Overview
Definitions of complexity often depend on the concept of a "system"—a set of parts or elements that have relationships among them differentiated from relationships with other elements outside the relational regime. Many definitions tend to postulate or assume that complexity expresses a condition of numerous elements in a system and numerous forms of relationships among the elements. However, what one sees as complex and what one sees as simple is relative and changes with time.
Some definitions focus on the question of the probability of encountering a given condition of a system once characteristics of the system are specified. Warren Weaver posited in 1948 that the complexity of a particular system is the degree of difficulty in predicting the properties of the system - given the properties of the system's parts. (unsubstatiated citation: please read the discussions page) . In Weaver's view, complexity comes in two forms: disorganized complexity, and organized complexity. Weaver's 1948 paper has influenced subsequent thinking about complexity.
The approaches that embody concepts of systems, multiple elements, multiple relational regimes, and state spaces might be summarized as implying that complexity arises from the number of distinguishable relational regimes (and their associated state spaces) in a defined system.
Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as later set out herein.
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