Mandelbrot Set

Chaos

James Gleick

Have you ever wondered why the weather forecast is almost always incorrect? Or why no two snowflakes look the same? These curiosities, as well as many others, are thanks to the relatively new, but incredibly fascinating science of chaos. This is the subject which both lends its name to and is explored in James Gleick’s ‘Chaos’. The book delves into the mysteries of disorder and tracks the emergence of chaos into the fashionable science it is today. Starting from the very beginning, Gleick tells the story of the few scientists from very different backgrounds who dared to challenge the classical ways and brought to light the order hidden in the disorder, in a book which has captivated me and left me wanting to find out much, much more.

‘Chaos’ starts at the very beginning, with the man who started it all in 1960, Edward Lorenz. Lorenz was a physicist turned meteorologist who was unsatisfied with the guesswork style of weather forecasting. So, he built himself a ‘toy weather’ system on his computer and let it run. Through what can only be described as a fortunate accident, Lorenz one day decided to start mid-way through the cycle and input the numbers straight from the print out. What he saw next began the whole new science of chaos. The weather pattern he got and the weather pattern he had expected, as it was what he got before, diverged massively. This incredible finding led to the first paper on chaos “deterministic non-periodic flow” and the first idea that chaos is due to “sensitive dependency on initial conditions”.

From there the book follows other scientists, from a range of field, as they discover a different piece of chaos in their own way. Smale, a physicist studying the strange behavior of basic pendulums, Yorke and May, finding chaos in animal populations by discovering period doubling and bifurcations in ecology, and the brilliant mathematician Benoit Mandelbrot who discovered fractals. The book also explores strange attractors, visual representations of numbers in phase space which never overlap and are part of a non-linear non-periodic dynamical (chaotic) system, and universality, order within disorder discovered by Feigenbaum, as period-doubling arrives at a constantly accelerating rate. Furthermore, Gleick explains the development of more tangible experimental results, for example the little box of helium exploring the onset of turbulence by Libchaber, the Mandelbrot picture set and chaos aiding in the fight against deadly fibrillations in the heart.

What I found interesting about ‘Chaos’, besides the subject itself, was how Gleick describes the process of discovery, and the theoretical and experimental work which goes into proving a hypothesis. The books format consists of anecdotes about different scientists, telling the tale of how they reached their result, from the accidental methods of Lorenz or Feigenbaum to the careful, thought-out experiments of Libchaber and the Santa Cruz ‘Dynamical Systems Collective’ group. I found this intriguing, to see the different methods of working from different scientists. I also enjoyed ‘Chaos’ as Gleick included many diagrams and graphs, which made visualizing the content easier, and hence helping me to understand it better.

However, what Gleick did not include was much mathematics. This is not unusual for a pop-culture science book, but I often found that Gleick stated “…[scientist] did some calculation and found…”. I would be interested to know more details about the calculations involved, because although they may be complicated, it would be good to understand how said scientist got from theory to result. For example, in the case of Feigenbaum’s universality, he finds the Feigenbaum constant, 4.6692…, which is the ratio of the rate of the acceleration of the period-doublings in a chaotic system. I would love to know how Feigenbaum got to this constant, as it is a revolutionary number.

Furthermore, ‘Chaos’ is rather old, being written in 1988. This is around the time that the subject of chaos really began to become more supported and more thoroughly researched. ‘Chaos’ only describes the begin of the tale – although it is an awe-inspiring tale – and since it was written there have been many more breakthroughs in the subject. I would love to read more about the more modern research and discoveries in the field, as I was entranced by the story up to 1980.

What I loved most about the field of chaos, was the way it was applicable to every science. Anyone who knows me knows I have a certain joy in finding places where different scientific concepts overlap – mechanical systems in the atmosphere, chemical analysis in stellar astronomy or cell biology in organic chemistry. Chaos is a science for all the sciences. It was first discovered in meteorology, then applied to simple mechanics, then ecology, fluid dynamics, economics, seismology, stellar physics, information theory, cardiology… the list goes on. This is why I found reading ‘Chaos’ so interesting; there was such a range of applications and so many problems which chaos theory helped to solve. To me, that is the best kind of science, the kind in which discovering something will help research across a range of fields.

Overall, ‘Chaos’ gives an interesting and informative introduction into the birth of chaos theory. The book is easy to read and well-written, and Gleick’s enthusiasm for the subject is clear through the text. Chaos itself is a wonderful and fascinating new science with a bright future ahead of it, being applied to all kinds of problems in all kinds of fields. I am left having read ‘Chaos’ with a better understanding of the science of the unpredictable and an even bigger desire to find out more about it.


Mandelbrot Set