Book Description

Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations, and soliton dynamics. ... Read more

Book Description

The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory. ... Read more

Book Description

This book gives an in-depth introduction to the areas of modeling, identification, simulation, and optimization. These scientific topics play an increasingly dominant part in many engineering areas such as electrotechnology, mechanical engineering, aerospace, and physics. This book represents a unique and concise treatment of the mutual interactions among these topics.Techniques for solving general nonlinear optimization problems as they arise in identification and many synthesis and design methods are detailed. The main points in deriving mathematical models via prior knowledge concerning the physics describing a system are emphasized. Several chapters discuss the identification of black-box models. Simulation is introduced as a numerical tool for calculating time responses of almost any mathematical model. The last chapter covers optimization, a generally applicable tool for formulating and solving many engineering problems. ... Read more

Book Description

For almost 15 years chaos and fractals have been riding a wave that has enveloped many areas of mathematics and the natural sciences in its power, creativity and expanse. Traveling far beyond the traditional bounds of mathematics and science to the distant shores of popular culture, this wave captures the attention and enthusiasm of a worldwide audience. The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot Set, Julia Sets, Cellulair Automata, L- systems, Percolation and Strange Attractors. Each chapter is closed by a "Program of the Chapter" which provides computer code for a central experiment. Two appendices complement the book. The first, by Yuval Fisher, discusses the details and ideas of fractal images and compression; the second, by Carl J.G. Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals. ... Read more

Reviews (9)

A good introduction
Chaos as a physical theory began essentially in the 1970's, but as a mathematical field it has existed since the early 1900's. This book covers only the mathematical study of chaos, and is addressed to those readers who have a fairly strong background in undergraduate mathematics. A knowledge of dynamical systems and measure theory would help in the appreciation of the book, but are not absolutely necessary. The application of fractals and chaos to finance is now legendary, but other applications, such as to packet networks and surface physics are not so well-known. Current research in chaos is done predominantly in the context of information theory, wherein the goal is to understand the difference between chaos and noise, and develop mathematical tools to quantify this difference. The BASIC code in the book gives away its age, but can be easily translated to one of the symbolic computing languages available now, such as Maple or Mathematica.

This is a sizable book, and space prohibits a detailed review, but some of the more interesting discussions in it include: 1. The video feedback experiment, which can be done with only a video camera and a TV set. This is always a crowd pleaser, at whatever level of the audience it is presented to. 2. The comparison between doing iteration of a chaotic map on two different calculating machines: a CASIO and an HP. The difference is very dramatic, illustrating the effect of finite accuracy arithmetic. 3. The pictures illustrating the Chinese arithmetic triangle and Pascal's triangle as it appeared in Japan in 1781. 4. The space-filling curve and its relation to the problem of defining dimension from a topological standpoint. This discussion motivates the idea of covering dimension, which the authors overview with great clarity. They also give a rigorous definition of the Hausdorff dimension and discuss its differences with the box counting dimension. 5. The many excellent color plates in the book, especially the one illustrating a cast of the venous and arterial system of a child's kidney. 6. The difficulty in measuring power laws in practice. 7. Image encoding using iterated function systems, which has become very important recently in satellite image analysis. This leads into a discussion of the Hausdorff distance, which is of enormous importance not only in the study of fractals but also in general topology: the famous hyperspaces of closed sets in a metric space. 8. The relation between chaos and randomness, discussed by the authors in the context of the "chaos game." 9. L-systems, which are motivated with a model of cell division. 10. the number theory behind Pascal's triangle. 11. The simulation of Brownian motion. 12. The Lyapunov exponent for smooth transformations. 13. The property of ergodicity and mixing for transformations, the authors pointing out that true ergodic behavior cannot be obtained in a computer where only a a finite collection of numbers is representable. 13. The concept of topological conjugacy. 14. The existence of homoclinic points in a dynamical system. These are very important in physical applications of chaos. 15. The Rossler attractor and its pictorial representation. 16. How to calculate the dimensions of strange attractors. 17. How to calculate Lyapunov exponents from time series, which is of great interest in many different applications, especially finance. 18. The Julia set, which the authors relate eventually to potential theory.

Simply a fantastic book
I purchased this book when it first came out, during the
initial wave of popularity of fractals and chaos theory.
Although the fadishness of chaos and fractals has died
down, a number of solid applications for this theory have
appeared in areas like computer graphics, finance,
modeling computer network traffic and data compression.

I have purchased a number of books on fractals and chaos and
how these concepts can be applied in a number of areas. I
have yet to see a better introduction to the topic. This is
a core reference and I keep coming back to it again and again.

In the spectrum of popular science books, this is definitely
on the technical end. You do not need an advanced background
in mathematics as you do for some books on chaos and fractals,
but the authors do not shy away from equations. However, the
ideas are clearly presented. I have used this book as a
reference for developing software for fractal brownian motion
and Hurst exponent estimation.

"Chaos and Fractals" covers a great deal of material. On a few
occasions I found that the algorithms or explaination were
difficult to follow. In some cases, like the generation of
Gaussian random numbers, I found better, simpler algorithms.

When this book was written, fractals and chaos were fairly new.
It is difficult to avoid comparing this book to an even thicker
book, "A New Kind of Science" by Stephen Wolfram. Although
cellular automata, the core topic of "A New Kind of Science"
are not exactly new, Wolfram claims new and profound
perspectives. Many, including this reviewer, feel that Wolfram's
claims are overblown and egotistical (he has a bad habbit of
claiming credit for innovation, even as he cites other work).
The authors of "Chaos and Fractals" do not make exalted
claims for this work. Yet without any fanfare, this book
really does deliver profound ideas. This is simply a
fantastic book. I recommend it for anyone in the applied
sciences (e.g., computer science, quantitative finance,
geology, etc...). Even for the mathematically sophisticated it
will provide an valuable overview, which is difficult to obtain
anywhere else.

