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54 people found this helpful

ByOptimistixon 24 January 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!

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!

35 people found this helpful

ByA customeron 21 November 2001

It should be noted from the beginning that this is not a "Layman's guide to Chaos theory ". It is in fact a "Once upon a time" account of the birth and development of this fascinating science. The problem is, who this book is trying to fascinate.

The first half is certainly handled well, with Gleick balancing the building up of Chaos Theory with the lives and characters of its pioneers. It does however prelude what is to come in the book: At times, though the language is clear, the concepts become obscured, especially as the author tries to keep things broad and general.

It gets worse in the second half of the book, as it becomes less and less clear who the author is talking to: People with a background in Chaos theory, or people who know nothing about it? The first group would find nothing interesting here apart from happy memoirs, while the second would be left scratching their heads as they go over and over the same paragraphs, trying to decipher the deeper meanings.

As an Introduction to Chaos, the book suffers from over-generalisations and fast pace: Gleick seems happy to glide from the surface of tough concept to the surface of tougher concept and then get poetic with the conclusions, before an ordinary reader realises that there were actually any conclusions to be made. In his own comments the author even "winks" to those in the know, providing "inside jokes" that only the people he has interviewed would probably get. The rest of us outsiders are left baffled and frustrated.

However, as a documentation of Chaos, the book is decent. Well-researched and well-planned, if you already know the specifics of Chaos theory, you 'll enjoy reading a general review of how this breakthrough way of thinking came to be, survived "persecution" and eventually influenced everything it touched.

The first half is certainly handled well, with Gleick balancing the building up of Chaos Theory with the lives and characters of its pioneers. It does however prelude what is to come in the book: At times, though the language is clear, the concepts become obscured, especially as the author tries to keep things broad and general.

It gets worse in the second half of the book, as it becomes less and less clear who the author is talking to: People with a background in Chaos theory, or people who know nothing about it? The first group would find nothing interesting here apart from happy memoirs, while the second would be left scratching their heads as they go over and over the same paragraphs, trying to decipher the deeper meanings.

As an Introduction to Chaos, the book suffers from over-generalisations and fast pace: Gleick seems happy to glide from the surface of tough concept to the surface of tougher concept and then get poetic with the conclusions, before an ordinary reader realises that there were actually any conclusions to be made. In his own comments the author even "winks" to those in the know, providing "inside jokes" that only the people he has interviewed would probably get. The rest of us outsiders are left baffled and frustrated.

However, as a documentation of Chaos, the book is decent. Well-researched and well-planned, if you already know the specifics of Chaos theory, you 'll enjoy reading a general review of how this breakthrough way of thinking came to be, survived "persecution" and eventually influenced everything it touched.

ByOptimistixon 24 January 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!

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!

Byalephnulluk@yahoo.co.ukon 10 December 2001

This book left me looking at the world in a radically different perspective. It seemed to suggest that in the late twentieth century we were begining to pin down the extremely subtle mathematics that underpinned almost everything and as a consequence were suddenly gaining an incredible insight into what's actually going on behind the scenes of the universe.

You enter this book knowing chaos as a buzzword occasionally touched upon by the media and gradually realise that it describes the 'forces at work' behind a whole array of things from something as trivial as the Newton-Raphson procedure (who'd have thought a simple piece of A-level maths could give rise to cutting adge research?) to matters as important as the weather, the interepherence in phone lines, the populations in an e-cology, indeed (without meaning to give away the book's climax) it's the very set of theories and idea's that keeps human beings alive!

An absolute must for anyone who's ever wondered why they wonder!

You enter this book knowing chaos as a buzzword occasionally touched upon by the media and gradually realise that it describes the 'forces at work' behind a whole array of things from something as trivial as the Newton-Raphson procedure (who'd have thought a simple piece of A-level maths could give rise to cutting adge research?) to matters as important as the weather, the interepherence in phone lines, the populations in an e-cology, indeed (without meaning to give away the book's climax) it's the very set of theories and idea's that keeps human beings alive!

An absolute must for anyone who's ever wondered why they wonder!

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ByA customeron 30 January 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.

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.

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ByMesomorphic Mesopotamianon 26 December 2012

Delicately skirting round some complex mathematics and using physical reasoning instead, this book explores behaviour of physical systems: the way the intertwined populations of rabbits and foxes go through an intricate little dance, the rhythms of the human heart, the shape of leaves, the unpredictability of the weather. There are some beautiful pictures and some equally beautiful computer-generated graphics.

