Edgar Taschdjian has recently suggested that if cybernetics is to move byond 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". (64) 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." 3ust 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 (65), 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.