Polyhedral mapping reconciling value-goals and their antitheses in the light of ball-games

Refining the Value of Sustainable Development Goals (Part #5)

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Taking 17 as a point of departure on which a form of ("non-negotiable"?) global consensus has been achieved, how might the coherence of the set be comprehended -- beyond the conventional use of an inherently unmemorable checklist of bullet-points? The approach taken here is to seek ways of mapping the 17 value-goals onto polyhedra with varying degrees of symmetry, offering varying degrees of memorability (partially according to that symmetry). The numbers characteristic of the polyhedra (vertices, faces, edges) can then be placed in juxtaposition with the number of players in various well-known ball games.

The argument here assumes that the 17 value-goals might indeed be associated with particular polyhedra. However the psychosocial reality of interest is the manner in which they are challenged by their antitheses -- the value-goals with which they are in game-like competition, namely those of their opponents, perceived as "deadly".

In sport, it is not the values upheld by the "home team" which are of sustainable interest -- unless they are challenged by opponents who can be successfully defeated as an exemplification of the superiority of the values which the "home team" defends. The game derives its interest (as a "strange attractor") from its dynamics, not from any static juxtaposition of the opposing teams.

The existence of the globally agreed set of 17 value-goals is taken as the necessary point of departure for this exercise. For this reason polyhedra onto which they might be mapped are presented at the top of the table below -- whether the choice is made to map onto vertices, faces or edges. In each case however, accepting that the set acquires its interest and meaning from its dynamics with an opposing set, there is a need to consider what polyhedra the two "teams" of 17 might be mapped to provide a sense of the larger coherence of psychosocial dynamics. The shaded rows in the table therefore offer indications of suitable polyhedra with regard to both "teams", in contrast to the unshaded row for the singular set of value-goals alone. It is then in the shaded row that various ball-games can be identified (on the right), according to the number of players on each side.

It is appropriate to recall that the perspectives opposing any set of values are themselves typically associated with a contrasting set of values -- rather than being inherently meaningless in any absolute sense (whatever claims are made in this respect by the opponents). Like it or not, however "non-negotiable" the world view with which each is associated, it is within the game that "negotiation" takes place, whatever the conflictual dynamics involved.

Links have been provided in the table to depictions of some polyhedra, whether in terms of their interest (in relation to the set of 17), or because of their recognition in terms of regularity or semi-regularity. Such regularity is understood as an approximation to the global whole (implied by the relation of the polyhedra to their circumspheres). For any given case, there may be multiple polyhedral candidates, in which case the number is indicated (in parentheses in the table), but only the more common or "interesting" are listed. Many indicated are obscure, little known, or highly irregular.

Given the particularly unusual value attached to the set of 17 as exemplifying a global preoccupation, the associated polyhedra are presented visually beneath the table -- whether for the 17 alone, or for the game of 2x17 in which they necessarily compete strategically.

In what sense could it be understood that particular ball-games, with a distinctive number of players, are giving expression (unconsciously) to the elusive experiential coherence of a pattern of invariance indicated by a particular polyhedron? Are the passing patterns of any such game an exemplification of constraints implied by the polyhedral configuration?

With respect to the pattern of 17 value-goals, it could be considered remarkable the the number is central to to one of the most esteemed ball-games, namely golf. The esteem is all the greater given the association of the game with the person recognized as the "most powerful man on the planet" and his ownership of the courses on which it takes place. Golf courses of distinction typically have from 17 to 19 "holes".

The challenges are usefully reframed by the work of management cybernetician Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994). Although no reference is made to the players of a rugby game, for example, his research focused on "problem jostling" between 12 active perspectives in a game. These interactions he associated with the 30 edges of an icosahedron between its 12 vertices. Given his understanding of the role of the edges in the icosahedron, it is these edges which may be of special interest in representation of the dynamics of any game. Other insights may arise from consideration of the vertices and faces for that purpose -- as with the sense of "facing off" or "marking" a player in the opposing team.

• preparations for the preceding Agenda 21 gave rise to an exercise (Configuring Globally and Contending Locally: shaping the global network of local bargains by decoding and mapping Earth Summit inter-sectoral issues, 1992). Here the opposition was between "global" and "local", each being "hidden" from the other -- but otherwise.
• the 15 global strategic challenges identified by the Millennium Project were framed in terms of "wickidity" (rather than wickedness) to suggest the stimulus they constitute to innovation. They were presented as mirrored by 15 internal processes of a (futures research) conference (Embodying Strategic Self-reference in a World Futures Conference: transcending the wicked problem engendered by projecting negativity elsewhere, 2015) -- "external" and "internal" being respectively "hidden" from each other.

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