What links all these? There is some new(ish) mathematics which describes these patterns of behaviour. Chaos and fractals are two of the main courses on the menu, although the author avoids giving actual mathematics. (There may be a footnote or two with equations, or an appendix to follow up some more technical ideas.) James Gleick explores and discusses ideas which lie in a strange border zone, where behaviour is not so simple as to be purely predictable, but not completely unpredictable either. That fascinating border zone contains the jitters of the stock market, the population dynamics of all the species on planet earth, and the bursts and pauses in internet traffic. The fundamental ideas are very simple and surprisingly cross-disciplinary: for example, chaotic behaviour discovered by mathematicians turns out to describe the progress of an influenza empidemic. This explains why some of the ideas took so long to emerge and become accepted: biologists studying measles epidemics didn't have the depth of mathematical background, and mathematicians didn't realise that their ideas could be used to monitor the success of a vaccination programme.

James Gleick manages to describe all these fascinating systems, and the underlying ideas, without requiring the reader to get into deep mathematics. Speaking as a mathematician, I can read the physical descriptions and see the mathematics in the background, so this book will also be enjoyed by the mathematically-minded.

James Gleick gives the history of the discovery of various of these mathematical ideas, and the personalities involved. This is also a story of mould-breaking ideas and how they struggled to be accepted.

What links all these? There is some new(ish) mathematics which describes these patterns of behaviour. Chaos and fractals are two of the main courses on the menu, although the author avoids giving actual mathematics. (There may be a footnote or two with equations, or an appendix to follow up some more technical ideas.) James Gleick explores and discusses ideas which lie in a strange border zone, where behaviour is not so simple as to be purely predictable, but not completely unpredictable either. That fascinating border zone contains the jitters of the stock market, the population dynamics of all the species on planet earth, and the bursts and pauses in internet traffic. The fundamental ideas are very simple and surprisingly cross-disciplinary: for example, chaotic behaviour discovered by mathematicians turns out to describe the progress of an influenza empidemic. This explains why some of the ideas took so long to emerge and become accepted: biologists studying measles epidemics didn't have the depth of mathematical background, and mathematicians didn't realise that their ideas could be used to monitor the success of a vaccination programme.

James Gleick manages to describe all these fascinating systems, and the underlying ideas, without requiring the reader to get into deep mathematics. Speaking as a mathematician, I can read the physical descriptions and see the mathematics in the background, so this book will also be enjoyed by the mathematically-minded.

James Gleick gives the history of the discovery of various of these mathematical ideas, and the personalities involved. This is also a story of mould-breaking ideas and how they struggled to be accepted.

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ByMr P R Morganon 29 September 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)

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)

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ByA customeron 19 September 2000

Well worth reading if you've ever wondered how computers generate some of the complex patterns we so often see in science magazines. A perfect introduction into the mathematics and history of one of the less-known areas of science. It would be good if a follow-up was available to take us a few steps further, but it seems that the mathematics of chaos fell a bit stale in the 90's. Definitely THE book for the layman interested in fractal geometry. This book made me consider Feigenbaum (of 4.669201 fame) to be one of the great heros of science, but left me wondering if Barnsley is just a graphic artist!

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ByGregory Samson 11 December 2010

I was enjoying a two-year early instalment on my retirement when I read this book in 1990. I'd been in natural foods since the 60's and my ticket out came from selling the Vegeburger, a product I had created, christened, and popularized. There were five possible new projects on my backburner when a friend insisted I read Chaos by James Gleick.

Gleick made this brand new science understandable, demonstrating his journalistic skill to the max. It is an exciting story with graduate students ditching degree subjects and diving into chaos; researchers stumbling across great principles; and beautiful designs manifesting from thin air. Chaos theory is a hugely important addition to science, shedding light on countless areas formerly beyond scientific enquiry. For me the most exciting lesson to be learned from chaos theory is the one that bears upon the deterministic means by which we run our society. We do everything possible to exclude the organizational skills of chaos from our culture, preferring coercion as the driving force.

I was so moved by Gleick's presentation of this new science that I opened a shop by the Portobello Market dedicated to chaos theory, called Strange Attractions (Google for more on that). And as the ideas that were sparked by his book grew within me, I was moved to write a book exploring the social lessons in chaos theory - lessons that would never be explored by scientists, who don't venture into that arena. That book is Uncommon Sense: State is Out of Date

Whilst I may be plugging my own book here, the message is that James Gleick's book was so powerful that it prompted me to propagate the idea by opening a shop, publishing fractal art and spending four years writing Uncommon Sense. Not many books do that for me. Thanks Mr Gleick.

Gleick made this brand new science understandable, demonstrating his journalistic skill to the max. It is an exciting story with graduate students ditching degree subjects and diving into chaos; researchers stumbling across great principles; and beautiful designs manifesting from thin air. Chaos theory is a hugely important addition to science, shedding light on countless areas formerly beyond scientific enquiry. For me the most exciting lesson to be learned from chaos theory is the one that bears upon the deterministic means by which we run our society. We do everything possible to exclude the organizational skills of chaos from our culture, preferring coercion as the driving force.

