Product Description
The author of "Hidden Order: How Adaptation Builds Complexity" dramatically shows readers that the "emergence" of order from disorder has much to teach about life, mind, and organizations. From the ingenious checkers-playing computer that started beating its creator to the emotive creations of the poet, "Emergence" shows that Holland's theory of emergent models successfully predicts many complex behaviors in art and science.Amazon.com Review
"Emergence" is the notion that the whole is morethan the sum of its parts. John Holland, a MacArthur Fellow known asthe "father of genetic algorithms," says this seeminglysimple notion will be at the heart of the development of machines thatcan think for themselves. And while he claims that he'd rather doscience than write about it, this is his second scientific philosophybook intended to increase public understanding of difficult concepts(his first was HiddenOrder: How Adaptation Builds Complexity). One of the questionsthat Holland says emergence theory can help answer is: can we buildsystems from which more comes out than was put in? Think of the foodreplicators in the imaginary future of Star Trek--with somebasic chemical building blocks and simple rules, those machines canproduce everything from Klingon delicacies to Earl Grey tea. Ifscientists can understand and apply the knowledge they gather fromstudying emergent systems, we may soon witness the development ofartificial intelligence, nanotech, biological machines, and othercreations heretofore confined to science fiction. Using games,molecules, maps, and scientific theories as examples, Holland outlineshow emergence works, emphasizing the interrelationships of simplerules and parts in generating a complex whole. Because of thetheoretical depth, this book probably won't appeal to the casualreader of popular science, but those interested in delving a littledeeper into the future of science and engineering will befascinated. Holland's writing, while sometimes self-consciouslyprecise, is clear, and he links his theoretical arguments to examplesin the real world whenever possible. Emergence offers insight notjust to scientific advancement, but across many areas of humanendeavor--business, the arts, even the evolution of society and thegeneration of new ideas. --Therese Littleton ... Read more

Customer Reviews (12)

Great concepts, but a little repetitive at times
Having done some work with genetic algorithms, I was very excited to read a book by John Holland.I was hoping to learn more about how to create models of complex systems and how new behavior can be exhibited by computer programs that were not inherent in the programmer's intent or design.

I certainly came away with knowledge of how to create models because that seemed to be the main point that Professor Holland made throughout the book.Don't get me wrong.Modeling is critically important to understanding the world we live in and the phenomena we observe in the world.I just had no idea from the title or the blurbs that modeling would be such a central theme.In a way it is reassuring since modeling is something that I am very comfortable with, and to me, relatively straight forward.

The book covers such novel concepts as cell assemblies, anticipation, signaling, and indefinite memory in relatively easy to understand language.There is a fair amount of dense mathematical notation that adds a bit of depth if you are comfortable with the subject matter, but can be skipped by the casual reader.I also like the point Professor Holland made about macrolaws and microlaws - that once basic structures and patterns are in place (microlaws), emergent, higher level structures and patterns emerge (macrolaws) that can be explained without reverting back to a knowledge of the microlaws.This provides a road map to understanding more about emergent behavior as we better develop and understand the microlaws describing emergent behavior.

I do think that some of the material was repetitive.Although many reviewers liked the last chapter or two, the end of the book seemed to drag on for me.It was a combination of recap (which is fine), and a philosophical discourse on innovation and creativity.The material was fine, but it seemed just tacked on at the end, and was less interesting to me than the rest of the book.

I have not yet read "Hidden Order", so I cannot compare the two books.Overall, I am very glad I read the book.I learned many new concepts regarding emergent behavior, and reinforced my prior knowledge about things like neural nets, genetic algorithms, and game trees.

Another great book by Holland
Expands on Holland's previous book Hidden Order. It presents an interesting method for understanding complexity and emergence. Highly recommended for those attempting to understand complex adaptive systems.

First steps towards a future theory of emergence
I just read Emergence in preperation for my oral qualifying exams for a Ph.D. in computer science and cognitive science. I disagree with many of the negative reviewers -- this book is well-worth the read. I share some frustration over this book due to the way it seems to scratch the surface. The book's strength seems to be in asking the right questions and pointing the way towards some future science of emergent behavior.

The book is too short for my taste -- in many of the later chapters Holland makes thought-provoking, deep remarks, without the follow-up and commentary that they leave me hoping for. But again, his main purpose seems to be in making people think about the issues. And he provides some formalisms that might be part of some future theory -- his constrained generating procedures (CGPs) and the variable "CGP-v" recall constructs such as the Turing machine for studying computability.

The strengths of the book lie in:

1) Discussion of the nature of modeling in science, and computer modeling in particular. This is discussed with clarity and pragmatism.

2) The beginnings of a framework in which to study emergence in multi-agent systems.

3) Discussion of the importance of metaphor/analogy in the creative scientific process. I didn't expect this to appear in the book but it was very welcome, and especially appropriate due to the role played by Mitchell's and Hofstadter's "Copycat" model (of analog-making itself) as it motivates the expansion of CGPs to CGP-v's as the book progresses.

Overall, I recommend this book highly to readers interested in the beginnings of this exciting new science, that really is in its infancy. I gave it 4 stars just because I felt like Holland had a lot more to say in the later chapters and left too much "as an exercise for the reader." I hope he does follow-on work that clarifies his vision for a future science of emergence!

an undispensable completion of "hidden order"
After 7 years from its publication it still gives a valid and fundamental approach to the conceptsof emergence and its meaning

Toss Up
Parts of this book were interesting, but overall it was much ado about not much, and what was done was often overdone (I agree with another reviewer on this point). I see that Amazon has coupled this book with Hidden Order. I can't see why. It would be like buying the same book twice. Anyway, so much of this has been warmed over so many times now that it's frankly a bit dry. I'd like to see a book that really breaks new ground in complexity without overusing buzz words or talking down to me, holding my hand through simple things. Here, the topic is more attractive than the content I'm afraid. Anyone really interested in complexity and emergence will need to go into technical details well beyond this book. Others, like me, will likely find the details that are here to be a bit tedious. ... Read more

Product Description
THE HISTORY AND THE MEANING BEHIND THE GREAT THEORIES OF 20TH-CENTURY MATHEMATICS

"Further elucidates the power of mathematics to influence concepts outside the standard realm of numbers."–Science News on Five More Golden Rules

In this follow-up to his critically acclaimed book, Five Golden Rules, John Casti reveals the remarkable origins of some of the most monumental mathematical discoveries of the last century–and sheds light on how these revolutionary ideas have shaped our lives. Using a diverse and entertaining range of sources to explain the five world-changing theories he discusses, Casti probes the engrossing and seldom heard tales that lie behind the breakthroughs–and finds exhilarating power and beauty in even the most intimidating theories. Fascinating, informative, and fun, Five More Golden Rules will forever change the way you think about mathematics.

PRAISE FOR FIVE GOLDEN RULES

"Caviar for the inquiring reader....Casti’s gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory."–Christian Science Monitor

"If you’d like to have fun while giving your brain a first-class workout, then check this book out."–San Francisco Examiner

"This book has meat! It is solid fare, food for thought....Casti’s Five Golden Rules makes math less forbidding and much more interesting."–Hartford CourantAmazon.com Review
Bring more joy to your favorite math-head with Five MoreGolden Rules from science writer and national treasure JohnL. Casti.Though a quick glance through the book will cause anintense fight-or-flight response in the numerophobic, Casti's writingis lovely and lucid as ever, explaining not just equations andtheorems but their significance in our lives. Having discovered inFive GoldenRules that he couldn't restrict himself to just five important20th-century mathematical theories, this follow-up explores theintricacies of knot theory, functional analysis, control theory,chaotic systems, and information theory.Each of the five livelychapters introduces its subject with a seemingly unrelated anecdotethat is (of course) informed by the theory in question.Then it'sheadlong into the wonderful details of postulation and demonstrationthat make math so much fun.Unlike a textbook, Five More GoldenRules meanders and breaks away from its proofs to discoverrelations between the symbols and the real world, from the stock marketto the coastline of Norway.Besides giving the reader a break, thismakes the abstract, almost ethereal concepts concrete and provides adefinite advantage to the interested student.Perhaps textbookpublishers should take note of this technique; until they do, we'llhave to curl up with Casti's Five More Golden Rules if we wantto have fun with our higher math. --Rob Lightner ... Read more

Customer Reviews (7)

Dreadful
As a popular science/maths work - horrible. In the middle of the chapter on the Kalman filter he starts talking about Lie algebras without actually explaining what they are, or their relevance. The whole topic is just dropped in from above and then disappears from the discussion more or less without further comment.I understand what they are, but if I were coming to this as a layperson I'd be completely in "WFT??" mode.

Further examples of this abound in this chapter - econometrics is chucked in for no particular reason and then just dropped and ignored. A good example of a child on a swing is not fully explained. What is the variable 'l'?.I would guess the hinge point where the child's hands are on the ropes of the swing but that is never articulated. Langragian dynamics appears but it's just chucked in as a couple of formula without any identification of what it is or how he's going to use it. Technical phrases like "equation of state" are just used without any explanation.

To top it all off the chapter starts by asserting that the Kalman filter is one of the most important results of the 20th C but doesn't actually bother to state what it is until the last page, and then does a bad job of it.

