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26 Dec 2001 | Uncompleted

Coherent Patterns of Schism Formation, Bifurcation and Disagreement

and the associated bonding, encounters and agreements they evoke

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It is a characteristic of psycho-social processes that enunciation of a belief in something eventually evokes enunciation of a contrasting belief. Historically this has been most evident in the case of religion with the formation of schismatic, breakaway movements -- possibly formally declared to be heresies. It is also evident in the case of ideological movements and schools of academic thought -- and of therapeutic or psychotherapeutic approaches. The breakaway may be both dramatic and traumatic for many involved, leading to unresolved tensions for many decades -- as in the separation of Protestants from Catholics, or Jung from Freud. Such a process is also evident in personal relationships, with dramatic separations resulting from some fundamental disagreement. It is perhaps most explicitly acknowledged in the 18 contrasting schools of ** philosophy.

The question explored here is whether schism formation -- and the emergence of disagreement -- in any way follows a pattern. Might the nature of this pattern hold larger insights important to the understanding of the emergence of the requisite variety necessary to the viability of any self-organizing system -- such as an 'ecosystem' -- whether linking biological, social or knowledge entities?

And if there is a pattern to schism formation, might there also be some sort of a matching pattern to the emergence of encounters that give rise to agreement and bonding? If this proves to be the case, then it is at the level of the pattern that responses to fundamental differences between religions and belief systems should be sought -- especially when they are associated with bloody territorial conflicts. Reconciliation may indeed be seen as a desirable coming together, but it is only meaningful within a pattern that recognizes a necessary tendency to break apart -- a pattern that both connects processes and holds the larger quality that is expressed by such variety. Such patterns are perhaps best understood in certain forms of drama and music.

This pattern needs to be explored in relation to the nature of any integrative understanding as expressed in calls for 'unity', 'coherence', 'harmony', or other insights into 'wholeness'. Failure to do so renders such 'global' perspectives essentially unsustainable.

The emphasis here is on the experiential quality -- the way in which the separation is experienced as a consequence of disagreement or permanent schism.

Biological template

The most obvious model of 'schism' formation is in the process of cell division, notably following human conception. This has been extensively explored in terms of 'bifurcation' leading to cell differentiation.

This ontogenetic development associated with successive bifurcation of cells to constitute a given organism is recognized as echoing the pattern of phylogenetic bifurcations leading to the emergence of the species in question. Such a pattern of bifurcations creates a range of species adapted to fill a corresponding range of niches in the environment. If there is a niche in the ecosystem, a species will adapt to fill it by distinguishing itself advantageously from other species..

It might well be argued that much evolutionary learning has been invested in this process. This is therefore likely to carry over into socio-cultural, psycho-cultural and conceptual equivalents -- in preference to any alternate pattern. Do the disagreements dividing social groups emerge in a manner in any way similar to those of cell division or speciation?

Perceptions preceding schism

In a psycho-social context, a coherent belief system is eventually threatened by perceptions in the left hand column (in the following table). These lead to distancing, alienation and dissociation through a form of rejection. This may well be aided by processes of attraction (right hand column) to some other belief -- recognized progressively as a more powerful attractor.

Alienation from known Attraction of new possibility
Sense of distance Sense of attraction
Miscommunication Novelty
Sense of constraint Discovery Freedom to explore
Predictability, Sense of closure Unexpectedness, Unpredictability
Sense of going nowhere Learning
Sense of pattern repetition More meaningful
Boredom More correct, More truthful
Less meaningful, Inadequacy  

The new focus may successfully provide coherence for many. However some, possibly of a later generation, will eventually be exposed to the same processes of disassociation once again -- as they encounter, or evoke, some other attractor experienced as more powerful.

Pathways of bifurcation and encounter

The emergence of religious movements, breaking away from those which preceded them historically, provides a fairly well-recognized pattern. New movements continue to breakaway from those so formed. The same is true of schools of thought within many academic disciplines.

Such patterns are seldom presented visually -- often because those best informed have a vested interest in denying the legitimacy or viability of breakaway movements with contrary views (possibly to the point of denying their existence). There is therefore little sense that such speciation is occurring in order to fill an implicitly defined space of unknown geometry and extent.

