Some Basic Definitions

Extensity.                                                                                                                                                                                                       

As we know, the theory of energy recognizes not only a factor of intensity, but also a factor of extensity, the latter being a necessary addition in practice to the pure concept of energy. It combines the concept of pure intensity with the concept of quantity (e.g. the quantity of light as opposed to its strength) ...[and it] shows the dynamic measure of energy present at any time in a given phenomenon. (Jung, 1981, p. 20)

            High extensity leads to individuation because only where this factor is high can the individual break away from the “collective herd” and act independently. Intensity can move from place to place within the psyche without affecting structure. However, extensity affects psychic structure itself. Let us refer to this factor as the Greek letter epsilon , and mathematically define it by

            This equation says that , is the area of C in phase space (i.e., the sum of all of the individual C’s) at any time t. Extensity is a measure of personal conscious experience and increases with both progressive and regressive motion as long as the experience resulting from these motions can be assimilated. It is directly related to long term memory so that , % E_MEMORY. According to Nicolis and Prigogine (1989), for any complex system the parameter of extensity is “proportional to the size of the system” (p. 15). Thus , increases as the ego matures as indicated in our two-dimensional phase space (Figures 15 through 17).

Psychic Maturity.

            We can use the Greek letter sigma F to represent the area under the U_P curve in phase space for any time t so that

            We can now define psychic maturity as the ratio of the conscious to the personal unconscious. The Greek letter gamma ' is used where

            In most cases '#1 prior to psychic puberty, '=1 at or near psychic puberty, and  '$1 after psychic puberty. The right side of Figure 15 shows the result of an idealized individuation process where F approaches zero (F 6 0) and ' approaches infinity (' 6 4). Psychic maturity is a measure of self-realization and approaches infinity as the ego approaches transcendence.

The Angle of Consciousness and the Transcendent Function.

            For every position of consciousness there is a corresponding opposite unconscious position. Jung (1989) calls the “continual process of getting to know the counterposition in the unconscious” the transcendent function (p. 200). As personal unconscious contents become conscious, there is “a modification of standpoint” which is to say, a change in self-image and/or in  worldview. The transcendent function T “unites the pairs of opposites” within the psyche and allows for “the psychic process of assimilation and integration” (p. 203).

            There are angles of consciousness associated with each of the four quadrants that are shown in Figure 14. Figure 27 shows the angles of consciousness for the waking state. We have no units of measure for consciousness or for the personal unconscious, but we can construct a circle with a radius of 1 unit, whatever that unit may be, so that for the waking state we have

sin2 = C  

cos2 = U_P

and                                                                                                     

 We can then find T through any of these relationships where 2 is the angle of consciousness and T is equivalent to 2 at or near 90E (290), a temporary event that occurs briefly whenever U_P 0 as shown in Figure 27.   

Figure 27. The Transcendent Function

            Figure 27 shows the relationship between the personal unconscious and consciousness insofar as mental health is concerned. A relatively large 2 (greater than 45E where tan 2 =1) is essential for mental health. The transcendent function or 2 as it approaches or passes 90E, is equivalent to a transpersonal experience; the peak experience of Maslow (1968; 1971). A small 2 is associated with neurosis or even psychosis, and as 2 goes below 0, the psyche transitions to its dream state as shown in Figure 14. Furthermore, there exists some small but critical angle 2_C that can allow temporary regression to a past mental state such as that shown in Figure 21.

            We can now rewrite psychic maturity in terms of 2 as

            Both C and U_P, and therefore 2, can be found at any time t from Figures 15 and 27.

Psychic Mass.

The unit of basic psychic operativeness is the emotionally-charged image. (Whitmont, 1991, p. 28)

            We can define psychic mass, the psychic equivalent to physical mass, as the product of Jung’s “psychic intensity,” the Greek letter mu :, and his “psychic probability” 1/p, or :/p. Here, psychic probability 1/p is defined by Jung (1981) as a direct measure of archetypal activity. The relationship is an inverse one; p is the probability of randomness or chance so that 1/p is the probability of archetypal activity. According to Nicolis and Prigogine (1989), “Probabilistic evolution processes...form the basis of the description of dissipative systems” (p. 199). The inclusion of archetypal probability into psychic mass therefore seems a logical necessity in order to describe the psyche as a dissipative system. 

            For large values of p the psychic mass is small and the ego is relatively predictable (i.e., statistically predictable). However, as 1/p increases due to archetypal activity, the ego passes its threshold of complexity and in accordance with Prigogine’s uncertainty, the ego becomes highly unpredictable because its psychic mass is approaching infinity–a chaotic condition. Psychic mass :/p is thus a Lyapounov function, an indication or measure of chaos.

            Unlike the physical mass of the body, which increases up to adulthood and then levels off, psychic mass is constantly changing and can only be measured statistically.  When addressing the psychic mass of the ego, the intensity : is directly related to how much meaning there is in life. Whitmont (1991) says that the meaning of life is basically emotional and intuitive, and not necessarily logical. “Our culture is logic-oriented but in dealing with our most fundamental problems rational logic fails to offer us adequate answers to the understanding and living of life” (p. 17). Thus the psychic mass of the ego can be considered as a function of its sense of meaning in life and the degree it is influenced by archetypal activity and has nothing at all to do with conscious rational thought.                                          

Our definition of psychic mass and the fact that it is a Lyapounov function suggests the enormous importance of finding meaning in life. According to Frankl (1984), there is no general meaning of life, but rather we must find our own personal meaning. His Logotherapy insists that mental health requires a sense of meaning, and he cautions that “the meaning of life differs from man to man, from day to day and from hour to hour” (p. 113). A lack of meaning in life decreases the psychic mass of the ego rendering it easily overcome by a complex.

