Complexity is the natural state of the world. It is what gives life flavour, unpredictability and excitement. Complexity may be considered as the amount of chaos in a system or as a measure of interconnectedness.
An understanding of the habits of complexity in general can help us understand systems that are cannot be studied causally because they're too fuckin' complex. This is good news for those of us who've decided to find the secret of the universe, because the universe happens to be rather on the complex side. Complexity theory is all the rage these days, and has been applied, with varying degrees of success, to economics, neurology, physiology, military strategy, computers and meteorology.
In complex systems, every event sparks off a chain of results. Tinkering with one element leads to changes all over the system. These results in turn cause other events and there is a constant, dynamic, flowery flowetry of cause and effect.
Non-proportionality of results
An incredibly important concept is the concept of "sensitive dependence on variables". It is closely tied to chaos theory and is the nature of complexity. It is mathematically analogous to ill conditioned functions and matrices. These are ones where a small change in one number brings a large change in the overall system. This is a very good definition of the world's workings, a small change in one little thing eventually affects everything.
This is the nature of interconnectedness: an atom's momentary shift to the left could bring the downfall of a building, the downfall of an empire! This old rhyme here shows the idea, how small consequences escalate and escalate:
For the want of a nail, the shoe was lost For the want of a shoe, the horse was lost For the want of a horse, the rider was lost For the want of a rider, the message was lost
For the want of a rider, the message was lost For the want of a message, the battle was lost For the want of a battle, the war was lost For the want of a war, the kingdom was lost
And all for the want of a horseshoe nail.
Even taking away the catastrophic vision there, it is not only mistakes which compound. Every single action has consequences which themselves carry knock-on consequences into the future - the entire future is determined by every single action taking place.
Take, for example, eating a cracker at night time. Innocent enough, what could it possibly do to the future, right? Wrong! The cracker could be the straw that breaks the camel's back on a cavity, it could mean that the next night you feel like eating another and suddenly you have a huge cracker habit and need an intervention, it could mean that someone else in the house doesn't have enough crackers and needs to buy more, it could lure rats to your house due to crumbs... Wild possibilities abound, yes, but each action does have its long term consequences which propagate on and on into the future. They will often snowball in hard-to-see ways.
This complexity, the dependence of the current moment on every single action which has preceded it, can lend itself to magical theories and magical spells - in themselves a particular action, such as not crossing a black cat's path, does not have any meaning. But viewing it in the framework of every single action being important not just in itself but for the future, not crossing the path could have given you the attention necessary to not walk out in front of a car - a very good benefit indeed.
- The Complexity and Artificial Life Research Concept for Self-Organizing Systems. An excellent site about complexity theory.
- The Hypertextbook of Chaos