Towards configuring silences globally

Civilization as a Global Configuration of Silences (Part #9)

The argument above offers various two-dimensional representations suggestive of systemic relations assumed to be fundamental to comprehension of the dependencies of silence / ignorance / uncertainty in a global knowledge-based civilization. Presented that way in two dimensions any more global, integrative comprehension (requiring representation in a third dimension) is necessarily implicit rather than explicit.

Folding a two-dimensional pattern of symbols into spherical form: A further step in the visual argument can be taken by considering how a two-dimensional pattern of "silences" might be fruitfully wrapped or folded into global form in three dimensions. A variant of this possibility was considered by addressing the impossibility of mapping together in two dimensions the contrasting star symbols of Judaism and Islam -- 6-pointed and 5-pointed respectively. The geometrical tiling problem can however be resolved in three dimensions, as argued and illustrated separately (Middle East Peace Potential through Dynamics in Spherical Geometry: engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks, 2012).

The point to be stressed is the manner in which the star symbols are used to reinforce two-dimensional modes of comprehension whose incompatibilities are curiously associated with the only too evident territorial conflicts. With respect to the argument regarding silence, a case could be made that each star is indicative of a mode of silence of a higher order -- represented inadequately and implicitly in two dimensions.

Of particular interest in respecting these contrasting understandings of a higher order of silence is the sense in which -- in a two-dimensional modality -- each can be assumed to frame the other as representative of silence of a lower order. There is therefore a complex dynamic in which "White" is framed as "Black", and vice versa, as separately discussed in detail (Interplay of black and white in the Greater Game, 2013). This constitutes a form of mirroring -- as might be expected.

Symbolic stars embedded in corresponding polygons
5-fold Star	6-fold Star

Combinations of the above forms can be presented as a two-dimensional pattern (left image below) -- then folded into a global form (right image below).

Truncated icosahedron holding a pattern of 5- and 6-pointed polygons (images produced using Stella Polyhedron Navigator)
Image of unfolded net form	Animation of folded form

The animation below shows stages in the folding of the variegated 5-star and 6-star pattern into a global form. It is the spherical form which implies a silence of a higher order through which their differences are potentially "resolved" -- whatever that may mean as a challenge to comprehension for a global knowledge-based civilization. It suggests a fundamental (or transcendent) comprehension which does not readily lend itself to articulation, as tentatively discussed separately (Unthought as Cognitive Foundation of Global Civilization, 2012).

Animation of the process of folding (and unfolding) a truncated icosahedron
(generated using Stella Polyhedron Navigator)

Animation of Islamic star and Star of David into icosahedral form

Balls as a significant vehicle of global silence: As illustrated below, it could be said that there is an immense irony to the fact that the relationship between 5- and 6-pointed symbols of such controversial significance should be "resolved" through the form of a football. This is unique in being the focus of much attentive game-playing worldwide -- across the ideological, religious, cultural, educational and ethnic boundaries by which global civilization is otherwise divided. In contrast to any two-dimensional exercise in representing global civilization, the ball acquires special additional significance through the dynamics of play. Through its ready recognition by all classes of society, it merits careful consideration as a reflection of the complex dynamics of global civilization -- and potentially the most appropriate representation of it..

Truncated icosahedron compared with ball used in association football
(reproduced from Wikimedia entry)

However the images above also point to alternative interpretations of that representation with its 12 pentagonal faces coloured black and its 20 hexagonal faces coloured white. The images suggest the question as to whether there are footballs in which the 12 pentagonal faces are white and the 20 hexagonal faces are black. A quick check in Google images reveals no such alternative. Why not? Is the football appropriate to global civilization one in which the colours alternate?

The argument above regarding the alternation between colours (Interplay of black and white in the Greater Game, 2013) was made within the context of a discussion of a new variant of the game played by the great powers of the world (Playing the Great Game with Intelligence: Authority versus the People, 2013). The original form of such international realpolitik in Central Asia was known as The Great Game, now recognized as The New Great Game -- in process of reframing as noopolitik. It is highly appropriate to implications of this argument that football should also be recognized and promoted worldwide as "the great game".

That a representation of global civilization should acquire its significance to the world through the process of play suggests that conceptual exploration of that significance may need to be considered dynamically rather than statically -- through "serious" playful interaction, as may be variously discussed (Dynamic Transformation of Static Reporting of Global Processes, 2013; Humour and Play-Fullness: essential integrative processes in governance, religion and transdisciplinarity, 2005; Playfully Changing the Prevailing Climate of Opinion: climate change as focal metaphor of effective global governance, 2005; Enacting Transformative Integral Thinking through Playful Elegance, 2010).

In that spirit, the following are quick experiments in alternative colour codings -- to highlight the sense of unfamiliarity they offer.

