Complexity

Complexity describes the behaviour of a system or 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 i.e. Complex is composed of the Latin words com (meaning: "together") and plex (meaning: woven). This is best contrasted with Complicated where plic (meaning: folded) refers to many layers. A complex system is thereby characterised by its inter-dependencies, where as a complicated system is characterised by its layers.

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 like 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. However, a characterization of what is complex is possible. The study of these complex linkages at various scales is the main goal of complex systems theory.

In science, there are as of 2010^[update] a number of approaches to characterizing complexity; this article reflects many of these. 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 he 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. 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.

Warren Weaver posited in 1948 two forms of complexity: disorganized complexity, and organized complexity. Phenomena of 'disorganized complexity' are treated using probability theory and statistical mechanics, while 'organized complexity' deals with phenomena that escape such approaches and confront "dealing simultaneously with a sizable number of factors which are interrelated into an organic whole". Weaver's 1948 paper has influenced subsequent thinking about complexity.

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