Few writers distinguish themselves by their ability to write about complicated, even obscure topics clearly and engagingly. In Chaos, James Gleick, a former science writer for the New York Times, shows that he resides in this exclusive category. Here he takes on the job of depicting the first years of the study of chaos--the seemingly random patterns that characterise many natural phenomena.

This is not a purely technical book. Instead, it focuses as much on the scientists studying chaos as on the chaos itself. In the pages of Gleick's book, the reader meets dozens of extraordinary and eccentric people. For instance, Mitchell Feigenbaum, who constructed and regulated his life by a 26-hour clock and watched his waking hours come in and out of phase with those of his coworkers at Los Alamos National Laboratory.

As for chaos itself, Gleick does an outstanding job of explaining the thought processes and investigative techniques that researchers bring to bear on chaos problems. Rather than attempt to explain Julia sets, Lorenz attractors and the Mandelbrot Set with gigantically complicated equations, Chaos relies on sketches, photographs and Gleick's wonderful descriptive prose. --Christine Buttery

Order from Chaos, 29 Sep 2007
We all know things that are not predictable. These can be everyday occurrences like the weather, or more specialised events (whether the stock market will go up or down). The unpredictable plays a large part in "normal life". Yet for some of these matters, there is a nagging feeling that if sufficient information were known, the unpredictable would indeed be able to be forecast with as much certainty as whether the sun will rise tomorrow. Thus James Gleick introduces the topic of `chaos' - there can be a "sensitive dependence on initial conditions". If we were to know the initial conditions in all their details, predictability would be brought within our grasp. Thus the flapping of the wings of a butterfly in China could result in rainfall in Indianapolis.

At times I was lost in the small detail, but the strength of this book is that it paints a big picture. The mathematics (and physics, and chemistry, and biology, and .....) is sometimes beyond me, but the overall story is that there is `chaos' all around. Some of the chaos is linked into classic Newtonian mechanics, but strangely enough, chaos almost has in itself an order and `predictability' about it.

The three of the most significant scientific theories of the 20th century are reckoned to be Einstein's General Relativity, Quantum Mechanics, and ...... Chaos Theory. Before opening this very historical account of the last mentioned, I knew nothing about the theory of chaos. Now I have an awareness of the subject, and how experimentation can play a part in mathematics. Experimentation and mathematics are not normally uttered in the same sentence.

Look for the big picture, and do not get lost in the people and places, which can be bewildering. If you read this book, please ensure that it has colour photographs within it - the pictures are both staggering, and help to bring home the message. Some areas of chaos have their roots in self similarity, and the pictures from Mendelbrot sets are both staggering and fascinating. Self similarity can be best summed up by the classic (and anonymous) ditty: "Big fleas have on their backs small fleas to bite them, small flees have smaller fleas and so ad infinitum"

Gleick is strong on the history and roots of chaos, and how the ideas were received when initially tabled. There was shock and disbelief that others from external communities could have something to say that would have relevance to (say) population growth models, from totally different scientific disciplines. There was also reluctance initially to publish some of the ground-braking ideas.

Chaos is about non-linear dynamics, fractals, fractal boundary basins and much more. As `chaos' as a concept (and almost as a discipline) spread, rather than bringing order when chaos had existed before (and this could be described as one of the main purposes of `science'), evidence of more chaos emerges.

From study, it could be that there is more evidence of chaos than we thought hitherto. There could be chaos in space, and the onset of cardiac arrhythmias (heart attacks) seems chaotic. Gleick speculates that `evolution' is chaos with feedback. He has made me more aware of randomness. Classic determinism generates randomness. Perhaps, just perhaps, chaos is a way to reconcile free will and determinism. All in all, unlike the pure scientists of old, I now find myself positively looking for chaos.

Perhaps that is a mark of a well presented book.

Peter Morgan (morganp@supanet.com)


New wisdom, 18 May 2007
I love this book because of its association with systems theory and the concept of emergent properties. I also find the story about the struggle to get the ideas accepted by the establishment very reminiscent of the struggle to get new ideas into the world of work.


A Truly Enlightening Introduction to a Whole New World, 29 Dec 2004
I am educated to degree level, however my degree is not in any scientific discipline. I only recently developed an interest in science, and have since read many popular science books to try and fill a few of the gaping holes in my knowledge.

Before reading this book, I had no knowledge of Chaos Theory beyond the analogy that a butterfly flapping its wings in Peking could apparently cause a hurricane in New York. I never really understood this idea so I decided to read the book and find out about it.

Chaos: Making a New Science - unlike many other books in the popular science genre - doesn't talk down to the reader, and makes no apology for the complexity of the subject. Don't let this put you off, Gleick doesn't need to talk down to you, instead he relies on carefully and precisely explaining all of the facts. I have to admit to re-reading some of the more complex areas, however upon re-reading I found everything accessible despite my limited scientific education.

The book primarily tells the history of Chaos Theory and its scientists, which in itself requires a discussion of the theories involved. This means that it explains what the different concepts mean (The Butterfly Effect, non-linear equations, fractals etc.) but doesn't get lost in the very complex mathematics behind them. The theories in this book are often explained very effectively with good use of diagrams. I found these to be priceless, for example the description of a fractal left me a little confused until I saw the diagram of a Koch curve and suddenly understood that it really is possible for a shape to have a finite area and an infinite perimeter.

If you already know a lot about Chaos Theory and want to know more I recommend a text book, otherwise I recommend Chaos: Making a New Science.

Top Book, 30 Jan 2003
This was the first book I ever read on chaos theory. I am not involved in chaos theory at all, but I was interested in finding out more about it as it was big news at the time.

While at times the concept can be difficult to grasp, the author does go to great pains to make things clear. I think this book is aimed at people with some kind of background in maths, science or engineering ho know nothing about chaos theory.

THe story of how chaos theory came to be is enlightening and a real insight into how such ideas evolve over time.

By the end of the book I was quite able to create and run my own (basic) chaos equations. Quite a feat, really.

A delightful read !, 24 Jan 2003
This book is called 'Chaos : Making a new science' - so it should hardly
surprise anyone that it deals with the history of Chaos, bringing forth
the elementary concepts of the field along the way.
This book isn't, nor does it pretend to be, a textbook on chaos theory,
so one shouldn't expect too much maths or technical details. On the other
hand, a little maths is unavoidable for discussing even the most basic
notions of chaos theory, so the reader should be prepared for some
(not very demanding) maths.

The style adopted by Gleick is to interweave the personal lives of the
major players involved in the birth of chaos with a description the
concepts, thus giving the book a feel of an interesting story while
introducing a plethora of dazzling ideas at the same time.

The idea of self-similarity, of patterns composed of infinitely-repeating
tiny replicas of themselves, is astounding, to say the least. And to
learn that nature is full of such patterns is revealing indeed. The
implications to science and technology are far-reaching and often
surprising - researchers in Computer Networking have discovered that
network traffic in large networks such as the internet may actually be
following self-similar patterns !!

Personally, i found this to be a delightful read - Gleick's writing is
racy, the ideas involved are mind-bending, and the vivid imagery will
stay with you for a long,long time. I fell in love with fractals at
first sight and can gaze at a collection of beautiful fractals for hours.

In brief, this is a light, breezy account of the history of Chaos, with
a gentle introduction to the basic ideas of Chaos without much technical
details and only a minimum of maths.

One of the best 'Science for everyone' books i've ever read!

Order from Chaos, 29 Sep 2007
We all know things that are not predictable. These can be everyday occurrences like the weather, or more specialised events (whether the stock market will go up or down). The unpredictable plays a large part in "normal life". Yet for some of these matters, there is a nagging feeling that if sufficient information were known, the unpredictable would indeed be able to be forecast with as much certainty as whether the sun will rise tomorrow. Thus James Gleick introduces the topic of `chaos' - there can be a "sensitive dependence on initial conditions". If we were to know the initial conditions in all their details, predictability would be brought within our grasp. Thus the flapping of the wings of a butterfly in China could result in rainfall in Indianapolis.

At times I was lost in the small detail, but the strength of this book is that it paints a big picture. The mathematics (and physics, and chemistry, and biology, and .....) is sometimes beyond me, but the overall story is that there is `chaos' all around. Some of the chaos is linked into classic Newtonian mechanics, but strangely enough, chaos almost has in itself an order and `predictability' about it.

