Communicable insights: the geometry of connectivity

Review of Frameworks for the Representation of alternative Conceptual Orderings as Determined by Linguistic and Cultural Contexts (Part #18)

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The arguments of the previous section can be clarified and taken a step further using the work of Ron Atkin on q-analysis, namely the theory and application of mathematical relations between finite sets. He has applied this to the analysis of communication patterns within complex organizations. (34, 35, 36). 

The perceptual significance of this approach is well-illustrated by visual sensitivity to colours resulting from the three primary hues (red, green and blue). These may be represented on a simple triangle : 

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Place Figure 6 here

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Here the vertices (O-simplexes) represent the primary hues, the sides are twofold combinations (1-simplexes), and the combination of the three hues makes the central white (2-simplex). The 2-simplex, together with all its faces, forms a simplicial complex KY (X) where X is the vertex set (red, green, blue) and Y is the set of seven perceived colours. 

Now to be able to see all the colours, a person's vision needs to have the ability to function in the triangle as 2-dimensional 'traffic' on that geometry, moving from location to location adjusting to the complexity of the geometrical structure which carries the visual traffic. It however the person's vision is limited to 1-dimensional traffic, then white could not be perceived because the visual traffic of seeing is then restricted to the edges and vertices only. Similarly, if the person's colour vision is only O-dimensional, then it is restricted to the vertices. It can only see one vertex colour at a time and never a combination (as represented by an edge). If vision was 3-dimensional, it would allow traffic throughout the geometry, but would perceive other colours as well, calling for a fourth vertex in order to contain the full range of combinations. 

If the geometry represents concepts or languages (or even sets of issues faced by an organization) instead of colours, then it would be expected that some people, in relation to that set, would have O-dimensional comprehension (i.e. sensitive to isolated primary issuesonly) and others would have 1-dimensional comprehension (i.e. only sensitive to binary combinations of primary issues). The latter would be unable to maintain attention to three concepts simultaneously in order to perceive the threefold combination (the central, integrated 'white' issue). The threefold issue may then be termed a 2-hole in the pattern of communication connectivity amongst those involved. For 2-dimensional traffic however, the issue complex is coherent, comprehensible and well integrated. For the 1-dimensional traffic, it feels less secure as a whole, since the latter may only be experienced sequentially through a succession of experiences ('around the edges') from which the shape of the whole may be deduced but not experienced For O-dimensional traffic, the integrated concept does not exist, since experience is disconnected. 

'Generally speaking it seems to be confirmed that action (of whatever kind) in the community can be seen as traffic in the abstract geometry and that this traffic must naturally avoid the holes (because it is impossible for any such action to exist in a hole). The holes therefore appear strangely as objects in the structure, as far as the traffic is concerned. The difference is a logical one in that the word 'q-hole' describes a static feature of the geometry S(N), whilst the world 'q-object' describes the experience of that hole by traffic which moves in S(N)' (34, p. 75). 

As an 'object' this phenomenon is an obstacle to communication and comprehension and obliges those confronted with it to go 'around' in order to sense the higher dimensionality by which it is characterized. Communications 'bounce off' such objects. As a 'hole' this phenomenon engenders, or is engendered by, a pattern of communication. It appears to function both as 'source' and 'sink'. Atkin suggests that, in some way which is not yet fully understood, such object/holes act as sources of energy for the possible traffic around them. From the initial research it would appear that such objects/holes are characteristic of communication patterns in most complex organizations. It seems highly probable that they can also be detected in any partially ordered pattern of communication. As such 'societal problems', 'human needs', and 'human values' merit examination in this light from the perspective of different languages. 

