Book Description

In Aircraft Stories noted sociologist of technoscience John Law tells "stories" about a British attempt to build a military aircraft—the TSR2. The intertwining of these stories demonstrates the ways in which particular technological projects can be understood in a world of complex contexts.

Law works to upset the binary between the modernist concept of knowledge, subjects, and objects as having centered and concrete essences and the postmodernist notion that all is fragmented and centerless. The structure and content of Aircraft Stories reflect Law’s contention that knowledge, subjects, and—particularly— objects are "fractionally coherent": that is, they are drawn together without necessarily being centered. In studying the process of this particular aircraft’s design, construction, and eventual cancellation, Law develops a range of metaphors to describe both its fractional character and the ways its various aspects interact with each other. Offering numerous insights into the way we theorize the working of systems, he explores the overlaps between singularity and multiplicity and reveals rich new meaning in such concepts as oscillation, interference, fractionality, and rhizomatic networks.

The methodology and insights of Aircraft Stories will be invaluable to students in science and technology studies and will engage others who are interested in the ways that contemporary paradigms have limited our ability to see objects in their true complexity. ... Read more

Reviews (3)

Sublime stories on things in their making
While at no point downspeaking to its reader, this book poses a large number of essential questions on technology, science and design. Based on the case of the TSR-2 aircraft, it keeps on asking stubbornly like a detective investigating a crime, uncovering bit by bit how objects are not singular, homogeneous entities, but just as heterogene and active in the formation of society and things as the subjects. It makes very clear that the 'interpellation' between human and nonhuman actors is crucial to investigate, and is itself a paradigmatic example on how to conduct such studies. Its points on the relevance of oscillating between modernity and postmodernity are lucid, imaginative and very informing.

I still hate this book
I had to rate this a second time because my one star rating only reduced the overall rating (it's been reviewed by one other reader) to a two and a half and that's two and a half too many.

I feel like a chump for buying it, but I'm happy admitting my mistake to the world if it could save one helpless soul from having to read paragraphs like...:

"The book as a whole, then, is not treelike in structure. It is not an arborescence. Instead it takes the form of a rhizomatic network. It makes overlaps and juxtapositions, and it makes interference effects as a result of making these overlaps. So that is the fourth way of introducing the book. It is about writing fractionally." - p. 9 John Law, Aircraft Stories.

You really don't want to know about other three ways of introducing the book. I was struggling during the first two, the third had me gasping for air and number four was kinda it for me.

I was dubious at first
Unless you are very used to post-modern theory, you will not find Law's idea lucid at first. I believe that I shook my head in disbelief. His explanation of a fractal reality fell on death ears, but then I read more. Once I finished the book and discussed it in class, I realized that Law had altered how I viewed technoscience. This book is highly recommended and Law should be commended for his approach to a reconciliation of the modern and post-modern. ... Read more

Reviews (3)

Not really worth it
Perhaps I bought this book with expecting too much. The books does talk about general system thinking, but:
- I find the book itself rather unsystematic and jumpy
- The style really annoying
- Most of the material is primitive
On the positive side, if you do want to get a feel of system thinking, this might be one of the books. I would also recommend to check out popular books on Complexity (such as Complexity by Mitchell Walldrop).

Great Book -- Makes You Think
One of the wonderful things about the Weinbergs' early series of books -- and this one in particular -- is that the ideas and the examples really make you think. With examples chosen from many fields, the book illustrates its central ideas with a cross-fertilization that helps one think outside ones box.

It starts with a very simple idea -- stability. Things change so little most of the time we hardly notice. And yet stability usually requires active forces to sustain it. As an information systems designer, Weinberg helped me see why this simple idea, and a few simple ideas that follow, turn out to explain a great deal about why projects information technology projects fail, and how they can be made more successful.

