1. Nonlinear cybernetics
Edgar Taschdjan has recently suggested that if cybernetics is to move beyond its current preoccupation with the "simplified world of abstract models", it appears to be necessary to develop a "nonlinear cybernetics able to handle regulations which are time-dependent and dialectic rather than mechanistic". (1982). Many world modelling exercises are based on such simplified models.
Tashdjan argues that human behaviour is not constant and that "too much of a good thing can become a bad thing". Furthermore, the "bipolarity of human motivations permits switches from positive to negative, from attraction to repulsion", whether in the case of an individual or of a group. The classic concepts of negative and positive feedback fail to encompass this reality since the results of such interaction in a system are purely linear, in the sense that regulators either add or subtract output from the unit governed. Regulation maintains an "equilibrium". The negative feedback concept, based on nullifying deviations, is "not sufficient to explain the real behaviour of the steersman of a sailing vessel buffeted by changing winds, who has to "tack" first in one direction, then in another." Just as in the case of (development) policy-making, there is a need to "change the course abruptly and repeatedly in order to reach his objective", especially if he has to steer around an obstacle. On the other hand, the positive feedback concept, based on amplifying deviations, is only able to explain exponential growth, whereas "real growth processes are not exponential but sigmoid", namely a function of time. All growth is constrained by counteracting processes
Now in a situation where there are effectively two interacting regulators governing the same working unit, for example two alternative policies (political parties) by which a society is (successively) governed, this "three-body problem", even in mechanical systems, is not susceptible to deterministic analysis. The synergisms and antagonisms which emerge are essentially nonlinear interactions. Such double regulation is of great importance in natural systems and society.
The overall effect of such interactions is a continual disequilibrium. In the case of physiological systems, "Once the organism reaches equilibrium, it is dead." In attempting to regulate any such oscillating systems, timing of intervention is vital, as is evident in attempting to control a child's swing. The timing of any therapeutic treatment is as important as its nature and direction.
From these considerations Taschdjan concludes that "when we want to analyze and model systems existing in nature and society, the dialectic process of successive antagonistic actions requires the model to be quadripolar rather than bipolar". He points out that there is no difficulty in representing this mathematically since the totality of positive and negative real numbers constitute a bipolar system, representable on one axis. It is accepted mathematical practice to add another axis perpendicular to this to indicate the bipolar system of imaginary numbers, which then, as discussed by C Muses (1967), represent the temporal dimension necessary to describe nonlinear processes. For Taschdjan, therefore, "to say that a system of dialectic interactions is quadripolar, is merely another way of saying that the system is nonlinear". Analysis then requires the use of vectors and tensors rather than scalars, and these are multiplicative rather than additive.
2. Cyclic self-organization requirements
The previous notes have demonstrated the need for at least four distinct approaches to be able to "contain" the complexity with which society is faced. These are the minimum number of complementary languages through which a "rounded" understanding of human and social development may be achieved.
Whilst four distinct approaches are sufficient to contain a general conceptual understanding, Buckminster Fuller argues that specific, concrete instances require a fifth: "all recallably thinkable experiencings, physical and metaphysical, are fivefoldedly characterized...All conceptually thinkable, exclusively metaphysicalexperiencings are fourfoldedly characterized" (1975,II,1072.2123). For Fuller the fourfold is the basis for a minimal conceptual system, whereas fivefoldness "constitutes a self-exciting, pulsating propagating system" (1975,I,981.03). He demonstrates this in many structural systems.
The difficulty with the four languages, as Fuller implies, is the additional ordering required to get to grips with particular cases. As such they together only offer an unanchored potential for grasping the particular. The question is how distinct approaches interrelate, or "resonate" together (since linear or "mechanical" interlinkage is unlikely) to underpin and stabilize any new order, whether conceptual, social, or physical. This is clearly of central importance to any practical approach to human and social development.
In Jantsch's investigation of cyclic self-organization of social systems (1980), he draws attention to the work of Manfred Eigen in molecular genetics. Eigen explores the question of how new information originates (1978). This is a general problem of evolution, which Jantsch relates to development and to learning. The question is how the new information emerges to provide the basis for any new patterns of ordering. Any given language, or "answer domain", effectively functions like a self-replicating ecosystem. Margalef (1968) has described the evolution of such ecosystems as a process of information accumulation. Each such system seeks information from the environment, but only to use it to prevent the assimilation of more new information. Novelty is continuously transformed into confirmation. The question is how any new order can emerge under such circumstances.
