Chaos: Making a New Science

When I walk along the streets on a fine day, I see clouds and trees and the boundaries formed by blue skies and mountains. And also, I see buildings. After I read this book, I enjoy walking even more. The images of man-made structures are composed of regular shapes like lines, rectangles, and circles. But the images of nature seem to be fundamentally different. The shapes of nature are irregular and far more diverse, and are also more beautiful. The waves at the sea shore and the sounds of seagull purify and heal my mind. What makes nature so special that man cannot imitate it perfectly? Chaos theory can give an answer for the question. It claims the following:When a complex system in nature evolves in time, it does according to universal rules.For examples, consider a jellyfish and the ink dropping in water. Although one is a living being and the other is not, about shapes, they are quite similar. The lightening paths and the shapes of some trees are also such examples. The universal rules have some features breaking the common sense.1. Simple and determined (in every detail) systems can behave in an extremely complicated way, apparently random and almost unpredictable.2. Different systems can behave in the same way, caring not at all for the details of a system's constituent atoms.3. Butterfly effect: small change in initial condition can give rise to qualitatively different results.Moreover, if we try to analyze the complex system using geometry, then we come to encounter fractal geometry, not ordinary Euclidean geometry in which main objects are lines, rectangles, and circles. Shapes in fractal geometry again resemble shapes in natural phenomenon like clouds, trees, sea shore, etc. Chaos theory is really charming.Chaos theory emerged around 1960s. The meteorologist Edward Lorentz is recognized as the father of this theory. He found the butterfly effect and investigated the problem of how far aperiodicity is responsible for unpredictability. The author, James Gleick, successfully teaches us what chaos theory is. As a journalist, he interviewed many original inventors of chaos theory. Beyond simply listing materials from chaos references and interviews with inventors, he wrote another great book about chaos. Almost half of the story is about mathematics. Reading the book, I felt ashamed when I found that he fully understand modern mathematics although he is not a professional mathematician.Now, I want to say about some bad points of the book. In several places, its explanation is vague. For example, the author explains the work of Barnsley through several pages. He does it with comparison to the game of throwing coins. But even though I could understand the analogy, I couldn't understand anything of the work of Barnsley. There are several places like that. I think it's because the author tried to contain as much contents as possible in an appropriate sized book. Another example of vagueness is about turbulence. Turbulence is regarded as one of the most difficult problems in physics before the chaos theory emerges. The effort to understand turbulence was one of the major impetuses that produced chaos theory. The book describes how chaos theory contributed to understand turbulence. But even though I finished the book, I couldn't understand in what concrete sense - by concreteness I mean clarity of explanation accessible to general audience - chaos theory were helpful.But the bad points are few compared with the merits of the book. It deals with almost all major inventors and historical events in the early history of chaos theory so that readers, after reading the book, may safely say they learned a lot about chaos theory. That's a good point. For example, the following were really new ideas to me:1. Chaotic aspects of a living organism can serve as self-defending system.2. Some sudden irregular movement of organism of eye muscles and sudden blockage of blood vessels possibly happen without any external reason, but with only its internal rule of movements.3. Mode locking phenomenon: I am not sure that this is also a chaos phenomenon. Some firefly congregates in trees during mating periods, thousands at one time, blinking in a fantastic harmony. A radio receiver to lock in on signals even when there are small fluctuations in their frequency. Moon always faces the earth.4. Renormalization theory: In particle physics, when we compute equations according to old quantum mechanics, many times we encounter infinity. In nature, every quantity must be finite. So this is absurd. Renormalization is a technique developed from 1940s to 1970s to avoid this problem. After reading the book, I come to know that renormalization is closely related to chaos theory.If you read the book, you will find great intellectual amazement. I can guarantee you that the amazement will exceed that of when you first learn relativity or quantum mechanics.

