## Thursday, March 15, 2007

### Complexity for Regular Folks, Part 2

Well, i had this post half written, lost my connection to the internet and lost the whole thing. So, this is the second necessarily shorter version... And i am not an expert in any way, so if you have additions or corrections to this, please send 'em along.

Atractors and scalar invariance.

Attractors are the simple rules that determine the direction of a system, its stability, its general trend. There are three groups of attractors: single point, periodic, and strange.

Single point attractors pull the energy of a system to one point or goal. A magnet is one good example of a single point attractor. If you sprinkle iron filings or some pins on a peice of paper and then put a magnet underneath it, the filings and the pins will be drawn towards a single point--the magnet. Another example, from palaeontology (for my kids): Many of us have seen films of palaeontologists working to remove massive chunks of stone--everyone on the dig site is drawn towards the work, lends shoulders and hands to move the boulder. All of their energy is directed towards a single goal--removing the rock. Systems governed by single point attractors tend to produce heroic model management.

Periodic attractors oscillate between two points. We have many experiences of periodic attractors, seasonality in employment, rush hour, and the most common--breathing.
We can cope with and benefit from systems governed by periodic attractors. We can get clarity from goals based on our knowledge of the oscillation. And we can recruit and train heroic model leaders with skills in anticipating and navigating the fluctuations.

Strange attractors were first described in the 1960's by Edward Lorenz (Lorenz attractor and graph) as he puzzled out the mysteries of the weather. While local weather patterns seemed completely unpredictable, when Lorenz modelled more global weather data on a computer, an interesting regularity appeared. The equations consistenty produced graphs in the shape of butterfly wings. At a larger scale, there were obviously rules at play that produced a predictable pattern. What those rules were, however, was difficult to tell, hence the name strange.

Complex systems are shaped by strange attractors that can be governed by a few simple rules. For example the movement of flocking birds is governed by three simple rules: stay equidistant from your neighbour and other objects, maintain the same speed as your neighbour, head toward the centre of the group. These simple rules allow a flock of birds (or fish or bees) to be 50 times more sensitive to changes in their environment than any one individual. (So complex systems are not well suited to the heroic leadership model. They are governed by interdependence, and so need a more interdependent style of leadership.)

So, to recap, strange attractors affect the flow of energy in complex systems. Strange attractors are comprised of a number of simple rules that interact with one another to produce the visible results we can observe. Discerning what these rules are is supported by certain attitudes and behaviours that Westley et al delineate--and that i will chat about in another post (hopefully also drawing some links to Spiral Dynamics).

So what is scalar invariance? Scalar means scale, or size. Invariance means not variable, unchanging. So put together, scalar invariance means that complex systems tend to act the same whether you are looking at only a few individuals (the micro level) or a mass (the macro level). You can extrapolate the simple rules governing the attractors of large systems by looking at the parts of those systems. In very simple terms, you can see the whole in the parts. As Blake would say, "the world in a grain of sand."

Both of these characteristics of complex systems are important to those wanting to effect social change. Identifying the strange attractors, and then looking under the surface to find the rules governing the attractors will have more leverage than attacking the surface characteristics. And scalar invariance means that local knowledge and expertise can effect change with global impact. And that small-scale efforts and experiments

Which leads us to one last concept from chaos science: complex systems are highly dependent on initial conditions. I am linking this to concepts from Aikido. In Aikido we have a very simple math. All systems have an energy of 10. If someone is attacking you with a force of 7, you only need to respond with a force of 3 to complete the system. In dealing with complex systems, the attractors hold a lot of the energy of the system, so a small input of energy at the right place and time can have significant results on the outcome.

There is good news here for those of us looking for ways to influence change. No guarantees, but lots of possibilities.

There is a lovely little animated game using attractors that you can play over at thecleverest.
Strange Attractor equations and graphs.
Formal definition of attractor.
Interesting discussion with illustrations of the four attractors of chaos science with speculative parallels to consciousness.
Some very cool 3-D images of attractors and other fractals.
Good next step for those wanting more information on attractors and complexity theory: Attractors Everywhere.

Next: a few more additions to our growing list of skills and attitudes for thriving in complexity.