A Complex Equation
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)
: 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.
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 ECOMPLEX
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
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 %
For large values of :/8
or :/p coupled with poor defense
mechanisms, ECOMPLEX 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 (),
ECOMPLEX 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, ECOMPLEX 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 ECOMPLEX 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 FC from the relationship
:e/pe is the psychic mass of the ego,
:c/pc 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