Stuart Kauffman’s term for the way the internal dynamics of a system generates order spontaneously under the right conditions. This order is “for free” in that it does not need to be imposed or imported from outside the system. It is Kauffman’s conjecture that natural selection during the course of evolution takes place on already self-organized order. An implication is that particular biological adaptations or forms may result from constraints on possible designs due to the inherent mathematical dynamics of a system. In terms of organizations, it may be case that spontaneously emerging structures provide a crucial understanding of such system’s functioning.

See: Emergence; Self-organization
Bibliography: Kauffman (1995)

Variables in the mathematical equations used to model system behavior. Changes in the values of these variables can affect the system’s behavior.

Control Parameters: These parameters often model some kind of external influence on a system that facilitate a far-from-equilibrium condition or, in other words, expedite a bifurcation. An example is temperature in the Benard System, which at a critical value prompts self-organization and the emergence of hexagonal convection cells when a particular liquid in a container is heated from the bottom.

Order Parameters: Parameters that represent some global emergent characteristic of a system as opposed to variables of lower level components. The shift to order parameters signifies recognition that emergent phenomena need to be investigated on their own terms.

Lambda Parameter: A parameter used by the computer scientist Chris Langton to get at the range where self-organization is most likely in cellular automata. As such the lambda parameter is a control parameter.

See: Bifurcation; Cellular Automata

Bibliography: Haken (1981); Langton (1986).

An abstract mathematical space which is used to display time series data of the measurements of a system. The dimensions of phase or state space correspond to the number of variables used to characterize the state of the system. For example, the phase space of a pendulum would consist of two dimensions: the speed of the bob; and the distance of the bob from the vertical resting state. Phase space is very helpful for observing the patterns that result as systems evolve over time. Please note that time is usually not one of the explicit dimensions of the phase space, a role that time does play in a straight graphical depiction of a time series.

Phase Portrait: The geometrical patterns shown in phase space as a system evolves. These portraits may be attractors such as fixed point, periodic, and strange attractors. They can also include repellors (the opposite of attractors) and such interesting patterns as saddles (in which there are attractor(s) in one direction and repellor(s) in another direction) and separatrices, or boundaries between two basins of attraction.

See: Attractors; Chaos

Bibliography: Abraham, et. al. (1991); Guastello (1995)

9).

The geometrical patterns shown in phase space as a system evolves. These portraits may be attractors such as fixed point, periodic, and strange attractors. They can also include repellors (the opposite of attractors) and such interesting patterns as saddles (combination of attractor in one direction and repellor in another direction) and separatrices, or boundaries between two basins of attraction.

See: Attractors; Chaos
Bibliography: Abraham, et. al. (1991); Guastello (1995)

Experiments or deviations from the norm in a social system that can lead to positive change. The phrase itself “positive deviance” is a kind of oxymoron, since it pairs the constructive term “positive” with the negative term “deviance,” the latter term carrying quite a bit of pejorative associations precisely because it pertains to deviations from the norm. For example, members of a society practicing “fringe behavior” are often called deviants. However, branding “deviance” with such derogatory outcomes sets up a bias that protects the norm with a halo of righteousness while condemning deviations-from-the-norm as degenerate. If this bias were strictly enforced, we would never have gained most of the great scientific and social advances of human history. All such major innovations and transformations, in one way or another, relied on radical departures from the norm. Both the Copernican and the American Revolutions are cases in point.

A social interventional method termed “Positive Deviance” developed by Jerry and Monique Sternin identifies novel experiments in complex social systems—deviations from the norm—and harnesses them to generate positive outcomes. “Radical” ideas from organizational outliers are reframed as solutions with the potential of bringing about significant social system change. According to Jerry Sternin, in many communities facing seemingly intractable problems, there are certain individuals or groups (positive deviants) with the same access to resources as other community members whose special practices, strategies or behaviors generate better results.

Bibliography: Sternin & Choo (2000 ); Sternin (2003).

 

A method developed by the management/complexity theorist Jeffrey Goldstein which consists of a work group highlighting the discrepancy between their original purpose and the current activities or procedures being done. The purpose of purpose contrasting is similar to difference questioning: to increase the amount of information in a system and thereby facilitate self-organization. For example, in a bureaucratically organized business or institution, the bureaucracy itself becomes its own purpose, obscuring the original purpose of making a product or providing a service.

See: Difference Questioning; Information; Far-from-equilibrium
Bibliography: Goldstein (1994)

A type of mathematical pattern in which the frequency of an occurrence of a given size is inversely proportionate to some power (or exponent) of its size. For example, in the case of avalanches or earth quakes, large ones are fairly rare, smaller ones are much more frequent, and between these extremes are cascades of different sizes and frequencies which take place a moderate number of times. Power laws define the distribution of catastrophic events in self-organized critical systems. Systems with power law distributions are marked by invariance with respect to scale and universality, the latter term referring to remarkably similar dynamics across quite different systems. Power laws are associated with fractal-like patterns since the pattern is self-similar with respect to scale. In this regard power law signatures have been discovered in heart inter-beat variability and are suspected in many other physiological phenomena.

 See: Fractal; Scale-free Network; Self-organized Criticality; Sensitive Dependence on Initial Conditions

Bibliography: Bak (1996);Barabási (2002); Schroeder (1991); West (2006).

The existence of repetitive patterns or structures. In an important sense, redundancy refers to order in a complex system in the sense that order is defined as the existence of structures that maintain themselves over time (i.e., they are stable). In information theory, redundancy refers to repetition in patterns of messages in a communication channel. If the message contains these redundancies, they can be compressed further. For example, if a message contains a series of two hundred and fifty 1s, then the message could be compressed into a command which effectively says “and then repeat 1 250 times” instead of writing out all two hundred fifty 1s. Self-organizing processes demand some element of redundancy which can be considered as a “fuel” for the processes leading to emergence. In other words, novel patterns come from a recombination of redundant patterns.

See: Information; Novelty

Bibliography: Campbell (1982); Poundstone (1985).