High Anxieties: The Mathematics of Chaos

High Anxieties: The Mathematics of Chaos is a documentary film made by David Malone on the origins of chaos theory and its implications for our political and economic systems. It describes how advances in mathematics and physics have led to an understanding that we don’t live in a Newtonian ‘clockwork universe’ governed by simple rules of cause and effect. It concludes that there are practical limits to our individual and collective abilities to predict and control complex natural systems and man-made systems. Any observed instabilities and breakdowns of such systems may be inherent in the systems themselves and are not necessarily the result of an external shock. The programme was first broadcast by the BBC in 2008.

The programme provides a good introduction to chaos theory and to well-known concepts such as tipping points. It makes a number of good points particularly on economics. However, a few segments seem to push the concept of chaos too far. For example, it suggests that chaos was a major cause of our inability to plan the course of the First World War, and it somehow seeks to relate chaos to the development of nuclear weapons. Also, it ends with some conclusions about the inevitability of disastrous outcomes arising from man-made climate change, which I don’t think are warranted by the preceding arguments. The key point surely is that chaos theory suggests that phenomena such as climate change are unpredictable, and that the risks they represent should be taken seriously, but not that such phenomena will inevitably lead to disaster. Nevertheless, the programme is worth watching.

Watch High Anxieties, split into nine segments, below.

Segment
High Anxieties: Part 1 of 9
High Anxieties: Part 2 of 9
High Anxieties: Part 3 of 9
High Anxieties: Part 4 of 9
High Anxieties: Part 5 of 9
High Anxieties: Part 6 of 9
High Anxieties: Part 7 of 9
High Anxieties: Part 8 of 9
High Anxieties: Part 9 of 9

The programme mentions people such as Henri Poincaré, Aleksandr Lyapunov and Edward Lorenz. Interviewees include David Ruelle, Paul Ormerod, James Lovelock, June Barrow-Green, Peter Cox and Linda Gask.

Is the solar system stable?

In an introductory post, I wrote about Henri Poincaré’s attempts to model the behaviour of three bodies orbiting each other. He found that the mathematics of this problem showed that the behaviour of such a system was complex and could become unstable.

As the solar system is made up of a lot more than three bodies (one sun, eight planets, several moons, and many smaller bodies), the obvious question arising from Poincaré’s work is to ask whether the solar system is stable. Indeed, this question seems to have been one of the drivers of Poincaré’s work.

Ian Stewart has written a fascinating article which attempts to answer this question. The short answer is ‘probably not’. Luckily, the timescales involved are unlikely to worry us.

The article doesn’t require any prior knowledge of astronomy but it does use a few specialist terms such as Hohmann transfer orbits, Trojan points and Lagrange points.