I was so moved by Gleick's presentation of this new science that I opened a shop by the Portobello Market dedicated to chaos theory, called Strange Attractions (Google for more on that). And as the ideas that were sparked by his book grew within me, I was moved to write a book exploring the social lessons in chaos theory - lessons that would never be explored by scientists, who don't venture into that arena. That book is Uncommon Sense: State is Out of Date

Whilst I may be plugging my own book here, the message is that James Gleick's book was so powerful that it prompted me to propagate the idea by opening a shop, publishing fractal art and spending four years writing Uncommon Sense. Not many books do that for me. Thanks Mr Gleick.

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ByA customeron 21 November 2001

It should be noted from the beginning that this is not a "Layman's guide to Chaos theory ". It is in fact a "Once upon a time" account of the birth and development of this fascinating science. The problem is, who this book is trying to fascinate.

The first half is certainly handled well, with Gleick balancing the building up of Chaos Theory with the lives and characters of its pioneers. It does however prelude what is to come in the book: At times, though the language is clear, the concepts become obscured, especially as the author tries to keep things broad and general.

It gets worse in the second half of the book, as it becomes less and less clear who the author is talking to: People with a background in Chaos theory, or people who know nothing about it? The first group would find nothing interesting here apart from happy memoirs, while the second would be left scratching their heads as they go over and over the same paragraphs, trying to decipher the deeper meanings.

As an Introduction to Chaos, the book suffers from over-generalisations and fast pace: Gleick seems happy to glide from the surface of tough concept to the surface of tougher concept and then get poetic with the conclusions, before an ordinary reader realises that there were actually any conclusions to be made. In his own comments the author even "winks" to those in the know, providing "inside jokes" that only the people he has interviewed would probably get. The rest of us outsiders are left baffled and frustrated.

However, as a documentation of Chaos, the book is decent. Well-researched and well-planned, if you already know the specifics of Chaos theory, you 'll enjoy reading a general review of how this breakthrough way of thinking came to be, survived "persecution" and eventually influenced everything it touched.

The first half is certainly handled well, with Gleick balancing the building up of Chaos Theory with the lives and characters of its pioneers. It does however prelude what is to come in the book: At times, though the language is clear, the concepts become obscured, especially as the author tries to keep things broad and general.

It gets worse in the second half of the book, as it becomes less and less clear who the author is talking to: People with a background in Chaos theory, or people who know nothing about it? The first group would find nothing interesting here apart from happy memoirs, while the second would be left scratching their heads as they go over and over the same paragraphs, trying to decipher the deeper meanings.

As an Introduction to Chaos, the book suffers from over-generalisations and fast pace: Gleick seems happy to glide from the surface of tough concept to the surface of tougher concept and then get poetic with the conclusions, before an ordinary reader realises that there were actually any conclusions to be made. In his own comments the author even "winks" to those in the know, providing "inside jokes" that only the people he has interviewed would probably get. The rest of us outsiders are left baffled and frustrated.

However, as a documentation of Chaos, the book is decent. Well-researched and well-planned, if you already know the specifics of Chaos theory, you 'll enjoy reading a general review of how this breakthrough way of thinking came to be, survived "persecution" and eventually influenced everything it touched.

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ByRama Raoon 13 July 2010

This book is the first of its kind, which introduces a new branch of science, the chaos or chaos theory from the historical point of view. This theory is widely applied in the transdisciplinary field of meteorology, mathematics, physics, population biology, cell biology, philosophy, astrophysics, information theory, economics, finance, robotics, and other diverse fields. The author has done a tremendous job of putting this book together with very little mathematics. I found this book highly engaging.

A brief summary of the book is as follows: Chaos physics along with classical and quantum physics are required to fully describe physical reality. Physical laws described by differential equations correspond to deterministic systems. In quantum physics, the Schrödinger equation which describes the continuous time evolution of a system's wave function is deterministic. However, the relationship between a system's wave function and the observable properties of the system is non-deterministic (quantum physical phenomenon). The systems studied in chaos theory are deterministic. In general for a deterministic system, if the initial state of a system were known exactly, then the future state of such a system could be predicted. However, there are many dynamical systems such as weather forecasting that are highly sensitive to initial conditions. This sensitivity referred to as the butterfly effect which suggests that small differences in initial conditions (for example, rounding errors caused by limiting the number of decimals in numerical computation), yield different results, rendering long-term prediction impossible, hence they are called chaotic systems. In short these systems are deterministic; their future behavior is fully determined by their initial conditions, with no random elements involved. But that does not make it predictable, this behavior is known as deterministic chaos or chaos.

