Complexity theory is a relatively new discipline, about 40 years old, that looks to model and understand the behaviour of complex systems. The systems themselves can be as diverse as the weather, crowd movements, epidemic spread or the brain. The experts talking about it on In Our Time were Ian Stewart (University of Warwick), Jeff Johnson (Open University) and Eve Mitleton-Kelly (London School of Economics).
One of the important first steps in understanding what complexity theory is about is to distinguish between a complicated system and a complex system. Mitleton-Kelly talked about this and said that a jet engine is a good example of a complicated system – it has many parts, but it is still something that can be designed and its behaviour can be predicted precisely. A complex system is something like the movement of a crowd through a building – again there are many parts (each person, the building itself) but whilst you can change things or design things in the building to influence the system the system as a whole is not designable. It is also unpredictable in a mechanistic sense, in particular complex systems are very sensitive to changes in the starting conditions and so a relatively minor difference can change the eventual outcome significantly. However complexity theory can be used to build models of the system that can predict the sorts of things that are likely to happen.
Complex systems are generally made up of a network of interacting units – people in a crowd, neurones in a brain, etc. These units may be (are always?) governed by straightforward and knowable rules. An example is that each person in a crowd is trying to get somewhere, and as a space opens up in the right direction they move into it. The complex system itself emerges from the interactions between the individual units (emergent behaviour is one of the key concepts of complexity theory). Crowd movements are apparently a solved problem and there are commercial packages that can be used to model crowds in different situations. Whilst there’s no way of predicting where any given individual is going to be at any given time, nor precisely how many people will be trying to go from any given A to B, you can model what the crowd as a whole will look like under different conditions.
Feedback and equilibrium are two important concepts in thinking about complex systems. Normally when we think about these concepts we are thinking about a system like a central heating system. When the thermostat detects the temperature has dropped, the heating switches on and so the temperature rises again until it’s in the desired range at which point the heating switches off. So that’s negative feedback acting to keep the system in equilibrium. But in a complex system there may be many equilibria, and feedback between the units is more likely to be positive and to reinforce the change from the equilibrium. An example of positive feedback between units in a network was given by Johnson (I think) – think of a rumour which starts with person A. Person A tells person B it’s definitely true (whatever it may be) even tho they’re not 100% sure, person B passes it on to person C (“guess what I heard?”) who passes it on to D & E and so on. Eventually someone repeats it back to person A, who then thinks to themselves “see, I was right” and doubles down on telling people about this “fact”.
Because of how feedback works in this sort of complex system, and because there are multiple stable points, it’s unlikely that once the system is perturbed from one equilibrium that it will return to that one. It’s particularly unlikely that an attempt (following a more mechanistic model) to generate negative feedback to return the system to equilibrium will work as intended. This has important implications for controlling the economy. Mitleton-Kelly also talked about work she’s involved with in Indonesia in helping the government attempt to stop deforestation – just passing a law saying “don’t do it” as a negative feedback mechanism is unlikely to have the right effect. Instead her work is on trying to model the complex system that arises from all the factors that affect who cuts down the forest where, and why. Then the Indonesian government should be able to try several strategies in the model and see what sort of effect they have and then pick something more effective.
Another example, that Bragg brought up, of a complex system that’s been perturbed from one equilibrium and is gradually (hopefully) settling into another was the Arab Spring. Which also illustrated something else – the idea that the system might be in equilibrium but also be ripe for a change. The way the world has evolved with it being easier to interact with each other via the internet meant that the situation in the Middle East & North African autocratic regimes was actually changing before it became apparent. Then the effects from a key event in Tunisia rippled through the network, and the system abruptly moved away from equilibrium. And it’s still shifting and trying to come to a new equilibrium.
This was fascinating as a look at a new and still rapidly evolving discipline. I did think Bragg came across as a bit out of his depth tho – amazing how rarely that happens to be honest. There was also a slightly odd mix on the panel, with two theoreticians (and mathematicians) and one more applied practitioner of the science. Sometimes Stewart and Johnson seemed to be having a different conversation to the one Mitleton-Kelly was having.