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One of the problems in addressing complexity issues has been formalizing the intuitive conceptual distinction between the large number of variances in relationships extant in random collections, and the sometimes large, but smaller, number of relationships between elements in systems where constraints (related to correlation of otherwise independent elements) simultaneously reduce the variations from element independence and create distinguishable regimes of more-uniform, or correlated, relationships, or interactions.Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between "disorganized complexity" and "organized complexity".Complexity is generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts.Just as there is no absolute definition of "intelligence", there is no absolute definition of "complexity"; the only consensus among researchers is that there is no agreement about the specific definition of complexity.

A complex system is thereby characterised by its inter-dependencies, whereas a complicated system is characterised by its layers.Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.The stem of the word "complexity" - complex - combines the Latin roots com (meaning "together") and plex (meaning "woven").However, "a characterization of what is complex is possible". Neil Johnson states that "even among scientists, there is no unique definition of complexity – and the scientific notion has traditionally been conveyed using particular examples..." Ultimately Johnson adopts the definition of "complexity science" as "the study of the phenomena which emerge from a collection of interacting objects".Definitions of complexity often depend on the concept of a confidential "system" – a set of parts or elements that have relationships among them differentiated from relationships with other elements outside the relational regime.

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