Well worth the cost
This is possibly the best and most thorough of all books on fractals. The discussion is excellent, the illustrations superb. After all, these are the guys who developed the computer art exhibits that toured Europe and parts of the US in the 1980s.

The mathematics is somewhat advanced, but not so advanced that most persons with a thorough background in high school mathematics cannot understand it. After all, I used it as a primary reference for my book Fractals in Music!

Excellent for intermediate knowledge of chaos
This book is a great entertainer for anyone who wants to spend many evenings "playing with chaos". The code in the book is a little dated (BASIC), but you won't have problems to use it as a good reference. The book will guide you through the understanding of the exciting realm of chaos and its hidden monsters.

Chaos and fractals are subjects that sound modern, interesting and eye-catching in the most of the cases. However, the applications and implications of chaos in the real world constitute the great achievement of human knowledge that the concept represents.

The lecture of this book doesn't require an extensive knowledge of math (but it would be helpful), it requires many will and passion for rediscovering your conception of the universe instead.

Before reading this book I'd recommend "Chaos: the Making of a New Science" by James Gleick and for those who are looking for a more compact but challenging material "Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise" by Manfred Schroeder will be just fine.

Add some DEPTH to your "Recreational Mathematics"
I spent quite a bit of time looking for a good "fractals" book. For me, this is it. It is not a book for everyone, though. I'll try to offer guidelines to help you decide if it is for you. In summary: (a) its not just a picture book, but extremely visual, (b) its not math-intense but asks for math-comfort and offers options and (c) its not only for computer jockeys, but offers repeated links to that approach.

This book is doubtless great for a high-school or college course in fractals. But I think it is also a worthy buy, albeit a pricey one, for a certain type of layperson with a fascination for mathematics presented in some depth. If you enjoy math but find some of the "popularizations" a bit too shallow, then the realm of fractals and chaos is a great place to explore in depth. This is a fine guidebook for that exploration.

"Chaos and Fractals" is not a book for the reader who is primarily fascinated with the visual representations of fractals. BUT it i!s chock-full of b/w illustrations (686 by the authors count) and nicely sprinkled with gorgeous color plates. The visual element is not central, but is very strongly represented and I found that almost every important concept was enhanced by the addition of a diagram or illustration.

This is definitely a book that delves into the mathematics of fractals. It does so in a well-crafted dual-track form. The core of the book should be comfortable and enjoyable mathematical reading for anyone with a sound and fairly current familiarity with high school math (Not that such "currency" suggests its only for youngsters! This old-timer preserves essentially that level of math by regular exposure to recreational math and the like). On the second track, the book provides mathematically in-depth views of selected topics. This is really nice if you like to stretch your mathematical horizons since you can use the core to steady your foundation understanding of a topic and then dive int!o the advanced mathematical topics at will; mustering strategic retreat when necessary, without loss of face, but sometimes learning how more advanced mathematics can be used.

Finally, the book makes an effort to scaffold some computer exploration of fractal concepts that succeeded for me but might not for you. For every chapter the authors provide a "Program of the Chapter" which allows exploration of one or more of the fractal forms and concepts explored therein. These are usually quite short and are written in Microsoft BASIC. This latter might be a problem for some. Nowadays, users with more advanced operating systems might not know where to find their version of BASIC (and it might not even be supplied), much less how to fire it up.

I would not belabor the BASIC program element too much except that experimenting with such code is an excellent way for anyone to better understand an algorithmic process. A program is, after all, such a process - a sequence of !discrete steps. I'd urge you to search your Windows disk for something like an "oldmsdos" folder and dig out the Qbasic files found there and fire them up. Even if you've never written a program, this kind of applied-use is a fine way to learn!

For the right sort of reader, this is unquestionably a 5-star book. ... Read more

Amazon.com

Using a computer to beat Wall Street from afar is, arguably, the new American dream. While it will remain just that for most of us, an offbeat gang of academics turned financial wizards is showing it can be done. Led by acclaimed physicists Doyne Farmer and Norman Packard, the Santa Fe-based Prediction Company has proven since its 1991 founding in an adobe bungalow furnished with plastic lawn chairs and top-of-the-line Sun workstations that it is indeed possible to make millions in the world's financial markets by anticipating trends and developing software that automatically capitalizes on them. In The Predictors, Thomas A. Bass colorfully relates their tale of fiscal triumph--and reveals in the process how even an unorthodox group of antibusiness intellectuals in far-off New Mexico can make the world's biggest institutions sit up and take notice.

Long esteemed in the scientific community, Farmer and Packard have become legendary in hacker circles since their failed attempt to beat the roulette tables in Las Vegas with toe-operated computers was chronicled in Bass's well-regarded 1985 book called The Eudaemonic Pie. This time, though, the two hit the jackpot with their cutting-edge computer programs and the company they created to trade German marks, Chicago commodities, Japanese treasury bonds, Texas oil futures, and New York securities. Bass's prose is a bit flowery at times, but his perceptive you-are-there account is nonetheless entertaining and sure to cement the pair's reputation as today's ultimate masters of "phynance," the successful, and now oft-copied, merger of physics and finance. --Howard Rothman ... Read more

Reviews (32)

Anticlimatic
I am a trader. I traded in the pits for years. I traded over-the-counter. Futures and options, vanilla and exotic. I also hold degrees in physics and electrical engineering from MIT. I was hoping to relate to the characters in this book. I didn't at all.

