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Experiencing the forces of unseen connectivity -- mathematically described


Hyperspace Clues to the Psychology of the Pattern that Connects in the light of 81 Tao Te Ching insights (Part #3)


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The focus here is on comprehension by the individual in interacting with the contextual reality at any one moment. The question is whether there is any mathematically-based conceptual bridge that would clarify the relationship between "geometry" and "felt forces" in psychological and communication terms -- rather than in the material terms that are the focus of the metric tensor above.

One insightful approach is that of Arthur Young who was inspired by his experience in inventing the Bell helicopter, because of the need for the operator to control movement in three dimensions. His theory of process is a formal analytical model based on number theory, geometry and topology -- which endeavoured to relate to psychologically-oriented modes of knowledge and insight. Young used this model to help comprehend and integrate a number of disciplines and areas of inquiry. His original study Geometry of Meaning (1976), derived from an ordering of 12 dimensionless physical constants, offers a useful basis for exploring a diversity of issues relating to learning/action cycles, dialogue, sustainable development and experience of past-present-future complexes.

The mathematician who appears to have been most helpful in that respect is Ron Atkin (1972, 1974, 1976, 1977) -- whose ideas he has articulated more accessibly (Multidimensional man: Can man live in 3-dimensional space? 1981). Atkin proposed the use of simplicial complexes to analyze connectivity in social systems, like cities, committee structures, etc. Since then, Atkin's ideas have been developed further, resulting in a new combinatorial homotopy theory of simplicial complexes. In this setting, a graded group is associated to a simplicial complex, similar to the fundamental group of a topological space. However, the resulting theory is very different from classical combinatorial homotopy theory. Q-analysis is a combination of geometric and algebraic tools for studying relationships and connectivity among entities in a complex system. The research generalizes the idea of binary relation between two things, which underlies the highly successful theory of graphs and networks. Hypergraphs provide a first extension, allowing edges with more than two vertices. The methodology of q-analysis extends this by considering relational structure and multidimensional connectivity. Atkin was especially interested in traffic on hypergraphs.

A review of the relevance of insights from q-analysis to an understanding of the psychology of operating in complex communication spaces is given separately in Comprehension: social organization determined by incommunicability of insights (also in Comprehension and Organization). Peter Jackson explores Atkin's ideas on cover set geometry to education (The Geometry of Intention: values in the creation of curriculae)

Q-analysis has been used in the social sciences (Cullen, 1983; Macgill, 1985; Seidman, 1983), political science, industrial relations, community studies (Jacobson, 1998), planning (Johnson, 1981; Macgill, 1986), supply chain management (Rakotobe-Joel and Houshmand, 1999) and in organizational analysis [more]. It has been used to solve problems ranging from failure diagnosis in large-scale systems (Isida, 1985), traffic flows, organization of rule-based systems (Duckstein, 1988), multi-criteria decision-making (Chin, 1991). Q-analysis encourages inspection of data without distorting it -- contrasting with the conventional metric approach requiring manipulation of data involving some loss of information.

Using q-analysis for organizational analysis, in the Management of Technology Group of the Simon Fraser University (UK), the focus has been on change decisions and management, which are often the marking points in the life of manufacturing organizations where such analysis has been explored as a change management tool that allows the analysis of the change process. The task involved the analysis of the relationship between various organizational forms in the studied artefacts and their respective characteristics in order to unearth the connectivity between various forms. The result of the analysis was then used to assess the change from one organizational form to another. Keys to success were: (1) confirmation of groupings, (2) verification of evolutionary pattern, (3) exploration of the relationships between organizational forms and characteristics sets [more]. This preoccupation with change processes is of course the core focus of the "sister" classic to the Tao Te Ching, namely the I Ching (or Book of Changes).

Aron Katsenelinboigen (The Concept of Indeterminism and its Applications: economics, social systems, ethics, artificial intelligence, and aesthetics, 1997) says of Atkin:

I know of a single daring attempt (which is far from being completed) to formulate a rigorous mathematical procedure to compute predisposition. It was made by the British mathematician Ron Atkin (1972). He developed a concept of connectivity and applied it to such diverse fields as mathematics, politics, military strategy, chess, regional issues, family therapy, interaction of atoms and molecule, etc. (Atkin and Johnson, 1992). In the present context, the merit of Atkin's work is finding the formal language that adequately describes his concept. The formal constructs, borrowed from algebraic topology constitute an important step in the mathematical analysis of the problem, including its application to chess (Atkin, 1972, 1975).

Jacky Legrand (How far can q-analysis go into social systems understanding?) provides a detailed critical review of the applicability of q-analysis. She is concerned at the degree of "metaphorical discourse heavily flavoured by the methods of algebraic topology, abstract methodology, practical applications and their relationships" and the need to "separate the syntactic perspective from the semantic perspective". Her major conclusion is that "the gap between metaphorical discussion and woolliness is narrow. The understanding of some of Atkin's ideas has been too intuitive in the past. However the use of graphics as a language is a powerful thinking tool and Atkin has delivered a framework for thought".


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