The book explains the development of Non-Linear dynamics in different fields of science from a historical perspective. You might have heard of the Butterfly effect - a butterfly flapping its wings could cause a tornado at a distant place. It is a metaphorical example of what physicists call sensitive dependence on initial conditions. It means that with a slight variation in the initial condition, the system would behave completely in a different manner. This is more evident in the example of double pendulums. A double pendulum consists of 2 pendulums, where the tail of the second pendulum is attached to the bob of the first pendulum. Take 2 double pendulums. Start making them oscillate at the same time with nearly same initial angle. A difference of 0.5 degrees. You notice that both the double pendulums oscillate in sync till a certain period of time but later, they start behaving completely different. Just a difference of 0.5 degrees caused the large difference in behaviour in pendulums over time. Such systems fall under the category of non-linear systems.

A catchy alternate word for “non-linear” is chaos. The book does a wonderful job of exploring chaotic systems in different fields to a non-technical reader. But I think this book should also be read by people who know Non-Linear dynamics well. The superficial discussions might bore a technically equipped reader. But the story behind each discovery is worth knowing. The field of Chaos is relatively new(quantum mechanics and General Relativity are comparatively older). The book covers the resistance the pioneers of the field had to face. It requires courage and originality to work in a field that hasn’t been established yet and the path is uncertain. Stories of Lorenz, Feigenbaum, Robert Shaw, Mandelbrot and many other pioneers of Chaos are both interesting and inspiring for anyone who wants to understand the development of a new groundbreaking field in science.

One of the key reasons Chaos developed late was the advancement of computers. It is through computers, that we could visualise chaotic behaviour of different systems and study them. Leonard Mlodinow in his book Feynman’s Rainbow mentions that he didn’t like the computer approach of solving since it was like getting results from a black box and they would not provide any understanding. This is kind of true. When equations become too complex to solve analytically, we make assumptions to simplify the equations to solve them(assumptions like a particular term being small, making the equation linear for a small period of time). The assumptions will help you to understand the system to a certain extent. But you can’t get far with those assumptions. In such cases, computers are indispensable. As I read the book, I realised the key role computers had played in the development of the field. In fact, arguably the first paper on Chaos by Edward Lorenz was possible from the results of a computer.

A good motivation to learn about chaos would be its universality. Chaotic systems are ubiquitous. Turbulent flow of fluids, Neurons, Signals sent to heart, ecological systems, epidemics, financial markets, snowflakes, weather, so on and so on. It is interesting to learn what seems like completely different systems may have in common. A chaotist(non-linear dynamicist?) can use his/her methods to study almost any system by acquiring a bit of required domain knowledge.

So folks who appreciate non-linear dynamics, folks who are interested in knowing more in breadth and little depth about chaos, folks interested in learning historical developments of a new field in science. Pick up the book!

Chaos: The Science of the Butterfly Effect video by Veritasium can be considered as a trailer to the book

Watch more about Chaos

There are many good videos for different topics mentioned in the book. YouTube videos can be a good company as you read along the book. Like the one on Feigenbaum constant, one on Chaotic Waterwheel.

Post Scriptum

Reading development of different fields helps me discover some legends, whom I have not heard of and I feel should be more popular. Einstein, Feynman are household names. But there are other scientists whose story and life is inspiring and worth knowing.

Reading Black Hole Blues by Janna Levin helped me discover Rainer Weiss, a Noble laureate and a pioneer who worked on Gravitational wave detection. Here is a wholesome interview of the man. From the book Chaos, I found another such inspiring hero - Stephen Smale. A field’s medallist and a pioneer who helped the field of chaos grow. Smale bridged the gap between mathematicians and physicists in the field of Non-Linear dynamics. He also helped establish a campaign against the Vietnam war. Read Smale’s short biography here.