The three of the most significant scientific theories of the 20th century are reckoned to be Einstein's General Relativity, Quantum Mechanics, and ...... Chaos Theory. Before opening this very historical account of the last mentioned, I knew nothing about the theory of chaos. Now I have an awareness of the subject, and how experimentation can play a part in mathematics. Experimentation and mathematics are not normally uttered in the same sentence.

Look for the big picture, and do not get lost in the people and places, which can be bewildering. If you read this book, please ensure that it has colour photographs within it - the pictures are both staggering, and help to bring home the message. Some areas of chaos have their roots in self similarity, and the pictures from Mendelbrot sets are both staggering and fascinating. Self similarity can be best summed up by the classic (and anonymous) ditty: "Big fleas have on their backs small fleas to bite them, small flees have smaller fleas and so ad infinitum"

Gleick is strong on the history and roots of chaos, and how the ideas were received when initially tabled. There was shock and disbelief that others from external communities could have something to say that would have relevance to (say) population growth models, from totally different scientific disciplines. There was also reluctance initially to publish some of the ground-braking ideas.

Chaos is about non-linear dynamics, fractals, fractal boundary basins and much more. As `chaos' as a concept (and almost as a discipline) spread, rather than bringing order when chaos had existed before (and this could be described as one of the main purposes of `science'), evidence of more chaos emerges.

From study, it could be that there is more evidence of chaos than we thought hitherto. There could be chaos in space, and the onset of cardiac arrhythmias (heart attacks) seems chaotic. Gleick speculates that `evolution' is chaos with feedback. He has made me more aware of randomness. Classic determinism generates randomness. Perhaps, just perhaps, chaos is a way to reconcile free will and determinism. All in all, unlike the pure scientists of old, I now find myself positively looking for chaos.

Perhaps that is a mark of a well presented book.

Peter Morgan (morganp@supanet.com)


New wisdom, 18 May 2007
I love this book because of its association with systems theory and the concept of emergent properties. I also find the story about the struggle to get the ideas accepted by the establishment very reminiscent of the struggle to get new ideas into the world of work.


A Truly Enlightening Introduction to a Whole New World, 29 Dec 2004
I am educated to degree level, however my degree is not in any scientific discipline. I only recently developed an interest in science, and have since read many popular science books to try and fill a few of the gaping holes in my knowledge.

Before reading this book, I had no knowledge of Chaos Theory beyond the analogy that a butterfly flapping its wings in Peking could apparently cause a hurricane in New York. I never really understood this idea so I decided to read the book and find out about it.

Chaos: Making a New Science - unlike many other books in the popular science genre - doesn't talk down to the reader, and makes no apology for the complexity of the subject. Don't let this put you off, Gleick doesn't need to talk down to you, instead he relies on carefully and precisely explaining all of the facts. I have to admit to re-reading some of the more complex areas, however upon re-reading I found everything accessible despite my limited scientific education.

The book primarily tells the history of Chaos Theory and its scientists, which in itself requires a discussion of the theories involved. This means that it explains what the different concepts mean (The Butterfly Effect, non-linear equations, fractals etc.) but doesn't get lost in the very complex mathematics behind them. The theories in this book are often explained very effectively with good use of diagrams. I found these to be priceless, for example the description of a fractal left me a little confused until I saw the diagram of a Koch curve and suddenly understood that it really is possible for a shape to have a finite area and an infinite perimeter.

If you already know a lot about Chaos Theory and want to know more I recommend a text book, otherwise I recommend Chaos: Making a New Science.

Top Book, 30 Jan 2003
This was the first book I ever read on chaos theory. I am not involved in chaos theory at all, but I was interested in finding out more about it as it was big news at the time.

While at times the concept can be difficult to grasp, the author does go to great pains to make things clear. I think this book is aimed at people with some kind of background in maths, science or engineering ho know nothing about chaos theory.

THe story of how chaos theory came to be is enlightening and a real insight into how such ideas evolve over time.

By the end of the book I was quite able to create and run my own (basic) chaos equations. Quite a feat, really.

A delightful read !, 24 Jan 2003
This book is called 'Chaos : Making a new science' - so it should hardly
surprise anyone that it deals with the history of Chaos, bringing forth
the elementary concepts of the field along the way.
This book isn't, nor does it pretend to be, a textbook on chaos theory,
so one shouldn't expect too much maths or technical details. On the other
hand, a little maths is unavoidable for discussing even the most basic
notions of chaos theory, so the reader should be prepared for some
(not very demanding) maths.

The style adopted by Gleick is to interweave the personal lives of the
major players involved in the birth of chaos with a description the
concepts, thus giving the book a feel of an interesting story while
introducing a plethora of dazzling ideas at the same time.

The idea of self-similarity, of patterns composed of infinitely-repeating
tiny replicas of themselves, is astounding, to say the least. And to
learn that nature is full of such patterns is revealing indeed. The
implications to science and technology are far-reaching and often
surprising - researchers in Computer Networking have discovered that
network traffic in large networks such as the internet may actually be
following self-similar patterns !!

Personally, i found this to be a delightful read - Gleick's writing is
racy, the ideas involved are mind-bending, and the vivid imagery will
stay with you for a long,long time. I fell in love with fractals at
first sight and can gaze at a collection of beautiful fractals for hours.

In brief, this is a light, breezy account of the history of Chaos, with
a gentle introduction to the basic ideas of Chaos without much technical
details and only a minimum of maths.

One of the best 'Science for everyone' books i've ever read!

A great introduction to the subject of chaos, 13 Jun 2001
Book review of: Does God Play Dice? - The New Mathematics of Chaos by Ian Stewart

Beautiful fractals, the butterfly effect and unpredictable systems were the images that chaos conjured up in my imagination before I sat down and read this book. Within its pages the incredible diversity of chaotic systems; and the diversity is remarkable; is presented and explained. It is staggering to see the picture unfold, the gradual realisation that 'the' scientific statement of the eighteenth century; that the universe runs according to a set of immutable laws; is unable to explain much of the behaviour in even the simplest of classical systems. The discovery of a whole new world, and one that has been in existence since the beginning of the universe: chaos. This book is merely an introduction to a comparatively new and exciting area of mathematics; but using the word merely is doing it an injustice, since it encapsulates the topic superbly and leaves the reader with a desire to study the mathematics of chaos in more detail.

Fittingly the opening chapter commences with the backdrop to this word 'chaos'. Three hundred years ago, Newton published, 'The Mathematical principles of Natural Philosophy'. This work is unrivalled in the field of mathematics; its basic message has been absorbed into our culture: "Nature has laws and we can find them." Unfortunately, although mathematics allows us to calculate the solutions to many difficult problems, we are still left in an unordered world, where apparently simple motions, on closer inspection, become unpredictable and hence unexplainable in the language of mathematics. It is appropriate at this point to introduce the nature of chaos. Stewart is quick to point out that since this branch of mathematics is still in its formative stages, giving it a precise definition is not possible or wise. However to get us off the mark he gives the definition reluctantly reached by the Royal Society in 1986: "Stochastic behaviour occurring in a deterministic system." More roughly speaking, random behaviour in a system governed by laws.

Where is the dividing line between order and chaos? The chapter 'The Laws of Error,' introduces another field of mathematics, Probability theory - the mathematics of chance. Mathematicians had found that analysing the detailed workings of large systems was too involved and complex. Probability theory grew out of a need to simulate detail without actually having to examine it. As Stewart states: "Mathematicians could calculate the motion of a satellite of Jupiter, but not that of a snowflake in a blizzard."

The book continues with a look at one of the prime examples of chaotic systems in our World, weather systems. This century has seen many attempts to write equations that will linearize weather and use them to predict exactly how weather systems will behave. As we are well aware short-term predictions are accurate a large percentage of the time, but long term predictions are much harder to make. What we learned in the 'Strange Attractors' chapter can be applied here. The initial conditions that we feed into any model we have will have finite accuracy. Even if we obtain data exact to many decimal places, it will not take many iterations before it digresses from the path that the described weather system follows. Lorenz stumbled upon this when computing weather systems. After examining results from two separate calculations involving the same set of data, albeit with different rounding accuracies, he discovered that his results were very similar for a short period of time, but then diverged extremely rapidly and followed distinct paths. This breakthrough was later to be named the 'Butterfly effect', illustrating the manner in which a trivial dynamic can upset a disproportionably large system. .