One of the most infuential books I have ever read
An outstanding follow up to the first book Weinberg wrote(An Introduction to General Systems Thinking, 1975). Anyone who considers themseleves a systems thinker must read this book! Whereas the first book attempts to answer the first question in the systems triumvirate, "Why do we see what we see?", this books tackles the next question, namely "Why do things stay the same?" As a marriage and family therapist, understanding systems is crucial to my work. This book is clearly written, and provides real world examples of sometimes difficult topics. I have read this book cover to cover 3 times in the last 2 years, and continue to get something new from it every time. One of the best books around to think about the organization of systems, regardless of the context. ... Read more

Book Description

This significant volume is intended for advanced undergraduate or first year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas which will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry and biology, will find this text as useful as students of mathematics. Overall, this will be a text that should be required for all students entering this field. ... Read more

Reviews (1)

Effective overview of a useful subject
The subject of dynamical systems has been around for over a century now, having been defined by Henri Poincare in the early 1900s, but having its roots in Hamiltonian and Lagrangian mechanics in the 19th century. In this book ths author has done a fine job of overviewing the subject of dynamical systems, particularly with regards to systems that exhibit chaotic behavior. There are 292 illustrations given in the book, and they effectively assist in the understanding of a sometimes abstract subject.

After a brief introduction to the terminology of dynamical systems in Section 1.1, the author moves on to as study of the Poincare map in the next section. Recognizing that the construction of the Poincare map is really an art rather than a science, the author gives several examples of the Poincare map and discusses in detail the properties of each. Structural stability, genericity, transversality are defined, and, as preparation for the material later on, the Poincare map of the damped, forced Duffing oscillator is constructed. The later system serves as the standard example for dynamical systems exhibiting chaotic behavior.

The simplification of dynamical systems by means of normal forms is the subject of the next part, which gives a thorough discussion of center manifolds. Unfortunately, the center manifold theorem is not proved, but references to the proof are given.

Local bifurcation theory is studied in the next part, with bifurcations of fixed points of vector fields and maps given equal emphasis. The author defines rigorously what it means to bifurcate from a fixed point, and gives a classification scheme in terms of eigenvalues of the linearized map about the fixed point. Most importantly, the author cautions the reader in that dynamical systems having time-dependent parameters and passing through bifurcation values can exhibit behavior that is dramatically different from systems with constant parameters. He does give an interesting example that illustrates this, but does not go into the singular perturbation theory needed for an effective analysis of such systems.

An introduction to global bifurcations and chaos is given in the next part, which starts off with a detailed construction of the Smale horseshoe map. Symbolic dynamics, so important in the construction of the actual proof of chaotic behavior is only outlined though, with proofs of the important results delegated to the references. The Conley-Moser conditions are discussed also, with the treatment of sector bundles being the best one I have seen in the literature. The theory is illustrated nicely for the case of two-dimensional maps with homoclinic points. The all-important Melnikov method for proving the existence of transverse homoclinic orbits to hyperbolic periodic orbits is discussed and is by far one of the most detailed I have seen in the literature. The author employs many useful diagrams to give the reader a better intuition behind what is going on. He employs also the pips and lobes terminology of Easton to study the geometry of the homoclinic tangles. Homoclinic bifurcation theory is also treated in great detail. This is followed by an overview of the properties of orbits homoclinic to hyperbolic fixed points. A brief introduction to Lyapunov exponents and strange attractors is also given.

This book has served well as a reference book and should be useful to students and other individuals who are interested in going into this area. It is a subject that has found innumerable applications, and it will continue to grow as more tools and better computational facilities are developed to study the properties of dynamical systems. ... Read more

Book Description

Contains an edited collection of papers by experts from all disciplines of chaos which are the result of the International Workshop on Applications of Chaos, sponsored by the Electric Power Research Institute. Focusing on the actual and potential methodologies of the latest investigations in chaos dynamics, topics presented here run the gamut from the dynamics of electrocardiograph information and the instability of conveyor belts to the time series modeling and control of chaos. ... Read more