Very concretely, Atkin has investigated situations in which the 'vertices' (which could themselves be n-simplexes in a multidimensional geometry) are individuals or offices linked together through various committees. They could also be governments or disciplines. There will then be a lot of O-traffic and 1-traffic within and between offices due to the details of their intra-and inter-office (bilateral) operations. This traffic will circulate around the holes/objects which they constitute. Any n-level traffic can only be encompassed, or be brought to rest, by an (n+1)-level body (e.g. an executive or a committee). If the latter does not exist, such traffic will continue to circulate around the q-objects in the structure and, according to Atkin, may be defined as noise. An 'empire builder' (or any elite), for example, in such an organizational system will carefully create many q-holes underneath him (at the n-level), so that subordinate bodies answerable only to his appointees, are trapped in the flow of noise between them (34, p. 129). Atkin notes that even though the geometry may not have been rendered explicit, such structures generate the feeling throughout a community of some 'power behind the scenes' acting to outwit the formal structure. The special value of q-analysis is that it can clarify why action/discussion in connection with (development) issues tends to be 'circular' in the long-term, however energetic it may appear in the short-term. As such it shows how social change is blocked by the way in whichconceptual traffic patterns itself around the sensed core issue which is never confronted as such because the connectivity pattern is inadequate to the dimensionality of the issue. This would explain why so many issues go unresolved and why the process of 'solving' problems becomes institutionally of greater importance than the actual 'elimination' of the problem. 

When the elements of the triangle represent languages of different degrees of complexity/sensitivity the kinds of distinct languages discussed in the previous section would be represented by the vertices (just as they are in the cubic representation of Figure 5). It is possible for a person or an organization to conduct all its communication in one of these languages only. Communications in other languages would be incomprehensible and to some degree inconceivable. It is possible to envisage a different paradigm, corresponding to the 1-dimensional traffic, which would permit movement between the primary languages via intermediate languages. This would correspond to the mind-set of a polyglot or a polymath, for example. Presumably more complex paradigms could also be envisaged. Atkin analyzes much more complex situations in exploring information flows through the committee structure of a complex organization. He is especially concerned with how information on substantive issues gets moved around through appropriate committees without it being necessary to confront core issues or bring them into focus, namely the bureaucratic technique of handling information overload by avoiding use of that information. 

Q-analysis gives precision to the recognition that communication complex, traffic of different degrees of content connectivity finds (or creates) its appropriate level in any psycho-social presucmably including a language. Communicable insights are level-bound, especially where they are of high connectivity. In other words, at the level within which we can communicate, concepts cannot necessarily be anchored unambiguously into terms and definitions which 'travel well'. Precision introduces distortion which is only acceptable locally within any communicating society - although 'locally' must be interpreted in the non-geographical sense in which all nuclear physicists are near neighbours, for example. 

The relation between two personal or institutional structures, conceived as a multidimensional backcloth, carries whatever traffic that constitutes the communication between them. If this backcloth changes by becoming dimensionally smaller, then its geometry loses vertices and the consequent connectivity properties. This is first indicated by the failure of higher dimensional traffic which the geometry can no longer carry. Such 4-traffic, for example, must then move through the structure to some new haven of 4- dimensionality or it must change its nature and become genuine 3-traffic. This process of reducing communication expectations in order to continue to live within the new warped geometry is the classical problem of compromising. The feeling of 'having to compromise' is a painful one. It is the feeling of stress induced by the warping of the communication geometry, namely the direct experience of a structurally induced force, in this case a 4- force (34, pp. 146-7). It is the feeling associated with the distortion of an unsatisfactory translation between languages. This approach clearly provides a very precise approach to understanding more subtle forms of structural violence. Atkin has applied it to an analysis of unemployment (34, p. 148).

Such considerations suggest the power of q-analysis in clarifying approaches to human and social development in general. Reducing the dimensionality of the geometry on which a person (or group) is able to live is an impoverishment associated with repressive forces. Expanding the dimensionality induces positive, attractive forces through which a sense of development and enrichment is experienced (34, p. 163). Q-analysis seems to be a valuable new language through which precision can be given to intuitive experiences and their communication, particularly since it provides an explicit measure of obstruction to change. 

In the case of social development, it is probable that most continuing societal problems should be seen as holes/objects, especially given the well-established record of unfruitful action in response to them - however vigorous and dedicated. Typical examples are: peace/disarmament, development, human rights, environment, etc. Q-analysis could then provide understanding of why any action tends to be drawn into a vortex of futuility, however much it satisfies short-term political needs for visible 'positive' action. The participants in the action find themselves 'circulating' around a central concern of which they are unable to obtain an overview due to the geometries of the overlapping conceptual and organizational structures through which they work (or which they somehow engender). 

