Saturday, December 1, 2012

Hysteresis in complex interactions

Recently, a group of us have been discussing the flows of monies and values in and between high-tech entrepreneurial enterprises and various economic, financial, social/societal, and legal contexts.  This is harder to do than one would initially suppose, because these concepts can easily be conflated -- value is usually measured in money. The problem when modeling and simulating these flows is that they exhibit a hysteresis. One might say that money tends to follow value, but that is not always the case. In other words, money may "lead" or "lag" in its correspondence to value. Why is this important in modeling complex market systems?

Value, as in realization of a value proposition, is a problem because it is usually measured a posteriori, or after the fact -- meaning after it has been realized --and often in rather subjective, qualitative metrics. In other words, the realization of value leads or lags in a possibility space.  We see this, in a primitive conceptualization, as a level at some distance on Roger's Innovation Adaption Curve.  So, how can we measure potential value, if not directly by money?

How about value as generative of a probability distribution function, not as a location on a probability distribution?  We can do this by composing functions, hyper-dimensionally, in an indirectly encoded compositional pattern producing network (h-CPPN) according to open-ended fitness functions in each of the contexts of interest.  Value becomes an evolutionary function in a competitive, co-evolutionary system, meaning value is also a comparitive function from alternatives.

There seems to be adjunction in the natural transformations between functions of value, and the functions that generate revenue.  Identifying those natural transformations informs us of the complex system between monitary flows and flows of value - and similar to those seen in Lotka-Volterra systems.

Just a thought, but fast becoming a simulation ....