Communicable Insights

Passing Thoughts: Anthony Judge

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Geometry of connectivity

In this annex to Comprehension of Appropriateness, the arguments of the previous annex 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. (38, 39, 40). 

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.

Comprehension of insights based on triangular model of Ron Atkin
	0-dimension vision ("vertex"): Red, Green or Blue 1-dimension vision ("line"): Yellow (=Red/Green); Purple (=Red/Blue); or Turquoise (=Blue/Green) 2-dimension vision ("triangle"): White (=Red/Green/Blue)

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. If 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 modes of socio-economic 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 issues only) 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)" (38, 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 and modes of socio-economic organization. 

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/objectswhich 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 (38, 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 which conceptual 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. 

The elements of the triangle may also be used to represent different modes of socio-economic organization comprehensible under different conditions. It is possible for a person or an organization to conduct all its communication in terms of one of these modes or frameworks. Communications in terms of other modes or frameworks 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 modes via intermediate modes. 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 traffic of different degrees of content connectivity finds (or creates) its appropriate level in any psycho-social communication conmplex, presumably 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 i

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