Chaos: A Very Short Introduction

Very Short Introductions #159

by Leonard A. Smith

Chaos exists in systems all around us. Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.

Genres: Science, Nonfiction, Philosophy, Mathematics, Physics, Reference, Audiobook

180 pages, Paperback

First published January 1, 2007

Reviews

[Hassan · Rating 2 out of 5]

بإمكان رفرفة جناحي الفراشة إحدات إعصار في الجانب الاخر من الارض. هذا ما هو مشهور عن نظرية الفوضى المعروفة أيضا ب "مسمار في حدوة حصان" او "اجنحة النورس" او حتى "النموسة التي سحقها هومر سيمبسون". أو كما تعرف في الافلام وقصص الخيال العلمي بتأتير الفراشة. أي أن أفعالا نظنها تافهة قد تحدت نتائج عظيمة _أو كارتية_ في المستقبل. (فروق صغيرة في الحاضر قد تفضي الى فروق كبيرة في المستقبل). كما هو مبين في هذه الصورة بطريقة ساخرة:



ظننت ان هذا الكتاب سيكون كتاب فلسفي عن نظرية الفوضى التي شاهدنها كتير في الافلام والمسلسلات الامريكية. و ربما أيضا طريقة لتأكد من حقيقتها. نظرا لعدم وجود واقع ثاني لتجربة، والواقع الوحيد هو الواقع المعاش. ولكن.

ولكن الكتاب خيب كل توقعاتي فهو دراسة رياضية للمفهوم الفوضى ومحاولات العلماء لتحويلها لمعادلات رياضية تفسرها وتروضها. كترويض الظواهر الطبيعية وتوقهعا متل الاعاصير وحالات الطقس


الكتاب ليس بسيطا الفهم للجميع. على القارئ أن يمتلك على معرفة لابأس بها في الرياضيات، كالتمييز بين انواع الدوال وخصائصها وخصوصا الدوال الخطية والأوسية. ومعرفة المتثاليات العددية وأنواعها وطريقة حسابها ونهاياتها ومجال دراستها...

ورغم دلك يسيطر على الكتاب مزيج من الملل والغموض كل ما يمكنني القول ان الكتاب مخصص لأصحاب الخلفية العلمية وأصحاب التخصص.

الكتاب يصلح كمحاظرات على اليوتيوب اما على شكل كتاب فهو متعب جدا

[عماد العتيلي · Rating 1 out of 5]

‎‫‏‬‬‬‬‬‬‬‬

Before I read this book, I had a simple idea about Chaos and what it means. After reading it, I must confess that I didn’t gain much of information but I felt like I built a connection between me and Chaos!

I may sound crazy, but I really feel that I’m a part of that whole chaos! And I think we all are connected to it one way or another! You know, everything in this universe has a connection – however small – with Chaos. We all are the children of Chaos!



The book didn’t provide clear examples of that connection, but it hinted at the connection. It talked, shyly, about the connection between Chaos and other scientific theories (Evolution for example). In the heart of Evolution and Natural Selection, you find the effect of chaos, of simple and random changes, on the species!

You will find in everything a simple trace of Chaos. And that makes you wonder: What a beautiful world! Beautiful because it is hard to understand! Because it doesn’t make sense! Or makes sense, but in a senseless way!



BUT ... DON'T RELAX AND THINK THAT I LOVED THIS BOOK!

It is true it made me think about the connection I have with the universe, but also it BORED me to death!
BORING BORING BORING!

[Mark Abrams · Rating 5 out of 5]

I found this in an interesting, but difficult read. That is not to say it was not a very helpful introduction, but this is a very complex and potentially daunting subject. This 176 page read serves as a very good springboard to a whole lot more reading! Unfortunately, I can see myself doing a lot more studying in this area; but that's the fun of it! I must admit that I enjoy learning about math, science, and philosophy; and this has plenty of all those things! Pardon me, but my "geek" is showing! How embarrassing!

I would recommend this book to those who enjoy science or math, but beware, this can easily lead to much heavier reading. Consider yourself warned!

