THE COMPLEXITY OF NATURE

D. C. Mikulecky

Professor of Physiology

Medical College of Virginia Commonwealth University

http://views.vcu.edu/~mikuleck/

Complexity is the property of a real world system that is manifest in the inability of any one formalism being adequate to capture all its properties. It requires that we find distinctly different ways of interacting with systems. Distinctly different in the sense that when we make successful models, the formal systems needed to describe each distinct aspect are NOT derivable from each other.

This is the basic definition of complexity that I suggest everyone adopt. I will now show that it either leads to or is consistent with all the following attributes/properties/definitions of a complex system.

• It is non-fragmentable. If a complex system were fragmentable it would be a machine. We require the distinction to be dichotomous. Therefore complex systems are not fragmentable. That is not to say that they are incapable of being reduced to parts, but such reduction destroys important system characteristics irreversibly.
• Consists of real components that are distinct from its parts. At least one set of these components is defined by its functions. These functional components are not simply collections of parts. If they were the system would be fragmentable in the above sense. These functional components are therefore defined by the system and have their ontology dependent on the context of the system. Outside the system they have no meaning. Further, if they are "removed" from the system in any way the system looses its original identity as a whole system.
• Real (complex) systems have models as in the modeling relation. These models may be analytic or synthetic models. The analytic models differ from the synthetic. This must be so for consistency with the requirement for non-fragmentability. When synthetic models can replace analytic models, the system is fragmentable and is therefore a machine.
• There can be no "largest model". If there were a largest model, all other models could be derived from it and fragmentability would result.
• The system falls outside the Newtonian paradigm in some important ways. If it could be described by the Newtonian Paradigm it would have a largest model from which all others could be derived.
• Causalities in the system are mixed when distributed over the parts. There is final cause in the sense that functional components have their own ontology. These components are defined by their function. For this reason, the system can be "anticipatory". That is to say, it can have causal relations which arise out of some future event if these future events are contained tentatively in a model the system has of its environment (in the broadest sense, i.e., the system is included in its environment.)
• The nature of causality and, especially the definition of functional components, requires that there be closed loops of causality of a nature forbidden, or at least excluded, by the Newtonian Paradigm.
• The result of these traits is that much of the system's important attributes are beyond algorithmic definition or realization by algorithms and therefore non-computable in the usual sense. In that sense they refute Church's thesis.

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