A few weeks ago, Mark Moritz asked the ResearchGate community how many components are required for a complex system to be truly complex. He argued that “Two components is not enough to make a system complex.“, but (he went on to ask): “would three or four components be enough for a system to become complex? What would be an example of such a system?”
In this post, I would like to challenge the assumption that a system cannot be complex if it only consists of two components. A complex system, as I understand the term, is defined as a system that displays complex behaviour. This may sound like a cyclical definition, and we don’t even have a shared definition of what complex behaviour is (but let us provisionally accept that it is something along the lines of dynamic, non-linear, unpredictable-but-not-quite, chaotic). However, it is an important point to make, because it underscores that complexity is all about the system’s behaviour, not its structure.
The number of components that make up a system are a red herring, really. A Swiss watch might have hundreds of cogs and wheels and springs, but it does not behave chaotically. In fact, it is the exact opposite of a complex system: its behaviour is (almost) entirely predicable, and we can tell with near absolute certainty where the watch’s hands will be even 100 years from now. Well, unless someone smashes the watch, maybe. Moreover, a complex system is -by definition- open, or ambiguously-bounded. It does not exist in a void: rather, it is enmeshed in an environment with multiple components ‘outside’ its boundaries, which interact with the ‘inside’. This seems to suggest that the number of components is not quite so important.
So then, is there an example of a complex system (i.e., a system that behaves chaotically) that consists of just two components? Of course there is: the double pendulum!
Image: Fractal flame | Credit: Wikipedia | CC BY-SA