Cognitive insights from mathematics

Engaging with Globality through Cognitive Circlets (Part #6)

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A very helpful bridge between the precision offered by a mathematical description and the cognitive implications (associated with torque) is to be found in the work of Ron Atkin (Combinatorial Connectivities in Social Systems: an application of simplicial complex structures to the study of large organizations, 1977; Multidimensional Man: can man live in three dimensional space? 1981). As summarized elsewhere (Social organization determined by incommunicability of insights), this highlights the way in which social action (of whatever kind) can be seen as traffic in an abstract geometry descriptive of cognitive relationships -- and specifically how this can be manipulated by ensuring the presence of "holes" in that space "around" which communication is forced to take place:

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, whilst the world "q-object" describes the experience of that hole by traffic which moves in that geometry....

This suggests new ways of comprehending the nature of a problem. 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, object/holes act as sources of energy for the possible traffic around them. His use of 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 complex, presumably including a language:

Communicable insights are level-bound, especially where they are of high connectivity. In other words, at the level within which it is possible to communicate, problems cannot necessarily be anchored unambiguously into terms and definitions which "travel well"....

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...

In these terms, "cognitive torque" may be understood in terms of the experience of warped geometry:

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... 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 this approach to an analysis of unemployment. 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. 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 futility, 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).

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. By relating this geometry to that of society, Atkin introduces an 8-level scheme within which the degree of integration (or eccentricity of communication) can be clarified in terms of developmental or anti-developmental forces.

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 continuing 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-political issues. The question is then how such learning communication between these different levels of connectivity can weave itself together within a social structure.

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