Monday, August 8, 2011

The Fallacy of Fractal Geometry

One thing that I've struggled with for well over a year now is that "fractals" are typically described in terms of geometry and/or probability, while my fractal theory of cognition does not fit easily within that paradigm.

Within the last 24 hours, I realized that even the concepts of the fractal geometry of nature and fractal finance do not truly describe geometry or probability.  Rather, they describe the result of applying a force to an object.  In the case of a coastline's fractal geometry, the force is erosion, and the object is rock, soil, etc.  In the case of a stock price's fractal charts, the force is human decision-making, and the object is the stock price.

Viewed through this prism, my fractal theory of cognition is entirely consistent with the broader theory of fractals, which suggests that we can better understand the fractal geometry of nature by focusing on the physical constants at play, many of which are defined in terms of stress (force) per unit area.  In this sense, fractals are not a "geometry" at all but a very complex derivative of stress (force) and strain (reaction to force).