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Indicative implications for global governance (A)

Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors (Part #10)

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Communication interfaces: If it is assumed that each of the 12 conceptual modalities necessary for coherent governance might be modelled by one of the polyhedra, then the facets and points of contact between them are suggestive of vitally distinctive communication interfaces that could be fruitfully explored with distinctive electronic protocols (cf Patterning Archetypal Templates of Emergent Order: implications of diamond faceting for enlightening dialogue, 2002).

Each facet is effectively one of the "windows on the world" from that particular modality or organizational perspective. Note that "facet" is a technical term in the discipline of knowledge organization -- notably in relation to faceted classification. Such facets might for example, be significant for communication between distinct functional units (as in the case of complementary government ministries) or with "associated" organizations or concepts. As noted above, aspects of this have been explored by management cybernetician Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994) [more]. Team syntegrity is understood by Beer as the "intelligent design" for managing complexity (cf J. Truss, et al. The Coherent Architecture of Team Syntegrity: from small to mega forms).

An associate of Beer, Markus Schwaninger proposed, to the 47th Annual Meeting of the International Society for the Systems Sciences, the use of neural and polyhedron research as a method for design of democratic management and for heterarchy (What Can Cybernetics Contribute to the Conscious Evolution of Organizations and Society? 2003). In Gunter Nittbaur's presentation of his work (Stafford Beer's Syntegration as a Renascence of the Ancient Greek Agora in Present-day Organizations, Journal of Universal Knowledge Management, 0, 2005, 1), he notes:

Syntegration is a structured, non-hierarchical process for highly effective and efficient dialogue that leads to much faster, much more informed outcomes and aligns people behind the resulting decisions, messages and action plans with a high chance for implementation.

Polyhedral ordering of complexity: There would appear to be an intuitive recognition of the value of polyhedral orderings as indicated by their metaphorical use in various contexts:

  • The ability to make polyhedral use of the pillars of local information - data relating to space (the property register, land divisions), people and businesses - will make for a thorough reengineering of management processes. (Xavier Marcet i Gisbert, Local Authorities in the Digital City)
  • The polyhedron nature of the cultivated illegal interests and the capillary-like diffusion of the Nigerian presence in the world, guarantee a competitive potentiality and the rapid possibility of using the illegal instrument in favour of the most remunerative business in the current economic situation. (The Nigerian Mafia between Voodoo and the Computer, Gnosis: Rivisita Italiana di Intelligence, 2, 2005)

Polyhedral decision-related strategies: So-called "polyhedral strategies" are mentioned in literature with varying degrees of potential relevance to governance and global decision-making:

  • Choice-based conjoint analysis is used widely in marketing for product design, segmentation, and marketing strategy; a new test, using a "polyhedral" question-design method has been proposed that adapts each respondent's choice sets on the basis of previous answers. (Olivier Toubia, et al. Polyhedral Methods for Adaptive Choice-Based Conjoint Analysis, 2003)
  • In the two-person zero-sum case it has been shown that the set of "good" strategies of a player is a convex polyhedral subset
  • Nash bargaining games with quadratic concave utility functions and polyhedral strategy sets
  • František Turnovec (One Class of Polyhedral Games, Proceedings: Arbeitstagung Spieltheorie, Institut fur Hohere Studien and Wissenschaftliche Forschung, Wien, 1967).

Such explorations raise the question of the advantage of any isomorphism between them and any configuration of global governance strategies.

Identifying polyhedral configurations: In an online experiment within the framework of the Union of International Associations, an algorithm was used to select a polyhedron onto which relationships from a problem (say) were projected. Each facet thus becomes the interface to another problem. The polyhedron as a whole is thus a configuration of facets representing the problem as it interfaces with related problems. Clicking on the facets brings up the corresponding text profile. In that version, the selection of polyhedron is crude and the colouring was random. The virtual reality browser enabled the user to manipulate and explore the polyhedral structure [more]

This is a viable project within current web-based knowledge processing, as more simplistically illustrated in mapping institutional systems onto the facets of a polyhedron as shown below.

Mapping of problems and organizations onto selected polyhedra in virtual reality
extract from Exploring Intelligible Associations: Integrative modes and metaphors, 2006
as presented to the German Research Centre for Artificial Intelligence)
Selected issues relating to "discrimation against women" Selected components of the "EU system"
Problem polyhedron Organizatioal polyhedron

Such an experiment could be readily extended to configurations of strategies, organizations or values -- especially in the light of the data now available on corresponding networks and the challenge of pattern recognition to elicit more integrative understanding.

Negotiating tables: Another approach to comprehending the interrelationship of 12 governance modalities is through recognition of the challenge in practice of the "geometry" of any negotiating "table" designed to ensure appropriate communication between the stakeholders. This challenge may be transformed into three-dimensional geometry in terms of the "closest packing" of spheres (cf Bill Lauritzen, Closest-Packing or Gravitational Gathering of Spheres; Paul Bourke, Waterman Polyhedra, 2004; Russell Z Chu, Mapping the Hidden Patterns in Sphere Packing: Lattices, nets, tensegrity structures and synergy, 2003). Closest packing arrangements lead to higher density structures -- which might be understood as an analogue to more highly integrated governance teams.