At this stage in the book, Stewart leads us into a chapter entitled 'Recipe for chaos'. It firstly attempts to describe the workings of chaos as analogous to a recipe, presumably in an attempt to simplify the concepts and avoid any complex mathematics. It does not really achieve the desired effect. This chapter was the hardest to grasp, which is a shame since it contains many of the fundamental facts about chaos and its axioms if one can use such a word.

Fractals are important part of chaos that joins the discussion at this point. They present us with a language to describe what we see happening with chaos. A fractal, generally speaking, is a geometric object, which continues to exhibit detailed structure over a wide range of scales. Self-similarity exhibited again. Interestingly the method of describing the detail level of a fractal is by allocating it a dimension, known as its Hausdorff dimension. These dimensions tend to be fractional (hence fractal).

The final three chapters are new to this, the second edition of the book, and they describe some of the advances in the subject since 1989, namely the prediction and control of chaotic systems, which are both perfectly possible.

In its totality, this book gives any discerning reader an opportunity to delve into the World of chaos and come away with a greater understanding of the topic as a whole and a glance at the variety of areas and applications it covers. The mathematics of chaos is involved; this is not surprising since the initial discovery of the topic was due to the inability of conventional mathematics to describe certain behaviours. Nevertheless, on the whole Stewart does a good job of explaining concepts and then illustrating them with simplified examples, avoiding the need for much of the mathematics. However there were one or two places where his desire to seek analogies for his models overlooks the aim of aim of the analogy in the first place that is to aid the readers understanding of the topic. Helpful too, was the inclusion of a fair number of diagrams and schematics that in several cases proved invaluable to my understanding of the book. This is a great introduction to a subject that is becoming increasingly important and perhaps indispensable in mathematics.

Readable Introduction to Chaos Theory, 06 Feb 2001
Relatively easy to read, even the Maths (honest!), Ian Stewart writes with an obvious passion but injects some much needed humour at times. He delivers the bulk of the subject (including the historical theory) in a fairly concise way. Probably best used in conjunction with another introductory text (e.g. James Gleick's 'Chaos')

A incredible book...about Chaos.., 01 Feb 2001
This book explains in a easy way, all the mechanism related to Chaos Theory. Ian Stewart shows a clever & interesting way of describing it.

A good introduction to the science of Chaos, 11 Oct 2000
If you are interested in the subject of Chaos, this book can be a good introduction. Very readable and engaging, you will find accurate descriptions of the key discoveries of that science in a language easy to understand to everybody. I loved that book!

Order from Chaos, 29 Sep 2007
We all know things that are not predictable. These can be everyday occurrences like the weather, or more specialised events (whether the stock market will go up or down). The unpredictable plays a large part in "normal life". Yet for some of these matters, there is a nagging feeling that if sufficient information were known, the unpredictable would indeed be able to be forecast with as much certainty as whether the sun will rise tomorrow. Thus James Gleick introduces the topic of `chaos' - there can be a "sensitive dependence on initial conditions". If we were to know the initial conditions in all their details, predictability would be brought within our grasp. Thus the flapping of the wings of a butterfly in China could result in rainfall in Indianapolis.

At times I was lost in the small detail, but the strength of this book is that it paints a big picture. The mathematics (and physics, and chemistry, and biology, and .....) is sometimes beyond me, but the overall story is that there is `chaos' all around. Some of the chaos is linked into classic Newtonian mechanics, but strangely enough, chaos almost has in itself an order and `predictability' about it.

The three of the most significant scientific theories of the 20th century are reckoned to be Einstein's General Relativity, Quantum Mechanics, and ...... Chaos Theory. Before opening this very historical account of the last mentioned, I knew nothing about the theory of chaos. Now I have an awareness of the subject, and how experimentation can play a part in mathematics. Experimentation and mathematics are not normally uttered in the same sentence.

Look for the big picture, and do not get lost in the people and places, which can be bewildering. If you read this book, please ensure that it has colour photographs within it - the pictures are both staggering, and help to bring home the message. Some areas of chaos have their roots in self similarity, and the pictures from Mendelbrot sets are both staggering and fascinating. Self similarity can be best summed up by the classic (and anonymous) ditty: "Big fleas have on their backs small fleas to bite them, small flees have smaller fleas and so ad infinitum"

Gleick is strong on the history and roots of chaos, and how the ideas were received when initially tabled. There was shock and disbelief that others from external communities could have something to say that would have relevance to (say) population growth models, from totally different scientific disciplines. There was also reluctance initially to publish some of the ground-braking ideas.

Chaos is about non-linear dynamics, fractals, fractal boundary basins and much more. As `chaos' as a concept (and almost as a discipline) spread, rather than bringing order when chaos had existed before (and this could be described as one of the main purposes of `science'), evidence of more chaos emerges.

From study, it could be that there is more evidence of chaos than we thought hitherto. There could be chaos in space, and the onset of cardiac arrhythmias (heart attacks) seems chaotic. Gleick speculates that `evolution' is chaos with feedback. He has made me more aware of randomness. Classic determinism generates randomness. Perhaps, just perhaps, chaos is a way to reconcile free will and determinism. All in all, unlike the pure scientists of old, I now find myself positively looking for chaos.

Perhaps that is a mark of a well presented book.

Peter Morgan (morganp@supanet.com)


New wisdom, 18 May 2007
I love this book because of its association with systems theory and the concept of emergent properties. I also find the story about the struggle to get the ideas accepted by the establishment very reminiscent of the struggle to get new ideas into the world of work.


A Truly Enlightening Introduction to a Whole New World, 29 Dec 2004
I am educated to degree level, however my degree is not in any scientific discipline. I only recently developed an interest in science, and have since read many popular science books to try and fill a few of the gaping holes in my knowledge.

Before reading this book, I had no knowledge of Chaos Theory beyond the analogy that a butterfly flapping its wings in Peking could apparently cause a hurricane in New York. I never really understood this idea so I decided to read the book and find out about it.

Chaos: Making a New Science - unlike many other books in the popular science genre - doesn't talk down to the reader, and makes no apology for the complexity of the subject. Don't let this put you off, Gleick doesn't need to talk down to you, instead he relies on carefully and precisely explaining all of the facts. I have to admit to re-reading some of the more complex areas, however upon re-reading I found everything accessible despite my limited scientific education.

The book primarily tells the history of Chaos Theory and its scientists, which in itself requires a discussion of the theories involved. This means that it explains what the different concepts mean (The Butterfly Effect, non-linear equations, fractals etc.) but doesn't get lost in the very complex mathematics behind them. The theories in this book are often explained very effectively with good use of diagrams. I found these to be priceless, for example the description of a fractal left me a little confused until I saw the diagram of a Koch curve and suddenly understood that it really is possible for a shape to have a finite area and an infinite perimeter.

If you already know a lot about Chaos Theory and want to know more I recommend a text book, otherwise I recommend Chaos: Making a New Science.

Top Book, 30 Jan 2003
This was the first book I ever read on chaos theory. I am not involved in chaos theory at all, but I was interested in finding out more about it as it was big news at the time.

While at times the concept can be difficult to grasp, the author does go to great pains to make things clear. I think this book is aimed at people with some kind of background in maths, science or engineering ho know nothing about chaos theory.

THe story of how chaos theory came to be is enlightening and a real insight into how such ideas evolve over time.

By the end of the book I was quite able to create and run my own (basic) chaos equations. Quite a feat, really.

A delightful read !, 24 Jan 2003
This book is called 'Chaos : Making a new science' - so it should hardly
surprise anyone that it deals with the history of Chaos, bringing forth
the elementary concepts of the field along the way.
This book isn't, nor does it pretend to be, a textbook on chaos theory,
so one shouldn't expect too much maths or technical details. On the other
hand, a little maths is unavoidable for discussing even the most basic
notions of chaos theory, so the reader should be prepared for some
(not very demanding) maths.