I'm not sure I'd even accept this as a series of lecture notes. (It certainly reads as though it was sourced from a set though - a bad set.)

nice sequel to Five golden rules but heavy on the mathematics
In Five Golden Rules John Casti wrote a wonderful book about important theorems in mathematics that were discovered in the 20th Century. The style and description was such that a layperson could understand, enjoy and appreciate the results. All the theorems were discovered before 1950 and they all dealt with topics in applied mathematics and particularly game theory and operations research.
Perhaps he found the list of five golden rules too restrictive and thus comes the sequel "Five More Golden Rules". Again, it would be hard to argue the choices. Casti goes into the details of the theorems and the theory related to them much like he did in the first book. However, in this book, he has chosen topics from very abstract areas of mathematics. I have a masters degree in mathematics and a Ph.D. in statistics and yet I had no familiarity with knot theory. So I learned a lot from chapter 1 but found it to be difficult reading, more like a mathematics textbook than a popular book for the scientist and layman.

This feeling continued as I read the other four chapters even though I was treading on territory that was very familiar to me (e.g. the Kalman filter of control theory). It was reassuring to me to see that this impression was also shared by the three customers that had already written reviews on the book.

I recommend this book wholeheartedly for mathematicians and other with strong math training. The Hahn-Banach theorem was the most important theorem that I learned about when I took my functional analysis course at the University of Maryland some 26 years ago. But I have not had much use for it since and I completely forgot what it said. Casti provides me with a nice reminder and shows how this result is a generalization of very practical results that relate to quantum mechanics and other results in physics.

The latter part of the 20th Century saw a great deal of activity in nonlinear dynamics. This is connected by Casti to the Hopf Bifurcation theorem. That chapter deals with many topics that grasped the attention of applied mathematicians, including chaos and catastrophy theory, strange attractors and the beautiful geometry of fractals. This material is not for a layperson. On the other hand, the introduction to the chapter, covering what a dynamical system is, provides a wonderful analogy to a treasure hunt in Central Park that can be appreciated by everyone.

The Kalman filter provides an example of how linearization of real dynamic systems allows one to write a prediction equation for the state at the next time point recursively as a function of the current state and the new measurements. This recursive formulation leads to the same solution that Wiener had found much earlier, but because of the recursion, it is much more suitable for real time computer applications. This was essential to controlling space vehicles and is the important result that made the trip to the moon possible. Casti covers the theory of Kalman filtering very well but emphasizes many of the interesting abstract concepts rather than the more concrete aspects of the solution.

The finally chapter on the Shannon Coding Theorem takes us into the realm of information theory. Casti provides the key references. Electronic communication in the 20th century has benefitted from the efficient coding of information that makes transmissions faster easier and error free. This is very important work with unforeseen applications. Casti points to applications in genetics.

Another interesting feature of the book is the connection made between the knot theory associated with Alexander's polynomials and DNA sequencing, a subject to be further explored in the 21st Century.

MEANT for non-mathematicians???
I'm math and computer science student. I have studied linear algebra and know lots about linear spaces, n-dimensional vectors, matrices and other stuff. Still I sometimes found it hard to get out proof or just idea of those formulas. Why do you need formula, if you can't understant its essence. Then there are lots of calculus expressions. I DON'T think it's for everyone!

BUT, I found the book SPLENDID just because of those subjects covered - and covered quite generally without too deep details (although sometimes I wanted more).

I certainly don't agree with those folks who say that there is no explanation on subject's importance. There is ENOUGH! Then I ask you: "Why did you buy that book? Just randomly?" If you have little gray cells in your box then you'll understand why something is or isn't important. I DON'T have need for lengthy texts of explanations why this and not other subject. That is boring!

Where is the value added?
In this book, John Casti takes an academic's eye toward 5 interesting areas of mathematics.Unfortunately, his treatment of the material reminds me of sitting in all too many classrooms in graduate school, with a professor rambling and scribbling on the board without ever bothering to indicate why it even mattered.Like all too many of my professors, he leaves the truly interesting material (the impact) to the reader's imagination.Casti really missed the mark here.He had the opportunity not just to present mathematical proofs, but to show why this is really interesting stuff.Instead, the material is presented no differently than how it would appear in a graduate level textbook.So, why not stick with those graduate level textbooks?Where is his value added as an author?

Beauty that is not made accessible to the layperson
.

«The linear dynamical system (**) is completely reachable if and only if the block matrix C contains n linearly independant vectors, that is, rank C = N»

If you don't feel completely at ease with this sentence, do not read this book.Every page contains mathematical propositions of such level, and such level of mathematical fluency is required in order to fully appreciate the content of John Casti's book.The content is interesting but the reading is made rendered somewhat tedious by this high density of maths.I have a degree in engineering, and I often fast forwarded trough the equations in an effort to not lose sight of the big picture Casti want to show the reader.

At the end you will be smarter, but it will not have been a relaxed reading.If you are looking for food for toughts, I would recommand, among others, «Paradigms Lost : Tackling the Unanswered Mysteries of Modern Science», by the same author. ... Read more

Product Description
A reference for the history of chaos theory, told by the pioneers themselves, and eleven other authoritative contributions. Provides a historical introduction to all of the concepts of chaos theory. ... Read more

Product Description
Book DescriptionPublished in 1995, the bestselling first edition of Trading Chaos provided readers with the most practical and comprehensive guide for applying chaos theory to the real world of trading and investing. But today, the markets are different than they were even a few years ago. So with fresh research in hand, coauthors Bill Williams and Justine Gregory-Williams have updated their profitable methods and provide new techniques to help you take profits from the markets.

Trading Chaos, Second Edition will not only show you how to anticipate, recognize, and react to impending bull and bear market conditions, it will also introduce you to the latest findings in physics and psychology as applied to various markets--stock, bond, futures, indexes, and many others.

The first portion of this book is devoted to understanding how the rewards you’ll acquire in trading and investing are determined by what is happening inside of you. By digging through some very interesting and deep psychological principles, you can become a profitable "trade/vestor"--using technical techniques for good short-term entries and exits, but also holding on to long-term investments when the opportunity presents itself. Trading Chaos, Second Edition will help you build a solid psychological foundation before you enter the markets.

After you’ve learned how to gain an inner analytic edge, the authors will show you how the application of self-knowledge will improve your bottom line. Through numerous charts, checklists, and examples, you’ll be introduced to proven techniques that can make the unpredictable understandable and make your journey into the markets more profitable. You’ll learn how to:

Sharpen entries and exits, and reduce whiplashes with the powerful "Alligator" indicator Get into a new trend very early with proper use of the "First Wise Man" Add on aggressively after your first entry using the "Second Wise Man" with the help of the Awesome Oscillator (AO) Make fractal breakout trades with the "Third Wise Man"--these almost guarantee profitable follow-through on a trade

In this early part of the twenty-first century, you have a choice to either be a part of the last generation of traders and investors using linear (ineffective) techniques or the first generation using effective nonlinear (chaotic) techniques. By reading the Second Edition of Trading Chaos, you’ll learn how you can take your trading skills to the next level and make steady profits in any marke ... Read more

Customer Reviews (22)

too philosophical to a trader like me
I've been trading for more than 5 years since my graduation from college. This book offers lots of questions for philosophical speculation. Indeed, it raises many doubts about our assumptions upon this reality we reside in physically, mentally, or spiritually. Nevertheless, I will not position this book as a guidebook or a know-how methodology for beginners. This book was written or structured with a strong philosophical implications. Some chapters are nothing more than anecdotes of successful traders which I personally don't find appealingly entertaining or useful to my personal account.

Bill Williams Is A Great Teacher
Williams has been educating traders for many years, and is an effective teacher.His approach of "want what the market wants" and "follow the path of least resistance", are simple but essential lessons.You will learn about these lessons and more in this terrific book, and if you are open minded enough you will be able to benefit from his deeper understanding of how markets and traders behave.

Some of Williams' ideas are "out of the box" for traditional practitioners: he recommends meditation tapes to his students, tapping into a holistic method, and thinking in terms of a more global and universal energy that affects the markets and each trader's mind via their thoughts.

If you like Williams' approach, you may also find Bennett McDowell's system useful.He was a student of Williams' way back when, and has since gone on to become one of the newer educators in the field.McDowell's book, "The ART of Trading"The ART of Trading: Combining the Science of Technical Analysis with the Art of Reality-Based Trading (Wiley Trading)has the same energy that Williams work does, plus it offers money management techniques that complete the success picture.

Williams doesn't lecture at the trade shows anymore, but his teachings can be effectively mastered by reading his books and visiting his website.Recommended reading.

Contradicts his own theory
When I first started reading this book I thought it was going to be great.He really sounds good talking about Zen and Chaos theory and non-linear vs linear - and I think he is right that the markets behave under these concepts.However, he doesn't really tell us how to apply any of this to trading.Read this book and then look at a chart.Can you trade better now knowing that you should be using a non-linear, chaos approach?No!Why?Because he doesn't tell us how to apply that theory to trading.He tells us to be one with the market and flow with it etc.That's fine and dandy - but how do we do that?

He tells us that ta and mechanical systems don't work, then he reveals the system he uses to trade by - a mechanical system!!!I was shocked to see that his system is just another dime a dozen 3 ma system.How is his system using non-linear chaos theory?How is his system flowing with the market and making you more "in tune" with the market?It's just another mechanical ta system!!!(kind of sad really)

This book started with great promise but ended up being a total disappointment.

Unique Among Trading Titles
This is the finest trading-related book ever published; if you are just starting to learn about trading and investing, please pick up a copy of Trading Chaos before you spend another dime on newsletters, software or 'hot tips.'

It's not about trading a system, it's about trading your mind .......

Bill and Justine did a great job
Bill and Justine are made me aware of what is driving the markets. Before I met them I was caught in a circle of winning and losing money in trading. The first edition opened my eyes, new trading dimensions got me out of the dream. The home study course showed me that It is possible to trade consistently, The personal workshop with Bill taught me more than enough of the inside of the markets to grasp the why and how. Eventually workshops by Justine in the middle of Chicago made me implement it all.

