Transformation pathways in multivocal discourse

Improvisation in Multivocal Poetic Discourse (Part #13)

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The argument to this point has highlighted the value of framing the multidimensionalty (or hyperdimensionality) of the context of multivocal dscourse -- whether poetized or improvised. It is clearly important to associate this framing with a sense of the transformation pathways through that space -- as they may be relevant to the recognition of interest and originality as attractors of attention.

Pathways patterned by polyhedra: Beyond their use as mapping surfaces, it is appropriate to recognize how polyhedral geometry offers an especially valuable mnemonic aid in a spirit artfully emphasized (Frances Yates, The Art of Memory 1966; Marie-Louise von Franz, Number and Time: reflections leading toward a unification of depth psychology and physics, 1986).

As a mnemonic device a polyhedron can be understood as follows:

• A vertex (or point) in the geometry can be usefully associated with one or more focal points of poetic discourse.
• Any edge (or line) can be suggestive of "activated" poetic connotations, associations and resonances.
• A face (or side) can identify a thematic field, delimited by a configuration of lines and points.
• Together the configuration can circumscribe and imply or frame a singular focal theme (especially if symmetrical) -- but essentially inaccessible to explicitation

The geometry is then also suggestive of the distinctions made by Globokar in improvisation between imitation (reflection), opposition (complementarity), integration through embodiment (of an axis of symmetry), and hesitation (in relation to the timing of morphing between polyhedral forms).

These implications can be used to identify a pattern of potential transformation pathways, as discussed separately (Changing Patterns using Transformation Pathways, 2015; Memetic Analogue to the 20 Amino Acids as vital to Psychosocial Life? Number 37 as indicative of fruitful pathways of transformation? 2015). There is then particular relevance to the indication by Joxerra Garzia of the number of rhyming words used by a bertsolaris as a resource in the improvisation of a bertsos (The Art of Bertsolaritza: improvised basque verse singing. 2001).

Map highlighting distinctive relationships pathways between spherically symmetrical polyhedra (regular and semi-regular) F=faces, E=edges, V=vertices (Total of these in parenthesis) [Total reduced to prime number, other than 2, in square brackets]

Knight's move, Swastika and blame-game: In framing further exploration, particular consideration is appropriate to the problematic aspects of originality and surprise, as it is typically used to gain competitive advantage. This may be highlighted through relating the pattern of the Knight's move in chess (or its equivalent in go) with that of the Swastika -- with which the Lauburu has been controversially associated (Santiago de Pablo, El Lauburu: política, cu lturae identidad nacional en torno a un símbolo del País Vasco. Memoria y Civilización, 12 , 2009).

The relationship has been discussed separately and related to the widespread prevalence of the so-called blame-game (Swastika as Dynamic Pattern Underlying Psychosocial Power Processes: implicate order of Knight's move game-playing sustaining creativity, exploitation and impunity, 2012; Collective Mea Culpa? You Must be Joking ! Them is to blame, Not us ! 2015).

In a discussion of the current disruptive dynamics of global governance, termed "monkeying" for the purpose, a case was made for Reframing "monkeying" in terms of Knight's move patterns (2011). As discussed in another context (Navigating the psychological forces of "communication space", 2003), the Knight's moves in chess are especially interesting given their potential significance as the moves of a Knight -- as a "noble" rather than as a "commoner".

The counter-intuitive strangeness of the Knight's move, and its numerical symbolism, has traditionally been the focus of hypotheses connecting the origins and structure of chess with secret magical and religious rituals of ancient India. The operation of a pattern of Knight's moves at an archetypal round table of the wise and/or influential is especially interesting (Implication of the 12 Knights in any Strategic Round Table, 2014)

Further insight into the contrast between Predictability and pattern-breaking with respect to the Knight's move, was the focus of a subsequent exploration (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics,  2011). This notably featured in the following animation (left below).

The question here is how the Knight's move can also be associated with the "cognitive twist" offered in the (potentially humorous) word-play and verbal juggling of the bertsolaritza. It is then appropriate to explore the pattern of Knight's moves as the resource mined in the process of poetic improvisation. The pattern is potentially helpful with respect to avoidance of a central integrative perspective. This is notably the case with respect to the blame-game, given the avoidance of the centre characteristic of strategic discussions, as illustrated by the animations below.