[Marc Lamot · Rating 1 out of 5]

I could have known: this booklet went way above my head. And that is mainly because the author almost exclusively focuses on the phenomenon of chaos in physical systems (weather, climate, warming water etc.). By consequence there’s a lot of mathematics and statistics involved. For my purpose (the chaos factor in the study of the history) there wasn’t anything useful in here.

[Muna Abboush · Rating 2 out of 5]

ممل وغير مفهوم في كثير من فصوله :/

[Aaron · Rating 3 out of 5]

I think I understood about half of this book. The middle part went mostly over my head, when it discussed the various models. I know the author was trying to avoid putting formulas into the book, but when you're talking math (and how can you explain chaos theory without talking math?) it's often easier to understand if you actually include the formula, rather than explain what the formula does in words.

In any event, I learned quite a bit from this book. The most important thing? That the word "chaos" does not mean the same thing to mathematicians as it does to everyone else.

[Ragheb · Rating 4 out of 5]

رغم أن الكتاب من سلسلة مقدمة قصيرة إلا أنه لا يصلح لغير المختصين، لكن من هم المختصين؟ الرياضيين والفيزيائيين والإحصائيين، لكن من يمتلك منهم القدرة على فهم فلسفة الفوضى، فهي مفهوم فلسفي قبل أن يكون رياضي ومن ثم فيزيائي، ولولا الرياضيين المتفلسفين لما خرج مفهوم الفوضى بهذا الشكل
يميز الكاتب كثيرا بين نظرة الرياضيين ونظرة الفيزيائيين لدرجة أنه يفرد الفصل الأخير للمصطلحات مع شرح المصطلح حسب مايراه كل من الفئتين
الكتاب لا يحوي معادلات وهذا ما جعله أكثر صعوبة للفهم (عكس ما كان الكاتب يقصد) لأن الامر اصبح يشبه كتابة المعادلات الرياضية بلا رموز كما كان يكتبها الخوارزمي

[Duong Dang · Rating 2 out of 5]

Unless you have a background in the field of mathematics or physics, you are NOT going to get much out of this book. Rather than explaining about chaos in terms that general population can understand and how it relates to things, the book focus heavily on exemplifying the different encounters of chaos in various fields of study without delving deeply into any of them, which makes the whole section rather pointless. In my opinion, the book doesn't do the job it was set to do, that is to introduce the concept of chaos.

[Mark · Rating 4 out of 5]

I really appreciated how it kept hammering away on the differences between models and reality; numbers in our mathematical models, the numbers we observe when taking measurements in the world, & the numbers inside a digital computer; and models, computer implementations of our models, and the real world.

[Daniel Wright · Rating 1 out of 5]

The author's reluctance to explain his subject without using any maths beyond primary-school level makes it more difficult to understand, not less. Strip away everything that is thus incomprehensible and we are left with a few vignettes about how weird the world is and nothing much else.

[Mohammad Aloush · Rating 2 out of 5]

أفسدت محاولة الكاتب تبسيط مبادئ النظرية لغير المختصين أي فائدة مرجوة من قراءته ، فلا هو بسط المفاهيم بشكل واضح ، ولا قدم ما هو جديد لمن لديه اطلاع على النظرية فاضحينا أمام كتاب شبيه بالكتب المدرسية رديئة المحتوى .

او كما يقال لا طال بلح الشام ولا عنب اليمن

[Megan · Rating 1 out of 5]

I understood about 5 pages of this book.

[عبد الله القصير · Rating 2 out of 5]

لم أستطع إنهاء الكتاب!!

[Keso Shengelia]

This is a really short introduction, but it can be shorter. For example something like this - Chaos is a Ladder :)

[غادة · Rating 3 out of 5]

"جميع الفرضيات صحيحة،
جميع النماذج خاطئة،
جميع البيانات غير دقيقة؛"
أُختصر كل شيء عن نظرية الفوضى في ثلاثة جمل

[Adi · Rating 4 out of 5]

We are connected to everything and everything is connected to us.

