Pendulums provide a great metaphor for the behaviour of systems of all kinds.
A single pendulum behaves in a predictable way. Its movement is determined by gravity. A well-timed push can increase or decrease the amplitude of the movement by a predictable amount. The movement is predictable even when the pendulum’s starting position is 180 degrees from its resting position, and a second identically-designed pendulum behaves in the same way as the first.
In this respect, a single pendulum is a metaphor for the systemic behaviour of everything from the movement of the planets orbiting the sun to the movement of a bicycle. We tend to like such systems. We have conquered them through science and technology. We can predict their behaviour. We can control them. We can use them to shape the modern world and to improve our lives.
When two pendulums are connected to create a double pendulum, the behaviour of the resultant system changes dramatically. At low amplitudes, the behaviour of a double pendulum is different from that of a single pendulum but is still fairly predictable. A well-timed push can still control the movement of the system. However, as the amplitude of the double pendulum’s movement is increased, its behaviour becomes unstable and unpredictable. At this point, it becomes virtually impossible to control the system with a push. The complex behaviour of a double pendulum emerges because of the interaction between the two pendulums.
A double pendulum is a metaphor for the behaviour of systems where multiple causes can interact with each other to create an unpredictable effect. This includes natural systems as diverse as evolution, climate, weather and the movement of continental plates, and man-made systems such as economic systems, democratic systems, stock markets, and individual businesses and public-sector organisations. Our feelings toward such systems can range from awe to fear precisely because of their unpredictability. Our attempts to control and exploit such systems are always imperfect and sometimes inept, and, in some cases, we resort to semi-religious ideologies in our attempts to understand them.
The objective of this blog is to explore the behaviour of such complex systems and our successes and failures in mastering them.
Watch a simulation of a double pendulum below.
