A Complex Equation

In my study of the phenomena of association I have shown that there are certain constellations of psychic elements grouped round feeling-toned contents, which I have called “complexes.” The feeling-toned content, the complex, consists of a nuclear element and a large number of secondarily constellated associations. The nuclear element consists of two components: first, a factor determined by experience and causally related to the environment; second, a factor innate in the individual’s character and determined by his disposition.”  (Jung, 1981, pp. 10-11)

            An equation for a complex, as define by Jung, can be written as  

Energy of a Complex = Nuclear Element (Core) + Sum of Constellated Associations (Shell)

or

where

            : is the intensity of the nuclear element. This can be partially measured by the time of reactions during word association tests.

            8 is the assimilation factor; a measure of the ego’s ability to assimilate the emotionally-charged experiences both at the core and shell of the complex. It is also a measure of how much the complex can adversely affect the ego until fully assimilated.

            :/8 is )W which suggests that we are dealing with a repressed experience; here it is Jung’s “factor determined by experience” and the “constellating power of the nuclear element” (Jung, 1981, p. 12); as shown earlier, this is a Lyapounov function for the worldview and if large can drive the ego into instability.

            1/p is the archetypal activity associated with the complex. Jacobi (1974) argues that there is an archetypal element in every complex.

            ( is the repression factor 1/(N')² where (N')² is the square of the psychic integrity; a measure of the strength of the ego’s defense mechanisms. These defense mechanisms can diminish E_COMPLEX but conscious assimilation is required to eliminate the nuclear element (in Jungian psychology, the persona can be considered a defense mechanism).

            (/p is a measure of the ego’s defense against unwanted archetypal activity. It is Jung’s “factor innate in the individual character and determined by his disposition.”

            n is the number of secondarily constellated associations; the number of energy centers clustered around the nuclear element comprising a shell around the core.

            Z is the energy associated with any specific secondarily constellated association or any one of the energy centers surrounding the nuclear element. These secondarily constellated associations make up what is sometimes called the shell that surrounds the core of the complex and are each, in turn, functions of the instincts so that Z % E_INSTINCTS.

            For large values of :/8 or :/p coupled with poor defense mechanisms, E_COMPLEX can drain the ego of the minimal energy required to maintain itself; one result being the chaotic condition of dissociation. As the ego matures and psychic integrity increases (which decreases (), E_COMPLEX decreases. In this way, the energy of a complex is transformed into energy available to the ego.

            According to Kast (1992) a complex can be caused by a painful collision with a demand or an external event with which the ego cannot cope for one reason or another.  “Every emotionally charged event becomes a complex” (p. 32), and of course, the ego itself is a complex. The ego has to become aware of the complex and then assimilate it (which depends on the value of 8) in which case, “the energy inherent in a complex can vitalize the entire person” (p. 32). When this occurs, E_COMPLEX becomes a positive energy available to the ego. We all have many complexes. Being in love, for example, is a complex. According to Jungian psychology, by becoming conscious of any complex, the ego gains the energy E_COMPLEX for its own conscious purposes whereas until then this energy is a drain on the ego.

            The attraction between a complex and the ego is analogous to the gravitational attraction between two masses. The attractive force can be determined at any time as F_C from the relationship                               

where                         

            :_e/p_e is the psychic mass of the ego,

            :_c/p_c is the psychic mass of the complex,

            ( is the repression factor, and

            2 is the angle of consciousness.

            This equation assumes that only one complex acts on the ego.  In actuality, there are many complexes, each influencing the ego at the same time to produce a very complex situation. In essence, each complex acts as a fixed or limit cycle attractor which push or pull the ego in various directions.