Chaos

Summary

Chaos: Making a New Science is a non-fiction book by James Gleick that introduced the principles and early development of chaos theory to the public. In it he details the history of chaos theory, and gives a brief overview of the main concepts in the field and how non-linear dynamics play a role in the world around us.

The main idea is that the world has non-linear elements in it. This means that there are systems where small changes can have large, outsized effects, in a way that is mathematically proven to be intractable. You can't predict the weather, the stock market, or the behavior of a flock of birds, because these systems are chaotic. Furthermore, systems in principle don't have to be very complicated to exhibit chaotic behavior. As long as systems have feedback loops, they can be chaotic, one of the simplest sets of equations that we know of are the logistic map, or the Lorenz attractor. It's like 3 equations that are super simple on paper, yet they exhibit chaotic behavior.

The beauty of chaotic systems is in this fact: that they can be deterministic, yet unpredictable. That means you can know everything about the system, have all the equations and in theory should know how the system works, but in applying the equations to a certain set of input conditions, you can't predict the output anymore, anyways. This is because the system is too sensitive to initial conditions, and small changes in the input can lead to large changes in the output. Many fractals belong into this category.

The sensitivity to initial conditions is the famous "butterfly effect", where the idea is that a small change in initial conditions, like a butterfly flapping its wings in Brazil can be enough of a difference in the initial conditions to "cause" or not cause a tornado in Texas. The undeterminability of the future of chaotic systems makes them highly interesting to study, because they are so ubiquitous in the real world. All of fluid dynamics, weather, and even the stock market are chaotic systems, and this book is a great introduction to this field of chaos theory.

On the same topic there is the book Complexity by Walter Mitchell, which is a great follow-up to Chaos by James Gleick and dives more into the work of the Santa Fe institute, trying to make sense of non-linear dynamics and chaos theory in the real world. Because there is a sweet spot between total chaos and rigid order, where complex, dynamic systems (such as life) exist. And interestingly enough, vastly different systems can be described by the same underlying principles. There is a universality to chaos theory that is almost spooky. The Weather, the economy, the stock market, flocks of birds, population dynamics, fractals, how heat is distributed in a material, turbulence... they can all be described by the same ideas. This also challenges our notions of reductionism and free will. Two more books that intersect with this topic and it's implications on our brains are Determined by Robert Sapolsky and Gödel, Escher, Bach by Douglas Hofstaedter.

Another great book by James Gleick is The Information. It deals with the history and implications of information theory, and how it has shaped the world we live in, from the telegraph to the internet.