Especially interesting is experimental mapping of the pattern onto the traditional BaGua pattern of Chinese cosmology (right below). Note the switch in colour and direction -- to the "other" Swastika -- following each "move"

Animation of 8 of the Knight's moves (potentially suggestive of dynamics within the blame game and amongst the Knights of the Round Table)	Animation cycle showing emergence of "avoidance container" from merged Swastikas (left- and right-facing)	Animation of succession of Knight's moves across the BaGua engendering both forms of Swastika: left-facing (green) and right-facing (red)

In the light of the controversial association of the variants of the Swastika with the variants of the Lauburu, the latter may be substituted for the former in the animation on the right above. The BaGua pattern can however be presented in the traditional circular manner rather than as a grid pattern. The two variants of that pattern are used (below) over which two variants of the Lauburu are mapped and rotated. Each branch of the Lauburu can then be usefully understood as a distinctive Knight's move -- each offering a distinctive cognitive twist to be appreciated in any pattern of discourse.

To be stressed as relevant to this exploration, each trigram in either BaGua pattern traditionally has fundamental metaphorical associations -- with the encoding indicative of how these are understood to transform into each other. Associating the Lauburu dynamically in the animations is suggestive of how its "deconstruction" is able to hold 12 distinctive sub-transformations.

Experimental rotation of alternative Lauburu patterns over alternative BaGua patterns
Anti-clockwise over King Wen pattern	Clockwise over Fuxi pattern

The 3-fold distinctive colour-coding of each branch of the Lauburu is reminiscent of the codon triplets of the genetic code -- of which there are 64 variants (variously compared with the pattern of the I Ching). Only a sub-set is indicated by the following two animations. The patterns can be explored metaphorically as indicative of the metabolic pathways of "cognitive metabolism". Of relevance to the aesthetic preoccupation of this argument, the challenge of their memorable comprehension in microbiology has been framed by a set of songs (Harold Baum, Biochemists' Song Book, 1995; The Biochemists' Songbook MP3 Files).

With regard to the play on words characteristic of poetic improvisation, notably as practiced by bertsolaritza, it is appropriate to note the analysis by William S Huff (Homonym, Homonym and Homonym, and Other Word Pairs, Symmetry: Culture and Science, 1992). He has made creative use of the 8 trigrams of the Chinese BaGua system to distinguish 8 types of word pair (such as "peace" and "piece") according to meaning, pronunciation and spelling, as discussed separately (Discovering Richer Patterns of Comprehension to Reframe Polarization, 1998).

12-fold configuration of 5-fold dynamics: Of particular interest is the classical use of a 5-fold "container", namely the Hygeia (the original association with hygiene and health) and the Chinese Wu Xing processes, as discussed separately with respect to current use of such configurations (Memorable Dynamics of Living and Dying: Hygeia and Wu Xing, 2014; Cycles of Enstoning Forming Mnemonic Pentagrams: Hygiea and Wu Xing, 2012). Such a pattern of processes can be distinctively mapped onto the 12-faced dodecahedron, as used above in exploring the relationship between poetic, multivocal and improvisation.

Distinctive mapping of 5-fold processes onto dodecahedron
Hugieia Pentagram of Pythagoreans	Chinese 5-phase Wu Xing cycle	Mapping of Wu Xing to dodecahedron
Reproduced from Hygiea entry in Wikipedia (G. J. Allman Greek Geometry From Thales to Euclid, 1889, p.26) with labels added	Adapted from Wu Xing entry in Wikipedia Interaction arrows: black=generating; white= overcoming	Prepared with features of the Stella Polyhedron Navigator software package

