Patterns of resonance and their characteristic experiential challenges

Hearing the Variety of Voices in Climate Change Discourse (Part #16)

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Arguably there is far greater need for both visual and aural indications of patterns of resonance as they may relate to psychosocial situations and the challenges of governance (Cognitive dimensions of governance: 2, 3, 4, 5, 6, 7, 8? 2016). Games with distinctive numbers of competing participants are suggestive of clues to comprehension of resonance. Other clues are offered by the treatment of "tuples" in mathematics, computer science, relational algebra, linguistics, and philosophy.

Clues to the cognitive experience of such resonance between alternatives are to be found in the challenges of "dilemmas", potentially to be understood as Cognitive glass ceilings impeding integrative comprehension (2019). The latter discussed the more elusive nature of trilemmas, tetralemmas (quadrilemmas) and pentalemmas (quintalemmas). These are also discussed separately (Decision-making capacity versus Distinction-making capacity: embodying whether as weather, 2015) with respect to enhancing strategic discourse systematically using climate metaphors (Five-fold ordering of strategic engagement with time; Five-fold cognitive dynamics of relevance to governance?). That discussion mentions the even rarer use of hexalemma and heptalemma, although an octalemma is seemingly recognized by Edward Andersonto (Problem of Time in Quantum Gravity, 2012). The Euthyphro "dilemma" is restated as an octalemma by Richard Goode (Nothing Is Permitted: an argument for moral eliminativism). Consideration could therefore be given to Strategic Octalemmas (2009).

N-tuple resonance: The following articulation draws particular attention to the reinforcement associated with use of the "strategic pillar" metaphor -- potentially dangerously dysfunctional when understood statically in a dynamic evolving context. It has been adapted from a separate presentation (Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity, 2017).

• 2-voice resonance (binary): The case was made above for insights that might be obtained from the duets in birdsong. These can be understood as contrasting with the relatively simplistic insights associated with competition in politics, sport, business and otherwise -- and their focus on triumphant defeat of the opposition in zero-sum games (Transcending Simplistic Binary Contractual Relationships, 2012; Destabilizing Multipolar Society through Binary Decision-making, 2016). Alan Washburn Two-Person Zero-Sum Games, 2013).
  
  Such resonance could be considered as framing the question as to how variety is sustainably engendered in a 2-person relationship -- given the aspiration of one or other to hegemony, with only singular dominance. The paradox might be explored through the classical koan of the sound of one-hand clapping.
  
  
• 3-voice resonance (ternary / triple / triadic): The following animation is suggestive of the pattern of bonding in the case of a triple resonance, notably with respect to its application to the Triple Helix model of innovation: academia (universities), business and government. Of related interest is its relevance to the three pillars of sustainability -- economic, social, environmental -- as most recently recognized by the 2005 World Summit on Social Development. This contrasts with the three pillars of the European Union, defined in instititutional terms. The Three Pillars of the United Nations are human rights, peace and security, and development.
  
  Of interest is the possible audio resonant form of a 3-fold Borromean ring linkage (of which a molecular form is reproduced below centre from Wikipedia), as discussed separately (Borromean challenge to comprehension of any trinity? 2018). One musical rendering is illustrated by the image below right (Robin Hayward and Christopher Williams, Reidemeister Move plays Borromean Rings, Corvo, 2016). As described (with reviews), performing Borromean Rings might be compared to playing a board game such as chess. Notation is used to define a field of possible moves for navigating within harmonic space. Unlike chess however the idea is not to overcome the other player, but rather to challenge them to explore continually fresh avenues within the harmonic framework laid out by the score [Excerpts (mp3): I, II, III].
  
  

  Animation of 3-fold bonding pattern	Molecular Borromean link	Musical rendering?

  
  There is clearly an extensive variety of understanding of the way that musical and sung trios form a pattern of resonance.
  
  
• 4-voice resonance (tetrad / quaternary / quadruple): Various possibilities merit consideration in relation to the pattern of resonance bonding, notably as discussed separately (Alternatives to "2-stroke democracy" suggested by 4-sided ball games, 2016) . Especially intriguing is the challenge of any relationship to the Christian cross and to the extremely charged symbol of the swastika in its different orientations. The animations on the right were developed in a separate argument which notably referred to the pattern of Knight's moves in chess across a matrix of 3x3 cells (Swastika as Dynamic Pattern Underlying Psychosocial Power Processes: immplicate order of Knight's move game-playing sustaining creativity, exploitation and impunity, 2012). (Alternation exemplified in 4-fold pattern, 2010)
  
  

  Animations of 4-fold bonding pattern
  Quadrangular	Left-facing Swastika	Right-facing Swastika

  
  Clearly there is an extensive variety of understanding of the way that musical and sung quartets form a pattern of resonance.
  
  
• 5-voice resonance (quintuple / pentangular): In arguing for recognition of 5-fold resonance, it is somewhat ironic to note the correspondence between fundamental traditional understandings of East and West, as exemplified by the pentagrams of Hygeia and Wu Xing discussed separately (Five-fold cognitive dynamics of relevance to governance? 2015). The following images were reproduced from an earlier discussion (Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012). The image on the right derives from System Dynamics, Hypercycles and Psychosocial Self-organization: exploration of Chinese correlative understanding (2010).
  
