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1. Human rights: The three sets of human rights are discussed, and illustrated, in some detail in Dynamic Exploration of Value Configurations: polyhedral animation of conventional value frameworks (2008)
2. Traditional symbol systems: The screen shot of the animation of traditional symbol systems (on the left) is discussed in detail in Dynamic Exploration of Value Configurations: interrelating traditional cultural symbols through animation (2008).
3. Software: The transformations between each of the polyhedra shown are possible due to the wide range of features in the Stella: Polyhedron Navigator software package. The above images are only a sample of that range. An explanation of those features currently available is given in the associated manual. An earlier overview with informative examples was produced by the developer Robert Webb (Stella: Polyhedron Navigator, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, pp. 231-268, 2000 [erroneously indicated as 2003]). Although this is a very helpful introduction to Stella's capabilities, it was written in relation to Great Stella 2.0 in 2003. Many new features have since been added to subsequent upgrades (to Stella4D), notably those offering possibilities in 4D.
4. Pattern language: The possibility of such a language, notably using the Stella package, is discussed elsewhere (Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008)
5. Pillars, posts, stakes, etc: The constraining implications of such simplistic architectural metaphors in relation to values and strategies are discussed elsewhere (Coherent Value Frameworks Pillar-ization, Polarization and Polyhedral frames of reference, 2008)
6. Interweaving strategic dilemmas: The configuration of a set of strategic dilemmas on the occasion of the UN Conference on Environment and Development (Earth Summit, Rio de Janeiro, 1992), leading to the diagram presented here, was discussed on that occasion (Configuring Strategic Dilemmas in Intersectoral Dialogue: summary of analysis on the occasion of Earth Summit, 1992; Configuring Globally and Contending Locally: shaping the global network of local bargains by decoding and mapping Earth Summit inter-sectoral issues, 1992, 5 mb PDF). Edited portions of the text have been made available as commentaries in the Encyclopedia of World Problems and Human Potential (1994-5, vol 2) and may be accessed as a set of documents at Configuring Strategic Dilemmas in Intersectoral Dialogue. The contents of the report are identified in the General Checklist of Documents Describing the Rationale and Process.
7. Interlocking circles: The polyhedral coherence of the structures emerging from the pattern of strategic dilemmas is dependent on the architecture of the interlocking great circles fundamental to their geometry. These have only been separately coloured in one diagram on the right. The implications of such an approach are discussed separately (Spherical Configuration of Categories -- to reflect systemic patterns of environmental checks and balances, 1994; Spherical Configuration of Interlocking Roundtables -- Internet enhancement of global self-organization through patterns of dialogue, 1998; Spherical Accounting using geometry to embody developmental integrity, 2004)
8. Global governance: The polyhedral approach to governance is discussed elsewhere (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors (2008); Configuring Global Governance Groups: experimental visualization of possible integrative relationships; 2008; Configuring Global Governance Groups: experimental animations and video sequences, 2008; Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance, 2008)
9. Metaphoric progression: A degree of association and complementarity is implied in the image as a whole between:
10. CERN: The relevance of considering the pattern of thinking, from which the Large Hadron Collider emerged, is discussed separately, notably in contrast with that associated with the animation of the relationship between traditional symbols (Dynamic Interrelationship of Symbols of Coherent Experiential Representation of Nonduality, 2008). Potentially striking from a future historical perspective is:
11. Managing complexity: Irrespective of the casual use of the "black hole" metaphor for the current crisis (as with very extensive use climatic metaphors such as "financial hurricane", "financial maelstrom"), it is clear that the CERN initiative represents a new order of thinking quite distinct from the pattern of thinking with which fundamental global challenges are traditionally managed. It is notably of interest because of the circle-based technology required to handle the collision between two opposing positive energy beams -- at a time when global governance is based on "linear thinking" focused on "clashing civilizations" based on opposing values (deemed positive by their respective proponents) and their need to eliminate each other.
The CERN initiative is seen as a means of creating the original conditions from which the universe (as it is now known) is derivative. Given the quality of the mathematics involved in both cases, there is surely a degree of equivalence to be explored between that challenge and the destructive financial "derivatives" so creatively elaborated for the exploitation of a virtual world completely divorced from the original reality in which people live. Such a comparison notably has merit given the contrast between the integrative simplicity of lived experience and the complexity of that world of derivatives -- incomprehensible to all but the few.
12: Hyperdimensionality and emergence of an architectural analogue to the arch: The geometric progression beyond "pillars" and "poles" -- and a recognition of the potential for "variable geometry" in governance -- is helpfully carried by the capacity to make use of polyhedra of varying degrees of complexity. The potential of such a polyhedral pattern language becomes all the more apparent when the possible transformations of such polyhedra are considered as illustrated in the images above. Whilst the simpler polyhedra can already be used to carry sets of categories (values, strategies, organizations), the possible transformations offer interesting challenges to comprhension of their potential significance in resolving the strategic dilemmas associated with thinking of lower dimensionality. In contrast with the complexity of "derivatives" and the specialized knowledge held by many disciplines, polyhedra -- even of great complexity -- lend themselves readily to a higher degree of intuitive comprehension as visualizations. As such they are indicative of the wider credibility of structures of governance based upon them.
As a challenge to the imagination, the software package used raises valuable questions as to significance of the geometry of duals and the various ways of morphing to them. However its use raises the further challenge of 4-D explorations, that it enables, and the possibility that the kinds of reconciliation sought in governance may only be possible within structures of that kind.
As suggested by the CERN initiative, through which opposing beams of positive values are appropriately handled, there is the possibility that an institutional analogue to the fundamental architectural role of the arch may be achieved through such explorations. Such possibilities have been variously considered elsewhwere (Hyperaction through Hypercomprehension and Hyperdrive -- necessary complement to proliferation of hypermedia in hypersociety, 2006; Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006; Hyperspace Clues to the Psychology of the Pattern that Connects, 2003).
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