The style adopted by Gleick is to interweave the personal lives of the
major players involved in the birth of chaos with a description the
concepts, thus giving the book a feel of an interesting story while
introducing a plethora of dazzling ideas at the same time.

The idea of self-similarity, of patterns composed of infinitely-repeating
tiny replicas of themselves, is astounding, to say the least. And to
learn that nature is full of such patterns is revealing indeed. The
implications to science and technology are far-reaching and often
surprising - researchers in Computer Networking have discovered that
network traffic in large networks such as the internet may actually be
following self-similar patterns !!

Personally, i found this to be a delightful read - Gleick's writing is
racy, the ideas involved are mind-bending, and the vivid imagery will
stay with you for a long,long time. I fell in love with fractals at
first sight and can gaze at a collection of beautiful fractals for hours.

In brief, this is a light, breezy account of the history of Chaos, with
a gentle introduction to the basic ideas of Chaos without much technical
details and only a minimum of maths.

One of the best 'Science for everyone' books i've ever read!

A great introduction to the subject of chaos, 13 Jun 2001
Book review of: Does God Play Dice? - The New Mathematics of Chaos by Ian Stewart

Beautiful fractals, the butterfly effect and unpredictable systems were the images that chaos conjured up in my imagination before I sat down and read this book. Within its pages the incredible diversity of chaotic systems; and the diversity is remarkable; is presented and explained. It is staggering to see the picture unfold, the gradual realisation that 'the' scientific statement of the eighteenth century; that the universe runs according to a set of immutable laws; is unable to explain much of the behaviour in even the simplest of classical systems. The discovery of a whole new world, and one that has been in existence since the beginning of the universe: chaos. This book is merely an introduction to a comparatively new and exciting area of mathematics; but using the word merely is doing it an injustice, since it encapsulates the topic superbly and leaves the reader with a desire to study the mathematics of chaos in more detail.

Fittingly the opening chapter commences with the backdrop to this word 'chaos'. Three hundred years ago, Newton published, 'The Mathematical principles of Natural Philosophy'. This work is unrivalled in the field of mathematics; its basic message has been absorbed into our culture: "Nature has laws and we can find them." Unfortunately, although mathematics allows us to calculate the solutions to many difficult problems, we are still left in an unordered world, where apparently simple motions, on closer inspection, become unpredictable and hence unexplainable in the language of mathematics. It is appropriate at this point to introduce the nature of chaos. Stewart is quick to point out that since this branch of mathematics is still in its formative stages, giving it a precise definition is not possible or wise. However to get us off the mark he gives the definition reluctantly reached by the Royal Society in 1986: "Stochastic behaviour occurring in a deterministic system." More roughly speaking, random behaviour in a system governed by laws.

Where is the dividing line between order and chaos? The chapter 'The Laws of Error,' introduces another field of mathematics, Probability theory - the mathematics of chance. Mathematicians had found that analysing the detailed workings of large systems was too involved and complex. Probability theory grew out of a need to simulate detail without actually having to examine it. As Stewart states: "Mathematicians could calculate the motion of a satellite of Jupiter, but not that of a snowflake in a blizzard."

The book continues with a look at one of the prime examples of chaotic systems in our World, weather systems. This century has seen many attempts to write equations that will linearize weather and use them to predict exactly how weather systems will behave. As we are well aware short-term predictions are accurate a large percentage of the time, but long term predictions are much harder to make. What we learned in the 'Strange Attractors' chapter can be applied here. The initial conditions that we feed into any model we have will have finite accuracy. Even if we obtain data exact to many decimal places, it will not take many iterations before it digresses from the path that the described weather system follows. Lorenz stumbled upon this when computing weather systems. After examining results from two separate calculations involving the same set of data, albeit with different rounding accuracies, he discovered that his results were very similar for a short period of time, but then diverged extremely rapidly and followed distinct paths. This breakthrough was later to be named the 'Butterfly effect', illustrating the manner in which a trivial dynamic can upset a disproportionably large system. .

At this stage in the book, Stewart leads us into a chapter entitled 'Recipe for chaos'. It firstly attempts to describe the workings of chaos as analogous to a recipe, presumably in an attempt to simplify the concepts and avoid any complex mathematics. It does not really achieve the desired effect. This chapter was the hardest to grasp, which is a shame since it contains many of the fundamental facts about chaos and its axioms if one can use such a word.

Fractals are important part of chaos that joins the discussion at this point. They present us with a language to describe what we see happening with chaos. A fractal, generally speaking, is a geometric object, which continues to exhibit detailed structure over a wide range of scales. Self-similarity exhibited again. Interestingly the method of describing the detail level of a fractal is by allocating it a dimension, known as its Hausdorff dimension. These dimensions tend to be fractional (hence fractal).

The final three chapters are new to this, the second edition of the book, and they describe some of the advances in the subject since 1989, namely the prediction and control of chaotic systems, which are both perfectly possible.

In its totality, this book gives any discerning reader an opportunity to delve into the World of chaos and come away with a greater understanding of the topic as a whole and a glance at the variety of areas and applications it covers. The mathematics of chaos is involved; this is not surprising since the initial discovery of the topic was due to the inability of conventional mathematics to describe certain behaviours. Nevertheless, on the whole Stewart does a good job of explaining concepts and then illustrating them with simplified examples, avoiding the need for much of the mathematics. However there were one or two places where his desire to seek analogies for his models overlooks the aim of aim of the analogy in the first place that is to aid the readers understanding of the topic. Helpful too, was the inclusion of a fair number of diagrams and schematics that in several cases proved invaluable to my understanding of the book. This is a great introduction to a subject that is becoming increasingly important and perhaps indispensable in mathematics.

Readable Introduction to Chaos Theory, 06 Feb 2001
Relatively easy to read, even the Maths (honest!), Ian Stewart writes with an obvious passion but injects some much needed humour at times. He delivers the bulk of the subject (including the historical theory) in a fairly concise way. Probably best used in conjunction with another introductory text (e.g. James Gleick's 'Chaos')

A incredible book...about Chaos.., 01 Feb 2001
This book explains in a easy way, all the mechanism related to Chaos Theory. Ian Stewart shows a clever & interesting way of describing it.

A good introduction to the science of Chaos, 11 Oct 2000
If you are interested in the subject of Chaos, this book can be a good introduction. Very readable and engaging, you will find accurate descriptions of the key discoveries of that science in a language easy to understand to everybody. I loved that book!

Interesting but not easy, 18 Nov 2008
I was looking for a relaxed read on the tube. This book was more substantial and quite a lot heavier going than the title implies.

I didn't find this book all that easy to read even though I have studied economics, mathematics and physics to quite a high level.

Interesting, but not a very short introduction, 01 Jul 2008
This book aims to introduce the key concepts of chaos in a readable way, including no mathematics. The title is a bit misleading, since there are over 160 pages and the book covers some quite advanced concepts. Overall, the book attempts to cover too much material for a short introduction, and I feel that readers who are not already familiar with the topic will be left confused.

The first chapter leaps directly into the concepts of deterministic nonlinear systems and sensitive dependence, and includes a wide-ranging discussion of the work of scientists including Laplace, Newton, Franklin and Darwin.

The second chapter explains exponential growth nicely, with several examples. Chapter 3 introduces examples of dynamical systems and their associated concepts. Here, new concepts such as state space, fixed points and attractors arise very rapidly and I wonder whether they have time to sink in for the reader who is not already familiar with them. Some of the new concepts are not clearly defined.

Chapter 4, 'Chaos in mathematical models', describes the universal period-doubling cascade, the Lorenz system, the Henon map, delay equations and Hamiltonian chaos. Again, too many models are introduced too rapidly. Chapters 5 and 6 cover fractals, dimensions and Lyapunov exponents, the measures of chaos, and the book then moves on to real numbers on a computer, statistics, predictability, weather forecasts, climate change and finance, ending up with some philosophical remarks.

Although I quite enjoyed reading this book, I would not recommend it as an introduction to the subject.



Good. But you need a preliminary, 11 Jun 2008
The book introduces the chaos theory relatively in details (compared with "the quantum world" J.P which introduces the entire structure of quantum physics less than 90 pages). The chaos is a very new and popular theory. It is based on the dynamical system, or dating back further, integral by I.Newton. The book itself produces nothing extremely exciting but progressively, makes you learn a lot. I find it really helpful to scan the dynamical system part in my financial math textbook before reading it. My suggestion is that you understand some concepts on integral and dynamical system first. They may be rather naive compared with the chaos theory but they at least give you a basis to develop your thoughts.