[Gijs Limonard · Rating 4 out of 5]

3,5 stars; 4 stars for educational intent, certainly picked up some basic terms in chaos theory, subtracted half a point for not getting the subject matter palatable enough for the general public; in particular the mid-section gets pretty technical which is sure to inadvertently put off swathes of interested lay readers.

[Mike_dangerous · Rating 4 out of 5]

This book gets 3 stars (good job!) plus an extra star for the difficult task. Chaos is a complicated and nuanced enough subject that writing a book for the layperson is a losing proposition. It is complicated and nuanced enough that I don't know jack about chaos even though I enjoyed mathematics and classical mechanics in my physics training -- it was covered in my 1980s training, but never in depth. When you model a system with mathematics (even something as simple as a double pendulum, two idealized pendulums attached end to end), you get equations which are nonlinear, deterministic, and very sensitive to initial conditions; thus you formally have chaos, and you can observe some wild trajectories in the system. When analyzing the simplest one dimensional mathematical maps or super complicated weather/climate systems in nature or computationally, there are many fundemental problems to keep in mind. What is the model? What are the uncertainties? How is the noise in the system characterized? Are there random elements? When you have many measurements with what would normally be called good statistics (enough data, sufficiently reliable data), what can the statistics tell you? It is a complicated mess, and the author demonstrates some discipline in staying calm and describing what's what.

[Ninvella · Rating 1 out of 5]

Abandonado 60%

Creo que voy a tener pesadillas con las iteraciones.

Este libro empezó bien, y supongo que mi experiencia leyéndolo ha sido una metáfora de lo que todos pensamos que ocurrió con las matemáticas cuando éramos estudiantes. Era fácil de entender hasta que empezaron a meterle letras y logaritmos y cosas varias.

El caso es que compré este libro porque creía que era de divulgación, y como todos los libros de divulgación, debería - debería- ser fácil de leer para personas que no entendamos del tema. (Obviamente, no voy a comprarme un libro de divulgación de economía, que para eso estoy estudiando la carrera). Lo que he encontrado aquí - para mi horror - ha sido un texto muy denso y muy fuera de mi alcance sobre la teoría del caos.

Creo que es un libro que podría interesar a matemáticos y personas que tengan cierta soltura en este tema, grupo que tristemente no me incluye.

[First Hope · Rating 5 out of 5]

A fantastic book, amazes me how ones single book can involve art, philosophy, literature and physics. Chaos is something we have very little knowledge about in real life. The book is hard to understand and once you read the book you may not understand a lot that's written but it gives you a sense of connection with the world and the deeper meaning of life, society and order.

[Amy Do · Rating 4 out of 5]

I much appreciate the quirky humour in some sections. There are definitely some parts that i don't fully understand, but the book did a great job of helping me imagine the complications of dealing with chaos in various models.

[Bashayer]

توقعته كتابًا يتناول نظرية الفوضى ومبدأ "أثر الفراشة" من منظور فلسفي، لكن الكتاب يطرح الفكرة بمفهومها العلمي رياضيًا/فيزيائًيا
قد يكون ممتعًا للمهتم، قرأت بضعة فصول فقط وتركت الباقي

[Alasdair Hunter · Rating 3 out of 5]

This book avoids repeating or summarising Gleick's "Chaos" and Stewart's "Does God Play Dice?", and introduces an interesting spin on the topic, at least in the early chapters. He introduces the "Burns' Effect" , named after the poem "To a Mouse", and has elsewhere some apposite and interesting quotations, for example from James Clerk Maxwell, shown to anticipate sensitive dependence on initial conditions. The choice of "The Cheat With The Ace of Diamonds" is an interesting illustration and leads to an interesting discussion of different scientific philosophies. Later on, the book attempts to discuss the philosophical and practical implications of the existence of chaos/nonlinear dynamical systems for science. However, I did not end the book with a sufficiently clear and detailed grasp of what the author thought these were. Except a sense that the problems include the difficulty of: model validation, parameter estimation, and interpretation of ensemble forecasts. The author avoids the use of equations, instead sometimes substituting wordy descriptions of the meanings of equations. This is ridiculous. None of the equations so described are beyond school level algebra - anyone interested in this topic is bound to understand the simple equations involved.

