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Complexity Wikipedia. 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.

Contrast complicated where plic meaning folded refers to many layers. 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. 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.

Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Easily share your publications and get. Here are November s writing competitions and calls for submission, all with free, electronic entry. As usual Im passing these on in good faith but mistakes. However, a characterization of what is complex is possible.

Science as of 2. Zayed et al. 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. 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 1. 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.

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.

Disorganized vs. Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between disorganized complexity and organized complexity. In Weavers 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. A prime example of disorganized complexity is a gas in a container, with the gas molecules as the parts.

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 Newtons laws of motion.

Of course, most real world systems, including planetary orbits, eventually become theoretically unpredictable even using Newtonian dynamics as discovered by modern chaos theory. 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. The organized aspect of this form of complexity vis a vis to other systems than the subject system can be said to emerge, without any guiding hand.

The number of parts does not have to be very large for a particular system to have emergent properties. A system of organized complexity may be understood in its properties behavior among the properties through modeling and simulation, particularly modeling and simulation with computers. An example of organized complexity is a city neighborhood as a living mechanism, with the neighborhood people among the systems parts.

The source of disorganized complexity is the large number of parts in the system of interest, and the lack of correlation between elements in the system. 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.

See e. Robert Ulanowiczs treatment of ecosystems. 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 1. Turing machines can decrease even the complexity class of a function, language or set Burgin 2. This shows that tools of activity can be an important factor of complexity. Varied meaningseditIn several scientific fields, complexity has a precise meaning In computational complexity theory, the amounts of resources required for the execution of algorithms is studied.

The most popular types of computational complexity are the time complexity of a problem equal to the number of steps that it takes to solve an instance of the problem as a function of the size of the input usually measured in bits, using the most efficient algorithm, and the space complexity of a problem equal to the volume of the memory used by the algorithm e.

This allows to classify computational problems by complexity class such as P, NP, etc. An axiomatic approach to computational complexity was developed by Manuel Blum. It allows one to deduce many properties of concrete computational complexity measures, such as time complexity or space complexity, from properties of axiomatically defined measures.

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