First, my comments on the book as a story. I was interested at first, but was struggling to get through the last third of the book, as characters were developed that seemed like little more than filler. I tired of the endless descriptions of wardrobe and scenery. And, in the end, we don't really find out what happened. Some reviewers complain about lack of technical detail. The book was obviously not written as a scientific treatise, but as a story, so those readers really have no reason to be disappointed in that aspect.

Secondly, my thoughts about the science and the scientists featured in the book. Nonlinear dynamic systems have been studied by all Wall Street firms, even at the time Prediction Co. was doing it. I actually have a fair amount of distaste for this whole subject. What it amounts to is traders, banks, uber investors, etc. looking for the next quick money making opportunity within the latest development (fad some might say) in informational science. That in and of itself is not a bad thing, but a reasonable quest. The reason most of these kinds of endeavors fail is that unification of Wall Street and academia can only be successful if the researchers or modelers have a firm grasp of BOTH worlds. The models ultimately fail because what is really being modelled is human psychology and reaction. Numbers alone do not tell the tale. There is no (legal) way of knowing that the trader at MS just had a blow up with his risk advisor and is angrily dumping his yen position inefficiently, and that UBS knows MS is also long calls so they begin crushing call volatility since they know MS will liquidate them as well. Sure, a chart may have predicted a squeeze, but the details of the actual trading couldn't have been prophesied. Prediction Co. was running thousands of models? This should be the first tip off that they had no idea what the principal components of the market were. They were shooting in the dark.

This was a perfect example of banker types with no technical prowess whatsoever trying to work with ivory tower types with no street savvy. It doesn't work. "Well, traders and quants work together in most trading firms." True, but this is different because there was no established program or models that the quants were running. This was fly by the seat of the pants almost. While I admire the accomplishments of these researchers in academic realms, they were definitely not cut out to be businessmen with their communistic, hippy, and honestly, somewhat lazy, approach to life. Yes, some succeed, you have your accasional Bill Gates (although I would argue he was extremely business-headed), but not many. Look at the dot-com debacle. Same story.

Lastly, do you really think that anyone who truly tapped into the Holy Grail of trading would actually allow a book to be written about it?

You would learn a thing or two,
Well I picked up the book as I am interested in complexity science. Most of the reviews here are quite harsh, and probably it was bad expectations management on writer's / publisher's part.

Even though the book sometimes is promoted as an investing book, it is not. It is not meant for day traders who just expect to discover next holy grail of financial markets reading such books. There is no holy grail in markets, but thats another thing. With that said, it may be clear that it is not a TRADING / INVESTIING book.

The book is story of two renowned physicists turning to use their physics, specifically chaos theory, to model financial market. The story part is dealt with great care. I am sure you learn a thing or two reading this book. This book was quite reasy to read and time I spent reading was worth more than had I spent reading a Grisham novel or watching some stupid soap on TV. It is real life here folks.

Bass is not a novelist so I did not expect him write a literary piece here. He has written a true story in a very good way and struggle of Farmer and Packard in estabilshing a company and utilizing their knowldge in a productive way is very cleverly depicted. There are tonnes of other relevant information that come and go, and an intelligent reader would surely pick something here. There is a lot of current history explored here.

With that said, this is NOT a book for the NEXT TRADING SYSTEM, nor does it preach that their system was PERFECT.

Interesting Topic not Handled Well
I agree with many of the other reviewers. This book is 90% filler. Instead of discussing the topic at hand, we are repeatedly bombarded with a desciption of the weather, the El Paso fiesta season, etc... This is a story about a group of (in my opinion, uninteresting) characters, and not a book on Investing or Science. Not recommended.

Another book about a start-up
This book is less about the market and more about the personal relationships and dealings of a business start-up. I'm surprised that the book lists its category as BUSINESS/SCIENCE when truly it lies in the former. I guess mentioning chaos theory, neural networks and genetic algorithms was all that was needed.

Regardless, it was an entertaining story about a group of physicists, being totally ignorant of the market, decide that they can predict the market. The storyline follows what I would consider typical of any start-up; the fights, arguments, doubts, meetings galore, etc... As I said, entertaining but not too much different from any other story about a start-up.

My two biggest complaints:

1) The back cover from the San Francisco Chronicle calls this book "one of the best books ever written about commodities, currency, and derivatives trading." I don't think they even read the book since this book isn't about trading but all about the traders.

2) The over use of descriptive fashion and landscape. I lost track of how many times we needed to be told who was wearing what and how blue the sky was in Santa Fe. It really got annoying after awhile.

Full of adventure
Interesting adventures, better than the Hardy Boys! On one page Doyne's replacing the differential in his old van in the desert, several pages later he's suited up (unwillingly, presumably) dueling intellectually with the experts at Goldman-Sachs. In between he's writing checks to keep the fledgling company alive. Like I said, beats Hardy Boys hands down! Bass includes a good description of neo-classical economics ideas, still widely believed by many economicsts far and wide, as in the case of the failed LTCM, not to mention Enron, the IMF, world Bank, and US advisors to Mexico, Argentina, Brazil, thailand, Russia, .... . Significantly, LTCM was guided in part by two Nobel Prize winning neo-classical economists who characteristically proceded implicitly as if there would be 'springs' in the market to enforce the 'no arbitrage' assumption at long (but not too-long...) times. I personally don't believe that the future can be forecast reliably, but then according to a member of The Company they found a small (few %) advantage and sold it to UBS. A gambler with a small bankrole would suffer the gamblers' ruin while trying to bet on such weak correlations. Actually, the hat on the cover looks vaguely familiar, but then what's in a hat? ... Read more

Book Description

The maximum principle and dynamic programming are the two most commonly used approaches in solving optimal control problems. These approaches have been developed independently. The theme of this book is to unify these two approaches, and to demonstrate that the viscosity solution theory provides the framework to unify them. ... Read more

Reviews (1)

Wow: a general solution to stochastic control problems!
This book covers general stochastic control more thoroughly than any other book I could find.