It is difficult to determine if a physical system is random or chaotic, because in practice no time series consists of pure 'signal.' There will always be some form of corrupting noise, even if it is present as round-off or truncation error. Thus any real time series, even if mostly deterministic, will contain some randomness. Methods that distinguishes deterministic and stochastic (a process having infinite progression with random variables) processes rely on the fact that a deterministic system always evolves in the same way from a given starting point. Thus, given a time series to test for determinism, one can: Pick a test state; search the time series for a similar or 'nearby' state; and compare their respective time evolutions. Define the error as the difference between the time evolution of the 'test' state and the time evolution of the nearby state. A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error. Thus one can see that chaos is neither purely deterministic nor is it stochastic. Application of chaos into cosmology and quantum physical phenomenon illustrates that chaos theory is indeed an important feature of physical reality which requires further development of this field.

1. Does God Play Dice?: The New Mathematics of Chaos (Penguin Mathematics)

A brief summary of the book is as follows: Chaos physics along with classical and quantum physics are required to fully describe physical reality. Physical laws described by differential equations correspond to deterministic systems. In quantum physics, the Schrödinger equation which describes the continuous time evolution of a system's wave function is deterministic. However, the relationship between a system's wave function and the observable properties of the system is non-deterministic (quantum physical phenomenon). The systems studied in chaos theory are deterministic. In general for a deterministic system, if the initial state of a system were known exactly, then the future state of such a system could be predicted. However, there are many dynamical systems such as weather forecasting that are highly sensitive to initial conditions. This sensitivity referred to as the butterfly effect which suggests that small differences in initial conditions (for example, rounding errors caused by limiting the number of decimals in numerical computation), yield different results, rendering long-term prediction impossible, hence they are called chaotic systems. In short these systems are deterministic; their future behavior is fully determined by their initial conditions, with no random elements involved. But that does not make it predictable, this behavior is known as deterministic chaos or chaos.

It is difficult to determine if a physical system is random or chaotic, because in practice no time series consists of pure 'signal.' There will always be some form of corrupting noise, even if it is present as round-off or truncation error. Thus any real time series, even if mostly deterministic, will contain some randomness. Methods that distinguishes deterministic and stochastic (a process having infinite progression with random variables) processes rely on the fact that a deterministic system always evolves in the same way from a given starting point. Thus, given a time series to test for determinism, one can: Pick a test state; search the time series for a similar or 'nearby' state; and compare their respective time evolutions. Define the error as the difference between the time evolution of the 'test' state and the time evolution of the nearby state. A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error. Thus one can see that chaos is neither purely deterministic nor is it stochastic. Application of chaos into cosmology and quantum physical phenomenon illustrates that chaos theory is indeed an important feature of physical reality which requires further development of this field.

1. Does God Play Dice?: The New Mathematics of Chaos (Penguin Mathematics)

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ByDavid Everitton 29 May 2007

Chaos theory has become so embedded in popular culture that it is easy to overlook the remarkable impact it has had on our thinking.

The principal and now-familiar tenets state that small initial changes produce large end results and, at a point where things do not tend too much toward either order or disorder, they dance around in a state of 'chaos', following endless permutations within the limits of their boundaries, yet retaining a kind of fluid organisation which echoes many processes in the natural world, and enables some of them to be modelled.

Underpinning this are non-linear equations - seemingly simple (you can even try graphing the examples from the book in Excel) yet insoluble mathematical equations that, with the right input, generate an infinite and ever-changing series rather than a fixed result. Chaos theory also includes the fractal notion of self-similarity - that (for instance) the surface of a small broken rock resembles the face of a mountain, or zooming in on the Mandelbrot set again and again simply reveals endless permutations of similar patterns. Chaos explains how clouds or trees, although never identical, remain recognisable. It explores how dynamic systems, such as those seen in turbulence or the weather, are sustained.

James Gleick's book on the subject is an ideal starting point, combining a thorough overview with a great introduction to how this interdisciplinary branch of science came about.

The principal and now-familiar tenets state that small initial changes produce large end results and, at a point where things do not tend too much toward either order or disorder, they dance around in a state of 'chaos', following endless permutations within the limits of their boundaries, yet retaining a kind of fluid organisation which echoes many processes in the natural world, and enables some of them to be modelled.

Underpinning this are non-linear equations - seemingly simple (you can even try graphing the examples from the book in Excel) yet insoluble mathematical equations that, with the right input, generate an infinite and ever-changing series rather than a fixed result. Chaos theory also includes the fractal notion of self-similarity - that (for instance) the surface of a small broken rock resembles the face of a mountain, or zooming in on the Mandelbrot set again and again simply reveals endless permutations of similar patterns. Chaos explains how clouds or trees, although never identical, remain recognisable. It explores how dynamic systems, such as those seen in turbulence or the weather, are sustained.

James Gleick's book on the subject is an ideal starting point, combining a thorough overview with a great introduction to how this interdisciplinary branch of science came about.

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