Fractal Intelligence

Friday, April 29, 2005

Thoughts on Geometric analysis of Emergent Behavior

I was contemplating emergence within the context of physics the other day (yes, I know that sounds strange). What I mean by this is that I was contemplating communication between physical bodies over time that show emergent behavior. The reason that I was contemplating such a thing is that I have this nagging, strong belief, that physics is somehow at work in emergence. Ok, so any rate:

Such an exercise will quickly lead one to realize that when thinking of physical objects communicating (say billiard balls bouncing off of one another) over time, we have a stable and static four-dimensional system that can be analyzed (for billiard balls it is 3 dimensional, 2 spacial and one time). This much is obvious.

This thinking of billiard balls got me thinking. It is clear that one can analyze a billiard game using geometric techniques when the time dimension is considered a spacial dimension. But of course, billiards aren't so interesting in and of themselves, I bring the game up to provide a thought substrate (to calibrate my brain).

If we, instead, consider some simplified artificial life system instead of billiard balls, but using the same technique (e.g. time as a spacial dimension), then we have the makings for a geometrically analyzable system where we can draw out geometric relations in the artificial physical system that has been created.

The point of studying such a system with geometric tools would be to attempt to isolate self-organizing principals with geometric mathematics in such a way as to capture the essence of the emergent (self-organizing) behavior of the system. Once such relations are describable mathematically, one should be able to use them to make predictions.

This requires further thought...

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