This new edition of Trading Chaos is refreshing. It's not about "the magic system", it's not about how to design the perfect system. No it's about real life and how the markets fit in. The perfection in the chaos, the perfect repetition of the small in to the bigger picture.

Don't buy this book if you want to know which market to trade and make money.Don't buy this book if you are looking for the magical tip.
Do buy the book if you want to learn what the market is driving and how you can profit.

Do buy this book if you are clueless (like I was) about your trading mistakes.
If you are serious go for the book, think of the implications and contact Bill and Justine to do a follow up. I did it 10 years ago and never had a moment of regret.
... Read more

Product Description
Chaos & Nonlinear Dynamics in the Financial Markets explores both theory and empirical results related to non-linear determinism in the dynamics of asset prices. It includes a wealth of material on the properties of chaotic processes relevant to markets, along with statistical and other tests which have been developed specifically to detect the presence of chaotic behavior. This authoritative guide covers a comprehensive range of issues associated with chaos theory. It includes sections on theoretical foundations; evidence of chaos in the stock market, commodities markets, and money markets; and a section on advanced methodological issues. You'll also find included Chaos Explorer, a complimentary software package that graphically illustrates the chaotic processes that are referenced throughout the book. ... Read more

Customer Reviews (1)

A bible for the nonlinear traders
First of all, this book is only a collection of journal papers.However, all of the chapters provide the complete understanding of the new science - chaos theory and its underlying assumption of nonlinearity.In my opinion,this book is the bible for anyone who want to study on this area. ... Read more

Product Description
Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena focuses on explaining the fundamentals of the subject by studying examples from one-dimensional maps and simple differential equations. The book includes numerous line diagrams and computer graphics as well as problems and solutions to test readers' understanding.

The book is written primarily for advanced undergraduate students in science yet postgraduate students and researchers in mathematics, physics, and other areas of science will also find the book useful. ... Read more

Product Description
Written by one of the most respected mathematicians in the field, this book conveys the essential mathematical ideas in dynamical systems using a combination of theory and computer experimentation. This introductory look at dynamical systems includes investigating the rates of approach to attracting and indifferent fixed points to the discovery of Feigenbaum's constant; exploring the window structure in the orbit diagram; and understanding the periods of the bulbs in the Mandelbrot set. ... Read more

Customer Reviews (4)

There Are Better Choices
This is a fine text, and I was able to follow it fairly easily.However, it is rather dated (1992) and there have been improvements in the subject in several areas.I found Steven Strogatz's "Nonlinear Dynamics And Chaos" (2001) a significantly better book for both content and readability.

Has soul - but no cigar
The content of the book is great, only a little short and condensed. I wish more examples were available. Also I wish sometimes author would approach a topic from different angles, instead of leaving us behind after plowing through something...

Very poor print quality and layout, the colored pages are FALLING OUT from the book. Definitions are not always apparent and it is difficult to discern important parts in the book. Graphs are "grayscale" and are also of very poor quality.
I guess this is all due to the book being old, and it is printed on-demand, as shows in the font/typeface - which looks like it's been "xeroxed".

Nice begginers text
This text is a great begginners guide to chaotic systems, it provides very clear explanations and proofs as well as some examples to help you along.

Excellent book.Explains concepts clearly.
I went from knowing absolutlely nothing about dynamical systems to being able to look at a point on the Mandelbrot Set and visualize what the corresponding Julia Set looks like.Ever wonder why weather cannot be predicted accurately??Read this book... ... Read more

Product Description

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms.

From the reviews:

"Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik

Customer Reviews (2)

Great reference or grad school level course text on general nonlinear dynamics
This book served as the "hidden basis" for a course in nonlinear dynamics by the late John David Crawford back at the University of Pittsburgh (the overt basis was Glendinning's book, which has proved less appealing as a reference). It's subsequently been useful to me in its treatment of Melnikov's method, and to review ideas in bifurcation theory.

As the other reviewer pointed out, it is weak in the section on symbolic dynamics. In its defense, I only know of one book which treats symbolic dynamics in a way that isn't utterly confusing, so perhaps leaving a lot of it out helps keep the student on track towards what the author is trying to present. Certainly, if he stuck to his theorem heavy style, one could get very lost in symbolic dynamics land. I'll also complain he never mention's Painleve's property. There are probably deep "theorist" reasons I'll never understand for his not mentioning this weird little thing. I hear the full treatment of Painleve's property is pretty complex, but I have always found it very helpful in understanding what integrability really is, in my "seat of the pants" way. I also would have liked more detail on Peixoto's theorem. Sure it's only useful in R2; if you're on the 'applied' side of things (or a student, learning by examining practical examples) -how often will you leave R2-land?

These complaints are minor, and they're probably effectively complaints that the book's author has a different purpose in mind than I would for writing such an introductory text, were I actually qualified to do such a thing. Wiggins writes very clearly, and he writes for physicists rather than mathematicians, and brings an amateur in the subject to a fairly high level of sophistication by the end of the text. The problem sets are also excellent.

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

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Customer Reviews (3)

Interesting, but title concept remains murky
This is an interesting book, but both its ambitions and its accomplishments are of a much narrower scope then being "a book about everything," as another reviewer put it. Mostly, it's a book about interdisciplinary metaphors, and the philosophical foundations of a case for such metaphors' being useful. However, I'm not sure if the metaphor in its title is entirely successful.

The book's jumping-off point is the late-20th Century fad for "chaos theory." Although today most physicists don't recognize it as a distinct "theory," economists, lawyers and literature scholars, among others, were all to happy to suck it into their own academic papers. Some academics, especially some physical scientists, attack this kind of poaching as illegitimate. Stephen Kellert (SK), who is, as he often reminds the reader, a "disciplinary pluralist," sets out in this book to explore the factors that might legitimate such borrowings, and to consider criteria for judging when some borrowings are more justifed or successful than others.

SK approaches these tasks with the patience, and at times the fussiness, of an academic philosopher. Even though some fields -- e.g. rhetoric and linguistics (and esp. the subculture of the latter that calls itself "critical discourse analysis") -- set themselves tasks similar to SK's, he usually manages to be both broader and more even-tempered. For example, he has some interesting things to say about how facts and values are different but not always entirely distinct; but, as a pluralist, he can tolerate this ambiguity without feeling driven to accept relativism.And SK refuses to enter into some fights, such as over the legitimacy of neoclassical economics; he explains that the book's project "primarily focuses on the ways that borrowed knowledge is used within the fields of economics, law and literature as they are currently configured in the academy" (@91).

The proverbial general reader may find this deference to the academic status quo to be a limitation of the book. Moreover, some parts of the book seem to be spent on settling issues that only academics might find problematic. E.g., SK spends a couple of pages asking and answering "Why criticize metaphors?" (@122-124). To find such a question necessary, you'd probably have to be the same odd sort of person who doubts that your pet dog or cat has mental states. I often agreed with SK's conclusions about specific cases, e.g. about economists' use of value-laden terms like "efficiency" as if they were somehow "value-free," or about how some purported references to chaos were actually referring to, say, quantum mechanics. But these conclusions seemed for the most part quite obvious to any reader with some sensitivity to metaphor, and who took an intro college physics course or reads lots of popular physics books.

SK never provides a clear definition of "borrowed knowledge,", though he comes close when he describes how some economists "look over at physicists doing their first-order work [i.e., asking questions like, how do atoms work?], borrow some of their concepts or tools, and then use them to look back at their own objects of study in a new way. This is just the phenomenon of borrowed knowledge" (@27). We aren't ever given a clear definition of "knowledge" either, though SK reifies knowledge heavily. Not only can knowledge be "borrowed," but it can "produced" (mentions of "knowledge production" abound, e.g. 20, 30, 43-44, etc.), it "resides in a disciplinary location" (rather than in, say, peoples' heads) and can be "transported... and (hopefully) returned" (@13).

Some of SK's examples struck me as aptly described by "borrowed knowledge." E.g. he mentions an economics paper that pointed out how chaotic physical phenomena forced physicists to use a wider variety of mathematical models than they had previously; the authors concluded that economists ought to consider that, by analogy, their own simple linear equations might not be adequate to describe economic phenomena (which is different from saying that economic phenomena follow the new physical models). An even clearer example might be a paper that actually demonstrates deterministic chaos in the dynamical behavior of some economic phenomenon -- though that might better be termed an "integration" than a "borrowing".

But what about when someone name-drops "glamorous jargon" (@108) to make their own work, however irrelevant, seem more important, modern, worthy of funding, etc. Is it really *knowledge* that's being borrowed here? or is it something more like prestige or an air of trendiness?SK notes that "knowledge production is always at least partially a matter of persuasion (@60);" but this doesn't mean that persuasion (esp. of the name-dropping kind) necessarily entails knowledge production.

In addition to such persuasive uses of borrowed knowledge, SK is no less interested in "inventive" uses, which rest on metaphors. Metaphors can play a "role in generating hypotheses from current conceptualizations and transforming those conceptualizations" (@111), e.g. by "defamiliarizing stagnant assumptions" (@114). They can "induce structure" in a target field [sc. of knowledge] that lacks structure, or can "reorder part [of a highly structured field], temporarily or permanently" (@111). But here again calling something a borrowing of "knowledge" seems to depend on what you're doing (examples are my own):

A. "The Mississippi River was a strange attractor for Huck Finn." I've used a buzzword, or perhaps even a concept from chaos theory. But did I borrow knowledge?Are concepts sufficient to constitute knowledge? For example, is "blue" knowledge?