[Hank Hoeft · Rating 3 out of 5]

Chaos: A Very Short Introduction is an excellent primer on the concept of "chaos" in mathematics, statistics, physics, and computer science, and until I read this book, I did not realize the word "chaos" means something slightly different in all of those fields, and the meaning I carried in my head of what "chaos" is (basically, a synonym for randomness and unpredictability) matches none of those. Reading this slim volume has also forced me confront the limits of my own intelligence. I consider myself a fairly smart guy, someone in the upper percentages of the range of human intelligence, but the concepts in this book had me thinking to myself for large parts of it, "Huh?" I think even a very short introduction--even one as well-presented as this one is--requires a layman to go slow and digest it in small chunks. I checked this book out of the local college library, and I rushed my reading of it to finish it before it was due back. I think I would have understood more if I had slowed down. Maybe I can check it out again some time and chew on its contents more thoroughly.

[Rasmus Tillander · Rating 3 out of 5]

Vähän liikaa asiaa, vähän liikaa humanistille.

Kaaos on monella tapaa kiinnostava konsepti. Odotinkin kirjalta paljon aineksia filosofiseen pyörittelyyn. Kirjan lähestysmistapa oli kuitenkin matemaattis-tilastotieteellinen. Eikä siinä kysymykset tulevaisuuden ennustamisesta ja mallintamisesta ovat kieltämättä kiinnostavia. Kaaoksella tarkoitetaan tässä kontekstissa (epälineaarisessa) järjestelmässä vallitsevaa tilaa, jossa pienet muutokset alkutilassa tai välivaihessa saavat aikaan hyvin suuria muutoksia (mieti perhosefektiä). Matemaattisesta sillä tarkoitetaan järjestelmää, jonka Lyopunovin eksponentti on yli nolla. Tätä jälkimmäistä en ihan hahmottanut.

Kuitenkin suurin puute tässä lukukokemuksessa oli tällä kertaa lukijassa. Huolimatta siitä, että osa kirjasta meni aika ylin niin hahmotin kuitenkin ainakin jotain uusia asioita esimerkiksi tilastoista, sään ennustamisesta ja tietokoneista. Jälkimmäistä koskien olisi ollut kiinnostava myös lukea kaaoksen vaikutuksesta koneoppimiseen. Mutta siis jos haluaa jonkun kevyen johdatuksen kaaosteoriaan niin kannattaa varmasti katsoa muualle jos matematiikka ei ole oma leipälaji.

[عُلا Ula · Rating 3 out of 5]

- بعد طول صبر و مصابرة على هذا الكتاب الذي لا يتجاوز المئتي صفحة انتهيت و الحمد لله رب العالمين الذي بنعمته تتم الصالحات :D
- مجدداً أقول هذا الكتاب يتكلم عن الفوضى في النظم الرياضية و الديناميكية و مقدار اقتراب نماذج محاكاة الحاسب من الواقع و قياس الاختلاف بين هذه النماذج و النظم الطبيعية.
- أكثر ما قرأت عنه هو المفاهيم والمصطلحات التالية (النمو الأسي - اللاخطية -التفكير المنطقي - النظم الديناميكية - الخريطة اللوجستية - أساس ليابونوف -ديناميكيات عدم اليقين - الإحصائيات والفوضى -عدم اليقين -الحتمية والعشوائية).
- في البداية كان الحديث عن الفوضى في النظم الرياضية و كان مملاً للغاية و السبب أن الكاتب كان يضع شرحاً لمعادلات رياضية دون أن يقوم بوضع هذه المعادلات حتى، مما زاد الأمر سوءاً من وجهة نظري فالكاتب كالذي يتكلم عن صورة واضحة في مخيلته و يعتقد أن القارئ يرى هذه الصورة التي يراها هو.
- هناك مصطلحات فلسفية عن الفوضى معقدة.
- هو ليس بالكتاب الطويل أبداً و لكن يحتاج لفهم و بحث كثير حتى تصل الفكرة التي يريد إيصالها الكاتب.

