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Further to explorations and clarifications in the papers cited above, the focus here is on the insights to be gained by representation of a conference as a polyhedron of suitable complexity. This representation is understood as possibly evolving, through the dynamic of the conference, into some other polyhedron -- possibly in a dynamic whereby it will revert to the original form.
The concern here is with the challenge of how "bringing different perspectives together" is to be understood in a conference where that is an explicit or implicit objective. The challenge might be seen in terms of the recognized complexity of arranging representatives of factions around a conference table. It might be seen in terms of solving the jigsaw puzzle of thematic tracks and schedules as a resource allocation matrix.
However, the concern here is whether there are aspects to the configuration of thematic tracks, plenary sessions and workshop panels that might fruitfully call upon three-dimensional geometry in unusual ways. Specifically, given the challenge of integrating the different elements into a comprehensible whole, whether this geometry involves a degree of curvature and spherical symmetry to ensure that the structural elements reinforce each other in a sustainable, memorable way.
The challenge might be framed in the light of the call for innovation in every sector of society, and the reliance upon it. And yet the conception of meetings is still defined and constrained by tabular schedules, possibly enlivened by mind maps presented on flat surfaces. This could be readily defended it is was not increasingly recognized that the complex of problems, stratgegies and institutional resources required for sustainable outcomes can no longer be represented in this manner -- and that the conference environment is much challenged to give birth to coherent, memorable strategic initiatives that are themselves sustainable in practice.
It is assumed that there is already a metaphorical insight that attributes value to an understanding of institutional "geometry" and that this is meaningful in relation to the dialogue context of conferences. The sense in which complex institutions may be structured such as to have a "variable geometry" has also long been explored -- although not explicated in relation to polyhedra.
Beyond the matrix: Complex programmes conferences are typically organized with the use of some form of planning matrix -- tracks, schedules and room allocations (often in a cubic array of rooms).
A polyhedron is assumed to offer an interesting metaphor because of a degree of possible complexity appropriate to the most complex, mult-themed conference, whilst at the same time retaining a degree of integrity as a coherent whole. The basic arguments in support of this view are given in the introductory paper (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008).
Use of a polyhedral form, allows the array of events and the communicatuions between them to be configured in a manner which uses the integrative possibilities of the third dimension to interrelate the parts to form a whole of greater potential significance and coherence (***).
Conferences as polyhedra: The emphasis here is on the role of a conference in "bringing different sides together". It is typically expected that a set of themes, topics or threads are to be explored and interwoven in some way.
Panels: This may be done in a set of panels of different orientation -- which may both represent different sides of a global topic as well as corresponding to necessary dialogue between parties of contrasting views that is may be hoped to reconcile.
Tracks and themes: Whereas the panels clearly reflect one feature of the conference "geometry", these are typically organized in terms of a set of tracks or themes that define the conference as whole. It is assumed here that these thematic tracks are -- in terms of spherical geometry -- great circle pathways around the polyhedron (understood as approximating to a sphere). The panels are effectively positioned, or defined, as the polygonal zones of intersection of these various tracks. Such panels are therefore dialogue zones or areas between the tracks -- or some subset of them -- and necessarily of different orientation from each other in approprixating to the surface of the sphere.
Reporting back: For the conferrence as a whole, the challenge is of course to reach an integrative synthesis of the preoccupations of the set of panels and the themes they interweave. This tends to be done through a plenary session in which all the panels are represented by their respective rapporteurs.
Issues and points: It is of course the case that a conference is also typically characterized by particular controversial issues -- typically at the intersection of one or more threads of discourse. These "points" may be understood as the various vertices of the polyhedron. Usually they are articulated by a representative speaker reflecting the perspective of that point. Clearly the point is necessarily located on several threads through other points -- on pathways defining the larger geometry of the polyhedron. As such it is necessarily common to several panels, in each of which a number of such points are the focus of a distinct side of the conference dialogue.
Links: The notion of tracks or threads is helpful with respect to the larger geometry of the conference represented by a polyhedron. However the portions of any such thread, as sides of various polygonal panels of different orientation, stress the "linearity" of the linking relationshjips between those represented at the panels -- at their vertices. These links may be understood as local lines of argument through which bomnds are established and sustained between particular participants at a panel
Typically, following the principles of spherical geometry, any such polygon has a number of sides equivalent to that of a conference panel -- minimally 3, but seldom more than 8 or 10. The "unwieldiness" of a larger panel is conveniently to be related to the instability of a polygon of any greater number of sides in the structure of a polyhedron.
Were the conference to be virtual rather than face-to-face, and its communications necessarily computer-mediated, the patterns described above would be reflected in the movement of messages by track and the discussion forums associated with each panel seeking to reconcile contrasting themes and issues. Moderators would probably be involved in filtering and redirecting such communications, possibly assisted by automated filters. Both effectively act as gatekeepers for the "local" panel discussions and for movement and accumulation of messages on "global" threads.
However understanding the pattern of exchanges in terms of a polyhedral structure, and reflecting that structure to some degree in the filtration protocols, would allow for a more complex and integrative approach to the conference as a whole -- as opposed to the needs of its particular parts.
Whilst a single polyhedron offers a valuable template for a structure understood primarily in static terms, the whole purpose of a conference (as typically articulated) is to "bring the sides together" in some more powerfully integrative manner.
The stages in this process may be fruitfully represented through morphing the polyhedron into related polyhedral structures -- in the light of various emergent features and dynamics. There is a rich array of such structures which it is reasonable to expect offer a means of mapping a wide range of possibilities as required.
Of interest is whether recognition of these possibilities provides participants and organizers of directions in which their dynamic can move in order to achieve more integrative configurations.
One particular dynamic of interest is the morphing of an adequately representative polyhedron into its dual. In this process any face (panel) of the polyhdron defines a central point that becomes the vertex of an implicit polyhedron -- the dual of the first.
This alternative structure may be seen in terms of the concentration of the focus of a single panel of the conference -- as it might be representated by a rapporteur -- but rendering emergent the lines of relationship to other panels focused to a point in a similar manner. Naturally it gives rise to a different set of panels in which the "rapporteurs" are respectively the participants in the light of the geometry.
Clearly such transformation, whether in one direction, reversible, or in continuing alternation, lends itself to computer-enabled support.
Whilst there are many computer-enabled groupware software packages, a previous paper focused on the software capable of representing comprehensibly the polyhedral structures that might emerge (Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008).
Subsequent papers have illustrated (through images, animations and movies) the relevance pof the approach to the configuration of coalitions of groups and issues (Configuring Global Governance Groups: experimental visualization of possible integrative relationships, 2008; Configuring Global Governance Issues: experimental animations and video sequences, 2008)
The process is seen as a means of enahcning the capacity of networks, in this case as they are represented, form and are enabled in the conference environment (Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance, 2008).
Stafford Beer. Beyond Dispute; syntegrity team design. Wiley, 1994
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