Crossing a Mental Divide

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A traveler crossing the Rocky Mountains passes the Continental Divide. If they straddle this imaginary line they have an enormous, yet unseen power. Water poured on to the ground on one side will ultimately flow into the Pacific. Water poured inches away will flow into the Gulf of Mexico. This seemingly insignificant change will mandate the end result, regardless of all that happens to the water on its long journey.

This sensitivity to initial conditions is a common characteristic of natural systems. We are used to thinking about systems in more simplistic ways. A pendulum will ultimately come to rest at its lowest point, regardless of where the motion is started. There is no sensitivity to the initial conditions. It's an esy system to understand.

Because the motion of a pendulum always ends at a point, its dynamics have been called that of a point attractor. The end point doesn't attract like a magnet; but it acts that way. Next in complexity are two dimensional periodic attractors that don't end in a point, yet always repeat the same cycle. The rotation of the earth around its axis creates a daily periodic attractor. Adding a third dimension increases complexity again. The additional rotation of the earth around the sun is expressed as a torus (doughnut) attractor, which is what it looks like.

Those are the easy ones. What happens if more than 3 forces (dimensions) are in play? For most of history, these were called chaotic. They seemed to be beyond pattern or properties because of their complexity. Recent advancements in computers have enabled mathematicians to demonstrate this was a bad term. These systems do have properties, although some, like sensitivity to initial conditions, seemed strange at first. They have been called strange attractors and although they are extremely hard to visualize, understanding their emergent properties help us understand how the world really works.

Learning to appreciate both the order and the complexity of natural and social systems takes you across a mental Continental Divide. It is the single difference between developing a simple business solution versus a simplistic failure. An Active Investor develops a sense of caution and mental red lights begin to flash when any answer appear to be too quick and easy.