complexity

Definition : 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.

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. 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.

Complex systems

Systems exhibit complexity ( complex systems ) when difficulties with modeling them are endemic. This means their behaviors cannot be understood apart from the very properties that make them difficult to model, and they are governed entirely, or almost entirely, by the behaviors those properties produce.

Any modeling approach that ignores such difficulties or characterizes them as noise, then, will necessarily produce models that are neither accurate nor useful.

As yet no fully general theory of complex systems has emerged for addressing these problems, so researchers must solve them in domain-specific contexts. Researchers in complex systems address these problems by viewing the chief task of modeling to be capturing, rather than reducing, the complexity of their respective systems of interest.

While no generally accepted exact definition of complexity exists yet, there are many archetypal examples of complexity.

Systems can be complex if, for instance, they have chaotic behavior (behavior that exhibits extreme sensitivity to initial conditions), or if they have emergent properties (properties that are not apparent from their components in isolation but which result from the relationships and dependencies they form when placed together in a system), or if they are computationally intractable to model (if they depend on a number of parameters that grows too rapidly with respect to the size of the system).

See also

 biological systems
 biological structures