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Chaos: too cool for it’s own good

September 17, 2012

The term “chaos” can mean very different things, depending on whether or not you are a mathematician. Personally, I dislike how it has become a highly misunderstood buzzword outside of mathematics. Is the term perhaps too cool for it’s own good?

It was famously used in mathematics in 1975 by Li and Yorke in their paper “Period Three Implies Chaos“. Since then, chaos theory has become a field that has attracted much attention. In fields outside of mathematics, it seems as though many people hope it is the magic answer behind the nasty randomness that afflicts the universe. Fortunately, at a recent conference on complexity in acute illness, I was delighted to hear John Doyle and Sven Zenker both criticize the chaos bandwagon. Sven Zenker even suggested that human physiology probably does not contain any true chaos. While he intended this to be a side point to his main talk, the audience jumped on it immediately, and he had to fight to get the talk back on track.

Ironically, the basic misunderstanding about chaos theory may be one of the main reasons why it is so fascinating. That misunderstanding is a belief that chaos is a form of randomness, when in fact chaos and randomness are fundamentally opposites! I have been impressed with how many people outside of pure mathematics are aware of the importance of sensitivity to initial conditions in defining a chaotic system. However, I don’t think people understand that sensitivity is not in itself such an amazing thing. It is actually quite easy to make a system that is sensitive to initial conditions by simply adding noise. The reason that sensitivity is important is that it is not easy to accomplish without the use of noise.

I think the irony of the misunderstanding extends even further. In many cases, it is relatively easy to explain to a layman the difference between the fundamentals of chaos and randomness. Yet many such laymen are empiricists who ultimately want to understand the systems they observe. To me, the irony lies in the fact that discerning between chaotic and random (or stochastic) systems seems to be significantly harder to explain. As discussed in Lacasa and Toral (2010), this may require attractor reconstruction and quantification of divergence rates.

In the end, I have mixed feelings about the term “chaos”. On one hand, I find chaos theory very fascinating and I’m glad that so many others do too. On the other hand, I don’t think those people are all interested in it for the same reasons I am. I wonder if the term is so misleading that it gives false hope to those who misunderstand it. I am particularly frightened by its frequent use in neuroscience where researchers still struggle to understand the role of noise. Hopefully chaos theory will not one day just be a joke to the rest of the world because they misunderstood it.

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3 Comments
  1. If you define sensitivity to initial conditions as the exponential decay of information then adding noise doesn’t make a system sensitive to initial conditions as it only degrades information by a power law. I presume the cardiac guys jumped on Sven over chaos in physiology. I would argue that low dimensional chaos probably is unimportant but high dimensional chaos could be. In some sense, a noisy high dimensional system like an idea gas is a high dimensional chaotic system. Correlations decay exponentially because of molecular chaos.

    • Thanks, Carson. I think low-dimensional chaos is actually of the most interest because it offers the possibility of short-term prediction. Skinner has an article titled “Low-dimensional chaos in biological systems”, Nature Biotechnology 12, 596 – 600 (1994), that deals with the concept: http://www.nature.com/nbt/journal/v12/n6/abs/nbt0694-596.html. Seems to me that the addition of noise to a model is usually a way of approximating what is actually high-dimensional chaos.

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