Dynamics of discord anticipating the dynamics of concord

Time for Provocative Mnemonic Aids to Systemic Connectivity? (Part #8)

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Mapping discord processes? Use of Szilassi polyhedra as indicative of the dynamics of concord, and the possibility of mapping its dynamics, usefully frames the possibility of mapping the dynamics of discord prior to any such concord. The unusual visual and mathematical frameworks elaborated by Charles Gunn and Sergey Bederov lend themselves to slight modification to explore conditions prior to the integration variously illustrated above.

The 6 Szilassi polyhedra that form the final pattern can be usefully recognized as contrasting frames of references through which the requisite variety of a higher order of integration is comprehended. Indicative in this respect is the work of Edward de Bono (Six Frames For Thinking About Information, 2008; Six Thinking Hats: an essential approach to business management, 1985). Somewhat appropriate to this argument, the former primarily uses polygons (and a heart) as mnemonic aids. In any discourse the question is how these frames of references are "oriented" to one another in the dialogue process.

Prior to their reconciliation, such frames of references "dancing" around each other can also be understood as territories or intellectual properties for those identified with the perspective each offers. This recalls a provocative implication of fundamental physics (Einstein's Implicit Theory of Relativity -- of Cognitive Property? Unexamined influence of patenting procedures, 2007). To the extent that any frame of reference implies a form of arrogance (especially when presented with gravitas), the provocation can be taken further (Understanding models otherwise -- as centres of "gravity"; Arrogance as an analogue to gravity -- equally fundamental and mysterious, 2015).

"Disorientation" and discord? Through modification of the Szilassi depiction and the degree of orientation of one to the other, visualization of the resultant dynamics offers a means of elaborating different "stories" regarding the discord process anticipating any potential concord. For that experiment, the 21 edges (of 12 types) of the polyhedron can be rendered visually explicit, as well as the 14 vertices -- and potentially distinctively coloured -- in contrast the animations above. Especially interesting is the visualization of the dynamics between the 6 polyhedra when they are more or less "disoriented" to one another -- in contrast to the images above where their interlocking is a feature of the model and its dynamics. The degrees of disorientation, and the associated dynamics, then offer a valuable "language" for illustrating visually the complex processes in the quest for concord between distinctive frames of reference -- or in resisting it.

Whereas the dynamics of the model above derive from linking the 6 Szilassi polyhedra by their edges at right angles to each other, consideration could also be given to achieving a form of collective bonding by linking the longer edges. As a distinctive basis for interlocking frames of reference into a circular configuration, the result could probably only be rigid. It would however frame a circular tunnel around that configuration through the holes of the polyhedra so joined. Rather than a circular configuration, the polyhedra linked by the longer edges could constitute a form of serpentine chain -- another understanding of consensus. Consideration could also be given to interlocking the polyhedra by their matching faces.

Of particular interest from a discourse mapping perspective are the distinctions that could be associated with the 14 vertices of a Szilassi polyhedron in constituting a frame of reference -- the reference "points" by which it is framed (notably as key points in an argument). When bonded through the Schatz linkage illustrated above, each frame of reference shares 4 of its vertices with the two contiguous polyhedra -- 2 for each. Thus 10 vertices ("points") remain unique to each polyhedron, whereas in the configuration of 6 Szilassi polyhedra as a whole, each is effectively associated with 12 distinctive vertices in a pattern of 72. It is the pattern of 72 "points" which defines concord in a larger and more fundamental sense -- articulated in greater detail.

Theocracies: angels and demons? However controversial, the leadership of the world's acknowledged superpower is now recognized to be intimately associated with an evangelical perspective (Evangelicals' White House meetings illegal, church-state watchdog says, Religion News Service, 31 August 2018). Evangelism is understandably associated with an angelic worldview (Angel, Baker's Evangelical Dictionary of Biblical Theology; What does the Evangelical Church teach about Angels? Spokane FAVS; Saints and Angels, Evangelical Times, 2010). The pattern in the US is more general (Religiosity reigns in US, on the wane in Western Europe, Deutsche Welle, 7 September 2018). A very specific case can be argued (David Ray Griffin, The American Trajectory: Divine or Demonic? 2018).

