Possible applications relevant to psycho-social organization

Polyhedral Pattern Language: Software facilitation of emergence, representation and transformation of psycho-social organization (Part #7)

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Team building and associated strategy:

• syntegration: One potential area of application is in building up teams. Relevant in that respect is the work of Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1995) and the franchised process of syntegration. The focus in this case is in building psycho-social structures based on the icosahedron.
• social networking: Another variant of this is as an extension of social networking and the current interest in enabling visualization and mapping of such networks -- typically of friends and contacts. The question is whether more coherent structures can self-organize, effectively using suitable polyhedra as catalysts or templates. This might prove a desirable additional option for those already enabled to list out such networks by name or in some other order, or based on some criteria. One reason for such developments, beyond the simple naming of members of a network, is that there are complementary qualities and characteristics important to the construction of teams with coherence. There may be a case for having a diversity of such qualities. An early proposal to that end (Group Questing or Twelving: Proposal for a large-scale small-group development process, 1976) points to possibilities that have yet to emerge from social networking.
• online gaming guilds: As discussed in the earlier paper (Engaging with popular games), a more probable early use of polyhedral representation of teams is in the design and management of online interactive gaming teams ("guilds") -- especially where a given polyhedron holds the "secret" of the coherence of such a guild and therefore is fundamental to its strategy and competitive advantage. In that respect, given the increasing overlap between such gaming simulations and electronic warfare, it is probable that polyhedra of appropriate complexity may be the secret to strategic success in reality. However Peter Gould and Anthony Gatrell (A Structural Analysis of a Game: The Liverpool v Manchester United Cup Final of 1977, Social Networks, 2 1980, 3) used the q-analysis, or polyhedral dynamics, of Ron Atkin to define and operationalise intuitive notions of structure in a soccer match between Liverpool and Manchester United. They found that the injection of q-holes, or obtrusive objects, by the defence of one team appeared to contribute to the fragmentation and loss of the other.
• research laboratories and "centres of excellence": Given the interdisciplinary challenges of such environments, mapping relationships onto a polyhedral form of adequate complexity (such as to highlight complementarities) might fruitfully clarify the integrative nature of the undertaking (cf Meta-challenges of the Future: for Networking through Think-tanks, 2005). The approach could also be applied to the "networks of excellence" promoted by the European Commission.
• sporting teams: Mapping the members and/or functions of such teams onto polyhedra could provide an appropriately visible sense of the integrity of the group and its vital complementarities -- in contrast with the simplistic schematics used for this purpose, notably in communicating through the media. Of interest is whether complexifying the polyhedra used would enable additional insights to be conveyed in team training. Clearly of greater interest is the possibility that a set of interrelated polyhedra might reflect the repertoire of strategies that the team might deploy against an opposing team. Of further interest is the possibility that the two teams might be usefully mapped onto the same polyhedron. There is even the possibility that the set of teams in a competition might together be represented in this way -- raising questions about how, as with the planes of a crystal, cognitive fascination is activated and engaged by reflection and refraction amongst the set of teams as a whole. This consideration might open the way to development of multi-sided ("polyhedral") games -- beyond the ubiquitous, binary, polarizing pattern to which politics is typically reduced.

Complementarity vs Imbalance: Especially important to team building, and the formation of coherent coalitions of stakeholders, is to ensure a requisite variety of complementary elements (whether people, organizations, strategies, values or concepts). The symmetry properties of the polyhedra can be used to distinguish such elements, notably by colour. Use of polyhedra in this way also serves to highlight possible imbalance.

Mapping and encoding psycho-social functions: The value of a polyhedral pattern language is clearly associated with the degree to which cognitive significance can be usefully mapped onto its features such as to highlight and hold complementarities and contrasts. This may be primarily a matter of exploration within the contexts for which the mapping is to be used, whether a small group or a large community of interest. It may be a communication device, symbolizing an initiative, irrespective of whether the mapping is universally acceptable. The range of geographical projections of the world points to the kind of variety that is possible and variously considered desirable

In its simplest form, the question is if a set of specific psycho-social functions is distinguished -- whether as principles, action programmes, values, qualities, etc -- is it helpful to map these onto a polyhedral form rather than present them solely as a checklist? Many such sets have been elaborated with different numbers of elements. Clearly a match can be attempted purely on the basis of the number (Representation, Comprehension and Communication of Sets: the role of number, 1978).

An unfortunate feature of many such extant checklists is that, because of their simple structure, no attempt is made to consider the relationships between elements of the set -- relationships which may be of considerable importance to the integrity and viability of the set when applied. Agenda 21, as formulated by the UN Earth Summit (Rio de Janeiro, 1992) is an example of an asystemic set of articles in that the relationships between the disparate parts are not considered. A mapping onto a polyhedron may highlight useful questions about relationships implied by the polyhedral pattern. These can lead to useful reconfiguration of the set.

Of particular interest is the case of sets of functions that are considered well-defined and complete. The Myers-Briggs Type Indicator is one example, with its 16 types. These could be mapped onto the vertices of an octagonal prism or the edges of a square antiprism. Clearly the 12 astrological types, as with any other 12-fold set, may be mapped onto a wider variety of convex polyhedra of greater symmetry (vertices: truncated tetrahedron, cuboctahedron, icosahedron; edges: cube, octahedron; faces: dodecahedron,) as well as non-convex forms (edges: tetrahemihexahedron; vertices: cubohemioctahedron, octahemioctahedron, great dodecahedron; faces: octahemioctahedron, great dodecahedron) and less symmetrical forms. Even those with more complicated names are readily comprehensible visually.

