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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. A complex system is thereby characterised by its inter-dependencies, whereas 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.
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. Ultimately Johnson adopts the definition of “complexity science” as “the study of the phenomena which emerge from a collection of interacting objects”.
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. Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as later set out herein. Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between “disorganized complexity” and “organized complexity”.