The Abrahamic religions have traditionally cultivated a belief in angels. It is however somewhat extraordinary to note the extent to which the leading governments in these times, notably the Permanent Members of the UN Security Council (with one exception), could be understood to be "theocracies" of a kind -- or more accurately, to be under the influence of Christian religions to an unquestionable degree. Whilst a number of countries have political parties using "Christian" in their names, the case of the UK is perhaps the most obvious in that a significant proportion of the unelected members of the House of Lords are bishops of the Church of England. As noted by Polly Toynbee:

Our 26 bishops in the House of Lords seem a quaint anachronism compared with Iran's ayatollahs, but only Iran and the UK are still theocratic, with faith in their legislature. (The culture of respect for religion has gone too far, The Guardian, 28 August 2018).

The divisive conflicts of the world could then be understood as engendered together with governments similarly unwilling to disassociate themselves from other Abrahamic religions. The governments of all these countries are effectively unable to undertake initiatives contrary to the dominant faiths of their countries. This is especially the case when the strength of such influence may frame decisions to engage violently with the "evil" so widely declared to exist (Evil Rules, 2015; Existence of evil as authoritatively claimed to be an overriding strategic concern, 2016).

To whatever degree this may be appreciated or regretted, there is clearly a need to find a means of engaging with that worldview rather than assuming naively that it can be dismissed as meaningless.

Patterns of angels and demons? Deprecated or not, much has been made in the past of the number of angels and the manner in which they are ordered. Evangelism offers relatively little insight into the manner in which their qualities are interrelated or how they function systemically together. Given the extent of the conflicts engendered with religious complicity, there is a case for exploring their theologies in a proactive manner as ordered emanations of any comprehension of unity, as argued separately (Mathematical Theology: Future Science of Confidence in Belief, 2011).

Given the tendency to frame "problems" with "evil", potentially intriguing is the possibility that the "fallen angels" cast out of heaven could be discussed through visualization of the dynamics of disagreement and "hellish" disassociation from concord. "Problematique" as "Demonique"? Can configurations of problems be recognized as configurations of demons -- and a challenge to visualization (Transcending the wicked problem engendered by projecting negativity elsewhere, 2015)? In the quest for dominon over the Earth, has Genesis 1-28 been paradoxically misinterpreted: Be fruitful and divide, rather than Be fruitful, and multiply? (Risk-enhancing Cognitive Implications of the Basic Mathematical Operations, 2013).

In the surreal condition of global society, the pattern of 72 "points of light" -- framed by the dynamic pattern of Szilassi polyhedra -- offers one language through which engagement with such "hyperreality" might be discussed, if only in metaphorical terms (Engaging with Hyperreality through Demonique and Angelique? 2016; Mnemonic clues to 72 modes of viable system failure from a demonic pattern language, 2016; "Angelique": evangelisation of the resolutique in the light of angelology?, 2016). As discussed with respect to Hyperbolic reframing of the Demonique and Angelique of tradition (2016):

The focus here on 72 constitutes an interesting challenge to the conventional articulations of sustainability through sets of factors of a much more limited size and a far lesser degree of systemic organization. Mathematically 72 has particular properties, notably as 2³ x 3², which suggest that the set as a whole might then be especially conducive to comprehension. Clearly smaller sets may be even more conducive, but without necessarily offering the requisite variety for understanding the dynamic nature of "heaven" -- or sustainability. This suggests exploration of optimum set size as a balance between comprehensibility and distinguishable variety. The size of some circlets of prayer beads as mnemonic aids extends to 108, for example...

The traditional set of 72 is described in the Wikipedia entry on Shemhamphorasch with reference to a "hidden name of God" in Kabbalah (including Christian and Hermetic variants), and in some more mainstream Jewish discourses. It is composed of either 4, 12, 22, 42, or 72 letters (or triads of letters), the last version being the most common as the 72-fold angels of the Shemhamphorash. It is derived from Exodus 14:19-21 read boustrophedonically to produce 72 names of three letters.

Screen shots of animations with 6 Szilassi polyhedra variously oriented to each other (showing 84 angelic "points of light", but which are visible from what perspective?)
Animations created through slight modification of those produced above by Sergey Bederov and Charles Gunn based on the Schatz linkgage Interactive 3D variants (vrml; x3d); videos (solid mp4 ; wireframe mp4).

Emergence of fruitful dialogue? Beyond the difficulties of the disorientation visualized above, a different design metaphor may be used for for representing a dialogue process. As frames of reference the 6 Szilassi polyhedra can be presented as rotating each on their own vertical axis within a ring -- in cognitive terms, each "within its own world". Getting any dialogue into a coherent pattern is of course already a major challenge (implicit in the visualization programming). The dynamics of the configuration can then be used to imply that at particular moments the communication between the frames "flows" -- exemplifying a higher order of ("magical") coherence for that dialogue process -- whereas at others that possibility is "blocked".

