A brief primer on chaos

Chaos, first steps.

Chaos theory is the generic name for the study of complex systems and how they work. Catastrophe theory is an earlier name for the same thing.

A simple system, like a light switch, has two attractors, one of which is called `on' and the other `off'. There is a shift in the state of the system across a break point that takes it from one state to another, and we can generally rely on that system remaining stable and functional.

- would you like me to turn you into a chaotic system?
Chaotic behaviour.

Yet a small shift in the system can render it chaotic; if we take a pendulum which has at one end `left' and the other `right' and set the pendulum going under regular motion we quickly find that, while sometimes it oscillates neatly between left and right, at other times it takes new paths.   Sometimes the path is elliptical, sometimes it is a figure of eight. Any attempt to actually predict the path that the pendulum will describe is completely arbitrary in that the behaviour of the pendulum, while determinate, is not predictable and any influence, no matter how subtle, could change the path; it has entered the realm of the chaotic.

Strange Attractors.

When a system becomes chaotic, the left and right nodes in our example are said to become `strange attractors', and the path of the pendulum comes and goes through the `basins of attraction', making `phase-shifts' as it passes from one basin to another. Each time the pendulum swings it begins an entirely new relationship with the strange attractors, taking its qualities of speed and direction into a fresh relationship with them.


One of the most surprising things about chaos is that systems are often `chaotic' even when they appear to be stable; the best example is water. A still lake is more chaotic than a river; in turbulence the level of predictability is higher than in systems that have yet to organise themselves in a flow.

Beyond the pendulum...

If the motion of a simple pendulum is impossible to predict, how about when the system we are examining is a weather pattern, the flow of water, or a political movement? The furthest we can go is say that that the system will develop sets of tendencies and these are largely based on our understanding of the mathematics of complexity, or number systems that exhibit chaotic tendencies, such as the mandelbrot set.

From Maths to Poststructuralism

While the Mandelbrot set  and similar mathematical sets are able to show the path of chaotic systems, these systems also exist in other forms. The work of Deleuze, for instance, contains a similar set of functional abstractions: Talking very loosely the strange attractors are abstract machines, the paths taken by something in a basin of attraction are rhyzomes and the areas of phase-shift are plateaus or planes of consistency. Stable and Chaotic systems are characterised as molar or molecular, the first being efforts of a system to act in a `zero' state of fascism and the second are systems which are `becoming' something else.

This rough mapping allows us to examine concepts and ideas in a similar way to physical systems, though it should always be remembered that, like a physical experiment,  it's not always possible to fix both the `speed' and `position' at the same time. And following this, the position of the subject within a network affects both the network and the subject, changing it's path in relationship to many things, moral, intellectual, actual and virtual, and vitally effects what we think `meaning' is...

The Mandelbrot set is our current image of chaos. It is an iterative formula that is computed with initial values. The change in these values create phase-shifts that are pictured on the computer screen in the familiar pattern; in the mandelbrot set the absolute values of 1 and 0 are attractors that the set of numbers generated tend to move towards, without ever reaching these values. Because each instance of the mandelbrot equation is a potentially infinite set, the computer image we see is a map of part of that set. The `zoom in' effect is a recalculation of the numbers within the area that we choose to re-examine.
Identity as a system of attractors...
Language, definition and circulatory meaning..
Phase shifts; the abstract machine...