This is *not* a book on numerical methods. It is also not on the cases which yield closed-form solutions: there is a chapter on LQG problems, but for the most part, this book focuses on the general theory of stochastic controls -- which are not the easiest things to solve in general, as you may know. The book handles only diffusion processes with perfect knowledge of the past and present (natural filtration). If these sound like what you want, I doubt there's a more thorough treatment.

It starts with a chapter on preliminaries of prob. spaces and stoch. processes and the Ito integral. After that, the book briefly addresses deterministic problems in order to compare solution methods to the stoch. approaches. It approaches the problems using a stochastic maximum principle and a stochastic Hamiltonian system, and also from a dynamic programming point of view using HJB equations. The authors attempt to show the relationship between the two approaches.

This book is technically rigorous. Though it claims to be self-contained, the reader should certainly be familiar with functional analysis and stochastic processes.

The authors try to keep the solutions as general as possible, handling non-smooth cases as well as smooth ones. This is fine, except that they don't emphasize well enough (I thought), for instance, that the solutions are much simpler when functions are well behaved on convex bodies (it's mentioned as a note on p. 120), or when diffusions are not dependent on controls, and such.

Because of this tendency to present one solution which will handle any case, it could sometimes be difficult to figure out what all the terms are. In the end, it all works out. Each chapter ends with a few pages of "historical background": who did what piece of the theory when, with an excellent list of references. (I found the originals useful to help explain things, on occasion, especially to see simpler ways to do simpler cases)

Altogether, a very thorough piece on general solutions to stochastic control! I was quite impressed. ... Read more

Book Description

Self-organized criticality (SOC) maintains that complex behavior can develop spontaneously in certain multi-body systems whose dynamics vary abruptly. This is a clear and concise introduction to the field of self-organized criticality, and contains an overview of the main research results. The author begins with an examination of what is meant by SOC, and the systems in which it can occur. He then presents and analyzes computer models to describe a number of systems, explaining the different mathematical formalisms developed to understand SOC. The final chapter assesses the impact of this field of study, and highlights some key areas of new research. The author assumes no previous knowledge of the field, and the book contains several exercises. It will be ideal as a textbook for graduate students taking physics, engineering, or mathematical biology courses in nonlinear science or complexity. ... Read more

Reviews (3)

Excellent and honest
This book deserves 5 stars because it gives crystal-clear, precise, brutally honest and unbiased coverage of what "Self-Organized Criticality" is and what it is not. Don't waste your time reading Bak's book, read this one instead.

A GOOD FORMAL INTRODUCTION TO SELF ORGANIZED CRITICALITY.
This book is the first attempt to condense in a single text a mathematical introduction to the emergent field of self organized criticality (SOC). The author describes the main general ideas of SOC in the first two chapters. In the third chapter there are a presentation of some systems that can exhibit SOC. The fourth chapter is a presentation and a study of "toy models" in the spirit of SOC. The fifth chapter is about the search of a general mathematical formalism for SOC, which is still an open question. The author presents in this chapter some formalisms developed to explain SOC. In the last chapter, the author discusses essentialy to what extent we can observe SOC behaviour in real systems. There are five appendices, and the first three of these appendices present FORTRAN codes for three distinct toy models. I did not rate this book as five stars because in my opinion the author is very concise in some parts of the text. But this is a good book, and can be recommended to all those interested in the field of self organized criticality.

Good introduction to Self Organized Criticality
From the caracteristics of systems exhibiting SOC to their simulation and modelling as well as many classical and new examples of SOC systems. ... Read more

Book Description

This book integrates insights from complexity and computational theory with the philosophical position of thinkers including Derrida and Lyotard. ... Read more

Reviews (13)

Good introduction to complex systems
Of the two I've read, this is by far the better introduction to complexity. Though sometimes redundant, Cilliers's book fleshes out the skeletal abstractions, and makes Derrida palatable even to the general reader.

Complexity and Dead End
The book combines elements of different philosophies: post-modernism, structuralism, and deconstruction. It is a meeting of vague philosophical generalizations and scientific terminology (e.g., neural networks), and as such, it muddles things instead of making them clear. The hope being that, if things look complex and muddled, people will consider the book profound.

I have to say that stylistically the book is fairly well written, yet this is not something one would read for entertainment. Bottom line: this is an attempt at some sort of philsophical synthesis which, in reality, is an intellectual dead end.

Science is not pop music ...and philosophy didn't used to be
... in spite of the appearance of the reviews associated with this work and the work itself, there is a valid connection between postmodernism and (let me be patient!) complexity.

First of all, about terminology... isn't complexity theory a branch of computer science that deals with execution time as a metric of algorithms? I think the reviewers here want to refer to complex systems theory. Wasn't connectionism a fad which was piled on top of a catchily-conceived name for artificial neural networks .... which were the popularization of more serious works of people like Papert, Minsky, Grossberg...and doesn't the reviewer who pretends to know something about physical science understand what "irreversibility" is and that, indeed, classical mechanics is indeed reversible? J. Willard Gibbs would roll over in his grave if he could read the reviews on this page...

