Self Organisation

I think this is a very nice demonstration of the self-organisation of a complex system. An initial random state produces chaotic behaviour which via a process of feedback leads to the eventual synchronisation of all elements.

This behaviour is nothing new. The phenomena of pendulum clocks synchronizing is as old as, well, pendulum clocks. Mathematician, astronomer, philosopher and all round very clever fellow Christiaan Huygens (you have to be pretty important to have a spacecraft named after you) noticed that two of his pendulums clock that were mounted on the wall near to each other would gradually synchronise no matter how they were initially started.

This was something of a mystery which Huygens coined ‘odd sympathy’. Huygens thought that the synchronisation may be due to the (admittedly very small) forces that the pendulums were exerting on the wall and the beams that held the wall up. A few hundred years later, new research by scientists at the Georgia Institute of Technology published by the Royal Society confirmed this hunch. Their worked showed how the forces would have been sufficient to, over hours and days, progressively nudge each pendulum into synchronisation. In Huygens case the pendulums were in opposite phase – they swung away and then towards each other. But it was possible to get pendulums swinging in the same direction as well.

That’s the key to understanding the metronome video. Look carefully and you will see that the base they all stand on begins to move. The tiny forces produced by the metronomes’ motions produce an overall force on the base which is mounted so as to allow horizontal movement. Complete synchronisation is achieved in only a few minutes.

The cute thing about the metronome video is the sense of increasing order in the system. It starts in a completely disorganised, high entropy state and evolves into a organised, low entropy state. At the start, knowing where a single pendulum doesn’t tell us anything about where the others may be whereas by the end, looking at a single pendulum gives us a lot of information about the states of all the others. But doesn’t the second law of thermodynamics say that the entropy of a system should only ever increase (or its increase in entropy is extremely more likely, to give it its statistical interpretation)?

Why synchronising metronomes and pendulums do not contravene the second law or otherwise ‘breaks thermodynamics’ is similar to why the incredible increase in complexity we see in the biosphere over geological time is consistent with our understanding of the laws of nature. In the first instance, the Earth and its biosphere is not a closed system. It’s an open (well perhaps closed – if you don’t count meteorites), dissipative, non-equilibrium system. Perhaps just as important is that only looking at one part of the system or one particular behaviour (e.g. metronomes all swinging the same way) may lead us to forget to look at and think about all the other elements of the system and how energy is being transferred into, out of and within it (e.g. initial kinetic energy of metronomes being dissipated into heat via friction).

I will not speculate as to what the metronome video may tell us about the evolution of human societies and personal identity.

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