B. "Money is like energy, it can neither be created nor destroyed." Here I'm doing more than borrowing a concept, I'm also asserting something to be true about money's relation to other things (the universe, e.g.), based on my knowledge about energy in the physical world. So far so good, but the statement is false as to money, since the US Treasury can print more of it. Should one say that knowledge has been borrowed unsuccessfully, or just that it's a lousy metaphor (or simile, for rhetorical purists)? Does the answer change if the context shows that my intention was persuasive rather than inventive (e.g., that I was just trying to bamboozle my audience, who might know next to nothing about physics or money)? Now what if the statement turns out to be false about physics, too -- was there ever any "knowledge" to be borrowed?

My sense from the book is that SK would say *all* of these cases count as "borrowed knowledge". (SK does say that "getting the science wrong dooms an attempted metaphorical borrowing" sometimes, though not always, @129-130.) If so, then I think the phrase may be too broad to be helpful. Why not just use "borrowed concept" or "interdisciplinary analogy" for some of these cases, instead of lumping them all under the "borrowed knowledge" label? SK might justify this on grounds of being a "pluralist," but for the general reader "knowledge" is what SK calls a "thick" term, carrying a lot of evaluative connotations (like: dude, it's really true).

Parts of this book can be entertaining if you've studied some physics, and interesting if you're involved with interdisciplinary studies, or if you don't often read much about metaphors and discourse analysis. But the ambiguity of its definition of knowledge and the obviousness of some of its case studies ultimately made me suspect that the book is salted with a pinch of "glamorous jargon," itself.

A Book About Everything
When a friend of mine recommended this book to me, I asked him what it was about. He told me that it was a book about everything. I, of course, was skeptical. The subject matter seemed quite narrow: Chaos Theory and Pragmatic epistemology - neither of which are areas I know much about. But it did not take long into the book before I realized how accurate my friend's description really was.
Kellert does a fantastic job of cogently and concisely explaining, summarizing and arguing about chaos theory, philosophical pragmatism, epistemology, and their interrelation. With striking genius, Kellert is able to present deep and complex arguments about philosophically rigorous concepts so they are enganing on a very basic level, but also quite profound in the current debate on the nature of knowledge, its relationship with human value and meaning, and the interplay between those two around usefulness. That is, Kellert does a wonderful job of explicating the limits of certain forms or disciplines of knowledge by demonstrating the limits of chaos theory as it has been used in several disciplines outside of the natural sciences.
One of - in my opinion the - the most interesting strands of Kellert's thought is his discussion about why groups "borrow" knowledge at all. He offers unique insight not only into how academics and practitioners - such as economists and lawyers - borrow knowledge from natural sciences, but why they do so - and what that tells us about how knowledge is produced, used and manipulated.
Overall, this is a great read for anyone interested in epistemology generally. It does not require a great deal of background knowledge in chaos theory, epistemology, metaphilosophy, economics, or any of the grandiose topics Kellert engages, because he clearly presents those ideas on a level the novice can grasp. Still, this is not a book for beginners, either. Kellert adds very serious academic rigor and intellectual insight for anyone interested in chaos theory, epistemology or pragmatism generally. I strongly recommend this book!

A great read
A very fun and interesting read!

I'd definitely recommend it to anyone who is curious about the applications of Chaos Theory and how it relates to the world around us. ... Read more

Product Description
Do we live in a simple or a complex universe? Jack Cohen and Ian Stewart explore the ability of complicated rules to generate simple behaviour in nature through 'the collapse of chaos'. 'The most startling, thought-provoking book I've read all year. I was pleased to learn that most of the things I thought I knew were wrong' - Terry Pratchett. ... Read more

Customer Reviews (9)

From simplicity and complexity to simplexity and complicity
Jack Cohen is a biologist and Ian Stewart is a mathematician. It is interesting to see the impact of chaos theory and complexity theory to their specialized areas. This book represents thoughts beyond the new science made popular by James Gleick in his far reaching book Chaos: Making a New Science, in which his description of Edward Lorenz's notion of Butterfly Effect dramatically altered the perception of many people from a orderly world to a chaotic world. The overwhelmingly numerous occurring phenomenon of chaos in nature was brought to the attention of the scientific circle. Chaos was found to be actually complexity beyond the comprehension of our mind but there is also naturally emerging simplicity out of the complexity. The collapse of chaos is the path of the development of our thinking from chaos/complexity towards simplicity. The opening of the book presents the intertwining phenomenon of complexity and simplicity.

The first half of the book is devoted to explaining the current reductionist paradigm by which cosmology, evolution and human intelligence are the consequences of lower level and simpler theories of quantum mechanics, chemistry and the genetic code. The content of the chapters on prevailing science is amazingly rich. It gives a concise and clear description of the foundation of modern science. Just these few chapters alone, before examining the authors' arguments on the collapse of chaos, make the money spent on the book worth.

On physics, it is Newton's laws of motion and gravity, Einstein's theory of relativity and also the basis of quantum mechanics, explaining in their own way the cosmos starting from the Big Bang and all the way down to atoms and sub-atomic matter.

On chemistry, it is Mendeleev's periodic table, supplemented by the explanation of electron shells, and also the versatility of the carbon atom which make up the complex hydrocarbon molecules: the origin of life.

On evolution, it's Darwin's natural selection, DNA and the genetic code, and in particular the interaction between genes and the environment.

These are strong illustrations of the complexity around us. The simple rules from our discovery of the laws of nature do not necessarily and adequately explain all the observed occurrences of natural phenomenon. We are therefore living in a chaotic world full of events we do not understand, but we choose to explain a very small proportion of the chanced events which happen to fit our perceived laws.

Science explains complexities as the interaction of a huge quantity of possibilities by finding simple causes which could produce a proportion of the predictable complex effects, and call them the laws of nature. The result is used to explain predicted large-scale simplicities observed, among the complexities. We think that the laws of nature represent the underlying simplicities, and therefore these simple causes produce simple effects, despite complexities involved. However, we ignore the reality that our laws also produce complexities which are not accordingly explainable.

Cohen and Stewart explain that reductionism, i.e. the use of reducing behavior to the interactions of the smallest entity, has brought forth great advances in biology, chemistry, and physics. They believe, however, that the potential of such scientific approach is exhausted.

Starting from the middle of the book, the authors expand the new science of chaos theory and complexity theory to show how inadequate our laws of nature in dealing with complexity which is all around us. Chaos theory, made popular by the butterfly effect on the sensitive dependence on initial conditions, shows that simple causes can produce complex unpredictable effects. Whereas complexity theory suggests the opposite, that complex causes can produce simple effects.

Here, there are two main features emerging from the style of the authors. First, owing to the biology background of Jack Cohen, there are detailed examples and explanations on the complexity of evolution, the embryological growth and the development of consciousness and intelligence. They are eye-openers. Second, the authors introduce a conversation between human: the spaceship crew, and the alien: inhabitants of another planet. The core of the conversation is the difference in culture and the laws of nature between lives in different world. It proposes that our world is not unique and life form in another world may be developed along a completely different path, including the atom composition and DNA composition. The conversation is quite inspiring and humorous. However, it attracted criticism from some reviewers who have expectation of more serious writing from a supposedly science book.

The interaction between simplicity and complexity gradually escapes the paradigm of reductionism and the authors introduce two new terms: simplexity and complicity.

Simplexity refers to the tendency of a simpler order to emerge from complexity. It is the emergence of large-scale simplicities as direct consequences of rules. It covers any features that emerge from sets of similar ground rules.

Complicity is a kind of interaction between co-evolving systems that supports a tendency toward complexity. It is more like convergent evolution: different sets of rules generating similar features. Both concepts of simplexity and complicity bring about a collapse of chaos.

The moral of the book is on the inadequacy of reductionism, building toward the two explanatory principles of simplexity and complicity. For example, one cannot simply map a lower level of organization, such as the DNA code, into a living organism. There is a dynamic in which both content and context are critical.

