Movement and focus of attention

Evoking Authenticity: through polyhedral global configuration of local paradoxes (Part #8)

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Individual attention tracks endlessly around any container, often following habitual circuits -- as noted by many meditation masters and psychologists. Some control may be exerted as with the control of the traffic on a model train set of some complexity -- switching points, stopping/starting trains, etc. The circuit may be more complex still -- perhaps as with the circuit board of any piece of electronic gadgetry -- capacitors, resistors, etc -- or with an extensive electrical grid.

Attention may flow along pathways as along any decorative garden walk. Any particular stretch may be experienced like the string of an instrument -- it may be plucked to evoke resonances and harmonies with others elsewhere. Degrees of consonance and dissonance may be detected. Patterns of association may become perceptible as in the art of poetry.

As with any journey, there is a pull onward to the next junction, and the next -- the potential of distant green fields. Significance may be derived from such "tourism" -- with explication taking the form of travel journals as in the earliest exercises in linear route mapping.

In a formal organization the flow and focus of attention is ensured by arrays of subunits. A conventional organization chart might be seen to be an array vital to that body's knowledge management process. Typically this is hierarchical -- with daring excursions into matrix management and network organization models. These may all be considered to be different styles of array. They reflect equivalent arrays in conceptualization: hierarchy, matrix, and network. Interestingly the French term for a matrix-based conceptual array is grille de lecture, emphasizing that it is through the conceptual array that external phenomena are read -- as through a pattern of window panes (and, ironically, the Windows computer operating system offering a "gateway" to surfing the web).

It is also worth considering how many conceptual schemes, whether theories or in the form of operational plans, can be considered as arrays -- ranging from lists of concepts (as in web menus), through tables, to more complex structures. The organization of these may be of special significance in practice (see Representation, Comprehension and Communication of Sets: the role of number, 1978).

Although much studied, it is questionable whether array technology as applied to social organization is now as sophisticated as that applied to radio antenna design and operation. There has been little follow-up to Patrick Heelan's concern with "The Logic of Changing Classificatory Frameworks" (1974) in terms of the conceptual freedom of the lattices of non-Boolean quantum logic -- which is in complete contrast to the essentially mechanistic structure of conventional thesauri [more]. He noticed that meta-contextual languages able to unify two or more contextual languages are isomorphic.

One intentional community that made very intensive use of conceptual matrices (which they termed "screens") was the Institute of Cultural Affairs [collective research]. The question is how such conceptual arrays function to orient the flows of insights and control messages throughout a community -- or for an individual. Can polyhedral configurations be understood as arrays of differently oriented facets that focus disparate insights? As such do they effectively function as conceptual antennae for the detection of insights of higher dimensionality?

How does this contrast with processes based solely on logical chains of argument -- on a "line" of argument? Can an "argument" then be better understood as an array of reasons to be comprehended through insights into their complementarity and symmetry -- as with a configuration of paradoxes? This then raises issues about the kinds of visual literacy required to comprehend an argument, or conceptual complex, so presented. The work of mathematician Ron Atkin --- concerned with whether humans can live in only three dimensions -- is helpful in understanding the difficulties that may be experienced in holding an array of perspectives of any particular degree of complexity [more]. Forms of intelligence may be cultivated that are more adept at this than those whose strengths lie in conventional forms of literacy and numeracy.

There is a case for exploring radiolaria as arrays. They are holoplanktonic protozoa widely distributed in the oceans (and in the fossil record) and range from 30 microns to 2 mm in diameter [more; more; more]. They have long been an inspiration as art forms in their own right [more]. Many are spherical in structure. Extremely interesting efforts by Nicholas Shea have been made to generate such spherical radiolaria structures [more] with graphic software within the context of other generated spherical arrays [more], including buckyballs [more; more].The question is whether such structures could be used to configure semantic content spherically -- a spherical semantic network map. This would then provide a context for exploring whether some collective initiatives effectively involve the construction of such "closed" arrays as "grilles de lecture".

Do such structures:

• map complex closed conceptual systems?
• reflect a degree of "programming" in both the positive and negative sense?
• provide the degree of mutually reinforcement between the semantic components to perform an antenna-like function ?
• offer clues to the emergence of coherence in the forthcoming "semantic web"?

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