IF you are seriously trying to find out what this stuff is about, start out by getting Lars Skyttner's book on General Systems Theory. Use it as a guidebook. Then, if you want to understand the evolution of the ideas, read the opening sections of Kant's Critique of Pure Reason. After that, read Saussure and Piaget on structuralism and read Terence Hawkes' book, "Structuralism and Semiotics" After that, try to get at least a rudimentary understanding of the work of the process philosophers...Bergson, Peirce, James and, of course, "Process and Reality" by Whitehead. At this point, you should seriously consider getting at least a passing familiarity with the work of Karl Marx with the goal of understanding what was really bothering him - and of seeing that Marx's ideas are important in ways that he probably never even thought about.

At that point, if you are one of many for whom there is a schism between the culture of liberal arts and the culture of mathematics and science, you should, at this point read a few of the popular works of Richard Feynman - perhaps, "The Character of Physical Law" or the opening lecture of Volume I of "The Feynman Lectures on Physics". Compare what Feynman has to say about science to what Piaget has to say about structures and - hopefully, by now you are beginning to realize that mathematics is a liberal art - and that the so-called liberal arts are sometimes excuses for people who don't want to be very careful in their thinking....(not always, mind you) - go and read Sunny Auyang's wonderful books, "Foundations of Complex Systems Theories" and "How is Quantum Field Theory Possible?"

By this point, you should feel somewhat secure in addressing "Postmodernism" and being able to distinguish what is there because people want to sound "cool" for their friends, and what is valid and sometimes deeply disturbing for the evolution of humanity.

Crippled by Cilliers' Knowledge of Complexity Science
Frankly, I'm astonished by some of the favorable reviews this book has received. First of all, I still haven't figured out if this really is a book or if it's a collection of essays, due to the amount of repetition of content between chapters.

Cilliers attempts to demonstrate the mutual relevance of complexity science (CS) and postmodern philosophy, but his knowledge of CS and thermodynamics seems to go no deeper than what he's read on the dustjackets of pop-sci books. The number of claims he makes that are either blatantly false or not necessarily true are outnumbered only by the number of uninsightful comments and statements that appear to have been gleaned directly from more technical sources. Here are a few to make one's skin crawl:

On p. 6, as an example of a non-linear relationship: "money can receive compounded interest". In fact, this is a classic *linear* relationship (so common it's often used as an introductory problem the first day of a course in linear differential equations). The equation representing it is simply: dM/dt = n*M, where M is the amount of money in an account, and n is the interest rate. The solution is Mo * e^(nt), where Mo is the initial amount of money in the account and 'e' represents 'exponential'. (Simply because compounded interest generates an exponential curve over time does not make the relationship non-linear; the underlying equation is linear.)

On p. 4: "Any analysis of a complex system that ignores the dimension of time is incomplete, or at most a synchronic snapshot of a diachronic process." This is completely false - One of the very purposes of 'phase space' analysis is to *completely* represent a system without considering time. The elliptical relationship between velocity and momentum in a simple harmonic oscillator is a common example that many might remember from high school physics.

On p. 8: "In classical mechanics, time was reversible, and therefore not part of the equation. In thermodynamics time plays a vital role." This quote still makes me tear at my hair. The *exact opposite* is true: almost every equation in classical mechanics (projectile motion, harmonic oscillation, planetary motion) explicitly involve time as a dimension, while, because thermodynamics is only concerned with initial and final (equilibrium) states, few thermo equations do so.

On p. 3, Cilliers says: "The grains of sand on a beach do not interest us as a complex system." but includes later in the book a quote from complexity scientist Per Bak, who has achieved his fame specifically for the study of the 'self-organized criticality' of sand grains.

And this is just the first few pages! The list goes on and on: He repeatedly confuses the thermodynamic concepts of 'closed' and 'isolated' systems; He seems to think that 'non-linear' equations are all somehow phenomenally complex and unsolvable and that the phrase 'non-linear' is therefore a synonym for being non-reductionist, non-rational, and, in short, 'postmodern'. (In doing so, he falls into many of the traps Alan Sokal identified in Fashionable Nonsense.)

I think that the basic concept behind the book could have been interesting, but due to Cilliers elementary-level grasp of half the subject matter with which he deals, the statement Cilliers himself makes on p. 133 (in reference to a recent book by Rouse) applies equally well to this text: "For me, reading this book was about as pleasant as it would be to eat it."

All Without Referring to Wittgenstein?
I read this book primarily through an interest in the philosophy of language. Of particular relevance in this respect is the emphasis on a characterisation of complexity as being opposed to traditional notions of representation. Cilliers draws parallels between the philosophy of Saussure and Derrida and scientific developments in distributed representation, particularly with respect to connectionist approaches as implemented in neural networks. Cilliers argues that a classical representational theory of language that posits syntax as an instantiation of semantics does not sufficiently allow for the complexity evident in language, but rather that meaning is constituted by the dynamic relationships between both the components of language and the environment in which it is embedded. Cilliers explicitly rejects rule-based symbol systems as being adequete for modelling language, referring to recent scientific research using neural networks to simulate language learning indicating that "though rules may be useful to describe linguistic phenomena, explicit rules need not be employed when language is acquired or when it is used" (p. 32). In Chapter 4 (pp. 48-57), Cilliers considers the Chinese Room Gedankenexperiment from the perspective of his thesis. He suggests that the debate has unquestionably assumed that the formal model of language represented by the argument is correct, that is, that a rule-book such as the one supposed is even possible. Cilliers suggests that this assumes certain features of language: that a formal grammar for a natural language can be constructed and represented in a lookup table; that there is a clean split between syntax and semantics; and that language represents rather than constitutes meaning (p. 53).

