International Encyclopedia of Systems and Cybernetics

"A system made up of a large number of parts that interact in a nonsimple way" (H. SIMON, 1965, p.63).

SIMON comments his definition as follows: "In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interactions, it is not a trivial matter to infer the properties of the whole. In the face of complexity, an in-principle reductionist may be at the same time a pragmatic holist" (Ibid).

Thus, the two approaches are by no means exclusive. On the contrary, they should be considered complementary: the first one study the parts, components of subsystems, and the second one investigates the interactions.

As shown by SIMON in his "Architecture of Complexity" paper, this is by far the tallest order.

Another important paint is made by R. ROSEN: "Simple systems do not make errors; it is meaningless to regard a system of mechanichal particles as behaving erroneously. Therefore there has always been a relation between complexity and the capability for error" (1991, p.481).

This is consonant with the possibility of alternative choices and the need for decision making.

J.de ROSNAY describes the complex system in the following way:

"-It is composed of a great variety of components or elements, which possess specialized functions.

"-These elements are organized in internal hierarchical levels. (For example, in the human body: the cells, the organs, the systems of organs).

- The different levels and individual elements are connected by a great variety of linkages. As a result the density of the interconnections is very high.

- The interactions among the elements… are of a peculiar type. They are said to be nonlinear" (1990, p.96).

This is merely a static description of any instant state of a complex system. From the dynamics viewpoint, as stated by P.M. ALLEN et al : "… complex systems involving nonlinearities and feedback may possess multiple solutions, and the bifurcation of a particular solution is a common phenomenon" (1984, p.152). And, at every possible bifurcation: "… the system can probe the "validity" of its own state of organization, and either retain it nevertheless (stability), or move away to some other branch of solution, some other state of organization and perhaps of complexity" (Ibid).

According to J.L.LE MOIGNE (1990), a complex system must offer the nine following characteristics: 1) be identifiable; 2) be active; 3) be regulated; 4) be informed about its own behavior; 5) decide its own behavior; 6) be able to memorize; 7) be able to coordinate its decisions taken for action; 8) be able to imagine and conceive new possible decisions; 9) be able to pursue goals.

R. ROSEN also offered methodological suggestions about the pratical ways to study complex systems:

"a. The only way in which we know how to approach complex systems is to simplify or abstract them in some way;

"b. Such simplification amounts to splitting the system into subsystems, which are simple enough to be characterized in isolation, and such that our knowledge of the isolated subsystems can be effectively employed to give us information about the original system ".

This "splitting", unfortunately, merely reflects DESCARTES old dream, because it eliminates the dynamical interactions.

ROSEN himself recognizes this immediately: "In biology, the abstractions offered by physical reductionism do not in general satisfy proposition b, in that they are not generally compatible with the dynamics of the original system" (1972, p.61-2).

For more see: "Complex system".