A Great Introduction, 04 Oct 2006
A very readable introduction for anyone interested in nonlinear dynamics, time series, weather forecasting or climate modelling.

Order from Chaos, 29 Sep 2007
We all know things that are not predictable. These can be everyday occurrences like the weather, or more specialised events (whether the stock market will go up or down). The unpredictable plays a large part in "normal life". Yet for some of these matters, there is a nagging feeling that if sufficient information were known, the unpredictable would indeed be able to be forecast with as much certainty as whether the sun will rise tomorrow. Thus James Gleick introduces the topic of `chaos' - there can be a "sensitive dependence on initial conditions". If we were to know the initial conditions in all their details, predictability would be brought within our grasp. Thus the flapping of the wings of a butterfly in China could result in rainfall in Indianapolis.

At times I was lost in the small detail, but the strength of this book is that it paints a big picture. The mathematics (and physics, and chemistry, and biology, and .....) is sometimes beyond me, but the overall story is that there is `chaos' all around. Some of the chaos is linked into classic Newtonian mechanics, but strangely enough, chaos almost has in itself an order and `predictability' about it.

The three of the most significant scientific theories of the 20th century are reckoned to be Einstein's General Relativity, Quantum Mechanics, and ...... Chaos Theory. Before opening this very historical account of the last mentioned, I knew nothing about the theory of chaos. Now I have an awareness of the subject, and how experimentation can play a part in mathematics. Experimentation and mathematics are not normally uttered in the same sentence.

Look for the big picture, and do not get lost in the people and places, which can be bewildering. If you read this book, please ensure that it has colour photographs within it - the pictures are both staggering, and help to bring home the message. Some areas of chaos have their roots in self similarity, and the pictures from Mendelbrot sets are both staggering and fascinating. Self similarity can be best summed up by the classic (and anonymous) ditty: "Big fleas have on their backs small fleas to bite them, small flees have smaller fleas and so ad infinitum"

Gleick is strong on the history and roots of chaos, and how the ideas were received when initially tabled. There was shock and disbelief that others from external communities could have something to say that would have relevance to (say) population growth models, from totally different scientific disciplines. There was also reluctance initially to publish some of the ground-braking ideas.

Chaos is about non-linear dynamics, fractals, fractal boundary basins and much more. As `chaos' as a concept (and almost as a discipline) spread, rather than bringing order when chaos had existed before (and this could be described as one of the main purposes of `science'), evidence of more chaos emerges.

From study, it could be that there is more evidence of chaos than we thought hitherto. There could be chaos in space, and the onset of cardiac arrhythmias (heart attacks) seems chaotic. Gleick speculates that `evolution' is chaos with feedback. He has made me more aware of randomness. Classic determinism generates randomness. Perhaps, just perhaps, chaos is a way to reconcile free will and determinism. All in all, unlike the pure scientists of old, I now find myself positively looking for chaos.

Perhaps that is a mark of a well presented book.

Peter Morgan (morganp@supanet.com)


New wisdom, 18 May 2007
I love this book because of its association with systems theory and the concept of emergent properties. I also find the story about the struggle to get the ideas accepted by the establishment very reminiscent of the struggle to get new ideas into the world of work.


A Truly Enlightening Introduction to a Whole New World, 29 Dec 2004
I am educated to degree level, however my degree is not in any scientific discipline. I only recently developed an interest in science, and have since read many popular science books to try and fill a few of the gaping holes in my knowledge.

Before reading this book, I had no knowledge of Chaos Theory beyond the analogy that a butterfly flapping its wings in Peking could apparently cause a hurricane in New York. I never really understood this idea so I decided to read the book and find out about it.

Chaos: Making a New Science - unlike many other books in the popular science genre - doesn't talk down to the reader, and makes no apology for the complexity of the subject. Don't let this put you off, Gleick doesn't need to talk down to you, instead he relies on carefully and precisely explaining all of the facts. I have to admit to re-reading some of the more complex areas, however upon re-reading I found everything accessible despite my limited scientific education.

The book primarily tells the history of Chaos Theory and its scientists, which in itself requires a discussion of the theories involved. This means that it explains what the different concepts mean (The Butterfly Effect, non-linear equations, fractals etc.) but doesn't get lost in the very complex mathematics behind them. The theories in this book are often explained very effectively with good use of diagrams. I found these to be priceless, for example the description of a fractal left me a little confused until I saw the diagram of a Koch curve and suddenly understood that it really is possible for a shape to have a finite area and an infinite perimeter.

If you already know a lot about Chaos Theory and want to know more I recommend a text book, otherwise I recommend Chaos: Making a New Science.

Top Book, 30 Jan 2003
This was the first book I ever read on chaos theory. I am not involved in chaos theory at all, but I was interested in finding out more about it as it was big news at the time.

While at times the concept can be difficult to grasp, the author does go to great pains to make things clear. I think this book is aimed at people with some kind of background in maths, science or engineering ho know nothing about chaos theory.

THe story of how chaos theory came to be is enlightening and a real insight into how such ideas evolve over time.

By the end of the book I was quite able to create and run my own (basic) chaos equations. Quite a feat, really.

A delightful read !, 24 Jan 2003
This book is called 'Chaos : Making a new science' - so it should hardly
surprise anyone that it deals with the history of Chaos, bringing forth
the elementary concepts of the field along the way.
This book isn't, nor does it pretend to be, a textbook on chaos theory,
so one shouldn't expect too much maths or technical details. On the other
hand, a little maths is unavoidable for discussing even the most basic
notions of chaos theory, so the reader should be prepared for some
(not very demanding) maths.

The style adopted by Gleick is to interweave the personal lives of the
major players involved in the birth of chaos with a description the
concepts, thus giving the book a feel of an interesting story while
introducing a plethora of dazzling ideas at the same time.

The idea of self-similarity, of patterns composed of infinitely-repeating
tiny replicas of themselves, is astounding, to say the least. And to
learn that nature is full of such patterns is revealing indeed. The
implications to science and technology are far-reaching and often
surprising - researchers in Computer Networking have discovered that
network traffic in large networks such as the internet may actually be
following self-similar patterns !!

Personally, i found this to be a delightful read - Gleick's writing is
racy, the ideas involved are mind-bending, and the vivid imagery will
stay with you for a long,long time. I fell in love with fractals at
first sight and can gaze at a collection of beautiful fractals for hours.

In brief, this is a light, breezy account of the history of Chaos, with
a gentle introduction to the basic ideas of Chaos without much technical
details and only a minimum of maths.

One of the best 'Science for everyone' books i've ever read!

A great introduction to the subject of chaos, 13 Jun 2001
Book review of: Does God Play Dice? - The New Mathematics of Chaos by Ian Stewart

Beautiful fractals, the butterfly effect and unpredictable systems were the images that chaos conjured up in my imagination before I sat down and read this book. Within its pages the incredible diversity of chaotic systems; and the diversity is remarkable; is presented and explained. It is staggering to see the picture unfold, the gradual realisation that 'the' scientific statement of the eighteenth century; that the universe runs according to a set of immutable laws; is unable to explain much of the behaviour in even the simplest of classical systems. The discovery of a whole new world, and one that has been in existence since the beginning of the universe: chaos. This book is merely an introduction to a comparatively new and exciting area of mathematics; but using the word merely is doing it an injustice, since it encapsulates the topic superbly and leaves the reader with a desire to study the mathematics of chaos in more detail.

Fittingly the opening chapter commences with the backdrop to this word 'chaos'. Three hundred years ago, Newton published, 'The Mathematical principles of Natural Philosophy'. This work is unrivalled in the field of mathematics; its basic message has been absorbed into our culture: "Nature has laws and we can find them." Unfortunately, although mathematics allows us to calculate the solutions to many difficult problems, we are still left in an unordered world, where apparently simple motions, on closer inspection, become unpredictable and hence unexplainable in the language of mathematics. It is appropriate at this point to introduce the nature of chaos. Stewart is quick to point out that since this branch of mathematics is still in its formative stages, giving it a precise definition is not possible or wise. However to get us off the mark he gives the definition reluctantly reached by the Royal Society in 1986: "Stochastic behaviour occurring in a deterministic system." More roughly speaking, random behaviour in a system governed by laws.