Non-Elementalism As A Paradigm.
Jack Cohen with Ian Stewart in "The Collapse Of Chaos" attempt to show how Science must evolve.Theories such as Chaos, Quantum mechanics, Relativity, etc., require a new paradigm(methodology, worldview, etc., after Thomas Kuhn(1962)) as a way of organizing 'reality'.However since they have not been able to formalize a system(like many before them) involving emergent(Lao-Tse(c.600B.C)-whole is not the sum of the parts) phenomena, they have instead resorted to analogies, images, examples, discussion, etc.
Cohen with Stewart appear to recognize self-reflexiveness, that content has context for example; non-identity(an abstraction, anything, etc., is not the 'same') though only through diversity- natural selection as contextual; non-allness(cannot have 'all' abstractions, anything, etc) via the fact that DNA conditionally only directly codes for protein synthesis, further not even indirectly for 'all' the characteristics of the organism, instead context(nurture; mother's genes, hormones, etc; environmental factors like temperature, etc; etc) has a major role; related to non-allness, non-universality: laws are not eternal truths but context-dependent(relative) upon our method of investigation(for 'reality' has a tendency of throwing up facts['filtered' out] that does not fit our laws);etc.Though Cohen with Stewart are not aware that our current inadequate methodology traces back to Aristotle(c.350B.C.), further that just such a Non-Aristotelian paradigm(the foregoing as part) got introduced by Alfred Korzybski(1933).Unfortunately, Cohen with Stewart finally falter with non-elementalism(interchangeable, equivalent, reversible, etc., functional[non-linear-asymmetry-non-additive], packets, etc., emergent, holism), their main thrust.
Science has tended to explain complexities(actualities: the sheer multiplication of possibilities due to the 'interactions' of huge quantities) by finding deeper underlying simplicities(the consequence of the operation of simple rules on another level: simple 'causes' produce predictable complex 'effects'), as the laws of nature, etc., such that any large-scale simplicities (from complexities) that we observe, represent the underlying simplicities(simple 'causes' produce simple 'effects', despite complexities involved) becoming visible on a higher level, for example the spiral form of galaxies.Termed 'reductionism'('atomism', 'elementalism': Latin elementum, to 'analyse', 'atomize', etc.,- divide to the indivisible parts, the non-separable, contextually interchangeable whole(s) from part(s); etc), this represented Science's greatest achievement- where the complexity of one level becomes 'analysed' to a simplicity on another level.For example, that the 'interactions' of a range of fundamental 'particles'(-waves-fields) can account for the chemical 'elements', further how they 'react', bond, etc.
However this answer is no longer convincing.Chaos theory(for example, butterfly 'effect':"sensitive dependence on initial conditions") suggests that simple 'causes' can produce complex unpredictable 'effects', for example Mitchell Feigenbaum's(1979) number, the basis of Benoit Mandelbrot's(1977) Mandelbrot fractals, etc.; different from the underlying rules.Whereas complexity(Stuart Kaufmann's Anti-chaos) theory suggests the opposite: complex 'causes' can produce simple 'effects'.Echoing 'conventional reductionist' Science current findings that inside the great simplicities of the universe we find not simplicity, but over-whelming complexity.Here Cohen with Stewart introduce the terms complicity(defined as functioning as accomplice; becoming complex) representing chaotic systems, along with simplexity(defined as "comprising a single part"; "process involving simple features arising from a system of rules") representing anti-chaotic systems.
Though 'reductionism' appears occasionally great for quantitative mathematical calculations involving content.Our understanding of external large-scale functionings remains instead mostly descriptive, geometric, qualitative, etc.,- emergence involving context.Charles Darwin's(1859) principle of natural selection for example has no agreed upon laws, equations, etc., from which natural selection can become derived.Therefore Cohen with Stewart came to realize that emergent simplicities represent structural patterns created by external constraints, that collapse an underlying sea of random fluctuation- chaos.However though holism would thus appear as the obvious alternative to 'reductionism', yet it is not what Cohen along with Stewart want: "It considers a system as a unit and often ignores its context".Nevertheless though this may appear true for example, Kurt Goldstein's(1934) "organism-as-a-whole", other formulations have intermeshed context(equivalent to Korzybski's(1933) self-reflexive premise), again from Korzybski's(1933) Non-Aristotelian system:"organism-as-a-whole-in-an-environment".But before that we had Edgar Rubin's(1915) "reversible figure(s)-ground(s)" of Gestalt 'Psychology'; which can explain for example Mandelbrot's fractal as a holistic process.
Now the problem remains as to how to formulate this emergent process.Firstly our theories as 'generalized-universals' destroy facts, therefore we must formulate them as packets of reversible content(s)-context(s) relative uncertainties.Secondly we must mathematically bridge quantitative(content) with qualitative(context) phenomena as relative uncertainties.Mathematics as the Science of patterns(otherwise function of values), is not another 'reduction' but a language with which we can gain insights into how patterns arise.However Cohen with Stewart in the end fail to see the interchangeability of functional non-additive-asymmetry-non-linearity as mathematical emergence, which finally must have blocked their understanding.Though further diverse insights may well have assisted.
Nevertheless despite these flaws, Cohen along with Stewart have made a magnificent effort, for not many would have made it as far as they have.

Brilliant
I loved this book. I have never seen such a huge compilation of ideas from so many different topics compiled into one place. Not only that, but all the topics interlink to show the obvious as well as subtle connections. I especially like the fact that throughout the book, the authors manage to show numerous points of view, but without trying to force the reader to fall into any specific belief. I'll admit that not all the ideas are original in this book, but that fact is even stated within the book. For a second-year chemical engineering major such as myself, this was a real inspiration for thinking "out of the box", and really made me think about some of the "knowns" tought in science. A deffinite must. I have several friends in line to borrow this book already!

Disappointing
Not terribly impressive. The first two thirds of the book offer no new ideas, the authors just rehash material you'll find elsewhere. This part of the book spends *far* too much time on the subject of evolution and DNA in my opinion, perhaps because one of the co-authors is a biologist. How about cosmology or neurology, for example - both important fields in which low-level interactions give rise to high-level emergent behaviour ?

The final third of the book also fall a little flat, IMHO. The authors' grand insights seem trivial and unoriginal. One idea in particular seems to be 'borrowed' without acknowledgement from Douglas Hofstadter's amazing "Godel, Escher, Bach" : that a message and its context are inseparable (remember the dialogues with records and record players ?) I came away feeling distinctly un-enlightened.

One aspect that really annoyed me is the use of the awful hybrid words "simplexity" and "complicity", used to describe two quite different concepts. Every time they're used, the reader is left struggling to remember which word is which. I wish the authors had aimed for clarity, rather than playing silly word-games.

And finally, I have to mention the appalling design of the UK edition of this book. The type is far too small, and the cover (white text on bright yellow) is unreadable. There's a quote on the cover from Terry Pratchett, and his name is so prominent it honestly looks as though HE wrote the book. It is possibly the worst jacket design I've ever seen.

I really admired Ian Stewart's earlier books, but my advice is to avoid this one.

all they want to do is remake science
This is a witty and at times brilliant book.The authors argue that the reductionist approach to science, which has flourished over the last 300 years, for a more holistic or contrextual approach.In the reductionist approach, scientists have choped problems into manageable bits - lab experiments or discreet mathematical problems - that eventually they assume will be fit together into a coherent whole.Nature in this view functions as a vast machine they can reduce and separate into its component parts.

TO prove their point, the authors embark on a dazzling tour of biology, chemistry and physics.But something is missing say the authors.What we know, they claim, are tiny islands in a sea of ignorance; it is self limiting as the larger questions get neglected.It is the causes of simplicity, they say - the order that suddenly emerges - that researchers should explore.

So, they conclude, it is time for a new set of questions.Unfortunately, just when we expect something new, it is here that the book gets a bit vague, with the authors falling back on anecdotes and speculation.They try to coin a new vocabulary ("simplexity" for the old and "complicity" for theirs); offer some diagrams of what they want, including an odd picture of mixing smoke with a unicorn head; and they harp on strange and abrupt conclusions, such as the importance of squid fat to the evolution of the human brain.But they do not offer a coherent new paradigm.

An uneven effort, but fun and very funny at times. ... Read more

Product Description
In a totally new way of looking at financial economics, Nonlinear Pricing abandons the traditional assumptions of equilibrium in economics and randomness in a time-series. These shortcomings are becoming increasingly awkward given a superior technological infrastructure and advances in mathematics and the sciences. Despite these advances and their empirical proof, much remains confused or muddled. In this groundbreaking new book, leading hedge fund manager Christopher T. May explores the nature and role of nonlinearity, an inherent part of everyday reality, and illustrates a profit-making strategy.

One of the many striking applications of nonlinear technology in recent years, nonlinear pricing uses cutting-edge technology to identify and exploit patterns hidden within the seemingly helter-skelter rise and fall of daily stock prices. Nonlinear Pricing sheds much needed light on the principles behind this innovative view of reality and provides clear explanations of how it is employed to predict—at least partially—the unpredictable.

Beginning with an incisive introduction to the topic, May presents the roots of nonlinearity through the examples of calendrics, geometry, and music. He then illustrates the application and integration of various nonlinear technologies, including genetic algorithms, fuzzy logic, fractal imaging, and nonlinear dynamics, to such essentials as trading strategies, asset allocation, risk management, and derivative pricing and hedging. Along with practical methodologies and a wealth of real-world examples, this comprehensive resource contains a glossary of terms, a bibliography, and in-depth information on:

• Fractal analysis—power law distributions, fractional Brownian motion, and their relationships
• The Hurst Exponent—the KAOS screen and its practical implementation
• Resonance—time domain versus frequency domain, Brownian motion, and the Gaussian distribution
• Advanced concepts—Soros's Reflexivity, nonequilibrium economics, kernel of theoretical nonlinear pricing, May's Law, resolution and resonance.

"Nonlinear Pricing is an eminently readable book which I found satisfied both the theorist and the practitioner in me. For the theorist, there are new insights into the relationship between complexity and the markets. For the practitioner, there are practical ideas on how to fashion investment strategies. I highly recommend Nonlinear Pricing to all students of the markets."—Edgar E. Peters, Chief Investment Strategist, PanAgora Asset Management; author, Chaos and Order in the Capital Markets.

"Nonlinear Pricing goes further than any book I am aware of in drawing a connection between the real world of economics and the new ideas about economics coming from the science of self-organized systems. Written in a lively, informal style, this is a wonderful read for those of us who have been wondering whether anyone understands anything at all about how markets work."—Lee Smolin, PhD, Department of Physics, Pennsylvania State University.

"Required reading for the enlightened financial professional. Enjoyable for the intelligent investor. A dash of physics, bite-sized pieces of nonlinear concepts, and a broth of hands-on experience make this a cookbook for the modern trader."—Richard E. Morley, Potts Medal recipient and founder of the Breakfast Club.

"A real eye-opener—Nonlinear Pricing explains a complex subject in easy terms and makes the reader aware of the many opportunities offered by this new technology."—Richard Olsen, founder, Olsen and Associates, Zurich.

"I, of course, think highly of this book as it credits Dance of the Money Bees with inventing 'swarm theory,' now a discipline in computer science. There are many other splendid insights."—John Train, author and President of the Montrose Fund

"An extraordinary tour d'horizon, this book challenges conventional thinking about finance, investing, and much else besides. Brimming with ideas and eye-opening connections, it makes a powerful case for our need to understand the extent to which nonlinearity shapes our lives."—Andrew Freeman, Managing Editor, Financial Services, The Economist Intelligence Unit; coauthor, Seeing Tomorrow: Rewriting the Rules of Risk.

