In the preceding notes it has been sufficient to present the argument in terms of learning "cycles" within an alternation process. But such cycles are rather abstract concepts. They may constitute good descriptive "geometry", but the challenge is to find additional features whereby the abstract geometry is geared or anchored into the complexities of perceived reality. Additional design constraints are required to relate any such cycle to its environment and prevent it spinning out of control or losing its integrity. This question can be examined in very different ways, each of which, as a "language", throws a different light on the relationships and significance of the dimension required to structure a minimally comprehensible system of adequate complexity.
2. Interlocking cycles
The interrelationships of circles has been extensively studied by Buckminster Fuller (1975, 1979), an architect, as the basis for a model of the non-transient existence of energy and material systems. He makes the point that: "Not until we have three noncommonly polarized, great-circle bands providing omnitrangulation as in a spherical octahedron, do we have the great circles acting structurally to self-interstabilize their respective spherical positionings by finitely intertriangulating fixed points less than 180 degrees apart..." (1975, I, 706.20). Furthermore, the more minutely the "sphere" so delineated is subtriangulated by other great circles, the lesser the local structural-energy requirements and the greater the effectiveness of the integrity resulting from such mutual interpositioning. This interlocking is then spontaneously self-stabilizing (1975, I, 706.22).
Assuming the circular representation of cycles, Fuller is in effect saying that it takes at least three interweaving cycles before there is interaction (entrainment) of a type to stabilize the abstract processes within a minimal non-abstract form which their interlocking brings about, in this case a sphere. With less than three, the form can exist only as a transient phenomenon, if at all. In his terms, three cycles is the condition for a minimal system.
But whilst three such cycles can interlock to engender a system, the system can only become comprehensible if a fourth cycle (corresponding to the processes of the observer's involvement in a comprehended system) is added. With less than four, the system may be identified with, opposed, proposed, or participated in, but it can only be partially contained within any communication. Its totality is only apparent as a succession of experiences in time. The unity of a minimal system as a whole only emerges in terms of a minimum of four event foci (400.08). In Fuller's terms "Systems are aggregates of four or more critically contiguous relevant events..." (I, 400.26). All conceptually thinkable experiencings are fourfoldedly characterized (II, 1072.22). This is the basis for the "the minimal thinkable set that would subdivide Universe and have interconnectedness where it comes back upon itself" (I, 620.03) differentiated from its environment (I, 400.05).
As is clarified below, this suggests that not even a conceptual process involving the three classic processes of the dialectic can render any kind of meta-answer comprehensible. It is no wonder that unitary or dualistic answers are insufficient, even though they may be necessary as part of a larger scheme. These considerations cause Fuller to distinguish four interwoven processes which relate to the learning perspective. "Life consists of alternate observing and articulating interspersed with variable-recall rates of "retrieved observations" and variable rates of their reconsideration to the degrees of understandability". The four are: observation (or recall), (re)consideration, understanding, and articulation (513. 0607).
3. Quaternary consciousness: number and time
The concern with alternation cycles arises because of a collective need to obtain a more conscious awareness of integration in a developing world system. It is therefore appropriate to take account of the insights of psychoanalysis. Marie-Louise von Franz, in linking the work of Jung to modern physics, makes points which bear a strong relationship to the distinctions made by Fuller. She presents material indicating the fundamental role which numberplays in ordering both the psyche and matter.
"Taken as rhythm or dynamism, three thus introduces a directional element into the oscillatory rhythm of two, whereby spatial and temporal parameters can be formed. This step involves the interference of an observing consciousness, which inserts a symmetrical axis into the two-rhythm, or else "counts" the latter's temporal and spatial succession. In terms of content the number three therefore serves as the symbol of a dynamic process... three signifies a unity which dynamically engenders self-expanding linear irreversible processes in matter and in our consciousness (e.g. discursive thought)" (1974, pp. 103106).
Her remarks, citing Jung, clarify further the limitations of single-answer or dualistic thinking: "... at the level of one, man still naively participates in his surroundings in a state of uncritical consciousness, submitting to things as they are. At the level of two, on the other hand, a dualistic world...images gives rise to tension, doubt, and criticism of...life, nature, and oneself. The condition of three comparison denotes insight, the rise of consciousness, and the rediscovery of unity at a higher level...But no final goal is reached, for "trinitarian" thinking lacks a further dimension; it is flat, intellectual, and consequently encourages intolerant and absolute declarations." (1974, p.124125).
This suggests again that, despite the necessity of answers formulated in such modes, they are not sufficient at this time. The difficult step across the "incommensurability" between threefold thinking is effectively a progression from the infinitely conceivable to finite reality "based on the inclusion (no longer avoidable) of the observer in his wholeness within the framework of his processes of understanding" (1974, p.122). Citing both myths and sets of physical constants von Franz notes: "The fact that mankind's repeated attempts to establish an orientation toward wholeness possess a quaternary structure appears to correspond to an archetypal psychic structural predisposition in man" (1974, p.115).
For von Franz, a fourfold approach appears "to constitute the fundamental minimum means for subdividing and thus classifying the circle or wholeness" (1974, p. 121). "Two pairs of opposites, a quaternion, are required to set up a bodily unity" (1974, p.127). Below four the perception of wholeness is partly unconscious. As soon as the unconscious content enters the sphere of consciousness it has already split into four basic modes of awareness. "It is perceived as something that exists (sensation); it is recognized as this and distinguished from that (thinking); it is evaluated as pleasant or unpleasant (feeling); and, finally, intuition tells us where it came from and where it is going" (1974, p.121). As a minimum condition, if not incorporated into an "integrated" approach, they must be projected onto competing approaches in the environment, with all the intellectual and institutional consequences for any harmonious integration. Such a fourfold approach is a requirement for comprehending any "meta-answer".
The significance of a quaternary attitude is evident for any human and social development programme: "Instead of proclaiming absolute dogmas, a "quaternary" attitude of mind then develops which, more modestly, seeks to describe reality in a manner that will - if it is based on archetypal concepts - be understandable to others. One remains simultaneously aware of the fact that assumptions of the unconscious do indeed reflect outer or inner reality, but also that they are transformed, through their passage into consciousness, into constricted, time-bound language" (p.26).
The step to a fourfold approach to the world problematique was beyond the impotence of mental processes revolving about "intellectual theorizations" into those which partake of the creative adventure of "realizations in the act of becoming" (1974, p.131). Von Franz cites Ferdinand Gonseth's advocacy of a quaternary outlook which would no longer involve "the summary and brutal coercion of one variant over another, but the play of identifications and differentiation, agreements and complements, limitations and expansions, a game which can lead to dialectical synthesis, built up in four rhythms." (1955, p.583).>
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