The "highly entertaining" New York Times bestseller, which explains chaos theory and the butterfly effect, from the author of The Information (Chicago Tribune). For centuries, scientific thought was focused on bringing order to the natural world. But even as relativity and quantum mechanics undermined that rigid certainty in the first half of the twentieth century, the scientific community clung to the idea that any system, no matter how complex, could be reduced to a simple pattern. In the 1960s, a small group of radical thinkers began to take that notion apart, placing new importance on the tiny experimental irregularities that scientists had long learned to ignore. Miniscule differences in data, they said, would eventually produce massive ones--and complex systems like the weather, economics, and human behavior suddenly became clearer and more beautiful than they had ever been before. In this seminal work of scientific writing, James Gleick lays out a cutting edge field of science with enough grace and precision that any reader will be able to grasp the science behind the beautiful complexity of the world around us. With more than a million copies sold, Chaos is "a groundbreaking book about what seems to be the future of physics" by a writer who has been a finalist for both the Pulitzer Prize and the National Book Award, the author of Time Travel: A History and Genius: The Life and Science of Richard Feynman (Publishers Weekly).
Few writers write clearly and concisely about science and Mathematics. James Gleick, a former science writer for the New York Times, writes about the first years of the study of chaos.
Focusing on scientists rather than science, Gleick explains the thought processes and investigative techniques researchers applied to chaos problems. Rather than attempt to explain Julia sets, Lorenz attractors, and the Mandelbrot Set with complicated equations, Chaos employs sketches, photographs, and descriptive prose.
There are not many writers who have the ability to write on two planes. One is understandable by the general public. The other is appreciated by experts who grasp the subject matter and appreciate the author’s depth of understanding. I am not one of the latter. While reading the book, I found myself long for math that would connect the prose to the science.
Nevertheless, this book is a history of a new science. Limited as it is, it inspired me to further study. It is probably asking too much to expect more from a book about science’s frontiers.
Gleick sometimes strays a bit from his topic, as when he briefly talks about Darwinian thinking in biology. He writes, "In biology, however, Darwin firmly established teleology as the central mode of thinking about cause. [...] Natural selection operates not on genes or embryos, but on the final product. [...] Final cause survives in science wherever Darwinian thinking has become habitual." (se p. 201 in the original hardback edition) I don't know where he got his information, but he got it wrong. Darwinian evolution through natural selection is not teleological. In What Evolution Is, Ernst Mayr writes, "... those who adopt teleological thinking will argue that progress is due to a built-in drive or striving toward perfection. Darwin rejected such a causation and so do modern Darwinians ..." In Darwin's Dangerous Idea, Daniel Dennett writes, "The theory of natural selection shows how ever feature of the natural world can be the product of a blind, unforesightful, nonteleological, ultimately mechanical process of differential reproduction over long periods of time." The nonteleological nature of Darwinian evolution is one of the principle themes of Dennett's book.
Chaos is a long book about somewhat difficult ideas, mostly of a mathematical nature, but the mathematics is largely suppressed. One important point that I think he makes very clear is that very simple equations when iterated in real space can exhibit surprising behavior.
The topics of this book are mostly outside my areas of even limited expertise, but I was wondering as I read it how many of the phenomena it describes depend on the use of real numbers, i.e., numbers that in general require infinite precision, e.g. π. If physical theories were to be developed on the basis of discrete mathematics, would some of these problems of chaos disappear? Consider the very first topic in the book: the sensitivity of weather models to initial conditions. With limited precision measuring instruments there are infinitely many states of the weather, if described by real numbers, that cannot be distinguished. So, if small differences, below the precision of measurement, can make a big difference as the weather develops, we have a problem that limits predictability. But, if the physics of weather were described by a mathematics with finite precision, then we might be able to make completely accurate measurements of initial conditions—in principle.
I found Chaos interesting to read, but I am always skeptical about reading explanations of science written by journalists, just as I am skeptical of explanations of science written by philosophers.