Interlocking round tables: Elsewhere (Spherical Configuration of Interlocking Roundtables: internet enhancement of global self-organization through patterns of dialogue, 1998) it was argued that many issues and remedial responses are articulated through specialized thematic conferences and dialogues, whether face-to-face or electronically. Such events may usefully be termed "roundtables". It is characteristic of such events that they tend to make little reference to roundtables on related or contrasting themes. In this sense the roundtables are thematically "local" (in a non-geographical sense) and beg the question as to how their insights are to be integrated within a thematically "global" (or conceptually comprehensive) context. Aspects of this local/global question have been articulated in a separate paper (Future generation through global conversation, 1997).

This challenge of the global configuration of specialized dialogues had previously been explored as an exercise for the Inter-Sectoral Dialogue on the occasion of the Earth Summit (Rio de Janeiro, 1992). The approach is summarized in a document on Strategic ecosystem: configuring strategic dilemmas in intersectoral dialogue (1992). There it was shown how the issues relating to sustainable development could be configured around a sphere projected onto a flat surface, that could then be folded back into spherical form. Zones on the surface of the sphere could then be understood as "local" dialogue arenas together encompassing the "global" concern.

There is an interesting question as to the degree to which relatively isolated dialogues are themselves "sustainable" and can effectively discuss "sustainability" in a strategically meaningful way. The challenge of dialogue sustainability is discussed in Sustainable dialogue as a necessary template for sustainable global community (1995). A related issue is the necessary Varieties of dialogue arenas and styles (1992).

In this contexf it is therefore interesting to note that the ACP-EU Joint Parliamentary Assembly (Report on Sustainable Management and Conservation of Natural Resources in ACP Countries, ACP-EU 3590/03/fin., 11 October 2003), referring to Rio+10 in Johannesburg, notes:

The value added of the WSSD Implementing Plan adopted in Johannesburg lies precisely in the endorsement by world leaders of a multi-dimensional concept of sustainable development, by incorporating poverty eradication and environmental conservation, as well as the rest of Millennium Development Goals, by considering the problems related to trade liberalisation and the issue of good governance in developing countries. The main rationale behind the suggestions being submitted today for consideration are based on this multi-dimensional concept of sustainable development, in which poverty eradication, trade liberalisation, economic growth and good governance are inextricably linked to the reversal of environmental loss, all being inseparable facets of a polyhedron.

Options for institutional reform: At the governance level, the challenge of institutional reform is typically framed in terms of the number of "seats" at a table -- and in what way this can be rendered more approprtiate in response to various pressures. The UN Security Council is currently a much debated case in point. The question is whether new insights and options emerge for more coherent global governance through reframing the challenge in terms of sides of a polyhedron rather than seats around a necessarily flat table. This opens the possibility for more explicit consideration of:

  • complementarity between "sides" represented
  • requisite variety, namely critical number
  • axes of symmetry
  • necessary opposition
  • ensuring vital communication pathways to maintain integrity
  • options for variable geometry through transformation to alternative configurations
  • integrity of the whole in the light of the polyhedron onto which the structure can be mapped (especially with any additions)
  • relationships to other structures, whether more or less complex, more fundamental or less (usefully mapped onto concentric polyhedra)

The following table points to possibilities worth exploring in the light of Examples of Integrated, Multi-set Concept Schemes: Polygons and polyhedra (1984).

Possible mapping of governance bodies onto polyhedra (indicative)
(see other possibilities exemplified by G8 and G20)
Body Members Sides (faces)
Vertices Edges
UN Security Council (perm.) 5 trigonal prism - -
UN Security Council (elect.) 10 - - -
G8 countries 8 octahedron, hexagonal prism cube -
Group of 10 10 - - -
Group of 15 15 - - -
Group of 20 (industrial) 20 icosahedron dodecahedron -
Group of 20 (developing) 20 icosahedron dodecahedron -
Group of 24 24 snub cub, truncated cube truncated octahedron, rhombicuboctahedron cuboctahedron, rhombic dodecahedron
NATO 26 - - -
EU 27 - - -
Group of 30 30 - icosidodecahedron snub tetrahedron
OECD 30 - icosidodecahedron snub tetrahedron
UN ECOSOC 54 - - -
Group of 77 130 ? ? ?
UN General Assembly 192 ? ? ?

It is possible that the ability, or inability, to map global governance groups onto polyhedra may in some way be an indication of their degree of integrity, coherence and viability -- especially where the polyhedra are regular or semi-regular. The question has notably been explored by management cybernetician Stafford Beer with respect to the icosahedron in teams of people; Leroy White ('Effective governance' through complexity thinking and management science. Systems Research and Behavioral Science, 2001) has adapted that process to work with other polyhedral arrangements, most effectively the octahedron and the cube. Efficient communication patterns are also a concern in social network analysis.