Given the importance of duals in relation to the geometry of many polyhedra, the significance of any corresponding mapping is of great potential interest. A dual of a polyhedron is one in which the vertices of the first correspond to the faces of the second. This implies an interesting relationship in alternating, through the dual, between:

• vertices used to map the nodes in a network of people, institutions, problems, concepts, -- with the edges of the polyhedron then indicating the links between them,
• faces used individually to map people, institutions, etc -- namely one per face -- with the edges linking the interface to other people, institutions, concepts, etc (across the edge)

Potentially more intriguing is the manner in which the form of a polyhedron may be usefully "decoded", recognizing the specialized interests that have explored this -- such as anthroposophy with respect to "projective geometry" and others with various approaches to "sacred geometry".

Mapping systems to highlight viability: Governance of any kind is called upon to deal with systems of increasing complexity. Such systems may be represented on hierarchical charts or systems diagrams of many kinds -- in two dimensions. Recognizing the arguments of Buckminster Fuller that polyhedra are to be understood as systems, the possible corollary that systems may be represented by polyhedra merits exploration. In that sense complex systems could be, in principle, fruitfully mapped onto complex polyhedra such as to highlight vital complementarity and necessary communication patterns (notably feedback loops).

Seeding organization emergence: crystal / saturation / catalysis ***

Transformation of organization: Identification of pathways, and transitional forms, through which an organization might evolve from one polyhedral form to another such form, possibly more complex. Stella already offers a number of possibilities for such transformation.

Significant issues of cognitive perspective: The cognitive mapping onto a surface that can be formed into a sphere raises interesting issues:

• as a spherically symmetrical polyhedron, it can only be viewed from one "side" and therefore has to be rotated manually -- or set to rotate -- in order to expose the other "side", and see "over the horizon". This raises the question of how the whole is to be understood and integrated
• as an unfolded flat net, only one side can be seen, since it lies flat. This raises the question of the other "side" which is potentially trivial since the whole net map is visible -- unless any image can only be attached to one side. This is especially significant when the flat net is folded under user control into spherical form because then the image is typically on the outer surface of the polyhedron, namely on the side currently hidden when the net lies flat -- unless the image is somehow allowed to be visible through each face of the polyhedron
• from within the polyhedron, which is often an option for a user who may navigate in virtual reality though the side of the polyhedron to view it from within. Here the question again is whether any images are apparent and the cognitive significance of having to rotate the polyhedron to understand the whole from within.

Encompassing disagreement:

• reconfiguring factional "sides", notably in a dispute: This possibility was the basic theme of the earlier paper (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008)
• reconfiguring "territory": This possibility has been partially explored in an earlier paper (And When the Bombing Stops? Territorial conflict as a challenge to mathematicians, 2000), notably in relation to the Middle East crisis.
• configuring global "bargains": A different approach was taken with respect to the strategic dilemmas articulated at the 1992 Earth Summit (Configuring Globally and Contending Locally: shaping the global network of local bargains by decoding and mapping Earth Summit inter-sectoral issues, 1992). This followed earlier related consideration of incommensurability (Containing the incommensurable, 1995; Using disagreements for superordinate frame configuration, 1995; Insights evoked by intractable international differences, 1993; Reordering Networks of Incommensurable Concepts in Phased Cycles, 1988)

Communicating meeting outcomes: The process whereby an integrative synthesis is derived from the insights expressed at a meeting -- the global "sense of the meeting" in Quaker terms -- could be understood in terms of the ability to produce a mapping of them onto a suitable polyhedron. This could then be a visual complement to a press release -- even an index to its elements (on a web page).

Curiously this echoes the intuition associated with the use of gold "nuggets" as a significant meeting product, or even the discovery of "diamonds" in the meeting process. To the extent that the pattern of such insight is reflected in a concluding declaration, its elements could also be usefully mapped onto a polyhedron (Patterning Archetypal Templates of Emergent Order: implications of diamond faceting for enlightening dialogue, 2002; Structure of Declarations: challenging traditional patterns, 1993) possibly even to be associated with song (A Singable Earth Charter, EU Constitution or Global Ethic? 2006). In this context, in relation to discussion of tensegrity structures below, Ronald J. Barnett and Gregory W. Cherry have applied for a patent on Tensegrity Musical Structures.

Communication of more complex forms of organization: Just as a spiral staircase does not lend itself to comprehensible verbal description without any illustration (if only gestures), so there may be many forms of coherent organization that could well depend on the kind of cognitive prosthetic provided by a polyhedron of whatever degree of complexity. As with the spiral staircase, this may enable transition from one level to another. The polyhedron then functions as a mnemonic of a superior degree of order to bullet pointed charts, other checklists and complex organizations charts that do not enhance memorability. Without such support, higher degrees of ordered complexity become essentially unsustainable.

Configuration of the parts, with which people may variously and separately identify, helps to determine whether, as a confguration, a larger and deeper sense of identity and significance emerges. The question is then whether the emergent organization corresponds to a mode of organization with which people are already familiar (experientially) but for whose patterns no adequate description has as yet been found -- as with an "unformed" sense of community or team.

Insightful discussion of the associated communication and comprehension challenges is provided by mathematician Ron Atkin (Multidimensional Man; can man live in 3-dimensional space? 1981; Combinatorial Connectivities in Social Systems; an application of simplicial complex structures to the study of large organizations, 1977) as summarized elsewhere (Social organization determined by incommunicability of insights, 1995).

Such considerations point to the possibility of using interrelated polyhedra, of different degrees of complexity, to map psycho-social issues (over) simply, comprehensibly, and more challengingly -- such as to elicit a greater degree of imaginative engagement. Exploration of the transformations between these degrees of complexity enable learning pathways to be highlighted. They also point to patterns of insight and order that are more likely to be forgotten -- and which are effectively meta-stable and unsustainable, namely which lack adequate mnemonic reinforcement.

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