Where is the dividing line between order and chaos? The chapter 'The Laws of Error,' introduces another field of mathematics, Probability theory - the mathematics of chance. Mathematicians had found that analysing the detailed workings of large systems was too involved and complex. Probability theory grew out of a need to simulate detail without actually having to examine it. As Stewart states: "Mathematicians could calculate the motion of a satellite of Jupiter, but not that of a snowflake in a blizzard."

The book continues with a look at one of the prime examples of chaotic systems in our World, weather systems. This century has seen many attempts to write equations that will linearize weather and use them to predict exactly how weather systems will behave. As we are well aware short-term predictions are accurate a large percentage of the time, but long term predictions are much harder to make. What we learned in the 'Strange Attractors' chapter can be applied here. The initial conditions that we feed into any model we have will have finite accuracy. Even if we obtain data exact to many decimal places, it will not take many iterations before it digresses from the path that the described weather system follows. Lorenz stumbled upon this when computing weather systems. After examining results from two separate calculations involving the same set of data, albeit with different rounding accuracies, he discovered that his results were very similar for a short period of time, but then diverged extremely rapidly and followed distinct paths. This breakthrough was later to be named the 'Butterfly effect', illustrating the manner in which a trivial dynamic can upset a disproportionably large system. .

At this stage in the book, Stewart leads us into a chapter entitled 'Recipe for chaos'. It firstly attempts to describe the workings of chaos as analogous to a recipe, presumably in an attempt to simplify the concepts and avoid any complex mathematics. It does not really achieve the desired effect. This chapter was the hardest to grasp, which is a shame since it contains many of the fundamental facts about chaos and its axioms if one can use such a word.

Fractals are important part of chaos that joins the discussion at this point. They present us with a language to describe what we see happening with chaos. A fractal, generally speaking, is a geometric object, which continues to exhibit detailed structure over a wide range of scales. Self-similarity exhibited again. Interestingly the method of describing the detail level of a fractal is by allocating it a dimension, known as its Hausdorff dimension. These dimensions tend to be fractional (hence fractal).

The final three chapters are new to this, the second edition of the book, and they describe some of the advances in the subject since 1989, namely the prediction and control of chaotic systems, which are both perfectly possible.

In its totality, this book gives any discerning reader an opportunity to delve into the World of chaos and come away with a greater understanding of the topic as a whole and a glance at the variety of areas and applications it covers. The mathematics of chaos is involved; this is not surprising since the initial discovery of the topic was due to the inability of conventional mathematics to describe certain behaviours. Nevertheless, on the whole Stewart does a good job of explaining concepts and then illustrating them with simplified examples, avoiding the need for much of the mathematics. However there were one or two places where his desire to seek analogies for his models overlooks the aim of aim of the analogy in the first place that is to aid the readers understanding of the topic. Helpful too, was the inclusion of a fair number of diagrams and schematics that in several cases proved invaluable to my understanding of the book. This is a great introduction to a subject that is becoming increasingly important and perhaps indispensable in mathematics.

Readable Introduction to Chaos Theory, 06 Feb 2001
Relatively easy to read, even the Maths (honest!), Ian Stewart writes with an obvious passion but injects some much needed humour at times. He delivers the bulk of the subject (including the historical theory) in a fairly concise way. Probably best used in conjunction with another introductory text (e.g. James Gleick's 'Chaos')

A incredible book...about Chaos.., 01 Feb 2001
This book explains in a easy way, all the mechanism related to Chaos Theory. Ian Stewart shows a clever & interesting way of describing it.

A good introduction to the science of Chaos, 11 Oct 2000
If you are interested in the subject of Chaos, this book can be a good introduction. Very readable and engaging, you will find accurate descriptions of the key discoveries of that science in a language easy to understand to everybody. I loved that book!

Interesting but not easy, 18 Nov 2008
I was looking for a relaxed read on the tube. This book was more substantial and quite a lot heavier going than the title implies.

I didn't find this book all that easy to read even though I have studied economics, mathematics and physics to quite a high level.

Interesting, but not a very short introduction, 01 Jul 2008
This book aims to introduce the key concepts of chaos in a readable way, including no mathematics. The title is a bit misleading, since there are over 160 pages and the book covers some quite advanced concepts. Overall, the book attempts to cover too much material for a short introduction, and I feel that readers who are not already familiar with the topic will be left confused.

The first chapter leaps directly into the concepts of deterministic nonlinear systems and sensitive dependence, and includes a wide-ranging discussion of the work of scientists including Laplace, Newton, Franklin and Darwin.

The second chapter explains exponential growth nicely, with several examples. Chapter 3 introduces examples of dynamical systems and their associated concepts. Here, new concepts such as state space, fixed points and attractors arise very rapidly and I wonder whether they have time to sink in for the reader who is not already familiar with them. Some of the new concepts are not clearly defined.

Chapter 4, 'Chaos in mathematical models', describes the universal period-doubling cascade, the Lorenz system, the Henon map, delay equations and Hamiltonian chaos. Again, too many models are introduced too rapidly. Chapters 5 and 6 cover fractals, dimensions and Lyapunov exponents, the measures of chaos, and the book then moves on to real numbers on a computer, statistics, predictability, weather forecasts, climate change and finance, ending up with some philosophical remarks.

Although I quite enjoyed reading this book, I would not recommend it as an introduction to the subject.



Good. But you need a preliminary, 11 Jun 2008
The book introduces the chaos theory relatively in details (compared with "the quantum world" J.P which introduces the entire structure of quantum physics less than 90 pages). The chaos is a very new and popular theory. It is based on the dynamical system, or dating back further, integral by I.Newton. The book itself produces nothing extremely exciting but progressively, makes you learn a lot. I find it really helpful to scan the dynamical system part in my financial math textbook before reading it. My suggestion is that you understand some concepts on integral and dynamical system first. They may be rather naive compared with the chaos theory but they at least give you a basis to develop your thoughts.

A Great Introduction, 04 Oct 2006
A very readable introduction for anyone interested in nonlinear dynamics, time series, weather forecasting or climate modelling.

Accessible chaos, 30 May 2004
Strogatz's approach to Nonlinear Dynamics is suitable for anyone equipped with a good basic understanding of ordinary differential equations. He allows the reader to gradually build-up their understanding through a series of illustrations and examples - this is the sort of book that will be indispensable the night before a final year undergraduate Chaos and Nonlinear Dynamics exam. Not excessively mathematical, contains solid explanations and leaves you wanting to learn more about this fantastic area of physics.

Great undergrad text, 04 Aug 1998
I recently took an undergrad course which used this book as the text. This book is very easy to follow, contains great explanations and diagrams, and is just plain interesting to read. Anyone who has had a basic calc/ODE class background could understand this book.

Great intro to nonlinear dynamics with excellent examples, 28 Jul 1998
This book is an excellent introductory graduate level text on nonlinear dynamics for those who wish to understand the basic concepts before seeing the mathematical rigor at the heart of the subject. Strogatz avoids getting caught up in mathematical nuances which often cloud the big picture for non-math students, and thereby clearly impresses upon the reader the essence of nonlinear dynamics, eventually building up to chaos. The examples and problems are truly unique and inspiring. This book is an excellent starting place for someone who knows little or nothing about nonlinear dynamics but has done some basic work with linear differential equations and linear algebra.

A sufficiently elementary and yet thorough introduction., 17 Jul 1998
A very good book. Recommended for all readers familiar or even vaguely familiar with Ordinary Differential Equations and Calculus. Its informal style helps a lot. The examples are clear and enough background information is given to understand them.

A little complex..., 15 Apr 1998
This is an excelent text with challenging problems (which you should work at for a while and not give up!)and clear explanations. The book explains a mostly geometric approach, and leaves the ananlytical side to you. Buy this book even if you've never heard of "Nonlinear Dynamics". You'll be glad you did!