[Tom Hastings]

Can a butterfly flapping its wings really create a storm halfway across the world? Chaos theory studies how tiny changes can have big impacts. Chaos VSI is a quick introduction to the field of chaos theory. Chaos theory is devilishly complex and encompasses a number of different areas of mathematics and science. It is a science with real world, real time applications and implications in, to name just of many, weather forecasting and astronomy. Thankfully Leonard Smith is able to get the math digestable and the jargon and scientific terminology to the bare minimum needed to explain chaos theory. At 180 pages this is one of the larger volumes in the series yet it must still omit some of the granular detail in order to give us the big picture. If you have an interest in either the real world applications or just the math and science involved this is an excellent book to begin exploring Chaos Theory.

[Silverprince · Rating 5 out of 5]

This book is punchy, humorous and insightful. I appreciate the writer was not afraid to go technical when it comes to terminology or descriptions; that means Mr Leonard here respects us readers to be able to appreciate and (I guess kinda) understand Chaos.

Some key takeaways:
1. Chaos is what looks to be random but is, in fact, periodic and predictable (just super hard to do it);
2. Real-world observations may be very different from the forecasting model's observations because of "noise" or measurement inadequacy; and
3. We must all be mathematicians, physicists and philosophers all at the same time to discover and uncover Truth of the real world or Laws of Nature.

I felt I understood about 60% of the book. If you come across difficult concepts, re-read and try to understand them if you are curious enough, but if not, carry on—it's not worth trying to master every concept. 5/5 because I don't think I'll find a better book to explain such a beautiful Math and Physics concept.

[Ahmed Omer · Rating 3 out of 5]

يشرح ليونارد سميث الفوضى والجذور الاولى للمفهوم وتطوره والمجالات الفوضوية الواسعة مثل الطقس والمناخ الى علم الفلك والاحياء و الفوضى بشكل عام تساعدنا على التوقع بفعالية اكبر في النظم اللاخطية ويناقش وضع اللايقين و يبين الاشتراطات الاساسية لاي نظام فوضوي رياضي وهي الحتمية والاعتماد الحساس والتكرار فمثلاً تجربة ليوناردو بيزانو عن توقع عدد زوج الارانب في سنة اعطى ما يسمى بارقام فابيوناتشي وهي تتكرر في الطبيعية بشكل ملحوظ في مخروط الصنوبر والاناناس وبنية عباد الشمس والتجربة ككل تشكل لبنة اساسية لبنية النظام الفوضوي واي خطا في الرصد الاولى مع النمو الاسي يولد خلل كبير, الكتاب يضع حدود بين العشوائية والحتمية ويتسائل عن وجود نظم ديناميكية فيزيائية عشوائية .. الكتاب صعب وعلى الرغم من ان الكاتب التزم بعدم ايراد المعادلات لكن الكتاب يحتاج خلفية واسعة في الرياضيات حتى تتمكن من اللحاق بافكار الكاتب ومناقشاته

[P.T. · Rating 2 out of 5]

This is what it’s come to: reading mathematics textbooks for fun.

I only understood about 20% of this. And I’m someone with a PhD in measurement psychology, so I know my way around the linear models that this book trash talks (probably rightly so). I can’t imagine the average person understanding more than 10%. That makes it a hard book to recommend to anyone who’s not a mathematician already familiar with chaos—yet it’s (mis)labelled as an “introduction.”

I still got something out of it, though. I couldn’t follow the specifics, but I got the general idea: even simple math leads to some really messed up patterns, which means science is screwed, philosophy is screwed, we’re all screwed. It’s an exercise in cosmic horror as much as it is a mathematics text.