            Archetypal activity influences the ego in all four states. If repressed or ignored during the waking state, then this activity intensifies in a compensatory manner in dreams. Conscious awareness of this influence helps increase meaning and thus strengthens the psychic mass of the ego.  

Psychic Momentum.

            We can now define psychic momentum as the Greek letter nu < where

            From this relationship we see that psychic momentum (the susceptibility of the psyche to change) is directly related to intensity or meaning, archetypal activity, and consciousness. As archetypal activity decreases (i.e., as statistical probability p increases), momentum decreases. Psychic momentum is directly proportional to consciousness. As :/p is equivalent to the psychic mass of the ego, so tan2 is equivalent to its velocity; a measure of its motion in phase space at any time t.

            Progressive or regressive motions of the ego through phase space in the waking state are the result of the oscillations of consciousness. Motion when 2>45E is progressive and when 2<45E is regressive. When 2=45E there is no motion and the ego is at equilibrium. Both p and : can range in value from zero to one, so psychic mass, and consequently psychic momentum, can theoretically range from zero to infinity.

            The equation for psychic momentum suggests that for normal conscious awareness (tan2~1) when archetypal activity is lacking and the statistical probability of the ego is high, psychic mass becomes identical to intensity. However, when p is very low and archetypal activity is almost a certainty, psychic mass becomes very high providing there is at least some amount of intensity (Jung used the term numinous to denote high intensity). If 2>0 (i.e., if the ego is consciously aware of the influencing activity at the time) and psychic mass is high, then the ego trajectory will be propelled into far-from-equilibrium conditions in either a progressive or regressive direction and will only reach equilibrium when 2=45E.

Psychic Force.

            Psychic force F can now be defined as

            The force required to change the directional motion of the ego at any time t through phase space is equal to its psychic mass times the rate of increase (or decrease) of consciousness at time t. The rate of change in consciousness d2/dt is a measure of the relative acceleration of the ego’s progressive and regressive motions in phase space.

Self-Image.                                                                                                                                                   

Idealized fantasies involving our self-image cause a repression of those aspects that do not agree with it; we allow them to become our “shadow,” or unconscious.” (Kast, 1992, p. 54)

            The Greek letter phi N is used to represent the strength of our self-image; a function of memory, the strength of the ego’s sense of continuity, and the degree of self-worth or self-esteem present. The self-image is not the persona, although the two are related. The self-image is the way we really see ourselves as opposed to the persona which is the way we wish others to see us. In a sense, the persona is an idealized self-image. One of the goals of individuation is to equate the self-image with the persona in which case the persona is no longer necessary and its energy can be used elsewhere.

Psychic Integrity.

            We define the product of self-image and psychic maturity, N', as psychic integrity, the general or overall integrity of the ego. Psychic integrity is a measure of the robustness of the ego complex. A high psychic integrity implies a high degree of self-realization.

Repression Factor.

            The repression factor is denoted by the Greek letter gamma  ( and we define it by the relationship

or

where N is the self-image, ' is psychic maturity, and N' is psychic integrity. The repression factor is defined here as one divided by the square of the psychic integrity; a measure of the strength of the ego’s defense mechanisms.            

The Reality Factor. 

            The reality factor is denoted by X_e where 0 # X_e # 1 in the waking and transpersonal states as shown in Figure 28. This factor is caused by the projective characteristics of the anima/animus and is a measure of the extent to which the psyche can experience objective reality. The reality factor X_e is an inherited ability; the filter of the anima/animus. X_e varies with each psyche in the waking and transpersonal states, but remains relatively constant throughout the first half of life and increases through the individuation process during the second half of life. In the dream state, X_e approaches zero and in the sleep state it approaches one. Ideally X_e will equal one in all but the dream state which is, by its nature, a projective state.

Figure 28. The Reality Factor.  

The Objectivity Factor.

            The probability that an external experience or event is purely objective (i.e., without psychic projection) is CX_e, the objectivity factor, which can also be denoted by sin2 X_e (recall that sin2=C). Here C is a measure of consciousness at the time of the experience. CX_e = 0 at birth, and whenever the ego is in the dream or sleep states. In the waking and transpersonal states 0 # CX_e # 1 and after an ideal individuation process CX_e = 1 (it also approaches one in the mystical experience S high 2 in the transpersonal state). The inverse is 1/CX_e, the probability that an external experience is confounded by our own projections. When 1/CX_e is large, these projections result in hallucinations or fantasies.

                                                      1/CX_e % E_PROJECTIONS 

One result of individuation is that C increases so that projections decrease.

Psychic Mass Ratio. 

            We are so accustomed to regard meaning as a psychic process or content that it never enters our heads to suppose that it could also exist outside the psyche. (Jung, 1981, p. 482)

            Whenever the ego experiences the outer world, it has an internal psychic mass that we denote by :_i/p_i. Jung (1981) suggests that every objective experience itself also has a psychic mass, which we denote by :_o/p_o. The psychic mass ratio can then be defined as the Greek letter eta 0 where

            Using this definition, based upon the ego’s experience of the outer world, a coincidence occurs whenever 0 = 1 which is to say, whenever the psychic mass of the ego is equal to the psychic mass of the experience.