The overall picture of language that Cilliers develops has important parallels with the views of Wittgenstein, though, somewhat surprisingly, Wittgenstein is never explicitly mentioned (except with regard to his family concepts). Firstly, meaning is construed as occuring through dynamic processes (use) rather than static representations (the conception that Wittgenstein's private language argument criticises). Secondly, the idea that there is some fact of the matter (whether inside or outside human agents) that determines meaning is explicitly rejected. Finally, a straightforward split between syntax and semantics is denied (a distinction that the sceptical interpretation of Wittgenstein, offered by Kripke, takes advantage of).

In summary, I would recommend this book to anyone interested in making connections between dynamic systems theory and philosophy of mind or language -- Cilliers proves an effective communicator in both of the fields he wishes to connect. ... Read more

Book 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

Book Description

This book provides a comprehensive overview of modern particle physics accessible to anyone with a true passion for wanting to know how the universe works. We are introduced to the known particles of the world we live in. An elegant explanation of quantum mechanics and relativity paves the way for an understanding of the laws that govern particle physics. These laws are put into action in the world of accelerators, colliders and detectors found at institutions such as CERN and Fermilab that are in the forefront of technical innovation. Real world and theory meet using Feynman diagrams to solve the problems of infinities and deduce the need for the Higgs boson.

Facts and Mysteries in Elementary Particle Physics offers an incredible insight from an eyewitness and participant in some of the greatest discoveries in 20th century science. From Einstein's theory of relativity to the elusive Higgs particle, this book will fascinate and educate anyone interested in the world of quarks, leptons and gauge theories.

This book also contains many thumbnail sketches of particle physics personalities, including contemporaries as seen through the eyes of the author. Illustrated with pictures, these candid sketches present rare, perceptive views of the characters that populate the field.

The Chapter on Particle Theory, in a pre-publication, was termed `superbly lucid' by David Miller in Nature (Vol. 396, 17 Dec. 1998), p.642. ... Read more

Reviews (1)

Comprehensive and concise, but awkward prose
Veltman delivers the tale of phenomenological particle physics with enthusiasm and depth as one of its leading researchers. He attempts to cover the whole arena, from the complex behavior of quarks and gluons to the description of particle detectors. Woven throughout the book are small "vignettes" (his terminology for brief biographical sketches) of the many physicists, famous and not-so-famous, who contributed to the current understanding of our universe. He succeeds relatively well in his goal of explaining particle physics to the layman.

But don't look here for any coverage of the more esoteric and exotic ideas of theoretical physics like string theory. He unequivocally states,

"The fact is that this book is about physics, and this implies that the theoretical ideas discussed must be supported by experimental facts. Neither supersymmetry nor string theory satisfy this criterion. They are figments of the theoretical mind. To quote Pauli: They are not even wrong. They have no place here."

He is, of course, correct but I think he downplays the mathematically unifying power of string theory, for which experimental verification lies beyond today's technological reach and thus cannot be vindicated one way or the other. Mathematical beauty, while not a sure sign of physical truth, can at least serve as a powerful beacon for future physical insights.

Always the true scientist, Veltman should be praised for unapologetically declaring agnosticism if evidence for a theoretical idea isn't clear cut. For example, he writes several times that the neutrino is massless but will almost always parenthetically acknowledge that it might have a very small mass (which indeed it does, as experimental evidence of neutrino mixing has been since verified). He deems it worthy enough to have an entire section devoted to neutrino mixing and its implications.

I found one glaring problem with the book that prevented the 5 star rating it could have received: writing style. It just doesn't read all that smoothly, and I think it could have been cleaned up a bit more by a more astute editor.

Balancing the rocky prose, however, are wonderful color templates (excellently used during his description of anti-matter) to aid explanations, pictures of apparati and scientists to portray the human side of science, and clear diagrams of particle interactions.

If you want to learn what physicists empirically know about particle physics today and how they determine it, get this book; just don't expect smooth reading. Veltman is clearly passionate about his profession and it shows. ... Read more

Amazon.com

Neural network theory is shaking up fields as disparate as philosophy and ecology: the paradigm shift is here. The second edition of Connectionism and the Mind: Parallel Processing, Dynamics, and Evolution in Networks has been rewritten and restructured to accommodate the profound changes wrought during the '90s burst of research in the field. Authors William Bechtel and Adele Abrahamsen present their material clearly and accessibly, asking of their readers only a familiarity with algebra and formal logic. Covering the basics of representation, architecture, and rules, they move on to deep and exciting questions about connectionism's implications for artificial intelligence and neuroscience--thought-provoking reading for nearly everyone. The text is stimulating and offers hundreds of routes to further study through its well-integrated bibliography. Connectionism and the Mind is essentially a progress report on a very young discipline; its readers will see the future a little more clearly. --Rob Lightner ... Read more

Reviews (2)

A well-written, comprehensive introduction to the field
Cellular Automata: A Discrete Universe is a fascinating overview of the wide variety of discrete systems researchers have developed in the past quarter-century, and how these might be used to model a range of natural phenomena, including (in the book's most speculative section) the universe itself. Illustrations are supplied in all the right places--serving to enlighten, rather than overwhelm, the reader. The list of references is superb, making the book not only a great introduction and an important reference, but also a valuable guide to the field of complexity.