The truth is that the focus of Gleick's book is not so much chaos itself as it is the people who first explored chaos theory and eventually managed to make it respectable and bring it into the mainstream. As the book's subtitle hints, Gleick is concerned mainly with how a 'new science' is 'made', not necessarily with the actual science or math involved. This was not quite what I was expecting from "Chaos", but it is actually an advantage for the book, since its age becomes somewhat irrelevant: although chaos theory itself has been growing and evolving dramatically in recent decades, "Chaos" deals only with its roots in the '60s, '70s and early '80s. On the other hand, I was hoping for more discussion of the science itself, rather than the personalities involved in its early development.
I was also not that taken with the style of Gleick's writing. His narrative tends to jump around rapidly, often spending only a few pages on some person or event before moving on to another, commonly with little in the way of connection or logical transition. This is fine for short articles in newspapers and magazines, but it doesn't work so well in a 300+ page book. The vast cast of characters (meteorologists, physicists, mathematicians, computer scientists, biologists, ecologists and many others) spins in and out of view, and it can be very difficult to get more than a general impression how the little pieces all fit together in the big picture.
However, even though I'm complaining about the content and presentation, I'm still giving "Chaos" four stars. This is because "Chaos" managed to get me interested in and excited about nonlinear dynamics. Gleick was able to convey the sense of wonder and excitement that comes from looking at nature in a new way, through the lens of nonlinearity. He successfully presented the making of this new science as the greatest and most exciting scientific revolution since the development of quantum mechanics - with the difference that chaos is more accessible, more understandable, and applicable in a far wider range of fields.
In short, "Chaos" still achieves its goal 18 years after it was written. It gets the reader (this reader, at least) interested in and excited about nonlinear dynamics and eager to explore the topic in greater depth. Reading Gleick's book inspired me to pick up a copy of Robert Hilborn's "Chaos and Nonlinear Dynamics" from the library and take a more serious look at the science itself. "Chaos" should make a good read for anyone who knows little or nothing about chaos or nonlinear dynamics but is curious about the topic and interested in learning a bit about its early development.
My question, is in which ways can a marketing plan, which hinges on a pre-set aims of say competitive analysis be so far different that its results lead some companies to ruin, and others successful beyond their orginal projections.
The failure to mention Hilbert's "Entscheidungs", posed as building blocks of mathematics, is nothing more than a personal disappointment.. I am also keening over the failure to limn the shadowing "strange loops" of Hofstadter and the ramble Bertrand Russell made of Godel, but that probably just dates me. Highest marks for taking on Nature and our Understandings of It, with sympathy, clarity and grace. Filled with snappy, even snarky biographical material. Science, made plummy.
One of the compelling features of the chaos story is that this scientific breakthrough wasn't a physics, mathematics, chemistry, astronomy, or biology breakthrough; it was all of them. A mathematician turned meteorologist, Edward Lorenz, builds a "toy weather" on what's still a fairly early computer in the early 1960s, and in working with the parameters, concludes that long-term weather forecasting is doomed--a simple deterministic system is producing unpredictable results. Mitchell Feigenbaum, a theoretical physicist at Los Alamos in the early seventies, and two other scientists working together independently of him, are working on the problem of turbulence and.discover that it doesn't, as anticipated, build up gradually in an orderly manner. Reach the tipping point, and there it is.
Beloit Mandelbrot, an IBM mathematician working with an equation that produces fractals, arrives to give a presentation to an economics class and finds "his" equation already on the board; the patterns he's found in pure path also apply in economics, the reproductive rates and numbers of animal populations, and countless other places.
In each field, also, the initial work was most often either resisted or ignored. Precisely because chaos was popping up all over, with just a few people in each of many different scientific fields, it was easy for scientists in any field to notice a paper or presentation, note the fact that is was completely different from the methods, logic, math that had relevance for their own work, that much of the work was in fact being done in other fields--and dismiss it. For new doctoral students, there were no mentors in chaos theory, no jobs, no journals devoted to chaos theory. It completely upended ideas about how the natural world worked. It was heady, exciting--and much harder to explain than to demonstrate. Much of what the first generation of chaos scientists did is incredibly easy to demonstrate with a laptop computer today--but most of these chaos pioneers were working with handheld calculators, mainframe computers with dump terminals and limited and unreliable access for something so peripheral to the institution's perceived mission, computers whose only output device was a plotter.
Gleick very effectively conveys the science, the excitement the early scientists working on it felt, and the challenges that faced them.