Mapping of 12 distinctive 5-fold conditions onto unfolded dodecahedron
Each face of the dodecahedron offers an indication of 10 unidirectional processes (as indicated in the Wu Xing diagram above), or 20 reversible (bidirectional) processes. The challenge is to configure the 3 colours at the vertices shared between contiguous pentagram faces such that the colour combinations are distinctive. Given that there are 5 corner colours, of which 3 are shared at a vertex, this gives only 10 possibilities if there is no repetition and the order is not significant. However the dodecahedron has 20 vertices to be distinguished. The question is then how to allow for a distinctive second set of 10 vertices. This could be done by using 6 reflections of the Wu Xing ordering, thereby reversing the colour sequence around the pentagram vertices in the second set. This provides 2 sets of 10, namely offering a means of duplicating the 3-fold colour combination. Presumably these duplicates would be on opposite sides of the polyhedron -- as the extremes of the 10 axes through the 20 vertices. [The illustration on the right is only indicative; it remains to be completed] The pattern of processes can then be explored as a map of "cognitive metabolism" -- metabolic pathways in which the vertices constitute "cognitive vitamins". How the labels are to be appropriately positioned requires further consideration	5-fold Wu Xing patterns distinguished by colouring of 3-fold vertices

Embodying paradox in paradoxical geometry: The Möbius strip is widely used to hold a paradoxical relationship between opposites through a cognitive twist. Curiously opposite branches of the Lauburu can be understood as implying such a twist, with the Lauburu as a whole effectively constituting two interwoven Möbius strips. This suggests an animation (left below), potentially relating to the BaGua configuration (right below).

Interweaving Möbius strips as "paradox containers"
Animation of 2 interwoven strips	Subject/Objective pattern through 2 interwoven strips	BaGua FuXi arrangement embodied within 4 interwoven strips

Rotation of "electromagnetic field" as source of insight: The acknowledged focus of the work of Nikola Tesla was on electromagnetism -- more specifically on electricity. There is the possibility that his insights can be reframed and/or generalized, as discussed separately in relation to creativity (Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014). Using a variety of animations, this notably includes discussions of:

• Imagining a method for adapting Tesla's insights to a psychosocial context
• Detecting a meta-pattern of connectivity amongst Tesla's insights
• Potential implications of alternation and rotation in psychosocial fields

Clarification from an avant-garde perspective: For Vinko Globokar (Drama and Correspondences. Harmonia Mundi, 20 21803-1), regarding the principle of mutual psychological reactions and attempts to "join" four participants with each other and to make them increasingly dependent on each other. There are four levels:

• The musical material is entirely fixed, but the choice of instruments is left open.
• Each musician possesses only incomplete instructions. In order to be able to play, each musician must search for missing material in the performance of the neighbour (pitches from the first, length from the second, etc) and react to it in different ways: imitate, adapt himself to it (if need be, further develop), do the opposite, become disinterested or something else (something 'unheard of').
• The composed material is completely substituted by the description of the possibility arising from the reactions of the performers to their neighbours.
• On the last level, it is left up to the performers whether to cease playing or to continue; for not even the selection of reactions is now necessary

Clarification from a bertsolaritza perspective: As variously noted 6 modalities are commonly recognized in this tradition:

• Hasierako Agurra: "The Initial Greeting": the bertsolari has to address the audience at the start of the day's competition, usually with a free choice of metre and topicGartzelako Lana "Prison Cell Task": the bertsolari has to compose and sing a bertso to a given topic.
• Elkarrizketa "Conversation": two bertsolaris have to deal with the topic together, singing the stanzas in turns and responding to the previous statement. Again the topic is given.
• Puntua Jarrita "Point Given": the jartzaile sings a puntu and the bertsolari has to complete it, staying within the given tune and metre.
• Hitza Emanda: "Word Given": the jartzaile gives a key word to the bertsolari who has to compose a bertso containing this word.
• Oinak Emanda: "Rhymes Given": the bertsolari is given the four (or more, depending on the metre required) rhyming words and is required to compose the bertso "around" these rhyming words.
• Txapeldunaren Agurra: "The Winner's Farewell": here the bertsolari is allowed to compose their farewell to the audience.

Poetizing comprehensive insight of relevance to governance: The following experimental animation of the I Ching, uses the relevant Chinese character to imply a cognitive stance in the dance. An interpretation of the 64 conditions and the transformations between them is provided separately (Transformation Metaphors -- derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). The pattern has also been the focus of an experimental animation (Dynamic Exploration of Value Configurations: interrelating traditional cultural symbols through animation, 2008).

Pattern suggesting 64 contrasting styles of engagement with otherness (corresponding hexagram from the circle indicated bottom right)

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