The term 'futility' used above is however only appropriate if the sole considerations were the elimination of such problems. In fact the existence of such problems is extremely important to the organization of society, to social development, and to the direct or indirect employment of many people. Just as the 'defence' business is vital to the economy of many countries, so is the 'social problem' business vital to many sectors of society. Eliminating social problems would be a disaster for many people, especially problem-oriented intellectuals, the employees of problem-solving agencies, or indeed those in need of stimulus and challenge. 

In the case of human development, Atkin shows how the individual can be defined in terms of a multidimensional geometry requiring a minimum of four levels (34, p. 111). By relating this geometry to that of society, Atkin introduces an 8-level scheme (34, p. 162) within which the degree of integration or eccentricity of communication can be clarified in terms of developmental or anti-developmental forces. 

Concerning such levels, the question arises as to whether their hierarchical order is fixed. Preoccupations associated with Schumacher's 'small is beautiful', for example, may well modify the order. The ordering may be a question of orientation in which the 'top' and 'bottom' elements selected depend on the preferred concept and direction of development (e.g. 'top-down',, 'bottom-up'). This would be more consistent with the concept of order as an (existential) choice as discussed above in connection with the various fourfold 'languages'. 

In such a multidimensional geometry it is clear that, whether in the case of an individual, a group or society as a whole, it is not possible to eliminate 'underdevelopment' as associated with low dimensionality. Such a geometry will necessarily continue to have traffic of very low-level connectivity co-present with that of increasingly higher level connectivity. The simplest illustration arises from the continual birth of infants who will, when resources permit, continue to be educated through to the level of connectivity to which they can respond. But there will always be communication at both low and high- connectivity levels, especially about socio-politicalissues. The question is then how such learning communication between these different levels of connectivity can weave itself together within a social structure. 

It is the status of the holes/objects in relation to development which could provide an interesting point of departure for further investigation. As noted above, it is not a question of attempting vainly to eliminate such holes, especially when some of them may arise from alternative concepts of 'development'. Rather it is a question of how configurations of holes can be identified and/or designed. It is such configurations of holes which provide the minimum structure (and communication dynamics) to stabilize and give form to the co-presence of the differing 'answers' to the challenge of development. 

In effect such holes exist at a lower connectivity-level than the 'macro-hole' of higher connectivity constituted by the world problematique at this time. This macro-crisis hole 'absorbs' the development initiatives of society by engendering the immense volume of action/communication traffic around the hole so defined. This draws attention to the developmental implications of the probable presence of holes of yet higher dimensionality than can be readily sensed or made the subject of acceptable public (consensual) communication. 

How then are 'better' holes to be engendered within such configurations? Now from one point of view it is necessary to avoid introducing an element of evaluation, because from each hole the perception of other holes will be distorted so that no communicable assessment can be usefully formulated. On the other hand, it may prove to be the case that, at the level of the configuration as a whole, more than one such configuration can be identified/designed in order to interrelate the perspectives associated with the set of holes. And at this level, without privileging any particular hole, more adequate interrelationships between the elements making up the holes can be identified. 

Expressed differently, introducing evaluative judgements into the relationships between the holes within a particular configuration can only contribute to the dynamics between such holes in terms of perceived advantage/disadvantage. Excessive emphasis on this runs the risk of tearing the configuration apart. The identities associated with the holes can be respected in each of the configurations in a series constituting progressively more adequate or richer formulations of the relationships between 'developments'. There is consequently a multiplicity of concepts of development operative in society. Individuals and groups may 'progress' from one to another, possibly with a general tendency towards those of higher connectivity. But other individuals and groups will emerge and find the concepts of lower connectivity more meaningful before moving on, if they do, to those of higher connectivity. (In this sense the 'ontogenesis' of an individual tends to repeat the 'phylogenesis' of his/her society). Society in this sense is the arena within which individuals and groups refine their concept of development. 

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