It is not to be expected that a fivefold grasp of a developing reality is sufficient. It is a minimal requirement for a certain degree of comprehension of that reality. For example, Jantsch notes:

"If, in the development of the organism, two types of non-linear processes play the main role, namely genetic and metabolic processes, the number rises to at least six in ecosystems (competition for niches, predator-prey, symbiosis, and optico-acoustical communication)....All these processes bring their proper rhythms into play..." (21, p. 247)

As he remarks, similar coupling of oscillations occurs to an even higher degree for sociocultural systems resulting in structures of "autopoietic and temporarily harmonious nature which are capable of carrying a great deal of creativity" (21, p. 248). In material systems Fuller also distinguishes six basic ways in which a system can "move" in relation to its environment, namely spin, orbit, inversion (inside-out), expansion-contraction, torque, and precession.

"The six basic motions are complex consequences of the six degrees of freedom. If you want to have an instrument held in position in respect to any cosmic body such as Earth, it will take exactly six restraints...Shape requires six restraints. Exactly six interrestraints produce structure. Six restraints are essential to structure and to pattern stability." (46, H, 400.664)

Fuller also notes that it takes a minimum of six interweaving trajectories to establish a boundary (insideness-outsideness) between any system and its environment (46, I, 240.32). It is thus a pre-condition of individuality (46, I, 458.05-11), and consequently of characteristic patterns of interference resultants: tangential avoidance, modulation, reflection, refraction, explosion, and critical proximity (46, I, 517.05, 101-12).

As an interesting confirmation of Fuller's statements, six muscles outside the eye govern its four basic movements in tracking any object - "restraining" it in order to be able to bring it into focus. The movements towards and away from the nose are each controlled by one muscle; the upward and downward movements are each controlled by two. Other movements involve a combination of muscles. Focusing is achieved by a muscular ring, the ciliary body, within the eye. This suggests that the distinct languages required to restrain a phenomenon conceptually could usefully be thought of as "counteracting together in a manner somewhat analogous to such muscles.

The learning dimension is introduced by Arthur Young in attempting to formalize how a free agent "interferes" with any system. The resulting freedom or unpredictability is then part of the system. He points out that a minimum of six observations are then required to determine the behavior of the free agent:

1. To know the position of a body in space, we need one instantaneous observation (for instance, the photo finish of a race).
2. To know its velocity, which is computed from the difference in position of the body and the difference in time between the two observations, we need two such observations.
3. To know its acceleration, we need three observations.
4. To know that a body, for example, a vehicle, is under control, and thus distinguish it from one in which the controls are stuck, we need at least four observations. That is, we need three to know acceleration and one more to know that acceleration has been changed. (This still does not tell us the body's destination or goal.)
5. To know the destination, provided the operator does not change his mind or try to fool us, we need five observations.
6. To know the operator has changed his mind or is trying to fool us, we need six observations. (70, p. 18)

Young notes that observation "categories five and six repeat the cycle", the fith falling into a position category (like the first), and the sixth falling into a velocity category (like the second). This shows the relationship between the minimum of four categories required for any analytical grasp and the six observational elements to encompass the behavioural complexity.

It is to be expected that the degrees of freedom of sociocultural systems call for a "corresponding array of conceptual "restrainers" in order to grasp their nature or contain them. This would also be true of any new order based on a hypercycle. Jantsch points out that the cyclical organization of any such new order may itself evolve if the participating (sub)systems mutate or new processes become introduced -- namely the hypercycles exploitation of its degrees of freedom. "The co-evolution of participants in a hypercycle leads to the notion of an ultracycle which generally underlies every learning process" (21, p. 15)

The term "ultracycle" was originally proposed by Thomas Balmer and Ernst von Weizaecker (71) to clarify the co-evolution of subsystems of an ecosystem. In such an ultracycle, according to Jantsch, the evolution of higher complexity does not result from competition, as in the hypercycle, but from interdependence within a larger system (21, p. 106). Each self-replicating "answer domain" in a hypercycle would then represent a niche within a sociocultural ecosystem, each such niche constituting a smaller ecosystem. Each "mutation" in a niche then catalyzes changes in other niches with which it is in contact - an increase in the complexity of one tending to increase in the complexity of others. The result of the co-evolution within the domains is then the evolution of the overall system. Jantsch sees this as applying to national economic systems, for example, but he does not focus on the inequalities in such development (21, p. 195-6)

"The ultracycle is a model for the learning process in general. Learning is not the importation of strange knowledge into a system, but the mobilization of processes which are inherent to the learning system itself and belong to its proper cognitive domain....Learning may generally be described as the co-evolution of systems which accumulate experience - a capability already characteristic of simple chemical dissipative structures. In the ultracycle information is not only transferred but also produced." (21, p. 196)