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In Weaver's view, disorganized complexity results from the particular system having a very large number of parts, say millions of parts, or many more.Though the interactions of the parts in a "disorganized complexity" situation can be seen as largely random, the properties of the system as a whole can be understood by using probability and statistical methods.
Some would suggest that a system of disorganized complexity may be compared with the (relative) simplicity of planetary orbits – the latter can be predicted by applying Newton's laws of motion.These correlated relationships create a differentiated structure that can, as a system, interact with other systems.The coordinated system manifests properties not carried or dictated by individual parts.In the case of self-organizing living systems, usefully organized complexity comes from beneficially mutated organisms being selected to survive by their environment for their differential reproductive ability or at least success over inanimate matter or less organized complex organisms. For instance, for many functions (problems), such a computational complexity as time of computation is smaller when multitape Turing machines are used than when Turing machines with one tape are used.Random Access Machines allow one to even more decrease time complexity (Greenlaw and Hoover 1998: 226), while inductive Turing machines can decrease even the complexity class of a function, language or set (Burgin 2005).From one perspective, that which is somehow complex – displaying variation without being random – is most worthy of interest given the rewards found in the depths of exploration.
The use of the term complex is often confused with the term complicated.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.Of course, most real-world systems, including planetary orbits, eventually become theoretically unpredictable even using Newtonian dynamics; as discovered by modern chaos theory.Organized complexity, in Weaver's view, resides in nothing else than the non-random, or correlated, interaction between the parts.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.