disappointing
This book is clearly a labor of love and contains a great wealth of material. However, it sorely lacks focus, the presentation is unclear and the results are often out of date. Here is a selection of more particular criticisms. Many rules remain undefined and the reader has to guess their details. The writer seems to be unfamiliar with the last five years worth of research, so particularly the chapter on probabilistic CA is not worth much. Far too many parts of the book are outlines of original papers (or books) with details omitted. Many claims in the said papers are accepted without scrutiny. (Two examples: (1) There is absolutely no evidence that any cellular automaton studied by Packard and Wolfram has a shape that is close to circular. (2) It has been discovered as far back as 1989 that the famous FHP lattice gas does NOT approach the two-dimensional Navier-Stokes equation, due to the fact that viscosity increases to infinity with increasing size of a finite system.) World Scientific editors need to do a much better job. ... Read more

Book Description

The goal of this book is to provide a comprehensive and systematic introduction to the important and highly applicable method of data refinement and the simulation methods used for proving its correctness. The authors concentrate in the first part on the general principles needed to prove data refinement correct. They begin with an explanation of the fundamental notions, showing that data refinement proofs reduce to proving simulation. The topics of Hoare Logic and the Refinement Calculus are introduced and a general theory of simulations is developed and related to them. Accessibility and comprehension are emphasized in order to guide newcomers to the area.The book's second part contains a detailed survey of important methods in this field, such as VDM, and the methods due to Abadi & Lamport, Hehner, Lynch and Reynolds, Back's refinement calculus and Z. All these methods are carefully analysed, and shown to be either imcomplete, with counterexamples to their application, or to be always applicable whenever data refinement holds. This is shown by proving, for the first time, that all these methods can be described and analyzed in terms of two simple notions: forward and backward simulation.The book is self-contained, going from advanced undergraduate level and taking the reader to the state of the art in methods for proving simulation. ... Read more

Book Description

A comprehensive, up-to-date presentation of the indispensable core concepts of geometric modeling

Now completely updated to include the most recent developments in the field, Geometric Modeling, Second Edition presents a comprehensive discussion of the core concepts of this subject. It describes and compares all the important mathematical methods for modeling curves, surfaces, and solids, and shows how to transform and assemble these elements into complex models. Written in a style free of the jargon of special applications, this unique book focuses on the essence of geometric modeling and treats it as a discipline in its own right.

It integrates the three important functions of geometric modeling: to represent elementary forms (i.e., curves, surfaces, and solids), to shape and assemble these into more complex forms, and to determine concomitant derivative geometric elements (i.e., intersections, offsets, and fillets).

With more than 300 illustrations, Geometric Modeling, Second Edition appeals to the reader's visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. An extensive bibliography lists many supporting works, directing the reader to more specialized treatments of this subject.

Geometric Modeling, Second Edition serves as an invaluable guide to computer graphics and CAD/CAM specialists, applications designers, scientific programmers, teachers, and students. ... Read more

Reviews (4)

An entry level book on geometric modeling
This book is a definitive introduction to geometric modeling. However, the sections on solid modeling and surface-surface intersection are lacking in depth. A serious reader may consider consulting books by Farin and Piegl for Geometric modeling and Hoffman/Mantyla for solid modeling.

Ultimate book on Geometric Modeling
The book covers every commonly used geometric model as well as many related topics in an easy to read style and good layout. It also covers the mathematical methods used in the text making it the only book you will ever need for modeling.

Mortenson does it again!
I have come to rely on Michael Mortenson's books as my prime resource for programming computer graphics. Most books on this topic expect the reader to have an advanced degree in mathematics. But Mortenson has the ability to talk to you regardless of your prior knowledge of the topic (indeed, you'll feel you have earned a math degree after reading this book without even trying).

This book is so complete that I feel it is the only book you'll ever need to understand the topic of geometric modelling. I highly recommend it (and any Mortenson book) to everyone interested in serious computer graphics programming.

A good introduction in GEOMETRIC MODELING!
This is an authorative, first-stage book on geometric modeling. I think everyone who is interested in geometric modeling will find it's beneficial for research as well as for applications.

Chen-June Kao

Solid Modeling Lab, ME, NTU, Taipei, Republic of China ... Read more

Book Description

This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications. ... Read more

Book Description

* Covers the modelling and simulation of mechatronic and micromechatronic systems using HDLs.
* Provides an overview of the design of digital and analog circuitry and software for mechatronic systems.
* Presents practical guidance on both chip and systems design for a wide range of mechatronic applications.
* Focuses on a practical approach to the design and simulation of electronic hardware and components of mechatronic systems. ... Read more

Reviews (1)

Get This Book
This is a must book for those interested in integral studies. While much of the work is similar to Ken Wilber's at least in structure, this book in many ways transcends Wilber's works with some real original thinking. Not surprisingly, the author is an authority on integral thought without trying to parrot Ken Wilber's view. Combs is a very clear and insightful writer, with no polemic axe to grind nor does he cling only to his view. ... Read more

