Tuesday, February 17, 2004

Chaos Theory and Boundaries of Society

People like lines. They prefer to see clean edges and smooth surfaces in the things they create. When compared to the myriad of shapes in nature, even baroque stylings are straightforward by comparison. The aesthetic value of lines appeals even beyond the physical. We draw boundaries on our world that try to be straight lines dividing right/wrong, true/false, good/evil, moral/immoral.

Chaos Theory has emerged in the past three decades in an attempt to describe the uncertainty of natural phenomena. The link is an excellent first primer for those whose only exposure to the field was nattering of Ian Malcolm, played by Jeff Goldblum, in the original Jurassic Park. Malcolm's pessimism about attempts to confine life do arise from Chaos Theory, but by necessity the basics had to be skimmed over for the purpose of feeding a lawyer to a T. Rex.

Perhaps the first realizations that lead to the development of Chaos Theory is that simple equations (rules if you will) can provide tremendously complex results when the equation is iterated, when the answer of the first application of the rule is then put back into the equation, then that answer is put back in, and so on. The Mandelbrot Set is the quintessential example. The linked article includes a description of the equation used to generate the image linked here. The black portions of the picture are points that belong to the set, while the rest are not. Things become interesting when one looks at the boundary of the set. The boundary is said to be infinite because the complexity of the curves and swirls never ends. This is a picture that was created by a simple mathematical procedure, yet the result is complex beyond all imagining.

I believe that we can take an analogy from this and apply it to our human experiences in society. Each of us makes decisions constantly about what is the best for ourselves practically every moment. Each moment, each scenario is different, much like the different points of the Mandelbrot Set. We then make a judgment of value and decide if each situation is good/bad for ourselves. When we come together in societies, we choose to accept common boundaries for that society, what the society considers to be part of the good set and that which is not. These decisions, when made by consensus or dictate, must happen beforehand, as there is no time to make a consensus when the situation arises.

However, these boundaries (rules and laws) must be of a simple form in order to be properly communicated. Simple communication implies a linear form. If one were to draw such a bright line along the boundary of our social Mandelbrot Set, one can not help but discover that there are many points are excluded that our moment-by-moment experiences would say belong in the set of "right" while other points are included by the law that should not be. A famous quote (by a Supreme Court Justice whose name escapes me for a moment) brings this dilemma into light: "I can't define pornography, but I'll know it when I see it."

When the line fails to include or exclude properly, we think of it as a miscarriage of justice. We try to keep track of precedents and exceptions and extenuating circumstances. The truth of human experience, however, is that the boundary between right and wrong is by extension of the mathematical analogy infinite. This is why I believe that individuals must remain empowered to decide for themselves what is right and what is wrong, and to have the power to grant reward or exact punishment, even if in the slightest amount. Government and law will always be too clumsy, no matter how well intentioned.

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