Synergetics

            Mainzer (1994) states, “Synergetic principles (among others) provide a heuristic scheme to construct models of nonlinear complex systems in the natural sciences and the humanities” (p. 13). Probably chief among the reasons why synergetics seems so well suited to this task, is its use of the slaving principle and the ordering parameter. 

            When a ferromagnet is heated above a certain threshold temperature, it suddenly loses its magnetization. When the temperature is lowered below that threshold temperature, it regains its magnetism. Such a transformation is called a phase transition.

            According to synergetics, as complex systems undergo phase transitions, a special type of ordering occurs at the microscopic level (with ferromagets, for example, the atomic particles become dislocated at high temperatures and point randomly, and then return to their directional order at low temperatures). Haken (1983) has shown, mathematically, that instead of addressing each of countless atoms in a complex system undergoing a phase transition, we can address their modes by means of an ordering parameter. This has the mathematical result of drastically lowering the degrees of freedom to only a few parameters. He also demonstrates how these ordering parameters guide complex processes in self-organizing systems.

            When a system ordering parameter guides one or more subsystems, they are said to slave the subsystems, and this slaving principle is the key to understanding self-organizing systems. Complex systems organize and generate themselves at far-from-equilibrium conditions, where:

In general just a few collective modes become unstable and serve as “ordering parameters” which describe the macroscopic pattern. At the same time the macroscopic variables, i.e., the order parameters, govern the behavior of the microscopic parts by the “slaving principle. In this way, the occurrence of order parameters and their ability to enslave allows the system to find its own structure.  (Haken, 1988, p. 13)

            Because complex systems have many components, they have  many degrees of freedom. By addressing one or two ordering parameters (that which describes the macroscopic order and simultaneously “orders” or slaves the components) the degrees of freedom are reduced to one or two, allowing for mathematical and especially statistical approaches. In this way, Haken (1987) concludes “In general, the behavior of the total system is governed by only a few order parameters that prescribe the newly evolving order of the system” (p. 425). 

            A circular causality is formed when the subsystems collectively determine the order parameters and the order parameters determine the behavior of the subsystems. Haken (1987) also proposes that models of complex systems must include an interplay between function and structure. Structures are formed through the process of receiving information.  The incoming signals or patterns from the senses, for example, can be addressed as ordering parameters which can either cooperate or compete with one another within the psyche.

            Jung’s psyche functions with circular causality. The central archetype of the psyche is the Self which, together with the ego, determine the order parameters of the entire psyche (biases, dispositions, likes and dislikes, values, and so on). These parameters then determine the behavior of the ego and Self. The behavior of the ego can be determined from personality characteristics and traits (Jung, 1971). The behavior of the Self can be determined from careful analysis of dreams (1974) because when the ego falls asleep it goes through a phase transition. He (1981) was familiar with the idea of ordering parameters because he wrote that “the unconscious uses number as an ordering factor” (p. 457) and said that number was an “archetype of order.”  (p. 456)