Book Description

This book provides a clear, understandable, and motivated account on the subject that spans both conventional and modern materials about discrete event systems, material that, up to now, has been presented in the literature in different fields, such as the graph theory, the probability theory, the automata's theory, and the queueing theory. The book gives a complete introduction to the discrete-event system theory and simultaneously applies the theory to practical problems. The book gives students of computer sciences, system sciences, and of electrical engineering, a clear, unambiguous, and relevant account of discrete-event systems. Numerous illustrations are included for better understanding. Problems as well as their solutions are included in each chapter. It can be used as a basic introduction for undergraduates and graduate students. Although it is logically self-contained, it presupposes the mathematical maturity acquired by students with two years of calculus. ... Read more

Reviews (1)

Exhaustive and clear
Tornambe' treats all the basics of discrete-event systems theory, from queuing theory and Markov chains fundamentals to more advanced topics like BCMP queues. I recommend it to whoever wants to learn the subject following a clear, exhaustive style and a very structured approach. ... Read more

Book Description

Designing Autonomous Agents provides a summary and overview of the radically different architectures that have been developed over the past few years for organizing robots. ... Read more

Reviews (1)

Designing Automonous Agents: a Review
This book contains a well-chosen sample of what I would like to call some of the "classic" papers in the AI/Robotics research field over the last decade. Maes includes some of the most well-known studies of subsumption architecture, planning, knowledge and goal representation, and behavioral studies. This is a great book for a student of AI/Robotics or just anyone who wants a good basis of understanding in these fields. If you have a robot of your own, this book is an excellent source of detailed descriptions of different architectures developed for organizing robots. While the papers in this book are not on the cutting edge, they provide a good foundation for exploring those that are. ... Read more

Book Description

This book provides an introduction to nonequilibrium statistical mechanics applied to ideas in chaotic dynamics. The author illustrates how techniques in statistical mechanics can be used to calculate quantities that are essential to understanding the chaotic behavior of fluid systems.Beginning with important background information, the volume goes on to introduce basic concepts of dynamical systems theory through simple examples before explaining advanced topics such as SRB and Gibbs measures. It will be of great interest to graduate students and researchers in condensed matter physics, nonlinear science, theoretical physics, mathematics, and theoretical chemistry. ... Read more

Reviews (10)

Most powerful math tool
This book is a nice introduction to non-linear dynamics study (Chaos, roughly speeking, the very complex behavior from a simple set of equations). The author wrote it in a way that you understand how the Chaos was developed historically and he sometimes stops the narrative to introduce an easy aspect of chaos that anyone can understand. Thus you'll indeed develop Chaos behavior even if you're not Ph.D. in mathematics, because he will show you, for example, a very simple equation that produces chaos. However, what really catches me in this book was the power of this new approach of chaos. This is exactly what Santa Fe Institute needs. See, why is that when we apply a classical physics equation in a system it does not behaves exactly as it was expected? Because we certainly did not considered details (e.g. friction). The non-linear dynamics show us that we can, from a exceptionally simple equation, create a very complex behavior that can simulate the true behavior. Thus I think in a near future non-linear dynamics will be able to break that famous wall in Science: can't explain that in details because that would generate an almost impossible-to-solve math equation. Now we can do that!

An intelligent non-technical introduction to chaos.
Being a physicist I frequently get bored with "science for the layman" books (for instance, Hawking's "Brief History of Time"). This was not the case with Stewart's "Dice" book. It is very well researched and written, in a style that wisely combines historical information with new discoveries, which are, therefore put into perspective. You can even try your hands in simple calculations with your PC. On the whole, a very balanced exposition, without, thank God!, the usual exageration on the place of chaos in the future of science. A very good place to start.

A thorough explanation of chaos theory
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.

Fighting religion with religion
This book is almost religious in its championing of Darwinian evolution. It is a shame that what are actually sound scientific points are presented with a religious fever that distracts or is even counter-productive in coverting open minded believers in creation.