"Nonlinear Pricing: Theory & Applications by Christopher T. May makes nice reading even for people like me who are not economists. This is an ambitious book as it presents economics starting from fundamental physics. It deserves a large readership."—Ilya Prigogine, 1977 Nobel Laureate, Chemistry; author, The End of Certainty; and world's foremost non-equilibrium scientist.

Written by one of the few practitioners using this breakthrough methodology to trade the markets successfully, Nonlinear Pricing fills an important niche in investment literature. It is a must read for anyone seeking to understand—and capitalize on—twenty-first century financial economics. ... Read more

Customer Reviews (20)

Completely Useless
Optimistically I bought this book expecting an insight into non-linear models of price behvaiour, maybe some thoughts I could use to flesh out my own experience - a peek into other approaches to managing price volatility perhaps. What I got was a rehash of technical analysis with a glaze of chaos theory. Don't bother.

Not worthy to present itself as a serious work
I expect that I am not the only reader to conclude that Christopher May has only a cursory grasp of nonlinearity. As a reader of philosophy and religion and a mathematician with research experience in nonlinear dynamics, I kept wondering when the "hand waving" and "name dropping" were going to yield to some cold, hard analysis or practical application.I might even have settled on a few unproved practical pricing applications!

To add insult to injury, this book was poorly edited: papers were discussed as if well-known, then introduced five paragraphs later; whole paragraphs were repeated several times, as if the book had been a series of independent pamphlets stapled together; anecdotal musings ran on for pages with no purpose apparent other than to impress the reader with the author's erudition; typographical errors peppered the few mathematical expressions.

I have similar complaints with Edgar Peters' books, but at least Peters understands nonlinearity sufficiently to have applied some famous techniques to problems in financial valuation. One can hardly escape the suspicion that Christopher May is a long-winded "poseur."

Ego trip with virtually no useful baggage
If you're looking for a good primer in fractal economics, do not waste your money, or worse, time with this book. You can get more information and less noise from E. Peters's "Chaos and Order in the Capital Markets". The most useful information you'll get from this book is a description of the Hurst exponent; the rest is, well...

I don't mind random musings with an articulate friend after dinner, but please don't do it in a pedagogical-sounding, inflated tome. Let the quotes describe themselves:

"... this chapter will present a challenge because it exists at a rarified level of understanding."

"I maintain, as any good scientist does, that the theory must fit the facts".

"The mathematics in this chapter may be complex to the financial economics professional" (I found the series summation as the most complex math in that chapter.)

Errors and carelessness are so prevalent, this book really brings down my opinion of the JW editors. Concepts of dependent and independent variables are mixed up, atrocious-looking graphs of normal and Levy distributions are shown, notations like "m2" are printed instead of "m(superscript)2" to mean m-squared, etc.

Most of the time is spent waxing philosophical connections among shallowly described concepts like Fourier transform, superstrings, the scriptures, Brownian motion, Socratic logic, etc. To be fair, if this sort of shooting-the-breeze provides a relaxing read for you, this book might fit the bill.

The author breathlessly describes "original concepts" like fixing risk for varying returns in security portfolios: this is already done with instruments like mortgage securities.

Perhaps the author's own quotation of Occam's Razor should have been heeded, "That which is not needed should not be included".

I did find the Bloomberg KAOS screen description on page 128 useful. If you use Bloomberg, you can also get that from the manuals.

Contains no substance or even one concrete idea
Very poor treatment of the topic. The author doesn't seem to know where the nonlinearity lies in "Nonlinear Pricing". He sees it "everywhere". One wonders whether he even knows the difference between a linear and a nonlinear function, and if so why he seems to thinkthat a Gaussian distribution pertains to "linear", and anythingelse to nonlinear. It is clear that his understanding of mathematics is atbest vague; unfortunately not even his concepts bear much merit."Genetic", "Fuzzy", "Non-equilibrium" aresimply used as buzzwords to create the air of beingmathematically-sophisticated (the mathematical community knows that"genetic algorithms" are essentially a characterization of"stabbing in the dark" in the absence of a better searchprocedure, or often, of knowledge). He even dares to toy with concepts fromphysics which he can't even start to fathom.

I see some readers fairlyimpressed with the book. If you don't have much understanding of math andthe fundamental sciences, you might be. But you'll also be left with nounderstanding at the end of the day ( you might attribute the lack ofunderstanding to your background in "humanities", but it willreally be because the book has no substance ).

With his writing style,the author could perhaps have given Deepak Chopra a run for his money hadhe concentrated more on the religious part and had he sounded less cocky.Only religion/metaphysics would marvel at theunsubstantiated rhetoric onefinds in this book. However, this is scientific ground he is attempting totread on.

Just read Mandelbrot's original book ...

Hand Waving and Puffery
The book can be summarized in 11 words: "Genetic fractal neural fuzzy chaotic nonlinear stuff good.Traditional finance bad."

There is no real information in the book.There are unsupported anecdotes and amyriad of quotes from non-financial sources.The lack of substance in thetext leads one to suspect that the author himself doesn't understand theunderlying mathematics himself.

For a better source, Chapter 12 ofEconometrics of Financial Markets by Campbell, Lo and MacKinlay has moreinformation on nonlinear modelling than the whole of this book (and it hasa couple hundred pages on traditional financial economics.) ... Read more

Product Description

Why, in a scientific age, do people routinely turn to astrologers, mediums, cultists, and every kind of irrational practitioner rather than to science to meet their spiritual needs? The answer, according to Richard J. Bird, is that science, especially biology, has embraced a view of life that renders meaningless the coincidences, serendipities, and other seemingly significant occurrences that fill people's everyday existence.

Evolutionary biology rests on the assumption that although events are fundamentally random, some are selected because they are better adapted than others to the surrounding world. This book proposes an alternative view of evolving complexity. Bird argues that randomness means not disorder but infinite order. Complexity arises not from many random events of natural selection (although these are not unimportant) but from the "playing out" of chaotic systems -- which are best described mathematically. When we properly understand the complex interplay of chaos and life, Bird contends, we will see that many events that appear random are actually the outcome of order.

Customer Reviews (4)

poor understanding of biology
The author of this book might be an expert on chaos, but he clearly has no formal training in biology.This book is full of mistakes that imply a poor understanding of the current state of biological research, or a deliberate misrepresentation of that research.For example Bird denigrates the contribution of molecular biology by suggesting that the chemistry of life isn't actually biology (it is), and that molecules can't be connected to the formation of organisms (they can and have been).Furthur, Bird argues that natural selection can't explain diversity because it would take too long for chance to create a protein, dna molecule, or cell.However Bird misunderstands the theory when he implies that life came about by chance.While chance may produce variation, it is selection that preserves good variants and eliminates bad.Selection IS the organizing principle that Bird calls out for.

Additionally, there are clear logical errors in the arguments in the text (e.g. argument through false analogy, appeal to authority, begging the question, etc...).The author should have consulted with one or more practicing researchers before sending this to press.

There are also factual errors, and incorrect citations (e.g. Bates, not Bateson, proposed the theory of mimicry).

This book is a typical autodidact's "theory of everything" and you will be disappointed if you expect better.

For those who want to learn about chaos theory, fractals, and how they might tie in to biology, Wolfram's "A new kind of science" is much more compelling.

Disappointing
The title "Chaos and Life" implies a model of how chaos is at the core of life.The core of life in this book, on the other hand, is a throwback model: the Turing machine.That's not to say that the topic of chaos is absent from this book - merely that it is not at its ultimate center.

Bird suggests that each living cell is a computer.I'll buy that.But then he goes on to suggest that since DNA resembles the symbol tape in a Turing machine that it in fact *is* the symbol tape in a cellular Turing machine.More than that, the symbols in DNA represent *numbers* and so addition, subtraction, multiplication, and so on, are taking place in each cell.RNA is used as registers in this model.I call this a throwback model in the sense of cognitive science, in which the Turing machine is the "classical" but largely discredited model of cognition, having subsequently been replaced in favor of connectionist and embodied dynamics models.

Is it unreasonable to argue that each living cell is a Turing machine carrying around its program in its DNA and storing data in its RNA?No.It's merely unexpected in a book that purports to be establishing a fundamental connection between chaos and life.Where is a proposal that the computation going on in each cell is a result of the complex network of non-linear interactions going on between the cell's genes, proteins, and environment?Where is a proposal that the computational states in each cell are a result of a series of leaps from strange attractor to strange attractor?Those are the kinds of ideas I would have expected to be at the heart of this book - unfortunately, at its core this book is more along the lines of "Turing Machines and Life".

A Thought-Provoking Book
Bird makes a strong case for the use of Chaos theory and Fractals to model life. But he sometimes goes too far and seems to ascribe more power to the mathematics than it actually has; he makes it sound mystical at times. On page 266, the paragraph starting with Chomsky is very profound but isolated and not developed in the remainder of the text. All in all, I recommend the book.

Critique of Neo-Darwinism
This fascinating voyage braiding evolutionary thinking with chaos theory starts with a cogent critique of current Neo-Darwinism in a fashion reminiscent of Robert Wesson's _Beyond Natural Selection_. Students of evolution are seldom aware of the criticisms of Darwin springing from scientists themselves, or of the attempts to really grapple with the problems without the distractions of the current Darwin debate, which is mostly propaganda. ... Read more

Product Description
Almost every scientist has heard of catastrophe theory and knows that there has been a considerable amount of controversy surrounding it. Yet comparatively few know anything more about it than they may have read in an article written for the general public. The aim of this book is to make it possible for anyone with a comparatively modest background in mathematics - no more than is usually included in a first year university course for students not specialising in the subject - to understand the theory well enough to follow the arguments in papers in which it is used and, if the occasion arises, to use it. Over half the book is devoted to applications, partly because it is not possible yet for the mathematician applying catastrophe theory to separate the analysis from the original problem. Most of these examples are drawn from the biological sciences, partly because they are more easily understandable and partly because they give a better illustration of the distinctive nature of catastrophe theory. This controversial and intriguing book will find applications as a text and guide to theoretical biologists, and scientists generally who wish to learn more of a novel theory. ... Read more

Customer Reviews (4)

A concise intro
This is a concise intro to catastrophe theory that is aimed mainly at undergrad level folks, or those who are looking for a streamlined version of Rene Thom's groundbreaking _Structural Stability and Morphogenesis_.