The question here is whether there are interesting and meaningful ways to think about the nature of such a space and its geometry. Hence the interest of the 18 schools of Indian philosophy.***

Before exploring this question, it is important to recognize that speciation has a consequence, namely encounter between species. If two distinct belief systems are formed by a speciation process, representatives of these species will tend to encounter each other. They will have to develop behaviour to deal with each other. The encounter may be associated with hostility or even violence. More interesting however are encounters, between species that are not immediate, direct descendents of the original undifferentiated belief system. Eight types of inter-species encounter have been described (***). These encounters may involve recognition of complementarity, even of attraction of opposites, namely a form of bonding that is important to the viability of the psycho-cultural ecosystem as a whole. In particular contrasting species may learn from each other -- a process much extolled in relation to inter-disciplinary, inter-faith and multi-stakeholder dialogue.

Encounters, especially those associated with learning or development of interdependency, therefore constitute a kind of temporal mirror image of bifurcation -- perhaps partially to be denoted by reconciliation. They may be especially significant in the case of personal relationships and bonding. But of course the coherence of such bonding is itself subject to subsequent bifurcation processes, if, and when, those involved go their separate ways.

Thus although bifuraction creates differences, these nevertheless lead to new 'encounters'. The next encounter is like a 'reverse bifurcation' or 'mirror' event. Encounters involve recognition of 'similarities' -- leading to binding events between/across dissimilarities, namely a form of 'marriage'. These are not to be confused with 'complementarities' which may be limited to similarities across the space (ie non-contiguous).

Curvature of bifurcation-encounter space

An ecosystem that effectively gives rise to a number of species, say 30, may possibly be describable by the network of bifurcation and encounter pathways that have separated the species over time and bring them together in time. This network may indeed be considered as without any particular structure. However it is interesting to consider the implications of two interrelated forms of structuring features. The first is 'curvature' and the second is 'polyhedra' as approximations to a sphere.

Curvature provides an interesting metaphor through which to understand the 'horizon effects' which impede visibility of very distant features on what might otherwise be understood as a flat landscape. Curvature also provides some sense of focus and containment of significance that otherwise tends to be eroded by flat perspectives.

Such curvature offers a greater sense of integrity if it iis understood in terrms of a sphere, with the pathways over its surface. Such a sphere provides a kind of memetic equivalent to a 'gravitational' effect that constrains those on its surface to exploration of the closed curvature. There are significant challenges to getting 'off' the surface. (centrifugal / centripetal -- Atkin?***)

Polyhedral approximations to spherical curvature

The integrity of episystemic bifurcation space can indeed be fruitfully associated with a closed curved surface such as a sphere, as an ideal template for insights into the integrative dimensions of unity. But to hold the reality of the contrasting understandings created by bifurcation, it is useful to acknowledge explicitly the 'flat earth' quality of each such individual 'holding'. Like tectonic plates, each subdivision of the whole can be imagined as a relatively flat surface. Different flat surfaces then meet at fault lines where the orientation of the surface changes. Together the many such surfaces then make up (and cover) the spherical surface -- constituting the integrity of the whole. Each such flat surface may be usefully understood as a 'field' of knowledge.

One of the most helpful ways to explore how flat surfaces might be joined together by bifurcation pathways to approximate a sphere is through the set of Platonic or Archimedean solids. Matching these 3-dimensional polyhedra are characteristic 'nets' generated by rolling each solid on a flat surface such that the edges of each of its surfaces represent links in the network consituted by the edges and apices of the solid. Discussion of networks is normally focused on what may be represented in 2 dimensions in this way. But 2--dimensional networks may also be understood as wrapped around matching 3-dimensional polyhedra.

This approach is especially interesting when 'networks' are understood as representing systems of relationships, as in ecosystems or communication systems. R Buckminster Fuller has extensively explored the argument that all systems are polyhedra.

Each polyhedron, or its matching net, then defines a viable pattern of variants -- that might in turn be represented by coordinates on the surface of a sphere. The coherence of the (eco)system represented is then associated with the properties of the polyhedron or its net.

This metaphor then suggests an interesting distinction between:

The surface net effectively defines a kind of wrap-around periodic table -- projectable onto 2D with various distortions and assumptions -- to provide a classification of the extant species within that system. Simpler systems of lower species variety would be described by simpler tables. Nesting the nets would gives a sense of how the corresponding paradigms are related to one another -- matching apices, faces, edges, duals, etc.





Speciation pathways

Filling structural / dynamic niches (theoretical biology? Consilience?)

Transaction analysis

may have 'jumps' to another solid/net

species/characteristic 'A' engenders 'not-A'


apartness: email dialogue


genetic ?

meaning / demeaning ?

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