Mind-Blowing Maths for kids!
Not being particularly mathematically minded, I found some sections of this book a bit of a struggle. Nonetheless, Stewart's somewhat disarming, slightly off-the-wall style of writing is very engaging, and on the whole the book is very readable. The implications of chaos will become clearer in the next decade or so I should imagine, so this book is timely and topical. A definite "must read". ... Read more

Amazon.com

We'd better get used to chaos because it certainly isn't going anywhere. Mathematician Ian Stewart--who is also a very talented writer--shares his insights into the history and nature of the highly complex in Does God Play Dice: The New Mathematics of Chaos. While his delightful phrasings will draw in nearly every reader, those with a strong aversion to figures and formulae should understand that it will be slow going. Chaos math suffuses everything from dreaming to the motion of the planets, and Stewart's words can never match the precision of his numbers. Persistence pays off, though; there are so many "aha" moments of insight herein that it almost qualifies as a religious text. The second edition has been partially revised in the wake of 1990s research, and three exciting new chapters report on prediction and other applications of chaos mathematics. --Rob Lightner ... Read more

Reviews (2)

Good tasting without indigestion
(1st edition '89) Stewart's book gives the reader as strong a flavor for the constructs of chaos as possible without formulas everywhere. The author makes great use of figures to depict ideas and even gives readers home-projects to test for themselves. Further reading is given (with difficulty levels indicated) for the brave-hearted. Unfortunately, the book is lacking as a reference due to it's vague table of contents and sparse index. But as compared to Mark Ward's "Beyond Chaos", Stewart gives the reader a deeper understanding of the subject matter. Overall good read.

The best chaos for layman
This mesmerizing historical overview of nonlinear science, full of seedy ideas and fascinating expositions (from heartbeat to weather forecast) is well worth reading. One of those "aha !" books that will broaden your understanding of the universe (and the rest), it is very "visual" and..well, a friend of mine said she considered it a "mental thriller" since it touches on the great old questions of determinism and predictability. As for "mathematics" in the title- don't be put off. The book is virtually mathless. ... Read more

Book Description

The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level.It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas.These same qualities characterize this revised and expanded second edition.Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model.This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos.This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level. ... Read more

Reviews (2)

From the pendulum to chaos in straightforward steps
Books that take you from undergraduate physics to a nontrivial understanding of nonlinear dynamics, chaos and fractals are rare. Chaotic Dynamics does the job ellegantly. The familiar pendulum is used to illustrate the basic techniques and concepts in nonlinear dynamics. The reader is gently introduced to phase diagrams, Poincare sections, basins of attraction and bifurcation diagrams. Computer code is included in the Appendix. The interested reader can use this code to further illustrate the lessons of the text or to embark on his/her own exploration of the pendulum and other dynamical systems. Having used the pendulum to establish a firm conceptual platform, Baker and Gollub progress gracefully into the logistic map to illustrate concepts such as period doubling, Lyapunov exponent, entropy, stretching and folding, and various measures of fractal dimension. The presentation is nicely rounded off with studies of other maps and nonlinear dynamical systems from a range of fields in physics, chemistry and fluid dynamics.

Chaos and True Basic Code
The gateway to experimental chaos research comes through here! The mathematics, the examples and code that illustrates the book is here. It is somewhat narrow in it's beginning approach, but delivers after careful study a beginning of understanding with some real industry. Not for the mathemaically shy or Professors like Ruelle, but for real people wanting real answers! Your unique Associates ID is: thefractaltransl. ... Read more

Reviews (1)

Very helpful and detailed.
There are a dozen of similar Simulink books in the market but this is the one you should get.This book clearly explains how to use each simulink block with concise and useful examples.This text also covers the details which other Simulink books are assuming you to know.The way this book is written satisfies both beginners and experts. ... Read more

Book Description

CHAOS: An Introduction to Dynamical Systems was developed and class-tested by a distinguished team of authors at two universities through their teaching of courses based on the material. Intended for courses in nonlinear dynamics offered either in Mathematics or Physics, the text requires only calculus, differential equations, and linear algebra as prerequisites. Spanning the wide reach of nonlinear dynamics throughout mathematics, natural and physical science, CHAOS develops and explains the most intriguing and fundamental elements of the topic and examines their broad implications. Among the major topics included are: discrete dynamical systems, chaos, fractals, nonlinear differential equations, and bifurcations. The text also features Lab Visits, short reports that illustrate relevant concepts from the physical, chemical, and biological sciences, drawn from the scientific literature. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulation, designed to be used with any software package. And each chapter ends with a Challenge, which provides students a tour through an advanced topic in the form of an extended exercise. ... Read more

