Networks, Complexity & Emergence

“[In the late 1000s, Taoists and Neo-Confucianists] taught that all was in flux but that everything structured itself according to inner principles that governed it. Now we’d call those laws. They said principle is one, but its manifestations are many. In other words, things in this world emerge from elements that structure themselves. The mind, they said, is not a vessel to be filled with facts or ideas. It too emerges. The mind is an emergent phenomenon.”

[Thanks Peter for this.]

Networks often (maybe always?) exhibit emergent behaviour. Emergence is another buzzword, but less flakey than memes. (It’s got a thousand year history for a start!). Anyway, I know I’ve said networks is the next sensible place to start examining for, but network science is very much a subset of complexity theory.

I don’t want to get dragged into Complexity Theory here – but if your interested Roger Lewin’s book Complexity: Life at the Edge of Chaos is a great read. Anyway, I thought, just to keep things clear in my own head, I’d reiterate the basic, basic idea behind complexity theory. And if I’m completely wrong please say …

1. First we had a clockwork universe. It was a) linear, and b) static. That’s to say, from a set of known inputs, a result could be predicted. Newton’s laws of motion etc.

2. Then we had chaotic universe. It was a) non-linear, and b) dynamic. It was non-linear in that it wasn’t easily predicted. A classic example of this is weather the butterfly effect. A butterfly flaps its wings on a beach in the Mediterranean, and as a result it pisses with rain for months in England. It was dynamic in that the universe comprised lots of little interacting things. And there are lots of non-linear dynamic systems in nature: economies, embryos, etc

3. Now we have a complex universe. It is still non-linear and dynamic, and retains a lot of the features of the chaotic universe. However, this time there is feedback into the system from the emerging results. So whereas in the chaotic universe, the butterfly is unaffected, in the complex universe the rain it causes makes a whole load of Englishmen take a holiday in the Mediterranean, where they affect the environment including (hopefully) the butterfly. Chaos theory is, I think, a subset of complexity theory – a unidirectional version of it if you like.

Now some of the things that seem to go hand in hand with complexity theory are:
– emergence: the order that emerges from the interaction of all the component parts of the system (e.g. an emergent property of the brain is consciousness, an emergent property of an embryo and the cells it contains is a mature individual etc)
– self-organisation: the way these systems seem to stabilise themselves.
– simplicity: the idea that apparently complex behaviour can be described by some very simple rules (e.g. Boids)
– transition: systems seem to be balance somewhere between “solid” and “gas”

That’s pretty much all I have to say for now, other than perhaps the Taoists were wrong. My mind may well not be an emergent phenomenon.