Development through Alternation

4.1 Omnitriangulation: interlocking cycles

Anthony Judge

The interrelationships of circles has been extrensively studied by Buckminster Fuller (46), 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 ISO degrees apart..." (46, 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 (42, 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 (#2). 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 (#3).

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 (46, I, 400.08). In Fuller's terms "Systems are aggregates of four or more critically contiguous relevant events..." (46, I, 400.26). All conceptually thinkable experiencings are fourfoldedly characterized (46, 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" (46, I, 620.03) and is differentiated from its environment (46, 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 (#4). 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." These four are therefore: observation (or recall), (re)consideration, understanding, and articulation. (46, I, 513.06-07)