Reviews (4)

Look no further for your first intro to the subject!
It's now been a decade since the time of a college course on Chaos and Fractals, when the textbook "Fractals Everywhere" by Michael F. Barnsely was used for teaching our class. For the several ensuing years the subject leapt into the background as I persued my studies in physics and later on in pure mathematics. Recently I have regained interest in some applied subjects such as dynamical systems and chaos, control theory, symplectic geometry, and information theory. Indeed the book by Alligood, Sauer, and Yorke was a somewhat recent recommendation by a college professor who had taught his students from it. I recall at the time there was a discussion as to whether Robert Devaney's book would have made for a better first course. He mentioned that Devaney only deals with the discrete dynamical systems, while ASY treats both discrete and continuous, and so the choice was clear. The topics discussed in the 13 chapters of the book include: one and two dimensional maps, fixed points, iterations, sinks, sources, saddles, Lyapunov exponents, chaotic orbits, conjugacy, fractals and their dimension, chaotic attractors, measure, Lotka-Volterra models, Poincare-Bendixson theorem, Lorentz and Roessler attractors, stable manifolds and crises, homoclinic and heteroclinic points, bifurcations, and cascades. There're also answers and solutions to the selected exercises, as well as extensive references at the back, making up an ideal setting for self-study. The level and style of exposition is targeted towards an advanced undergrad or beginning grad student who is into applied math or engineering fields. The authors justly tend to emphasize concepts and applications, instead of getting bogged down in too much mathematical rigor or heavy use of the abstract machinery. All in all, an excellent first excursion/introduction to one of the most fascinating areas of applied math, whether for classroom use, or for self-study.

The definitive guide to dynamical systems!
When I purchased this book three years ago, I had only a rudimentary understanding of dynamical systems. Thankfully, all that was needed to get me started was some intermediate calculus and some basic college-level linear algebra. Since I had been doing both from the time I was a sophmore in high school, I had no trouble getting comfortable with it. The authors present dynamical systems in an easy-to-read style with tests that appear at the end of each chapter after you've had time to catch on.

If you're seriously thinking about getting started in dynamical systems, get this book!

great introduction to dynamical systems
I was enrolled in a course at GMU in which the draft version of this text was used. The math was not as difficult as some of the graduate texts, therefore it serves as a good intoduction for someone with as little as 2 years of undergraduate math. The challenges at the end of each chapter are more difficult than the regular problems, but they are meant to be. Many of the systems can be modeled on a spreadsheet. If you have any interest in Chaos, this book will only strengthen it.

For my Taste One of the Best Undegraduate Texts
This book presents brilliantly the foundations to Dynamical Systems and Chaos. You need to have some Linear Algebra, Calculus and Multivariable Calculus and Differential Equations knowledge. Full of exercises, computer experiments and Challenges. I think that the text looses some substance due to the lack of presenting more or all the solutions to the Exercises. They should be solved detailed in a Solutions Manual. Don't try to e-mail the authors for more solutions, they will not get them to you. This point is the only pitty in a text that is a great companion through chaotic dynamics. Also Very Brilliant for me at this Level are: Strogatz-Nonlinear Dynamics and Chaos, Kaplan-Understanding Nonlinear Dynamics, Gulick-Encounters with Chaos, Hilborn-Chaos and Nonlinear Dynamics, Devaney-An Introduction to Chaotic Dynamical Systems and A First Course to Chaotic Dynamics, Holmgren-A First Course in Discrete Dynamical Systems. More sofisticated maths but not too far away are: Schuster-Deterministic Chaos(graduate) and Ott-Chaos in Dynamical Systems (graduate). ... Read more

Book Description

Until recently, such phenomena as the volatility of weather systems, the fluctuation of the shock market, or the random firing of neurons in the brain were considered too "noisy" and complex to be probed by science. But now, with the aid of high-speed computers, scientists have been able to penetrate a reality that is changing the way we perceive the universe. Their findings -- the basis for chaos theory -- represent one of the most exciting scientific pursuits of our time.