Book Description

A new approach to understanding nonlinear dynamics and strange attractors
The behavior of a physical system may appear irregular or chaotic even when it is completely deterministic and predictable for short periods of time into the future. How does one model the dynamics of a system operating in a chaotic regime? Older tools such as estimates of the spectrum of Lyapunov exponents and estimates of the spectrum of fractal dimensions do not sufficiently answer this question. In a significant evolution of the field of Nonlinear Dynamics, The Topology of Chaos responds to the fundamental challenge of chaotic systems by introducing a new analysis method-Topological Analysis-which can be used to extract, from chaotic data, the topological signatures that determine the stretching and squeezing mechanisms which act on flows in phase space and are responsible for generating chaotic data. Beginning with an example of a laser that has been operated under conditions in which it behaved chaotically, the authors convey the methodology of Topological Analysis through detailed chapters on:
* Discrete Dynamical Systems: Maps
* Continuous Dynamical Systems: Flows
* Topological Invariants
* Branched Manifolds
* The Topological Analysis Program
* Fold Mechanisms
* Tearing Mechanisms
* Unfoldings
* Symmetry
* Flows in Higher Dimensions
* A Program for Dynamical Systems Theory
Suitable at the present time for analyzing "strange attractors" that can be embedded in three-dimensional spaces, this groundbreaking approach offers researchers and practitioners in the discipline a complete and satisfying resolution to the fundamental questions of chaotic systems. ... Read more

Book Description

Magic and science may seem like strange bedfellows, but in this captivating and far-ranging book, respected science journalist Roger Highfield nimbly illustrates how the two disciplines are actually deeply intertwined in the Harry Potter books. Like Highfield's The Physics of Christmas, The Science of Harry Potter teases out the scientific explanations and surprising factual foundation of marvels and mysteries-only this time instead of reindeer and Santa, Highfield trains his eye on dragons, broomsticks, and all the wonderful oddities of J. K. Rowling's enchanted world.Highfield uses the amazing elements of the Harry Potter books as a springboard into discussions of fascinating scientific issues. He delves into the archaeology of witchcraft, tracing the origin and uses of wands and cauldrons as revealed at ancient European dig sites. He speculates on the astounding connection between hallucinogens and flying broomsticks and the bizarre drug-taking practices of medieval witches. The potions and charms that Harry has so much trouble replicating in Snape's class are in fact grounded in the science of ethnobotany. Here too is a plausible account of the cutting-edge physics that explains the invisibility cloak and the genetic engineering behind the creation of Fluffy the three-headed dog.

As Highfield reminds us, "wizard" actually means wise man-and wizardry and science were closely related fields before Newton. As enlightening as it is delightful, The Science of Harry Potter sheds light not only on Harry Potter's magical realm, but also on the magic that is taking place in labs and science classrooms in our own "muggle" world.

This book is not authorized, prepared, approved, licensed, or endorsed by J.K. Rowling, Warner Bros., or any other individual or entity associated with the Harry Potter books or movie. Harry Potter is the registered trademark of Time Warner Entertainment Company, L.P. ... Read more

Reviews (15)

Review of The Science of Harry Potter
Woah- This book was obviously very well researched and thought out. Whats-his-name went to a lot of effort to write this book. Though, as an obsessive 15 year old harry potter fan, it didn't make me happy! It took all the magic out of the books. it explained how every bit of magic the book had could be really happening, but with out magic! He took the all the fun out of it! When i bought it i thought it would tell me how the magic worked, not how it wasn't real. i was highly offended.

A good book to think on
This book is for people who enjoy reading about what people have tried/done in the past and what people will be trying and doing in the future

This book is not really directed towards children more to someone who enjoys reading about science. From start to finish a lot of names, ideas, experiments, and questions are given. A great read for anyone who likes to wonder. This book provokes hundreds of what if questions and the reader is left to just wonder how the world would be with these things.

The thoughts and ideas in this book are LOOSELY based on the 'magic' in Harry Potter. The ideas in the Harry Potter books are expanded and talked about at great length with not only what if questions but how scientists in the past and present are (without first seeing it in Harry Potter) trying to achieve real life 'magic'

The science of Harry Potter?
I received this book as a gift and, upon reading it, now consider it a valuable addition to my collection. There are a few things, however, that I've noticed some other reviewers pointing out that I would like to go into. The author of the book considers himself a Harry Potter fan. In fact, the majority of scientists he consults are also supposedly fans of the series. The book, however, is less about Harry Potter and more about science. Essentially, it is a book describing and explaining the realistic possibilities of scientifically creating the "magic" used by the wizards in Harry's world. If anything, the book should be retitled, "The Science of Harry Potter: How Muggles Use Technology to Acheive What Magic Already (Potentially) Does."

It is, however, incredibly well researched and is obviously a labor of love and dedicated interest. I would suggest this book to any Harry Potter fan who also enjoys reading about science. It is not, on the other hand, what the average Potter fan would consider casual reading. This is a science book, discussing topics ranging from quantum physics to ethnobotony and could very well be considered boring by most people's standards.

Ignore the writing style and enjoy the information
This book does an amazing job introducing the "magical" world of science. I am amazed at the author`s research and discussion of emerging scientific fields--such as levitation and teleportation--in layman`s terms. Anyone with science or Harry Potter in his/her heart will love this book. Sit back and relax and enjoy the tid bits of information the author offers. However, if you expect the author to stay on topic, totally relate to the Harry Potter books, or draw any comprehensible conclusions...you will only frustrate yourself. Ignore the writing style and enjoy the wealth of information.

A set of lively scientific insights
The immensely popular Harry Potter fantasy books are used as source material in The Science Of Harry Potter as a foundation for discussions of scientific and historical issues ranging from connections between hallucinogens and flying sensations to the science of ethnobotany. Readers of Harry Potter will find here a set of lively scientific insights which go far from Harry's world and into the world of real science. ... Read more