Eigen uses the term "hypercycle" to denote any such new order. A hypercycle is a closed circle of distinct transformatory or catalytic processes in which one or more participants act as autocatalysts. For Jantsch: "Hypercycles...play an important role in many natural phenomena of self-organization, spanning a wide spectrum from chemical and biological evolution to ecological and economic systems and systems of population growth." (1980,p.15). Eigen, in reporting on his detailed analysis with Peter Schuster of the emergence of such new order (1979), states: "The self-replicative components significant for the integration of information reproduce themselves only in a coexistent form when they are connected to one another through cyclic coupling. The mutual stabilization of the components of hypercycles succeeds for more than four partners in the form of nonlinear oscillations..." (p.252).
Such a hypercycle can be seen as a linking process between the participating (sub)systems, themselves cyclically ordered. The formation and maintenance of such a cycle which runs irreversibly in one direction and reconstitutes its participants and thereby itself, is possible only far from equilibrium. Its rhythm is controlled by the cycle of the slowest acting participant, thereby liberating transformative energy steadily rather than explosively (p.90).
From this one could conclude that whilst an adequate new (world) order can be envisaged with the aid of four internally consistent, self-replicating languages, it could not be rendered practicable without a fifth language of some kind.
For Eigen "the hypercyclic order is a theoretically justifiable, essential requirement for the integration of subsystems capable of replication into a unit of greater informational content" (p.255). It alone is capable of integrating and stabilizing such otherwise competing (sub)systems. Simple connections "would not be sufficient for cooperative stabilization of the components" (p.255). From a multitude of such replicative units, the hypercycle can discover those appropriate to one another and, if the combination offers some advantage, amplify them selectively. In this manner a totally novel order comes into being through "sympathetic" interaction which does not change the nature of the participating (sub)systems, although it may optimize their characteristics (p.256).
Eigen, through his hypercyclic ordering principle, addresses directly the question of the nature of the non-Darwinian constraining mechanism in an environment in which each "species" would otherwise expand exponentially. This is a problem with any individual answer domain, whether discipline, ideology or religion. "Coexistence of competitors requires some sort of stabilization, which confirms the exponential growth law, or the formation of niches that uncouple the competition." (p.247). Eigen's "decisive question" is also of interest for the emergence of any new world order: "The decisive question for the evolutionary ability of an information-integrating system is that of the stability of the respective coupled reaction systems, whose components must be coexistent, at the same time behaving in toto selectively with respect to other competitors." (p.251). The latter would then presumably be those hypercyclic features characterizing the old order.
3. Encompassing system dynamics: sixfold restraint
It is not to be expected that the 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..." (1980, 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" (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." (1979,II,400,464).
Fuller also notes that it takes a minimum of six interweaving trajectories to establish a boundary (insideness-outsideness) between any system and its environment (1975,I,240.32). It is thus a pre-condition of individuality (1975,I,458.0511), and consequently of characteristic patterns of interference resultants: tangential avoidance, modulation, reflection, refraction, explosion, and critical proximity (1975,I,517.05,10112).
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 "counter-acting" together in a manner somewhat analogous to such muscles.
4. Encompassing system dynamics: learning
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 behaviour of the free agent:
- To know the position of a body in space, we need one instantaneous observation (for instance, the photo finish of a race).
- 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.
- To know its acceleration, we need three observations.
- 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).
- To know the destination, provided the operator does not change his mind or try to fool us, we need five observations.
- To know the operator has changed his mind or is trying to fool us, we need six observations." (1978,p.18).
Young noted that observation "categories five and six repeat the cycle", the fifth 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 behavioral complexity.
5. Ultracycles and hypercycles
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 hypercycle's 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" (1980,p.15).
The term "ultracycle" was originally proposed by Thomas Balmer and Ernst von Weizaecker (1974) 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 (1980, 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 catalyses changes in other niches with which it is in contact - an increase 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 (p.1956).
"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." (p.196).