Analogous considerations apply, for example, in the configurative organization of computer memory for communication efficiency (cf F. Quilleré, et al. Generation of Efficient Nested Loops from Polyhedra, In: International Journal of Parallel Programming, 2000, 28, 5; F. Quilleré, et al. Optimizing Memory Usage in the Polyhedral Model, In: ACM Transactions on Programming Languages and Systems, 2000, 22, 5). As explained by Fabrice Baray, et al (Federating Polyhedral Tools, 2004):

Present-day tools for embedded system design have trouble handling loops. This is particularly true for logic synthesis systems, where loops are systematically unrolled (or considered as sequential) before synthesis. An efficient treatment of loops needs the polyhedral model.... The polyhedral model is now widely accepted... Most of these are research projects, but the increased involvement of industry... is a favorable factor.

The polyhedral approach is basic to supercomputers. For example, the STAR-CCM+ contains "the revolutionary new polyhedral-based finite volume solution approach, which is both robust with respect to automatic meshing and accurate solution of very complicated geometry and faster than other methods for even the largest problems being attacked in industry today".

Clearly, from the above, the G8 and G20 would then exhibit greater integrity than other bodies. Questions might however be fruitfully asked about the viability of the UN Security Council as a current focus of global governance.

Mapping of the G20 Group of 20 industrial countries onto an icosahedron
then complexified to an icosidodecahedron
with subsequent morphing to a yet more complex form
suggesting increasing challenges (and possibilities) of communication and integration amongst the set of countries so mapped
(mapping and exploration done in virtual reality in Stella as described in
Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization)
Mapping of the G20 Group of 20 industrial countries onto an icosahedron Mapping of the G20 Group of 20 industrial countries onto an icosahedron (for transformation) Mapping of the G20 Group of 20 industrial countries onto an icosahedron (for transformation)
Further complexification of the G20 Group below onto a rhombicosidodecahedron
(with representation of the unfolded polyhedral net)
Complexification of mapping of G20 Group onto a rhombicosidodecahedron Again the 20 country groups are mapped onto the 20 triangles of the spherical polyhedron figure. In this case the pentagonal faces are coloured green (instead of transparent as above), and the additional square faces are rendered transparent. The triangular, square and pentagonal areas raise useful questions about different typecs of 3, 4 and 5 party dialogues between countries. The net diagram highlights the possibility of interlocking "roundtables" if only virtually.. Complexification of mapping of G20 Group onto a rhombicosidodecahedron
Such an exploration could also be undertaken with respect to the Group of 20 developing countries

Curiously, whereas games of various kinds elicit a well-understood need to "make-up" a team (a "fourth" in bridge, for example), no such need has emerged in relation to the challenges of global governance -- a greater game by any standards, and with more at stake. Clearly the configurations currently considered appropriate for such governance are based on a less cvomplex understanding of the necessary opertational feedback loops (well-noted by Stafford Beer). Typically the focus is more simplistically on ensuring that there is a "quorum", if such is required -- without any sense of the communication pathways which particular numbers of members render possible in ensuring the greater integrity of the group.

Of potential interest is the possibly unsuspected integrity of groups of larger number -- appropriately selected, with the implied complementarities and communication pathways. There are many such polyhedra, less regular in structure, suggesting other possibilities for governance (see George W. Hart, Virtual Polyhedra: The Encyclopedia of Polyhedra, 2000; Marcus J. Wenninger, Polyhedron Models, 1974). The variety of such structures -- and their various degrees of relationship to each other -- is suggestive of the need to explore their relative advantages (singly or appropriately configured together) in institutional design and reform. Such imaginative exploration should be facilitated by software enabling their construction (Robert Webb, Stella: Polyhedron Navigator. Symmetry: Culture and Science, 11, 2000, 1-4, pp. 231-268, with a 4D variant: Stella4D).

It is possible that the ultimate challenge and opportunity of global governance is represented in some way by the most complex example of group symmetry, the so-called Monster group (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).

Recognition of degrees of disagreement: There is a dangerous tendency to focus on consensus formation and to mask degrees of disagreement that might be indicative of the need for more complex structural arrangements. Thus John Beatty (Masking Disagreement among Experts, Episteme: A Journal of Social Epistemology, 2006) explores why scientific experts may mask disagreement and endorse a position publicly as "jointly accepted", notably in the case of technically difficult issues, but also in matters of social and political importance. Assessing "degrees of disagreement" was the purpose of an opinion poll on the important issue of climate change (Fergus W.M. Brown, et al., Is there agreement amongst climate scientists on the IPCC AR4 WG1?, 2007) Speaking on the Future of Transatlantic Relations, with respect to Iraq, the Chairman of the Committee on International Relations (U.S. House of Representatives) noted:

While the approaches and strategies needed to accomplish our common or individual national agendas have been the subject of much discussion and varying degrees of disagreement, I certainly do not believe that Americans and Europeans are in effect from two different and distinct planets.

The question with respect to the configuration of "sides", to constitute a polyhedron, is whether any "degree of disagreement" can be usefully correlated with the geometry of the angle of one side to another. Such an approach could shift understandings of consensus beyond "masking" of disagreement whilst avoiding implications of a degree of dissociation consistent with "different and distinct planets". The approach not only offers a visual representation of the relationships between perspectives but also provides the basis for initiatives based on complex partial agreements, possibly especially appropriate to the complexity of the governance challenge.

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