In the light of the arguments above concerning fourfoldness as providing the basis for the minimal conceivable system through which distinct domains could be related, it is possible, as Mushakoji noted (see above), 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 Thorn demonstrated that, irrespective of their nature, there are only seven qualitatively different types of discontinuity then possible (19). 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 catastrophy theory has demonstrated that in systems with five control factors, a further four types of characteristic catastrophy 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 catastrophy", 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. A related problem in cultural anthropology has however been explored by a philosopher, W T Jones (162). He is concerned, like Maruyana, 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 transition "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:
- Order vs disorder, namely the range between a preference for fluiditity, muddle, chaos, etc. and a preference for system, structure, conceptual clarity, etc.
- Static vs dynamic, namely the range between a preference for the changeless, eternal, etc. and a preference for movement, for explanation in genetic and process terms, etc.
- Continuity vs discreteness, namely the range between a preference for wholeness, unity, etc and a preference for discreteness, plurality, diversity, etc.
- Inner vs outer, namely the range between a preference for being able to project oneself into the objects of one's experience (to experience them as one experiences oneself), and a preference for a relatively external, objective relation to them.
- Sharp focus vs soft focus, namely the range between a preference for clear, direct experience and a preference for threshold experiences which are felt to be saturated with more meaning than is immediately present.
- This world vs other world, namely the range between a preference for belief in the spatio-temporal world as self-explanatory and a preference for belief that it is not self-explanatory (but can only be comprehended in the light of other factors and frames of reference).
- Spontaneity vs process, namely the range between a preference for chance, freedom, accident, etc. and a preference for explanations subject of laws and definable processes.
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 formes (46, I, 1040-1042.05). He shows that if each axes 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 (46, II, 1041.12-1041.13). If each extreme mode (or "domain") on Dones 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" (21, p. 240). But he draws attention to the reality of such a sevenfold system in Hindu thinking concerning human development.