In the light of the arguments in previous notes concerning fourfoldness as providing the basis for the minimal conceivable system through which distinct domains could be related, it is possible, as Mushakoji noted, that recent work on catastrophe theory can clarify the kinds of discontinuity which might then become apparent. Clearly knowledge of the forms such discontinuities take is necessary if the dynamics of such a developing system are to be encompassed conceptually.
If the behaviour of the minimal conceivable system interrelating the domains is determined by four control factors only, Rene Thom (1980) demonstrated that, irrespective of their nature, there are only seven qualitatively different types of discontinuity then possible. In other words, while there are an infinite number of ways for such a system to change continuously (around an equilibrium position), there are only seven structurally stable ways for it to change discontinuously (through non-equilibrium states). "To put it very simply, in a wide range of situations - physical, biological, even psychological - where experience tells us that 'something's got to give'...there are only seven fundamentally different ways it could happen".
Recalling the importance of fivefoldness for implementability, it is appropriate to note that subsequent work on catastrophe theory has demonstrated that in systems with five control factors, a further four types of characteristic catastrophes emerge, making a total of eleven. Above five there are no unique patterns.
The question is then what are these possible "catastrophes" or discontinuities as they emerge in human and social development? What are these processes with which people are presumably intimately acquainted, but which are seemingly difficult to "objectify" despite their importance ? In a sense the discontinuities are "irrationalities" to which man is subject in the development process. Thus the "cusp catastrophe", for example, has been used to explore the flight/fight and love/hate transitions. The nature of such developmental discontinuities does not seem to have been determined.
2. Varieties of communication
In cultural anthropology, a related question has however been explored by a philosopher, W T Jones (1961). He is concerned, like Maruyama, with discontinuities in communication which prevent people, supposedly concerned with the same subject, from achieving any effective dialogue. To clarify this situation, he demonstrates that the discontinuities can be described in terms of the different positions of the participants (or schools of thought) on [seven pre-rational axes of bias]. These differences are reflected in aesthetical, theoretical, value, life-style, policy, and action preferences, as well as in the preferred style of discussion. Any difference between people in position "along" an axis gives rise to discontinuity which it is difficult to handle within a rational frame of reference. The axes identified by Jones are:
It is worth noting that in Fuller's analysis of systems, conceptual and otherwise, he identifies a total of [seven axes of symmetry necessary for the descriptions of the variety forms] (1975,I,104010 42.05). He shows that if each axis passes through two distant planes, then the fourteen resultant planes together encompass all possible asymmetries in relationships, as typified by arrays of biological cells or bubbles (1975,II,1041.121041.13). If each extreme mode (or "domain") on Jones axes (above) is represented by a plane, then the variety they represent together could be "contained" by a "space" of fourteen facets. Much of Fuller's work is concerned with the fundamental significance of the regenerative transformations possible with systems represented by such a fourteen-faced figure.
Jantsch attributes a seven level structure to the autopoiesis and evolution of man. He notes that such "a concept of multilevel life presents considerable difficulties to Western thinking" (1980, p.240). But he draws attention to the reality of such a sevenfold system in Hindu thinking concerning human development.
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