Unraveling Complexity - Chaos by James Gleick

Winding down to the end of my pappapermisjon* while tending to this little source of entropy, I’m also flipping through the final pages of Chaos by James Gleick.

The extent of my knowledge of the subject was limited to the butterfly effect, snowflakes and fractals (although I never really understood what they had to do with chaos). So, I thought I’d expand my mind and try to learn something new before going back to work. Call it the frequency illusion** or just plain spooky, but ever since I began reading the book, I’ve been seeing it everywhere. Netflix even released "3 Body Problem" last week, named after a popular book by Liu Cixin, but referring to the difficulty of predicting the motion of a system of more than two bodies for all times in the future, because of complex ways in which the forces between them interact (generally known as the "n-body problem").

Think of the word chaos and what readily springs to mind is the idea of disorder: no rules or discernible patterns, only randomness, and tending further and further away from any semblance of order. Such a system offers no way to tame it or to learn anything about it. And therefore, that way of thinking is uninstructive, even if mystical and serves up good lines in movies. Instead, the science of chaos is about finding the order in chaos, and the sources or causes of chaos.

We have a deep-seated craving to be able to explain everything that we witness. We want to understand the motion of the Sun, the planets and the stars across the skies, the patterns of the weather, the causes of pathologies, the global and local economies, and much else. So, we seek to learn as much as we can about them. The most popular way to do this has been (and continues to be) to reduce these systems to their most basic parts, understand those parts, and thereby try to deduce the properties of the whole***. Which is why we break matter down to atoms and subatomic particles, and living things to cells and chromosomes. On top of that, we like to pretend that geometries are straight lines and neat curves, that bodies move along them in perfect trajectories and cycles as instructed by classical rules, that systems tend to stable equilibrium, and that, given initial conditions, we can predict any future state.

Even in the domain of Data Science where I work, we start with the assumption that there is a pattern underlying data, hidden away for us to find, and it is undesirable to have outliers and noise, and you try really hard to get rid of them. If something breaks pattern, it is ignored as a low-probability outcome or an error in measurement, and you hope to high heaven that it does not recur.

The truth is anything but. Things don’t neatly add all the way up to the everyday phenomena we observe around us. A swinging pendulum never quite returns to a state it has been in before. Weather systems don’t obey simple additive laws. As the book concludes, simple systems give rise to complexity and complex systems obey simple rules. Classical models, while useful, and functional under tightly defined conditions, break down at the boundaries.

The most fundamental shift from the previous era was to start looking at these systems as dynamic, as flowing through space and time, always changing and evolving, and when similar, never quite the same. It is possible to model them to a great degree of fidelity by mathematical equations° that run recursively on themselves, thus rendering them almost predictable and demonstrating that even in the disorder, there are patterns.

No discussion of chaos theory is complete without the mention of Fractals. Fractals are hugely popular for their aesthetic appeal as for their utility in modelling physical structures°°. When you plot the Mandelbrot set°°°, you discover a shape that is self-similar across scales, never ending and mesmerizing.

To cut a long story short, if you are intrigued by this, you should give this book a try. The birth and development of nonlinear dynamics was the result of people who weren’t satisfied with perfect solutions to an imperfect world, and this book is a chronicle of the same, starting from its earliest days and its pioneers. It is very light on the technical details, but the author, not a “chaotician” by profession, demonstrates deep understanding of the concepts and intuitions of the various phenomena he details, the tools and techniques used in their analysis, together with the stories of the physicists and mathematicians and their lives in true journalistic style, making it a refreshing and informative read. The only thing I have against the book is that it is too long and repetitive for its own good. Overall, a good layperson introduction; if I ever find myself in a nerd bar and the discussion veers towards phase maps and strange attractors, I can at least nod in recognition.

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P.S. No LLMs were harmed in the making of this post (except for the title of the article), but an image generator, LinkedIn's Designer (Preview), to create the cover photo of this post.

Footnotes

* Norwegian for paternity leave

** See “Baader-Meinhof phenomenon ”.

*** Reductionism

° Difference or quadratic, for example

°° The Eiffel tower ?!

°°° Set of all numbers c in the complex plane obtained by running the equation:

on itself again and again on the condition that the absolute value does not diverge to infinity.