Order from Chaos, 29 Sep 2007
We all know things that are not predictable. These can be everyday occurrences like the weather, or more specialised events (whether the stock market will go up or down). The unpredictable plays a large part in "normal life". Yet for some of these matters, there is a nagging feeling that if sufficient information were known, the unpredictable would indeed be able to be forecast with as much certainty as whether the sun will rise tomorrow. Thus James Gleick introduces the topic of `chaos' - there can be a "sensitive dependence on initial conditions". If we were to know the initial conditions in all their details, predictability would be brought within our grasp. Thus the flapping of the wings of a butterfly in China could result in rainfall in Indianapolis.

At times I was lost in the small detail, but the strength of this book is that it paints a big picture. The mathematics (and physics, and chemistry, and biology, and .....) is sometimes beyond me, but the overall story is that there is `chaos' all around. Some of the chaos is linked into classic Newtonian mechanics, but strangely enough, chaos almost has in itself an order and `predictability' about it.

The three of the most significant scientific theories of the 20th century are reckoned to be Einstein's General Relativity, Quantum Mechanics, and ...... Chaos Theory. Before opening this very historical account of the last mentioned, I knew nothing about the theory of chaos. Now I have an awareness of the subject, and how experimentation can play a part in mathematics. Experimentation and mathematics are not normally uttered in the same sentence.

Look for the big picture, and do not get lost in the people and places, which can be bewildering. If you read this book, please ensure that it has colour photographs within it - the pictures are both staggering, and help to bring home the message. Some areas of chaos have their roots in self similarity, and the pictures from Mendelbrot sets are both staggering and fascinating. Self similarity can be best summed up by the classic (and anonymous) ditty: "Big fleas have on their backs small fleas to bite them, small flees have smaller fleas and so ad infinitum"

Gleick is strong on the history and roots of chaos, and how the ideas were received when initially tabled. There was shock and disbelief that others from external communities could have something to say that would have relevance to (say) population growth models, from totally different scientific disciplines. There was also reluctance initially to publish some of the ground-braking ideas.

Chaos is about non-linear dynamics, fractals, fractal boundary basins and much more. As `chaos' as a concept (and almost as a discipline) spread, rather than bringing order when chaos had existed before (and this could be described as one of the main purposes of `science'), evidence of more chaos emerges.

From study, it could be that there is more evidence of chaos than we thought hitherto. There could be chaos in space, and the onset of cardiac arrhythmias (heart attacks) seems chaotic. Gleick speculates that `evolution' is chaos with feedback. He has made me more aware of randomness. Classic determinism generates randomness. Perhaps, just perhaps, chaos is a way to reconcile free will and determinism. All in all, unlike the pure scientists of old, I now find myself positively looking for chaos.

Perhaps that is a mark of a well presented book.

Peter Morgan (morganp@supanet.com)


New wisdom, 18 May 2007
I love this book because of its association with systems theory and the concept of emergent properties. I also find the story about the struggle to get the ideas accepted by the establishment very reminiscent of the struggle to get new ideas into the world of work.


A Truly Enlightening Introduction to a Whole New World, 29 Dec 2004
I am educated to degree level, however my degree is not in any scientific discipline. I only recently developed an interest in science, and have since read many popular science books to try and fill a few of the gaping holes in my knowledge.

Before reading this book, I had no knowledge of Chaos Theory beyond the analogy that a butterfly flapping its wings in Peking could apparently cause a hurricane in New York. I never really understood this idea so I decided to read the book and find out about it.

Chaos: Making a New Science - unlike many other books in the popular science genre - doesn't talk down to the reader, and makes no apology for the complexity of the subject. Don't let this put you off, Gleick doesn't need to talk down to you, instead he relies on carefully and precisely explaining all of the facts. I have to admit to re-reading some of the more complex areas, however upon re-reading I found everything accessible despite my limited scientific education.

The book primarily tells the history of Chaos Theory and its scientists, which in itself requires a discussion of the theories involved. This means that it explains what the different concepts mean (The Butterfly Effect, non-linear equations, fractals etc.) but doesn't get lost in the very complex mathematics behind them. The theories in this book are often explained very effectively with good use of diagrams. I found these to be priceless, for example the description of a fractal left me a little confused until I saw the diagram of a Koch curve and suddenly understood that it really is possible for a shape to have a finite area and an infinite perimeter.

If you already know a lot about Chaos Theory and want to know more I recommend a text book, otherwise I recommend Chaos: Making a New Science.

Top Book, 30 Jan 2003
This was the first book I ever read on chaos theory. I am not involved in chaos theory at all, but I was interested in finding out more about it as it was big news at the time.

While at times the concept can be difficult to grasp, the author does go to great pains to make things clear. I think this book is aimed at people with some kind of background in maths, science or engineering ho know nothing about chaos theory.

THe story of how chaos theory came to be is enlightening and a real insight into how such ideas evolve over time.

By the end of the book I was quite able to create and run my own (basic) chaos equations. Quite a feat, really.

A delightful read !, 24 Jan 2003
This book is called 'Chaos : Making a new science' - so it should hardly
surprise anyone that it deals with the history of Chaos, bringing forth
the elementary concepts of the field along the way.
This book isn't, nor does it pretend to be, a textbook on chaos theory,
so one shouldn't expect too much maths or technical details. On the other
hand, a little maths is unavoidable for discussing even the most basic
notions of chaos theory, so the reader should be prepared for some
(not very demanding) maths.

The style adopted by Gleick is to interweave the personal lives of the
major players involved in the birth of chaos with a description the
concepts, thus giving the book a feel of an interesting story while
introducing a plethora of dazzling ideas at the same time.

The idea of self-similarity, of patterns composed of infinitely-repeating
tiny replicas of themselves, is astounding, to say the least. And to
learn that nature is full of such patterns is revealing indeed. The
implications to science and technology are far-reaching and often
surprising - researchers in Computer Networking have discovered that
network traffic in large networks such as the internet may actually be
following self-similar patterns !!

Personally, i found this to be a delightful read - Gleick's writing is
racy, the ideas involved are mind-bending, and the vivid imagery will
stay with you for a long,long time. I fell in love with fractals at
first sight and can gaze at a collection of beautiful fractals for hours.

In brief, this is a light, breezy account of the history of Chaos, with
a gentle introduction to the basic ideas of Chaos without much technical
details and only a minimum of maths.

One of the best 'Science for everyone' books i've ever read!

A great introduction to the subject of chaos, 13 Jun 2001
Book review of: Does God Play Dice? - The New Mathematics of Chaos by Ian Stewart

Beautiful fractals, the butterfly effect and unpredictable systems were the images that chaos conjured up in my imagination before I sat down and read this book. Within its pages the incredible diversity of chaotic systems; and the diversity is remarkable; is presented and explained. It is staggering to see the picture unfold, the gradual realisation that 'the' scientific statement of the eighteenth century; that the universe runs according to a set of immutable laws; is unable to explain much of the behaviour in even the simplest of classical systems. The discovery of a whole new world, and one that has been in existence since the beginning of the universe: chaos. This book is merely an introduction to a comparatively new and exciting area of mathematics; but using the word merely is doing it an injustice, since it encapsulates the topic superbly and leaves the reader with a desire to study the mathematics of chaos in more detail.

Fittingly the opening chapter commences with the backdrop to this word 'chaos'. Three hundred years ago, Newton published, 'The Mathematical principles of Natural Philosophy'. This work is unrivalled in the field of mathematics; its basic message has been absorbed into our culture: "Nature has laws and we can find them." Unfortunately, although mathematics allows us to calculate the solutions to many difficult problems, we are still left in an unordered world, where apparently simple motions, on closer inspection, become unpredictable and hence unexplainable in the language of mathematics. It is appropriate at this point to introduce the nature of chaos. Stewart is quick to point out that since this branch of mathematics is still in its formative stages, giving it a precise definition is not possible or wise. However to get us off the mark he gives the definition reluctantly reached by the Royal Society in 1986: "Stochastic behaviour occurring in a deterministic system." More roughly speaking, random behaviour in a system governed by laws.

Where is the dividing line between order and chaos? The chapter 'The Laws of Error,' introduces another field of mathematics, Probability theory - the mathematics of chance. Mathematicians had found that analysing the detailed workings of large systems was too involved and complex. Probability theory grew out of a need to simulate detail without actually having to examine it. As Stewart states: "Mathematicians could calculate the motion of a satellite of Jupiter, but not that of a snowflake in a blizzard."