Most terms and concepts are explained adequately. The text is essentially a narrative for the algebra and differential equations that comprise the primary explanatory mechanism of the book. There is far less reliance on topology in this book than Thom's, and it tends to appear mainly in the things like the visualization of the obligatory seven elementary catastrophe types.

The applications given are intended to be fairly simple to understand (in keeping with the lack of specialization of the intended audience), so they are fine for an intro book, but I would tend to call them only "examples" rather than "applications".

I contrast this book with Thom's by saying that this intro book will give you the mechanics of catastrophe theory and some examples, whereas Thom's book paints a much broader conceptual picture with many profound speculations on the applications of catastrophe theory. Both books have their respective value and I feel they are good complements to each other to the newcomer to catastrophe theory.

A concise intro
This is a concise intro to catastrophe theory that is aimed mainly at undergrad level folks, or those who are looking for a streamlined version of Rene Thom's groundbreaking _Structural Stability and Morphogenesis_.

Most terms and concepts are explained adequately. The text is essentially a narrative for the algebra and differential equations that comprise the primary explanatory mechanism of the book. There is far less reliance on topology in this book than Thom's, and it tends to appear mainly in the things like the visualization of the obligatory seven elementary catastrophe types.

The applications given are intended to be fairly simple to understand (in keeping with the lack of specialization of the intended audience), so they are fine for an intro book, but I would tend to call them only "examples" rather than "applications".

I contrast this book with Thom's by saying that this intro book will give you the mechanics of catastrophe theory and some examples, whereas Thom's book paints a much broader conceptual picture with many profound speculations on the applications of catastrophe theory. Both books have their respective value and I feel they are good complements to each other to the newcomer to catastrophe theory.

A concise intro
This is a concise intro to catastrophe theory that is aimed mainly at undergrad level folks, or those who are looking for a streamlined version of Rene Thom's groundbreaking _Structural Stability and Morphogenesis_.

Most terms and concepts are explained adequately. The text is essentially a narrative for the algebra and differential equations that comprise the primary explanatory mechanism of the book. There is far less reliance on topology in this book than Thom's, and it tends to appear mainly in the things like the visualization of the obligatory seven elementary catastrophe types.

The applications given are intended to be fairly simple to understand (in keeping with the lack of specialization of the intended audience), so they are fine for an intro book, but I would tend to call them only "examples" rather than "applications".

I contrast this book with Thom's by saying that this intro book will give you the mechanics of catastrophe theory and some examples, whereas Thom's book paints a much broader conceptual picture with many profound speculations on the applications of catastrophe theory. Both books have their respective value and I feel they are good complements to each other to the newcomer to catastrophe theory.

A concise intro
This is a concise intro to catastrophe theory that is aimed mainly at undergrad level folks, or those who are looking for a streamlined version of Rene Thom's groundbreaking _Structural Stability and Morphogenesis_.

Most terms and concepts are explained adequately. The text is essentially a narrative for the algebra and differential equations that comprise the primary explanatory mechanism of the book. There is far less reliance on topology in this book than Thom's, and it tends to appear mainly in the things like the visualization of the obligatory seven elementary catastrophe types.

The applications given are intended to be fairly simple to understand (in keeping with the lack of specialization of the intended audience), so they are fine for an intro book, but I would tend to call them only "examples" rather than "applications".

I contrast this book with Thom's by saying that this intro book will give you the mechanics of catastrophe theory and some examples, whereas Thom's book paints a much broader conceptual picture with many profound speculations on the applications of catastrophe theory. Both books have their respective value and I feel they are good complements to each other to the newcomer to catastrophe theory. ... Read more

Product Description

The Chaos Theory of Careers outlines the application of chaos theory to the field of career development. It draws together and extends the work that the authors have been doing over the last 8 to 10 years.

This text represents a new perspective on the nature of career development. It emphasizes the dimensions of careers frequently neglected by contemporary accounts of careers such as the challenges and opportunities of uncertainty, the interconnectedness of current life and the potential for information overload, career wisdom as a response to unplanned change, new approaches to vocational assessment based on emergent thinking, the place of spirituality and the search for meaning and purpose in, with and through work, the integration of being and becoming as dimensions of career development.

It will be vital reading for all those working in and studying career development, either at advanced undergraduate or postgraduate level and provides a new and refreshing approach to this fast changing subject.

Key themes include:

Factors such as complexity, change, and contribution

People's aspirations in relation to work and personal fulfilment

Contemporary realities of career choice, career development and the working world

Customer Reviews (4)

An interesting overview.
There are several versions of this book; or at least books with the same title that are being reviewed together. The description of the book given by Amazon states that the text of the Amazon.com review refers to another, earlier, edition of a book with the same title.This earlier edition was written by Richard Mankiewicz, with a forward by Professor Stewart. It was published in 2001, whereas the book description lists a publication date of 2008.The one that I read was written by Ian Stewart and was published in 2008.However, it does not have the cover shown in the Amazon insert; it has the cover that was provided by a customer.I believe that the negative comments of some reviewers (small print and many pictures in place of text) refer to the 2001 Mankiewicz edition.I had no trouble with the size of the text, and I find it difficult to read books with small print.Furthermore, while there are pictures, they are not the focus in my edition and, unlike the 2001 Mankiewicz edition, none were in color.A prospective buyer should check to make sure of the edition that is being purchased.This review refers to the 2008 edition authored by Ian Stewart.

The book is an overview of the development of mathematics.It is part math, part biography and part history.It covers mathematics from the earliest ideas of the Egyptians, Babylonians, Chinese, Indians and Greeks, to the most modern ideas group theory, set theory, topology, and non-linear dynamics.Each chapter, starting with counting and numbers, is self-contained but there is a flow that relates each chapter to what has gone before and what will come next.The text is only 278 pages long, so only a brief overview of each topic can be provided.The development is generally chronological and historical and in addition to the development of the math there are capsule biographical inserts concerning the mathematicians involved with that development.Each chapter also contains a capsule summary of why this topic is important not only for the development of mathematics but also "what it does for us", so even if the reader does not completely follow the mathematics they can see why the topic is important and how it fits into the whole of mathematics.

This is a good book for advanced high school and college students who are interested in the way in which mathematics developed.Equations are provided, but are generally not derived or developed fully.The introductory chapters on numbers and the development of geometry and algebra are good supplements to what students are learning in math class, but many will likely find the latter chapters a bit too advanced.Be forewarned, however, that this is not a mathematics book in that it does not aim to teach the reader how to solve problems.The treatment is more historical and aims at describing how mathematics evolved.

Mathematics is a difficult subject to cover in a cursory manner and Professor Stewart does as good a job as any that I have read, but frankly I found that some of the latter chapters were somewhat incomprehensible. I guess this is unavoidable as there was just not enough space to include a more complete exposition of the topics.It is for this reason why I could give the book only 4 stars.Nonetheless, I did learn what the basic ideas were and why they were important, even if I could not completely follow the all mathematics. Mathematicians will likely find this book too elementary, but the historical and biographical elements will possibly interest them.

Some good, some bad
The book is about 20 or so chapters of around 10 dense pages each, with each chapter concentrating on a particularly portion of mathematics.The chapters are arranged somewhat chronologically while maintaining a good sense of order.Amongst each chapter, Steward describes a problem, the insights around it, the prominent figures behind it, what was accomplished, and why it is important.The chapters range from simple numbers to multi-dimensional geometry.Overall, with so much information, which is good, it was hard to caught up in the book itself.If anything, this is not a page turner, but informative.

This books is a bit schizophrenic when it comes to quality.Stewart, who seems to have a knack of presenting complex mathematics in layman terms, is very inconsistent.The beginning chapters are very slow and dull.The middle chapters get extremely complex, and if you haven't taken a mathematics class on that particular subject, be prepared to get lost.Trudging through the group theory chapter game me a headache.However, there are some extremely fascinating topics that I never considered, and Stewart does a superb job of explaining it, like the chapter about the fundamentals of mathematics near the end.

All in all, it was some chapters made me feel smarter, some chapters got me excited about mathematics, and some chapters made me feel dumber and frustrated; making it an average book.

Despite production values, a good high level overview of Mathematics for the Non Mathematician
Mathematician and scientist Ian Stewart writes some popular books on the subject (I keep meaning to read his annotated Flatland).The Story of Mathematics is devoted to an overview and history of Mathematics, and what it was good for in the past and what its good for now.

With lots of sidebar digressions on figures and topics, this volume reminded me, in some respects, of my beloved "The Math Book" textbook that I recently found for sale again, used and purchased. The Story of Mathematics takes on Mathematical topics of increasing complexity and difficulty. Each topic is placed in context with how and why it was invented and developed.

So the volume begins with tallies and basic number systems, showing how tallies turned into Babylonian and Egyptian number systems. We progress through basic geometry, our own number system (with sidebars on things like the Mayan and Chinese systems), trigonometry, logarithms, algebraic geometry, number theory, calculus, differential equations, and all the way up to modern chaos theory.