No better introduction to this find could be found than John Briggs and F. David Peat's Turbulent Mirror. Together, they explore the many faces of chaos and reveal how its law direct most of the processes of everyday life and how it appears that everything in the universe is interconnected -- discovering an "emerging science of wholeness."

Turbulent Mirror introduces us to the scientists involved in study this endlessly strange field; to the theories that are turning our perception of the world on its head; and to the discoveries in mathematics, biology, and physics that are heralding a revolution more profound than the one responsible for producing the atomic bomb. With practical applications ranging from the control of traffic flow and the development of artifical intelligence to the treatment of heart attacks and schizophrenia, chaos promises to be an increasingly rewarding area of inquiry -- of interest to everyone.

Reviews (5)

A step deeper guild of Chaos Theory to layman
I've finished this book's Chinese version today. In the last year, I'm trying my best effort to absorb knowledge of Chaos Theory, Complexity, and Catastrophe Theory. It's quite hard to get a in-depth guild of the above knowledge to common people in Hong Kong.

My purpose to get the above knowledge is just in order to find the hidden order of financial market, and, of course, to make profit from the market. That's why I find this book is good to serve my purpose. It explained clearly on fractals, the relationship between chaos and order, and non-linearness.

I knew E. Peters has using fratals / Elloit Wave Theory to analyze financial market. Of course, it needs more intra-day data to try to find such fratals in a small scale period, e.g. in a 5-minute charts. But I guess that, such fractal are existing in the market, if you watching index movement everyday.

On another aspest, the technique of plotting data in a phase space is a tool to get the picture of financial market to me. This tools can be compared with weighted moving average, MACD, or other technical indicators. Though, phase space analysis is quite uneasy to a man without advanced mathematics. I'm quite sure such mathematical technique may apply to financial trading.

Besides, the idea of "quasi-periodic" is likely describing financial market. Though I got less knowledge from the book on this topic. It sounds like some ideas from William Gann, and other cyclist writings.

Hince, I'm benefitted from the book to enlighten new view point to see the world, and the market. I recommend any financial market practitioner to read this Chaos Theory guild and then reread some technical analysis classics, and reviewing their trading strategies. I believe that shall be worthy in one's trading life.

N.B. The picture 2.7 is missing (P.76), and there is some printing errors in its Chinese version which printed in 20.6.1997

Science or Science Fiction
While this book does make some interesting points about chaos, I found that the book's blatant disregard for accepted science very hard to stomach. I currently attend Harvey Mudd College, a small, but highly regarded science and engineering school, so I like to think that I know something about the subject.

For example, at one point the authors are describing solitons (a term I had never heard before), states a theory that by generating an extra bit of energy we could put the universe out of the unstable equilibrium it currently exists in and cause it to "begin to boil." While this is all well and good, it makes vast assumptions that the authors neglect to mention. Most importantly it assumes that the universe is in an unstable equilibrium, a fact which although highly unlikely is not impossible. Secondly it assumes that the universe is completely clean of these bits of extra energy currently. They draw this parallel to an example of superheating water because without external particles to build upon no bubbles can form to release the steam. This is also true, but it is still impossible because it is impossible to have a perfect system like this. There are always going to be minute cracks in the pot, or imperfections in the water (fractal theory, covered earlier in the book, even states this!), and so while this might be theoretically possible it will not happen in any real world environment. The book has many other places like this where the authors conveniently leave out details that might weaken their arguments. I find this to make the book as a whole very frustrating to read, even if some of their points are valid.