The book continues with a look at one of the prime examples of chaotic systems in our World, weather systems. This century has seen many attempts to write equations that will linearize weather and use them to predict exactly how weather systems will behave. As we are well aware short-term predictions are accurate a large percentage of the time, but long term predictions are much harder to make. What we learned in the 'Strange Attractors' chapter can be applied here. The initial conditions that we feed into any model we have will have finite accuracy. Even if we obtain data exact to many decimal places, it will not take many iterations before it digresses from the path that the described weather system follows. Lorenz stumbled upon this when computing weather systems. After examining results from two separate calculations involving the same set of data, albeit with different rounding accuracies, he discovered that his results were very similar for a short period of time, but then diverged extremely rapidly and followed distinct paths. This breakthrough was later to be named the 'Butterfly effect', illustrating the manner in which a trivial dynamic can upset a disproportionably large system. .

At this stage in the book, Stewart leads us into a chapter entitled 'Recipe for chaos'. It firstly attempts to describe the workings of chaos as analogous to a recipe, presumably in an attempt to simplify the concepts and avoid any complex mathematics. It does not really achieve the desired effect. This chapter was the hardest to grasp, which is a shame since it contains many of the fundamental facts about chaos and its axioms if one can use such a word.

Fractals are important part of chaos that joins the discussion at this point. They present us with a language to describe what we see happening with chaos. A fractal, generally speaking, is a geometric object, which continues to exhibit detailed structure over a wide range of scales. Self-similarity exhibited again. Interestingly the method of describing the detail level of a fractal is by allocating it a dimension, known as its Hausdorff dimension. These dimensions tend to be fractional (hence fractal).

The final three chapters are new to this, the second edition of the book, and they describe some of the advances in the subject since 1989, namely the prediction and control of chaotic systems, which are both perfectly possible.

In its totality, this book gives any discerning reader an opportunity to delve into the World of chaos and come away with a greater understanding of the topic as a whole and a glance at the variety of areas and applications it covers. The mathematics of chaos is involved; this is not surprising since the initial discovery of the topic was due to the inability of conventional mathematics to describe certain behaviours. Nevertheless, on the whole Stewart does a good job of explaining concepts and then illustrating them with simplified examples, avoiding the need for much of the mathematics. However there were one or two places where his desire to seek analogies for his models overlooks the aim of aim of the analogy in the first place that is to aid the readers understanding of the topic. Helpful too, was the inclusion of a fair number of diagrams and schematics that in several cases proved invaluable to my understanding of the book. This is a great introduction to a subject that is becoming increasingly important and perhaps indispensable in mathematics.

Readable Introduction to Chaos Theory, 06 Feb 2001
Relatively easy to read, even the Maths (honest!), Ian Stewart writes with an obvious passion but injects some much needed humour at times. He delivers the bulk of the subject (including the historical theory) in a fairly concise way. Probably best used in conjunction with another introductory text (e.g. James Gleick's 'Chaos')

A incredible book...about Chaos.., 01 Feb 2001
This book explains in a easy way, all the mechanism related to Chaos Theory. Ian Stewart shows a clever & interesting way of describing it.

A good introduction to the science of Chaos, 11 Oct 2000
If you are interested in the subject of Chaos, this book can be a good introduction. Very readable and engaging, you will find accurate descriptions of the key discoveries of that science in a language easy to understand to everybody. I loved that book!

Interesting but not easy, 18 Nov 2008
I was looking for a relaxed read on the tube. This book was more substantial and quite a lot heavier going than the title implies.

I didn't find this book all that easy to read even though I have studied economics, mathematics and physics to quite a high level.

Interesting, but not a very short introduction, 01 Jul 2008
This book aims to introduce the key concepts of chaos in a readable way, including no mathematics. The title is a bit misleading, since there are over 160 pages and the book covers some quite advanced concepts. Overall, the book attempts to cover too much material for a short introduction, and I feel that readers who are not already familiar with the topic will be left confused.

The first chapter leaps directly into the concepts of deterministic nonlinear systems and sensitive dependence, and includes a wide-ranging discussion of the work of scientists including Laplace, Newton, Franklin and Darwin.

The second chapter explains exponential growth nicely, with several examples. Chapter 3 introduces examples of dynamical systems and their associated concepts. Here, new concepts such as state space, fixed points and attractors arise very rapidly and I wonder whether they have time to sink in for the reader who is not already familiar with them. Some of the new concepts are not clearly defined.

Chapter 4, 'Chaos in mathematical models', describes the universal period-doubling cascade, the Lorenz system, the Henon map, delay equations and Hamiltonian chaos. Again, too many models are introduced too rapidly. Chapters 5 and 6 cover fractals, dimensions and Lyapunov exponents, the measures of chaos, and the book then moves on to real numbers on a computer, statistics, predictability, weather forecasts, climate change and finance, ending up with some philosophical remarks.

Although I quite enjoyed reading this book, I would not recommend it as an introduction to the subject.



Good. But you need a preliminary, 11 Jun 2008
The book introduces the chaos theory relatively in details (compared with "the quantum world" J.P which introduces the entire structure of quantum physics less than 90 pages). The chaos is a very new and popular theory. It is based on the dynamical system, or dating back further, integral by I.Newton. The book itself produces nothing extremely exciting but progressively, makes you learn a lot. I find it really helpful to scan the dynamical system part in my financial math textbook before reading it. My suggestion is that you understand some concepts on integral and dynamical system first. They may be rather naive compared with the chaos theory but they at least give you a basis to develop your thoughts.

A Great Introduction, 04 Oct 2006
A very readable introduction for anyone interested in nonlinear dynamics, time series, weather forecasting or climate modelling.

Accessible chaos, 30 May 2004
Strogatz's approach to Nonlinear Dynamics is suitable for anyone equipped with a good basic understanding of ordinary differential equations. He allows the reader to gradually build-up their understanding through a series of illustrations and examples - this is the sort of book that will be indispensable the night before a final year undergraduate Chaos and Nonlinear Dynamics exam. Not excessively mathematical, contains solid explanations and leaves you wanting to learn more about this fantastic area of physics.

Great undergrad text, 04 Aug 1998
I recently took an undergrad course which used this book as the text. This book is very easy to follow, contains great explanations and diagrams, and is just plain interesting to read. Anyone who has had a basic calc/ODE class background could understand this book.

Great intro to nonlinear dynamics with excellent examples, 28 Jul 1998
This book is an excellent introductory graduate level text on nonlinear dynamics for those who wish to understand the basic concepts before seeing the mathematical rigor at the heart of the subject. Strogatz avoids getting caught up in mathematical nuances which often cloud the big picture for non-math students, and thereby clearly impresses upon the reader the essence of nonlinear dynamics, eventually building up to chaos. The examples and problems are truly unique and inspiring. This book is an excellent starting place for someone who knows little or nothing about nonlinear dynamics but has done some basic work with linear differential equations and linear algebra.

A sufficiently elementary and yet thorough introduction., 17 Jul 1998
A very good book. Recommended for all readers familiar or even vaguely familiar with Ordinary Differential Equations and Calculus. Its informal style helps a lot. The examples are clear and enough background information is given to understand them.

A little complex..., 15 Apr 1998
This is an excelent text with challenging problems (which you should work at for a while and not give up!)and clear explanations. The book explains a mostly geometric approach, and leaves the ananlytical side to you. Buy this book even if you've never heard of "Nonlinear Dynamics". You'll be glad you did!

A well structured account of a new field, 14 Feb 2007
There aren't really any text books on networks, at least networks as they're being studied by physicists today. You'll find maths books on graph theory but that is about all. This book is a collection of the most important papers through the recent (and not so recent) history of networks.

The reasons I really like this book are, firstly, the authors are among the best in the field. The papers they have chosen really are a good place to start if you want to know the story of networks. Secondly the introductions to each of the sections are very well written. There is a general introduction and then they go through each paper picking out its important point and placing it in the bigger picture.

I'm a postgraduate physics student and I'm learning about networks for my research. Along with Mark Newman's website I've found this the most comprehensive resource yet.