Computing Anticipatory Systems : A Generic Structure of Organization

A theory of organization of complexity was constructed in order to create a common semiotic lineage among the diverse symbol systems used by various disciplines (Chandler, t996, L997). The foundations of the theory are developed from observations on the nonlinear dynamics of organisms within ecoments -- ecoments being defined as the immediate surroundings of one hierarchical degree of an emergent system. Each system (sub-system, sub-sub-system ... ) is assigned four primitives attributes (closure, conformation, concatenation and cyclicity) which are subject to scaling and semiotic constraints. In principle, each of these four terms is enumerable for a local system. Degrees of organization (symbolized as Oo) are composed from lesser organized systems to higher organized systems in terms of the enumeration of the four primitives. The emergent organizations are enumerated: 1,2,3, ... The patterns of organization at any particular level, Oo, are composed from patterns at other levels. Thus, no particular science or philosophy is assigned a privileged role in the unfolding of the dynamics. Mathematically, the organized systems are composed under the scientific representations of categories as developed in Chandler, 1991, and Ehresmann and Vanbremeersch 1987, 1997. Categorical objects have the unique mathematical characteristic of creating a 'logical shell' for other classes of mathematical structures. (see S. Mac Lane, Mathematics, Form and Structure, 1986.) This 'logical shell' character of category theory is used here to construct hierarchical relationships between scientific observations and mathematical structures. This notation parallels natural history and allows the facile accounting of the molecular biological mechanisms within a living system. Implications of this theory of natural organization for the design of artifrcial hierarchical systems arc apparent.