I was prepared to hate this book, and it sat on my Kindle for about a year before I finally read it. I am an Electrical Engineer, a group not normally enamored with mathematicians, since Engineering is, almost by definition, the avoidance of pure math.I ended up loving the book. Probably proof right there that Chaos exists.While the book is certainly "technical", it is well within the range of anyone who is not afraid of math and willing to spend a little time considering what it says. I ended up spending about a week or so reading the book, a long time for me, because it takes time to digest some of the material and understand what it is saying.A very good example is Gleick's discussion of a common mathematical formula x(next)=rx(1-x). This formula, where R is a constant governs many common phenomena, including biological populations. (r is a constant, and x represents a level of population from 0 to 1). Just looking at the equation, you would expect it to be fairly well behaved, probably some sort of exponential or sinusoidal looking function with a nice regular period to it. In fact, as Gleick suggests, if you spend a few minutes playing with the equation in a spreadsheet, you see that it is anything but a neat, orderly function. Depending on the starting conditions and the value of the constant (scaling function R) that you use, the graph takes on numerous random shapes.In other words, even for populations with can be modeled with a simple formula, the math predicts that there will be occasional booms and crashes INDEPENDENT of any external influences. To put it another way, bald eagle populations might crash every once in a while, seemingly at random, whether anyone invents DDT or not- just because of the chaotic nature of how the universe works. (I am not trying to defend DDT, just using it as an example).I found this to be a startling revelation. It certainly goes against my engineering mindset, where things work the way they do, first time, every time, and randomness is really caused by some error or external force you don't quite understand. Chaos theory proposes that randomness is inherent in nature, and even the most carefully controlled conditions may result in unexpected results.No doubt Gleick has just scratched the surface, and watered down the math to the point where an average person could have a glimpse of concepts that trained mathematicians spend their careers on. From that standpoint, the book is a success. I walked away with an understanding of what chaos really means, how it influences real-world events, and why those fractal images aren't just pretty pictures, but actually have real meaning.The only criticisms I have of the book are its attempt to relate chaos and the works of philosophers (Goethe) and artists. While I am sure there is a high-level connection to be made, I found the comparisons tedious. Also, because the book is a very limited overview, it can get a little jumpy and choppy. It is really more of a series of essays than a complete narrative. Finally, in some cases I found the mathematical simplifications overdone, and it took a while to realize what Gleick was talking about simply because it was so oversimplified.All that said, I enjoyed the book, learned something, and walked away with at least a slight understanding of what all the chaos fuss is about. If you are at all interested in how the world works, some of the ideas put forward will amaze you. And while chaos theory is very much about the math behind it, don't let is scare you off. If you understood the first chapter of your algebra book, you are well on your way.

It’s so addicting I read the book in a couple days. Maybe because I’m a science freak but this did the trick for me.

Some books inform, some entertain, and a few completely change the way you think. Chaos by James Gleick did that for me.I expected a dry science book, but instead, I found a fascinating exploration of hidden patterns in what seems like randomness—weather, markets, even human behavior. The butterfly effect and fractals blew my mind, making me see the world differently.I came across this book through an anthropology course I found online, and it completely reshaped how I think about culture and society—not as fixed structures, but as dynamic, ever-evolving systems. Even if you're not into science, this book is eye-opening, accessible, and full of "aha!" moments. Highly recommend!

Gleick has done excellent research into an interesting subject, though I gather that it's now considered dated, like me. There's no deep math and the concentration is more on researchers' progress paths. However, I didn't care for the organization of the first half of the book. Take Lorenz, depicted, possibly incorrectly, as the originator of Chaos Theory. Maybe half of his work on chaos is described at the beginning. Then, as later researchers from other backgrounds discovered him, new aspects of his work were revealed in great detail. By the time I'd finished absorbing these new items, I'd almost forgotten why the later researchers were interested.This book needn't have been so difficult to read. BTW, I'm not entirely an ignoramus. I have solid qualifications in Engineering, so how this book became a best-seller is beyond me.