Another reason that I find the book to be very frustrating is that everything is very sensationalized. At the beginning of the description of fractals the authors say that the first person to think of a fractal curve created "a panic among mathematicians that took some fifty years to resolve." I find it truly hard to believe that the entire mathematical community was pulling their collective hair for fifty years trying to explain this curve, but by phrasing it this way the authors make it seem like science as a whole does not want to accept new ideas because it would make them look bad. In reality though I think the scientific community is ready to accept anything that can be strongly proven theoretically, or experimentally (just look at relativity, or quantum).

Because of all of these failings I would not recommend this book. I am sure that there are many other better books about chaos theory that do an excellent job of describing it without disregarding the rest of science, or trying to place it in places where it does not necessarily belong.

IGNORE CHAOS AT YOUR PERIL
Very well thought out survey of chaos theory presents a metaphorical mirror as a means to magnify and project into view the hidden world of turbulence. The advent of the computer has brought chaos and fractals out of the closet. Here the authors teach the reader how to navigate in the turbulent world from the submicroscopic realms to the distant galaxies. The authors dish up a huge concept list: fractal dimensions, strange attractors, holograms, soliton bubbles, bifurcation, quantum phase locking, coevolution of species and the earth as Gaia -- all in an attempt to teach the reader the folly of allowing the part/whole dichotomy to rule your perception of the universe.

The book is a stark attack on those the authors term reductionists -- those who seek answers in breaking the whole into ever smaller parts. The authors' pet writers are David Bohm, Lynn Margulis, and Llya Prigogine but they toss in another hundred ideas for irregular stepping stones to get where they are going. Where is that? They composed an evangelical message -- that man now has the tools and knowledge to step through Alice's Looking Glass into an entirely new and mystical perception of the whole. They see chaos as a source of future evolution and life.

I give the authors a high mark for original thought. Although using a hundred other science writers to frame their ideas, they direct the reader to go beyond existing theories and strike a path for the center of the turbulent mirror. The diagrams and illustrations also were very helpful. They pictured the brain as a strange attractor, with thought arbitrating between the two realms of order and chaos. My favorite metaphor was the slime mold which, when food gets scarce, merges from being a collection of individual cells to a collective entity moving across the forest floor. This was to show an example of quantum phase locking which "could provide a bridge joining classical, nonlinear reality with linear, quantum reality" (P. 188). Great Two Thousand year Philosophy.

Stunning Revelation about the World We Live in
What I read is a Chinese translation of the book. Although I do not fully understand the researches and examples involved in explaining the development from 'Order to Chaos' (the first few chapters), and I have not yet experienced some of the interesting events that described, I am amazed by the final few chapters about the possible role of chaos theory in the development of cells, organisms, RNA, DNA, and about creativity and 'nuance.' What I find most debatable is the responsibility of reductionism in creating the problems for nature and humanity, or detouring the course of science. I certainly believe that the scientists and thinkers before us forged the foundation for us, and from their experience, we discover the verity of past knowledge. I don't think Darwin would appreciate we calling him a reductionist because at that time, reductionism was the way of science, not to mention that 'reductionism' is a modern classification. The book also details a lot of examples to explain that most phenomenons are the results of nonlinear chaos complexity. I can't help but notice the strong implication of creationism, with chaos theory as the creator instead of God.

Terrific Book
This book provides a great introduction to chaos theory and strikes a devastating blow to reductionism. Using a historical approach, the book walks the reader through the discoveries and mathematics that underlie fractals, chaos and complexity. It also provides a short, fascinating interview with Ilya Prigogine and a great layperson's introduction to his ideas. Turbulent Mirror makes the point that because of "sensitive dependence on initial conditions" one can not really separate the whole from the parts - in essence there really are no "initial conditions." The only weakness of this book, IMHO, is the use of occasional Alice and Wonderland illustrations and a few too many quotes from eastern philosophy. These are not overpowering, however, so if you don't like them them can ignore them and enjoy the rest of the material which is truly great. ... Read more

Book Description

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry, Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas. ... Read more

Reviews (2)

Good introduction to the beginning student
This book gives a quick and elementary introduction to the field of chaotic dynamical systems that could be read by anyone with a background in calculus and linear algebra. The approach taken by the author is very intuitive, lots of diagrams are used to illustrate the major points, and there are many useful exercises throughout the book. It could serve well in an undergraduate mathematics course in dynamical systems, and in a physics undergraduate course in advanced mechanics. The author emphasizes the mathematical aspects of dynamical systems, and readers will be well prepared after finishing it to read more advanced books on dynamical systems.