In less than 300 pages, this means that no topic really is done in depth, a strength and a weakness. Similarly, too, the book remains at a high level overview strictly for non-mathematicians. This is not a volume by Eli Maor! In fact, the Mathematically trained might feel this is a bit dumbed down.

So, I believe that intelligent readers who are completely math-phobic and yet have an urge to know more about how it works and where it came from (without doing any math skull sweat) will be happiest with the book. Those fully trained in Mathematics might be frustrated at some of the lack of depth in topics (and probably would be happier with a volume on a more specific subject that they are interested in).

As for myself, I learned some things about fields of mathematics of which I am not very conversant. Stewart has a relatively easy style to follow, but its nothing special.As a production value, I do mention that to keep the volume under 300 pages, the print in the book is relatively small. Still, despite all of this, I enjoyed reading Stewart's Mathematical overview.

A readable survey of mathematics that is popular in style without sacrificing the inclusion of formulas
Light mathematical history is the best phrase to describe this book; it has too much math to be considered as mere history and not enough to be described as mathematics. It begins with the earliest of representations of mathematics, which was of course numbers. After that came the geometry of area representations for land surveying and the beginning of abstraction, where the idea became the mathematical concept traded rather than physical objects.
Most of the general ideas of mathematics developed since antiquity is at least mentioned, and Stewart is to be commended for including formulas when needed. His style of exposition is effective in presenting complex ideas in a manner that makes it very readable. Any reader with knowledge at the level of high school algebra will be able to understand the fundamentals of the concept even if the particular details are beyond their grasp.
This book could also serve as a text for a college level history of mathematics class for the elementary or middle school education major. If used as a source of ideas for classroom presentation, it could also be used as a text in a history of mathematics class for the math major.
... Read more

Product Description
We are surrounded by order that-until now-physics has been unable to explain.

The spread of veins in the back of our hands mirrors the spread of branches on a tree; fern fronds bear a resemblance to the outline of fjords; the best-loved classical music echoes the patterns of our heartbeats.

The theory of Universality is using fractal patterns to explain much of the world around us.Could it be that the same laws that govern systems in their critical states also govern some of the most unpredictable events such as earthquakes, avalanches, the growth of cities and stock market crashes-even the way businesses are run and the way fashions come and go?Is there a common principle, a universal affinity that binds us to the forces of nature?

A consensus is emerging on how complex structures grow and sustain themselves; phenomena that were once thought to be unique now appear to have a great deal in common.Mark Ward examines these theories, explores how they fit into an age-long quest to discover how the universe works, delves into their possible limitations and asks what we can do with this new knowledge.

While identifying patterns does not mean that we can always predict what will happen next, some of the trends scientists are noticing prove that life is not a series of random events.Universality deepens our understanding of natural phenomena and our place in the physical world.

We are surrounded by order that-until now-physics has been unable to explain.

The spread of veins in the back of our hands mirrors the spread of branches on a tree; fern fronds bear a resemblance to the outline of fjords; the best-loved classical music echoes the patterns of our heartbeats.

The theory of Universality is using fractal patterns to explain much of the world around us.Could it be that the same laws that govern systems in their critical states also govern some of the most unpredictable events such as earthquakes, avalanches, the growth of cities and stock market crashes-even the way businesses are run and the way fashions come and go?Is there a common principle, a universal affinity that binds us to the forces of nature?

A consensus is emerging on how complex structures grow and sustain themselves; phenomena that were once thought to be unique now appear to have a great deal in common.Mark Ward examines these theories, explores how they fit into an age-long quest to discover how the universe works, delves into their possible limitations and asks what we can do with this new knowledge.

While identifying patterns does not mean that we can always predict what will happen next, some of the trends scientists are noticing prove that life is not a series of random events.Universality deepens our understanding of natural phenomena and our place in the physical world.
... Read more

Customer Reviews (8)

Interesting Ideas, Unclear Presentation
I originally picked this book up because it was related to chaos theory and I happen to find chaos theory to be an interesting subject.

The book discusses "universality," a theory that purports to unify highly varying phenomena into one basic explanation. Instead of having to study bar magnets and avalanches separately, universality claims that at a certain point (the "critical point"), the details of certain systems no longer matter. All that matters is how the components within the system interact. Ward explains how "power laws" are a property of universality and how certain things, such as heart beats and breathing rates, are optimized through universality. All of these are (brief) examples of the interesting ideas Ward touches upon in this book.

That said, there's a lot that could have been improved. The first 40 pages or so add nothing substantial to the discussion. More egregiously, Ward never gives precise definitions for his terms, so unless a reader goes back occasionally to review what he means by them, one won't easily follow some of his later discussions. For example, Ward discusses something called "Self-organizing Criticality" at one point, and unless the reader is diligent, he/she might be be confused with how this term is at all different from universality.
Lastly, the book admittedly has a lot of speculation in it and Ward doesn't always do the best job distinguishing between what's fact and what isn't. Nor does Ward ever give a satisfying answer to the question of, "just how ubiquitous IS universality?"

Bottom line: If you're into chaos theory, this book might have some ideas that will pique your interest. Unfortunately, if you do read this, you'll have to go through the trouble of clarifying certain things for yourself; Ward doesn't do a good job of it himself.

Irritating and pointless
After reading the first three pages of the introduction, I thought "this must get better". I skipped to chapter 1 and read two more pages of vague, disconnected repetition. So I turned to Amazon reviews to see if it was worth my while to persist. It isn't. On to the next book...

Lots of speculation, no substance
The book is disjointed and speculative so that it is hard to take any of the arguments seriously. It is strange to find this in a book about science, but then perhaps it is not a science book! Some remarks comparing scientific research today with demonology several hundred years ago make you wonder. It is almost as bad as `The Web of Life' by Fritjof Capra (conversely if you liked that book, you will like this one too). Oddly enough, although the book claims not to be about Chaos but about `Universality', it is Chaos that appears in the title. I am fairly familiar with the research into chaos theory, but having read this book I still cannot really tell you what `Universality' is, other than that it seems to involve everything (!). In any case, the book presents even the better data on the subject poorly.

On a general note, in thinking of fractals (discussed extensively but loosely in the book) I wonder if we are not over-interpreting the data. After all, mathematicians have known all along that mathematical models can represent a variety of natural processes and yet have no causal relation to them. Similarly, when we see fractals in a wide variety of biological structures and processes, is it because fractals are fundamental to them, or because, as I suspect, a fractal can be used to model anything? Is it the chicken or the egg?

Know it's place
Understanding why you're reading this book makes all the difference.I used this book as a carefree nightly read around an interesting topic, and it worked!Using this book to solve problems would be a mistake.There's not enough detail and it won't work.
The author approached Universality from enough angles to brighten my world to possible unexplored connections.Unfortunately, the author's light dimmed a bit when he didn't stay "on-message" 15% of the time, wherein I skipped forward some pages.Hense, the 3 stars.
Overall, read this book as an intro, and lighten up!

Long, empty, boring,not worth the time
One would think that 300 pages discussing science theory would have some substance but this book could have been edited down to an eight page magazine article with little loss of content.And not a "heavy" magazine for scientists but a "popular" type magazine.I forced myself to stay with it hoping that the author would eventually get serious but the book stayed chatty and anecdotal to the end.According to the bio Mr. Ward is a science writer for the BBC and I did get the feeling of a TV narration purposely kept light in order not to scare off any viewers.

I found myself rereading series of pages because I had the feeling that I had missed something and then finding that I hadn't missed a thing,there was simply no content to retain.This happened repeatedly and made this book a real chore to finish and ultimately unrewarding.A shame too because the premises Mr. Ward teases the reader with are intriguing but the book fails miserably to live up to the promises made on the dust cover.Budding authors should seek out his agent however,that individual is well worth his fee! ... Read more

Product Description
Fractals and chaos are currently generating excitement across various scientific and medical disciplines. Biomedical investigators, graduate students, and undergraduates are becoming increasingly interested in applying fractals and chaos (nonlinear dynamics) to a variety of problems in biology and medicine. This accessible text lucidly explains these concepts and illustrates their uses with examples from biomedical research. The author presents the material in a very unique, straightforward manner which avoids technical jargon and does not assume a strong background in mathematics. The text uses a step-by-step approach by explaining one concept at a time in a set of facing pages, with text on the left page and graphics on the right page; the graphics pages can be copied directly onto transparencies for teaching. Ideal for courses in biostatistics, fractals, mathematical modeling of biological systems, and related courses in medicine, biology, and applied mathematics, Fractals and Chaos Simplified for the Life Sciences will also serve as a useful resource for scientists in biomedicine, physics, chemistry, and engineering. ... Read more

Customer Reviews (1)

Excellent! Make it a permanent part of your Library!!
This book is amazing. It should be a requisite book of anybody who is interested in Fractals and Chaos Theory, whether they be a student in High School or an expert in rigorous mathematics. The book jumps right to the important points and conclusions of this beautiful area of mathematics, and develops intuition without resorting to mathematical rigor, which is a boon to any beginner.

This book makes a solid introduction to Fractals and Chaos Theory, and should allow any motivated student in this area to later jump to more mathematically/technically rigorous textbooks later. For students in biological and medical sciences, whom may only have limited mathematical training compared to students of other disciplines (Physics, Mathematics, Computer Science, etc..), this should be a required book to read. More and more current research is indicating that biological systems - Immune system, Heart Dynamics, Vision - are fundamentally ruled and described by chaos and fractal based processes. The book goes over several biological applications, and does a great job of calibrating the student to the promise that this area of mathematics will revolutionize our understanding of biology and medicine in addition to highlighting specific open research questions to help focus the thoughts of the motivated student.

Overall, get this book ASAP!!!!! ... Read more