“There’s a fundamental presumption in physics that the way you understand the world is that you keep isolating its ingredients until you understand the stuff that you think is truly fundamental. Then you presume that the other things you don’t understand are details.”

This book is maybe the most popular one ever written about chaos science and nonlinear dynamics in general. Gleick kind of wrote a non-fiction novel that is very accurate even if non-technical. It’s even a better read than Hawking’s books because it has all the details to understand some concepts without the really lengthy, almost document-like history parts. It may be a personal preference of course, but I’m not that interested in scientists lives than their actual work.

I’m just presuming things of course, but it may be an effect of the online anonymity I’m used to, and the idea that paradigm shifts happen on their own, certain persons just accelerate the advancing tendencies, so in the terms of a historical scale they are not that relevant. You can see it in several places, and I don’t question the genius of great scientists but no work can exist without a strong background, there is no genius without context.

In general, nonlinear systems and chaos is like everything in physics besides the textbook examples. Turbulence, meteorology, population growth, market prices, but the famous example of Mandelbrot about the coast of Britain can show one how easy is it to find such phenomena in everyday things. The example is about scaling – you ask how long is the given coast, and give an answer in kilometers or miles. With a smaller scale you measure it again, like in inches or centimeters, so the coast seems bigger. Next you could move on and start measuring in nanometers, then so on until the very core of matter.

The problem shows that in nature a circle is not a circle, a coast is not a line, but most of the systems are turbulent, almost chaotic in the sense of physics. This is not the real problem yet even, as you can get quite close values by working with lines and circles, but some things are more sensitive to (their initial) values than others. Friction, weather, fluids… Extremely little changes can lead to entirely different results. This is why chaos is important.

When you talk about this subject, usually you can’t be really technical and careful wording is important. After all, fully understanding this matter takes years of mathematics and physics studies lots of people including myself, don’t have. Non-linearity in general is a concept that is well-defined, but without giving the certain area we use it in, there’s not much to say about it unless you state something like “functions that change in a way that don’t resemble to a line”. Little changes lead to big ones, they have ups and downs, often hills and mountains seemingly randomly, as the output of such a system is not directly proportional to the input.

Actually we meet such things a lot, because even the trigonometric functions or anything with an x on power is in fact, not linear. As these systems change in time, their corresponding differential equations require linearization or other tools so we can handle them.

The book starts with introducing us to Feigenbaum and Lorenz with their adventures in meteorology and modelling weather environment with computers. Gleick carefully avoids real details of the field, that is kind of understandable because of their complexity. He does not skip through important ideas or parts, though. Very early in the book we meet strange attractors and phase space, and they are difficult enough to fill a whole book with fully explaining them, but in elegant manner the author skips the little details to give us a picture of them we can grasp.

Although these systems seem unpredictable, an approach is finding strange attractors that are like small areas of regular behavior in the mentioned phase space. The phase space is not real space but an abstract map of a whole system. All possible states are represented, with each possible state of the system corresponding to one unique point in the phase space.

Through the stories of people we learn new concepts like fractals, turbulence and the state and frequency changes leading to such behavior, how population biologists use chaos theory as well, and such fields of science discovering the methods of chaos for themselves. Calling it chaos is misleading, the most important thing is that the methods Gleick writes about can predict numerous systems that were believed to be truly chaotic, like signal noise in cable transmissions.

Though being 300+ pages this book is an easy read, so really recommended in my opinion to anyone interested in a (new) field of physics. Yeah, well. It’s not new any more since decades, but still extremely fascinating.

Pictures:

http://mathworld.wolfram.com/LorenzAttractor.html

http://fractalfoundation.org/OFC/OFC-10-4.html