chaos theory and nonlinear dynamics, including their relationship to topology, history of discovery, and projections into the future. in particular enjoyed learning about poincare sections and how they relate to phase portraits and attractors. also chaotic control (von neuman's dream). excellent introduction to chaos theory and nonlinear dynamics, including their relationship to topology, history of discovery, and projections into the future. in particular enjoyed learning about poincare sections and how they relate to phase portraits and attractors. also chaotic control (von neuman's dream).

  23. 4 out of 5

    Trystan Hopkins

    Read this and one other book on Chaos theory. The author misrepresents Einstein's theories at many points in the book, i presume in order to promote his own relativistic views as if they were supported by Einstein himself. Ultimately, it reads like a book whose author didn't fully understand the topic at hand. Read this and one other book on Chaos theory. The author misrepresents Einstein's theories at many points in the book, i presume in order to promote his own relativistic views as if they were supported by Einstein himself. Ultimately, it reads like a book whose author didn't fully understand the topic at hand.

  24. 5 out of 5

    Bradley Gram-hansen

    Ian Stewart writes many books, including this one, which cater to both mathematicians and non-mathematicians. Although, no mathematical knowledge is required, they are very insightful books and are a great bit of fun!

  25. 5 out of 5

    Marcos

    Not my cup of tea, but very interesting indeed. Some concepts are hard to follow for a layman, but all in all, Stewart uses accessible language and lots of examples, so you get a general idea. I'd recommend it as an introduction to the subject. Not my cup of tea, but very interesting indeed. Some concepts are hard to follow for a layman, but all in all, Stewart uses accessible language and lots of examples, so you get a general idea. I'd recommend it as an introduction to the subject.

  26. 5 out of 5

    Carroll Straus

    Superb, even for a lay reader. Enchanting.

  27. 4 out of 5

    Carlisdania Mendoza

    I liked it. Very fun to read, quite challenging.

  28. 5 out of 5

    Artur Edward

    Years ago opened teenager's eyes wide! Years ago opened teenager's eyes wide!

  29. 5 out of 5

    Piya

    Tedious at times, I would recommend one to first read Lorenz's book. But the chapter on quantum mechanics (+ argument of what's really random) is very interesting. Tedious at times, I would recommend one to first read Lorenz's book. But the chapter on quantum mechanics (+ argument of what's really random) is very interesting.

  30. 5 out of 5

    Kiran

    You'll enjoy it if we can appreciate the ubiquitous mathematics in our world! You'll enjoy it if we can appreciate the ubiquitous mathematics in our world!

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