Inverting the colours in the above image	Recolouring the above image

Any alternation between the pattern of colours enables the ball to be recognized as the focus for a range of currently "unspoken" questions -- as a potentially valuable configuration of silences:

why is the football design effectively restricted to a single black-and-white pattern:
- is this an indication of conceptual "lock-in" -- of restriction to "in-the-box" thinking, or a single pattern of discourse?
- does it reflect the fact that football is primarily a "men's game" -- in a global civilization?
- why not use balls of alternate colour pattern -- in the two halves of a game (for example)?
how significant is the black colouration of the pentagonal forms:
- so appropriate to the dubious role of the Pentagon in the pattern of global silence?
- so appropriate to the manner in which Islam is framed by cultures more closely identified with the white-coloured hexagonal form?
are the 12 black-coloured forms indicative of a 12-fold pattern of silences -- inadequate or "lost" modes of expression, as separately argued (Enabling a 12-fold Pattern of Systemic Dialogue for Governance, 2010)?
what "qualities of silence" might be suggestively inscribed on the 32 polygons -- whether understood problematically or constructively as the experience of civilization?
to what extent are the 12 pentagons and 20 hexagons indicative of a particular strange alliance -- regarding what is not being said?
given the typically noisy context in which the game is played, how does this relate to any higher order of silence -- possibly as the ultimate symbol of systemic neglect through the distraction the game enables?

As a design challenge, it is appropriate to note that some premium-grade 32-panel footballs use non-regular polygons to give a closer approximation to sphericality. It might be asked why less universally-played ball games, such as basketball, use other simpler designs.

It is intriguing that the focus should be placed on a singular polyhedral pattern when there are so many others that are spherically symmetrical, as separately explored (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008; Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008; Configuring Global Governance Groups: experimental visualization of possible integrative relationships, 2008). Many are potentially capable of holding a greater variety of any combination of "silence/ignorance/uncertainty" -- especially where there is alternation between what each represents globally. Possibilities are illustrated below.

Global configuration of values fundamental to civilization (examples based on articles from the Universal Declaration of Human Rights reproduced from Dynamic Exploration of Value Configurations Polyhedral: animation of conventional value frameworks, 2008)
Partially folded pattern	Faceting diagram	Simulated "4-dimensional" view

Mapping conditions of change into spherical form: A seemingly quite different approach can be taken in the light of the classical coding of conditions of change in the Chinese Yi Jing (I Ching). The question is whether there are insights to be gleaned regarding silence from some such configuration. As an exploratory exercise, the twofold set of problematic/constructive modalities of the threefold set of silence/ignorance/uncertainty might be represented by the classical combination of trigrams, perhaps as follows -- using the unbroken lines to signify "constructive", and the broken lines to signify "problematic" (for example).

Use of trigram encoding to distinguish patterns of constructive versus destructive
Silence (+/-) Ignorance (+/-) Uncertainty (+/-)

Some such articulation offers useful pointers to the ambiguities of the relationship which each of the eight conditions then characterizes in a knowledge-based civilization. The argument can be taken a stage further through combining any of the eight with each other to constitute the 64 hexagrams encoding the range of possible decision situations -- with one set of eight framing the condition for the individual (decision-maker), with the second the condition for the collective. It is these which could then be configured globally as indicative of global civilization. One approach to such configuration is that of József Drasny, as indicated below (with the numbers indicative of the standard sequence of the hexagrams from 1 to 64).

*Selected images of the Yi-globe* of József Drasny** reproduced with permission from The Image of the Cosmos in the I Ching: the Yi-globe (2007)

These images point to the possibility of a correspondence between the spherical organization of conditions of change and the more familiar understanding of how the Earth, as a globe, is exposed to light and darkness. The approach is however especially useful in offering a way of switching from light/dark to their metaphorical equivalents based on sound. It is suggestive of ways of configuring contrasting qualities of silence whilst implying a more central understanding of "higher order". It is instructive to consider the traditional decision-making dilemmas of the 64 conditions of change as implying "moments of silence" in anticipation of the decision taken. Any such "strategic silence" can be understood as corresponding to the "creative silence" of the artist protective of emerging insight.

Curiously, with respect to the previous case regarding the 32 polygonal panels of the football, the 64 hexagrams could be associated with a "dynamic high-tech football" whose colours alternated between black and white -- giving 2x32 possibilities. It is otherwise quite problematic to associate the 64 conditions of change distinctively with any such a form. One unique possibility is the drilled truncated cube with 64 edges onto which those conditions can be mapped, as discussed separately (Enabling Wisdom Dynamically within Intertwined Tori: requisite resonance in global knowledge architecture, 2012).

Drilled truncated cube of 64 edges with abridged hexagram names (some faces transparent, see other variants)

Appropriate to this argument, this form is closely related to the cube-connected cycles used as a network topology in parallel computing.

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Towards configuring silences globally