Yes - I figure joining the Batman-bandwagon might get more readers. And I know I suggested that this would be a substantive blog - not too much pop psyc. But after going to see the new Batman movie on Sunday night, it occurred to me that the film is essentially based upon the distinctions among chaos, order, and chance; which we would have needed to cover anyway as central topics to future blog entries. So I'm going to use these characters, their relationships with one another, and their roles within the plot of the film as examples of these three common dynamics. Before we get into the nonlinear dynamics themes in the film, however - "yes," the film was as good as they say, "yes" about Heath Ledger giving an incredible performance too, and "no" I won't give away any more than the typical movie critic in the posts that will follow. So you may read on without worrying about that. Anyone who knows the comic will know about the characters and what they represent: 1) The Joker = chaos, 2) The Batman = order; 3) Two Face = pure chance. There are many lines in the film which "spank your face" with these metaphors, and if the acting was not as good as it was, the joker's lines in particular could have easily been over the top in making the deeper, existential questions within the film appear too obvious and contrived for most moviegoers.

And a warning from the outset. This post turned out to be a lot longer than I had planned. So I've sliced it up into sections. So please be patient. It may take several weeks to dole them out. There is a lot of research folded into the supped-up movie review that will follow in the next few weeks. And beyond the differences among chaos, complexity, and chance, we are going to identify at least two different types of chaos, and how the interactions among these three general dynamics impacts resiliance, growth, and conflict resolution within us as individuals, in our immediate relationships, and also at broader levels of society. We will also be tackling questions of free will that Perez kindly and aptly introduced in his reply to our first, introductory post last week. It is going to be a pretty deep ride I think. By the time we get to the end, I believe that you will look back and be glad I didn't hit you with it all at once. Plus, this will give everyone time to go see the film once or twice (I am going back to see it again on I-Max myself) in the process. So let's start first with chaos.

The Joker: Chaos incarnate?

Okay - so what are the technical distinctions of these three aspects of nonlinear dynamics as they relate to psychology? "Chaos," as in "Chaos Theory" is not necessarily the same as the bad, destructive chaos portrayed by The Joker. In fact, the paradox of chaos theory is that chaos is not actually random, that chaos contains order, and that order contains chaos, in a Yin-Yang sort of manner. Chaos occurs when the behavior of a system is: a) determinist and b) bounded (meaning it conforms to an "attractor" for its behavior), and at the same time displays: c) non-repeating trajectories, and d) sensitive dependence on initial conditions (SDIC). The easiest example of a chaotic system is when you tie 3 pendulums together, end to end (technically three coupled periodic oscillators). If you hold the top pendulum's string and move your hand (to add energy), the bottom pendulum will potentially display chaotic movement. The movement will be completely a) deterministic (i.e., you could model it with three simple motion equations) and b) bounded (there is only so far the pendulum will swing), but c) the trajectories (direction and velocity) will never repeat exactly (although they come close, and so there is some beautiful patterning within chaos), and d) any small change in motion at an initial point in time will make big differences in predicting later positions. Another way of saying (d) is that predictability of the system decreases over longer time spans, such that the output of chaotic systems will often appear random, unless you look at a very long series of behaviors. This is one of the ways that researchers can distinguish chaos from randomness, by looking at how autocorrelation (i.e., momentum in a sense) drops off over time. In highly chaotic systems the drop off is fast, in low-level chaotic systems the drop off is slower, and in random processes the drop off is immediate.

Finally, all of this means that things are not chaotic or orderly. There is a range. A system may be a little bit chaotic, as in "low dimensional" chaos. Or it may be very chaotic, as in "high dimensional" chaos. And you can measure the degree of chaos in a system in a research context. Above, you can see the Lorenz attractor, which comes from Lorenz's weather forecasting models of the early 1960's. The funnest chaotic attractor to explore visually is probably the Mandelbrot set, a mathematical fractal generated by graphing the iterated outputs of a very simple equation involving real and imaginary numbers. When you iterate the equation (start with some intial value and then plug in the output as the next value over time) and then plot the solutions from different starting values as color codes, you get rich beautiful patterns that repeat at smaller and smaller scales (sorry if I'm off here, I'm not a mathematician). If you follow this link, you will see clearly the ‘fractal' nature of such chaotic attractors - that if you travel down into them you find infinite complexity that repeats, the parts of the attractor contain the whole. I would recommend you follow that link above. Or, if you want an animated trip into the Mandelbrot, just go to You Tube and search for Mandelbrot. I tried to link directly, but couldn't figure it out. It is very cool to go deeper into the set of solutions visually.

Yes - the ideas of: structural infinity arising out of simplicity, infinite detail, inherent unpredictability in deterministic systems, order and chaos being mixed together in yin-yang fashion, and so on are all very deep, and these ideas serve to draw in many different types of folks - from mathematicians to New Agers. So is this type of chaos bad? Does this type of chaos really match what we see in the motives of the Joker? How is this type of chaos distinct from the principled order of The Batman and the pure randomness of Two Face? What the heck does any of this have to do with psychology? And if Heath Ledger wins as best actor, will we all secretly wonder if his sad and untimely death had anything to do with it? These questions and more will be addressed in part two...stay tuned...