### 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

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...

*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...