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Chaos: A Very Short Introduction

Download Ebook Chaos: A Very Short Introduction

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Review

"Leonard Smith's Chaos (part of the Oxford Very Short Introduction series) will give you the clearest (but not too painful idea) of the maths involved... There's a lot packed into this little book, and for such a technical exploration it's surprisingly readable and enjoyable."-- popularscience.co.uk

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About the Author

Leonard Smith is a member of the Mathematics Faculty in Oxford and lectues on nonlinear dynamical systems and chaos.

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Product details

Paperback: 176 pages

Publisher: Oxford University Press; 1 edition (April 16, 2007)

Language: English

ISBN-10: 9780192853783

ISBN-13: 978-0192853783

ASIN: 0192853783

Product Dimensions:

6.8 x 0.4 x 4.3 inches

Shipping Weight: 5.6 ounces (View shipping rates and policies)

Average Customer Review:

3.7 out of 5 stars

22 customer reviews

Amazon Best Sellers Rank:

#117,441 in Books (See Top 100 in Books)

I read the book twice. The first time I read it in bits and pieces and, frankly, didn't get a lot out of it. The second time I sat down, focused and read it as a whole; the second approach was much more valuable. So, I recommend that you take the time to read the book in a focused matter; otherwise, if you're like me, you may not get the book's import.Next, you need to understand that the book has a number of mathematical concepts that for a non-mathematician like me, takes some effort to grasp. There are mathematical concepts that I believe that I only dimly understand even after some effort to do so. However, I concluded that this probably more on my shortcomings rather than the author's.So, if you're going to read the book, commit to do so, and, unless you've got a broader mathematical background than I have (one college calculus course), prepare to be challenged. The more I considered the book after my second reading, the more that I felt the challenges merited my effort. I think that it will reward your effort as well.What are the rewards? Most are familiar with the "butterfly effect;" the idea that a butterfly flapping its wings in Argentina, for instance, can cause a tornado in Kansas. The book discusses, among many things, "sensitive dependence," the reality that sometimes small changes can have exponentially large effects across time, and maybe a fairly short time. But there's much more.To my surprise, the book challenges the belief that mathematics can adequately, and always, describe reality. In doing so the book compares the realities faced by physicists and mathematicians. Chaos has defined the mathematical dynamical qualities, of being (1) recurrent, (2) deterministic and (3) sensitive dependence in its initial state. A physical system may be described as chaotic, but it may be difficult, or impossible, to be assured that it possesses all three of these qualities. The author describes why computers can't model chaos systems.Another surprising observation of the book is that we probably can't determine the initial physical state of a table, a garden filled with rabbits, etc., with as much precision as we think. This inability is due to the concept of "noise." Read the book to see what "noise" is and why it affects our ability to make predictions.Chaotic systems are non-linear. The book considers scientific inquiry prior to, and during much of, the 20th century, which dealt with linear systems, and how that experience, and some of the mathematical concepts developed for that experience, was upended by chaos as it developed during the 20th century. So, the book has a history of science component, which I found interesting.Models, such as the ones used for weather forecasting, are examined in detail. The strengths, weaknesses, and evolution of modeling receive careful examination. Can a model, even one with 10,000,000 variables ever truly permit accurate forecasting? Read to find out.Lastly, the author occasionally considers the concept of "truth." If the model and/or the math is bad or inadequate, can one get truth from any effort to model reality. He tells the story of three baseball umpires who explain their views of the game. One says: "I calls 'em as I sees 'me." The second says: "I calls 'em as they are." The third says: "They ain't, until I calls 'em." The author says that chaos pushes us towards the philosophical position of the third umpire. Focus and I think you'll find your efforts rewarded.

I enjoy this short introduction series. I have read several books from this series and have found that it is a good way to learn about topics I have always wanted to learn about but never found the time to study in depth. Nevertheless, I was a little disappointed with this book.I have heard about chaos theory for years and 'the butterfly effect,' that chaos theory invokes has almost become cliché. Yet, I didn't understand what chaos theory was. That is why I picked up this book. Now, after reading it, if I understand rightly, it seems like chaos is an apparent lack of order within a system and chaos theory is an attempt to measure and model uncertainty within particular systems. Even though there is apparent disorder there is an underlying order in which small events can lead to complex results, thus the famous 'butterfly effect.' of chaos theory. The theory actually arose from attempts to understand and model weather patterns, and to predict future weather. It was out of the need to understand uncertainty in weather that the science grew.That was about as far as I got in my understanding of the ideas contained within. The author claimed readers didn't need to be mathematicians to understand what he was saying about chaos. Sure, he never threw any formulas at me. Yet, much of the concepts and jargon was derived from math. I feel to really appreciate what he was saying about chaos theory one needs a solid background in math. I found some of the jargon and math ideas intimidating and didn't feel like I was comprehending all of the concepts that the author was trying to communicate.Again, could have the author communicated the concepts better, or does the reader need the background to understand what the author was saying?I will leave that up to other readers to decide. Maybe they will appreciate the thoughts contained within better than I did. Yet, regardless, I recommend books from this series. It is a good way to quickly get up to speed on intellectual topics in vogue. I hope that the editors continue to produce new books in this series.

This book is more than just an introduction to chaos. it is a deep dive in the question of uncertainty, noise and modeling accuracy, including mathematical, scientific, statistical and philosophical points of view. it offer a deep analysis and great food for thought. while the first part of the book is ready to follow down to the details, the second part becomes increasingly more complex, requiring a deeper know-how to be correctly comprehended. But at the dentist the goal of the book was just to be a short introduction.

I found this in an interesting, but difficult read. That is not to say it was not a very helpful introduction, but this is a very complex and potentially daunting subject. This 176 page read serves as a very good springboard to a whole lot more reading! Unfortunately, I can see myself doing a lot more studying in this area; but that's the fun of it! I must admit that I enjoy learning about math, science, and philosophy; and this has plenty of all those things! Pardon me, but my "geek" is showing! How embarrassing!I would recommend this book to those who enjoy science or math, but beware, this can easily lead to much heavier reading. Consider yourself warned!

This book takes a complex subject and adds even more complexity. The author good get to the point much more quickly than he does.

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