Saturday, April 9, 2011

The Ragged Edge


It started with my Plymouth's erratic behavior. It was stalling out all the time, but the number of times it stalled and when it stalled seemed different each time I drove it. I noticed that the car's pattern of stalling was quasi-predictable, more or less tied to the engine's operating temperature. It suddenly occurred to me that there were 3 zones of operation--cold, warm and hot--separated by a chaotic transition boundary. These boundaries marked the event of the engine stalling.

I visualize these "stall boundaries" as ragged edges. You can't tell your position with respect to a boundary until you hit it. And since it's a chaotic function, the boundary's shape changes upon each instance of starting the car and running the engine.

The two diagrams here illustrate the wildly unpredictable nature of the situation.  The black line is the car’s usual progression in its temperature.  Sometimes the car would stall very few times.  Other times it would stall many times.  The difference I attribute to the chaotic transition boundaries—the ragged edges.

Now, the chaotic ragged edge idea permitted me to visualize and explain the types of stalling I was getting. There was suddenly a "perceptible" pattern of behavior that could be defined as a set of rules. As time went on, I could tell that I was--with certainty--approaching, crossing and receding from first one, and then another of the stall boundaries. However, the ragged edge made it impossible to know precisely when the crossing would occur.

This strikes me as an exciting idea. First, the ragged edge concept is easy to visualize. Second, it delineates system states that are both highly predictable (in that that they will occur) and maddeningly erratic. This distinction is made by recognizing that there are points in a zone that are either far from or close to ragged edge transition boundaries. Third, it provides a model of knowledge that distinguishes experts from novices. Experts are notable for having accumulated reliable rules for detecting or anticipating ragged edge boundary phenomena.

Although the model is simple, I believe it can be employed in many situations where one desires to explain erratic or "turbulent" system behavior. Here are a few ideas:

  • Schizophrenia: transitions between lucid thinking vs. disconnected ideation
  • Investing: transitions between aggregate buying or selling behavior
  • Management: transitions between successful planning vs. crisis-driven periods
  • Cognition: changes in attention from very focused to scattered or distracted
I think the model works if it allows situations to be represented using the following simple structure:

  1. Any number of distinct operating states (zones)
  2. Boundary events that mark the transition between adjacent (and distinct) zones
  3. A single "driver variable" that correlates to a path through the (zoned) state-space
Element 3 is perhaps the most interesting component, and the one that most limits the model's applicability. How many situations, after all, resolve to a change in only a single variable?

Nevertheless, ragged edge thinking can reveal that situations that appear to be completely disorderly do, in fact, have an underlying structure. In other words, some systems might be fundamentally simple--consisting of only a small number of zones--but appear to be complex because ragged edge transitions mask this underlying simplicity and give these systems the appearance of being completely unmanageable.

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