Excerpted from Wikipedia
Source: http://en.wikipedia.org/wiki/Complexity
Date: 30-Jun-2012
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory.
In science there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article. Neil Johnson describes complexity science as the study of the phenomena which emerge from a collection of interacting objects.
In a business context, complexity management is the methodology to minimize value-destroying complexity and efficiently control value-adding complexity in a cross-functional approach.
Overview
Definitions of complexity often depend on the concept of a “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.
Some definitions focus on the question of the probability of encountering a given condition of a system once characteristics of the system are specified. Warren Weaver posited in 1948 that the complexity of a particular system is the degree of difficulty in predicting the properties of the system – given the properties of the system’s parts. In Weaver’s view, complexity comes in two forms: disorganized complexity, and organized complexity. Weaver’s 1948 paper has influenced subsequent thinking about complexity.
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 complexity vs. organized complexity
One of the problems in addressing complexity issues has been formalizing the intuitive conceptual distinction between the large number of variances in relationships extant in random collections, and the sometimes large, but smaller, number of relationships between elements in systems where constraints (related to correlation of otherwise independent elements) simultaneously reduce the variations from element independence and create distinguishable regimes of more-uniform, or correlated, relationships, or interactions.
Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between “disorganized complexity” and “organized complexity”.
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.
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, for example, with the (relative) simplicity of the planetary orbits—the latter can be known by applying Newton’s laws of motion, though this example involved highly correlated events.
Organized complexity, in Weaver’s view, resides in nothing else than the non-random, or correlated, interaction between the parts. 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 system’s parts.
…
Study of Complexity
Complexity has always been a part of our environment, and therefore many scientific fields have dealt with complex systems and phenomena. 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. In today’s systems, this is the difference between myriad connecting “stovepipes” and effective “integrated” solutions. This means that complex is the opposite of independent, while complicated is the opposite of simple.
While this has led some fields to come up with specific definitions of complexity, there is a more recent movement to regroup observations from different fields to study complexity in itself, whether it appears in anthills, human brains, or stock markets. One such interdisciplinary group of fields is relational order theories.
Complexity Topics
Complex Behavior
The behavior of a complex system is often said to be due to emergence and self-organization. Chaos theory has investigated the sensitivity of systems to variations in initial conditions as one cause of complex behavior. Complex behavior can be caused by multitasking of brain.
Complex Mechanisms
Recent developments around artificial life, evolutionary computation and genetic algorithms have led to an increasing emphasis on complexity and complex adaptive systems.
Complex Simulations
In social science, the study on the emergence of macro-properties from the micro-properties, also known as macro-micro view in sociology. The topic is commonly recognized as social complexity that is often related to the use of computer simulation in social science, i.e.: computational sociology.
Systems theory has long been concerned with the study of complex systems (in recent times, complexity theory and complex systems have also been used as names of the field). These systems are present in the research of a variety disciplines, including biology, economics, and technology. Recently, complexity has become a natural domain of interest of real world socio-cognitive systems and emerging systemics research. Complex systems tend to be high-dimensional, non-linear, and difficult to model. In specific circumstances, they may exhibit low dimensional behavior.