Chapter 1 introduces one-dimensional dynamics, with the analysis of the quadratic map given particular attention. Called the logistic map in some circles, this very important dynamical system has been the subject of much study, and exhibits generically the properties of chaotic dynamical systems. The author also gives a brief review of some elementary notions in calculus needed for the chapter, making the book even more accessible to a wider readership. The important concept of hyperbolicity is discussed in the context of one-dimensional maps and a good discussion is given on symbolic dynamics. Structural stability, which is really useful only in dynamical systems in higher dimensions, is treated here. The intuition gained in one-dimension is invaluable though before moving on to higher-dimensional examples. Sarkovskii's theorem, which states that a one-dimensional dynamical system with a period three periodic orbit has periodic orbits for all other periods, is proved in detail. In addition, the Schwarzian derivative, so important in complex dynamics, is defined here. The author also gives an introduction to bifurcation theory, which again, is most interesting in high dimensions, and introduces the concept of homoclinicity in this discussion. Maps of the circle and the all-important Morse-Smale diffeomorphisms, are treated in this chapter also. The author introduces the reader briefly to the idea of genericity when discussing Morse-Smale diffeomorphisms. Kneading theory, so important in the mathematical theory of dynamical systems, is introduced here also.

In chapter 2, the author generalizes the results to higher dimensions, and begins with a review of linear algebra and some results from multivariable calculus, such as the implicit function theorem and the contraction mapping theorem. This is followed by a treatment of the dynamics of linear maps in two and three dimensions. Whereas the canonical example of one-dimensional dynamics is represented by the logistic map, in higher-dimensional dynamics this is represented by the Smale horseshoe map. The author carefully constructs this map and details its properties. Then he takes up the hyperbolic toral automorphisms (or Anosov systems as they are called in some books). Both the Smale horseshoe map and the toral automorphisms are excellent, easily understandable examples of higher dimensional dynamics and the associated symbolic dynamics.

The concept of an attractor is also treated in chapter 2 in the context of the solenoid and the Plykin attractor. Both of these are of purely mathematical interest, but by studying them the physicist reader can get a better understanding of what to look for in actual physical examples of attractors (or the more exotic concept of a strange attractor). The author also gives a proof of the stable manifold theorem in dimension two. This is the best part of the book, for this theorem is rarely proved in textbooks on chaotic dynamics, the proof being delegated to the original papers. However, the proof in these papers is extremely difficult to get through, and so the author has given the reader a nice introduction to this important result, even though it is done only in two dimensions. This is followed by a very understandable discussion of Morse-Smale diffeomorphisms. In addition, the author introduces the Hopf bifurcation, of upmost importance in applications, and introduces the Henon map as an application of the results obtained so far.

The last chapter of the book is a brief overview of complex analytic dynamics. Complex dynamical systems are very important from a mathematical point of view, and they have fascinating connections with number theory, cryptography, algebraic geometry, and coding theory. The author reviews some elementary complex analysis and then reintroduces the quadratic maps but this time over the complex plane instead of the real line. The Julia set is introduced, and the reader who has not seen the computer graphical images of this set should peruse the Web for these images, due to their beauty. The geometry of the Julia set and the associated complex polynomial maps are given a fairly detailed treatment by the author in the space provided.

The best starting point.
This book covers almost every aspect of theory of discrete dynamical systems and by far the easiest explains and proofs with useful exercises, anyone with solid calculus and linear algebra background shouldn't have any problem absorbing this material and is highly recommended to whom wants to know about the theory of chaos from the scratch. ... Read more