Indication of various dysfunctional conditions in dialogue (particular "points" could be represented with disproportionate size to others, with all changes in size occurring dynamically)
Excessive extension of "lines of "argument"	Conflation of two frames of references	Inversion of some frames relative to others

In the following preliminary experiments, the "flow" between frames is indicated by distinctive circular rings (as illustrated below). The emergence of such moments could be indicated more clearly in improvements to the timing of the dynamics -- notably to be associated with "alignment" of particular vertices, whether at the top of the Szilassi polyhedra, or the bottom. Such alignment could be presented as bondng, reducing the total number of vertices to 72. When otherwise aligned, those vertices framing the holes in the polyhedra could similarly frame the larger ring when they are aligned -- a ring absent when they are not. This metaphor offers a sense of the systemic function of 84 vertices (whether or not 12 are to be excluded as not contributing actively to any coherence).

Screen shots of experimental animations of rotation of 6 Szilassi polyhedra oriented to each other in a ring (showing 84 angelic "points of light"; but which are visible from what perspective -- given the absence of transparency of the wireframe version on right)
Interactive 3D variants (vrml; x3d); videos (solid mp4; wireframe mp4).

Increasing the rate of the animation offers a visualization reminiscent of the experiments of Nikola Tesla with rotating electromagnetic fields -- an inspiration for the fruitful operation of dialogue (Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014).

Discourse as projective geometry? As argued, the strange numerical relationships between the polyhedra noted above provide a transformative framework for various stories about how to dance between configurations of perspectives. As noted, there is a certain charm to the common terminology of geometry and discourse -- points, lines, frames, and the like. It is remarkable that both discourse and geometry refer to "sides" or "faces" -- namely what is framed by a 2D polygon as the sides of a polyhedron. The challenge in divisive discourse is one of reconciling sides. Much is then made of "face", especially in the personalization of discourse and in the need for "face-to-face" encounters, and in the consequences of "loss of face" the means of avoiding it. It is intriguing that as the number of faces of a polyhedron increases -- approximating more closely to a sphere -- that immediately neighbouring faces are less readily visible from any given face (as in conference seating).

Especially provocative for the dyslexic is the relation between "angels" and "angles" -- as a confluence of perspectives and linear pathways. Formally, an angle is formed by two rays, termed the sides of the angle, sharing a common endpoint, termed the vertex. Through the transformations of polyhedra, the number of angles increases or decreases in an ordered way -- dancing curiously in relation to any 12-fold pattern. Faces and sides are characteristically oriented or angled with respect to the centre of a polyhedron.

More provocative is the deprecation of debate in the past on "the number of angels which can dance on a pin head". The phrase is now used to deprecate certain modes of discourse -- but with little indication of more frutiful alternatives. Curiously, however, it is pins which may be used in mapping ("bullet") points made during some dialogues -- possibly with relational lines between them. The question might then be reframed in terms of the number of such lines which can meaningfully converge on a point. There are constraints to this in the geometry of polyhedra. Cognitively these constraints can even be considered in the light of the much-cited study of George Miller (The Magical Number Seven, Plus or Minus Two: some limits on our capacity for processing information, Psychological Review, 1956).

Relation of 7-fold discourse to 12-fold dscourse? Much hs been made of the optimum size of a working group -- consistent with the "magical number seven". It is therefore of interest to use the unique combination of 7-fold and 12-fold characteristics of the Szilassi polyhedron to take the argument further. It is indeed the case that 7 Szilassi polyhedra (rather than the 6 used above) can be configured in an unexpected way to form an unusual structure indicative of the kind of coherence that might be expected of 7-fold discourse. This is illustrated below.

Screen shots of animations of 7 Szilassi polyhedra forming a ring indicative of dialogue modalities
Interactive vrml; Video mp4	Interactive vrml; Video mp4

It is intriguing to note that although the necessarily static images are somewhat suggestive of the complexity of the dynamics, and that the videos offer further insight, the selection required for both images and video obscures further insights. These are more evident in the interactive virtual reality models, although these in turn are based on particular selections of parameters which can be readily modified in the programs for such models (speed, colouring, axes of rotation, and the like).

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