  

  Pentangular bonding patterns
  Hygeia (Hugieia) Pentagram of Pythagoreans	Animation of 5-fold bonding pattern	Chinese 5-phase Wu Xing cycle	Hypercycle representation
  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	Reproduced from entry in Principia Cybernetica

  Concerns with strategy and principle might be usefully reframed in terms of resonance between any conventional static references to "strategic pillars", as with the Five Pillars of Islam or the Five Pillars of US cyber security. The fundamental principles of Wikipedia are summarized in terms of "five pillars". OECD distinguishes five pillars of effective development action. UNFPA distinguishes five pillars of population and development. Of relevance is the widely appreciated distinction by Peter Senge (The Fifth Discipline: the art and practice of the learning organization, 1990). The strategic significance attributed to The Book of Five Rings is noted below.
  
  As with the quartet, there is potentially an extensive variety of understanding of the way that musical and sung quintets form a pattern of resonance.

• 6-voice resonance (sextuple / hexangular): As suggested above, the molecular structure of benzene offers an archetypal insight into the significance of 6-fold resonance. The image on the left is derived from the commentary by Arusa Ehmet (Why is benzene stable? Socratic.org, 8 April 2018). The animation below right is suggestive in that respect.

  Resonance of benzene molecule
  Elements of the pattern of resonance	Animation of 6-fold bonding pattern

  
  Of relevance to bonding explorations, a more rigorous interactive approach to the 6 pointed star is offered under a pseudonym in the GeoGebra environment. A detailed mathematical description is provided by Harvey Heinz (Order-6 Magic Stars, 2003). Understood in terms of 6 pillars, examples include: The Six Pillars of Self-Esteem (1995) articulated by Nathaniel Branden; The Six Pillars of Character; Six Pillars of Knowledge Economics; Six Pillars of Peace. As argued by David Grebow, missing from the above-mentioned "fifth discipline" articulation is a learning technology required to teach and continuously support the other five disciplines (The Sixth Discipline, Brandon Hall Group, 2013).
  
  The framing offered by Edward de Bono could well be recognized in terms of a 6-fold pattern of voices variously evident (Six Thinking Hats, 1985; Six Action Shoes, 1991; Six Frames For Thinking About Information, 2008).
  
  As with the quartet and quintet, there is potentially an extensive variety of understanding of the way that musical and sung sextets form a pattern of resonance.
  
  
• 7-voice resonance (septuple / heptangular): Importance is conventionally attached to the effective size of decision-making groups, notably in relation to information processing capacity (George A. Miller, The Magical Number Seven, Plus or Minus Two: some limits on our capacity for processing information and size, Psychological Review, 63, 1956). Patterns of bonding in such contexts therefore merit consideration. As noted above, this raises distinctive problems in the case of the great circle approach advocated here and the related absence of symmetrically regular spherical polyhedra. Of interest is the recent elaboration of a "ritual of the heptagram" in the neopagan tradition -- specifically noting forms of relationship within the pattern which can be understood as distinctive forms pf bonding.

• Images of 7-pointed star, implying a 7-fold bonding pattern
  Reproduced from Wikipedia		Copyright Shutterstock

  A detailed mathematical description is provided by Harvey Heinz (Order-7 Magic Stars, 2003). It is potentially appropriate to note that the wrapping of DNA around the nucleosome core results in 7-fold compaction of DNA (N. Ramaswamy, et al, Structure of D-DNA: 8-fold or 7-fold helix? The EMBO Journal, 1983). With respect to recognition of any set of "seven pillars", many examples exist. Most memorable is perhaps the Seven Pillars of Wisdom (1926), as articulated by T. E. Lawrence, but featuring in Proverbs 9:1 (Henry M. Morris. The Seven Pillars of Wisdom, Institute for Creation Research). Other examples include the The Seven Pillars of Life (Science, March 2002) articulated by Daniel E. Koshland, the Seven Pillar of Ecosystem Management (Landscape and Urban Planning, 1998) articulated by R. Lackey, and the Seven Pillars of Democratic Governance (Synergy Associates, 2009) by Mel Gill.
  
  Miller's argument usefully highlights the experiential mystery of the relation between a 7-fold and 8-fold pattern of voices. This is curiously evident in the set of notes in an octave -- given that the 8th such note is a feature of the subsequent octave. However this is to be explained in logical terms, this experiential relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems".

• 8-voice resonance (octuple / octangular): The following animation is suggestive of the pattern of bonding in the case of an eight-fold helix.
  

  8-fold bonding pattern
  Animation	Image

  Of relevance to bonding explorations, a more rigorous interactive approach to the 8 pointed star is offered under a pseudonym in the GeoGebra environment. A detailed mathematical description is provided by Harvey Heinz (Order-10 Magic Stars, 2003). Expressed in terms of pillars, the Dali Lama and Archbishop Desmond Tutu have articulated Eight Pillars of Joy. Google allegedly operates in terms of Eight Pillars of Innovation. Extensive reference is made to the articulation of Eight Pillars of Prosperity (2011) by John Allen.
  
  Further clues to the nature of such a 8-fold pattern are offered by the insights into a coaction cardioid presented by Edward Haskell, as discussed separately (Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2005).
  
  The resonance inherent in any such 8-fold pattern can also be explored through the encoding offered by the Chinese BaGua system -- especially given the nature of the transformation between its 8 conditions to which the encoding gives precision, as indicated in the animations below-left. The animations below-right are reproduced from a discussion of Transformation pathways in multivocal discourse (2016) featuring the Lauburu pattern. The latter featured in an experimental depiction of 8-fold, 16-fold and 24-fold patterns (24-fold Pattern Implied by Dynamics of the Lauburu in 3D: visualization of the interplay of sets of voices in discourse, 2016)

  Use of 8-fold BaGua to suggest the resonant dynamic relationships between voices
  Alternative experimental animations indicative of transformations between BaGua "voices"		Experimental rotation of alternative Lauburu patterns over alternative BaGua patterns
  Later Heaven (King Wen) pattern of transformations	Earlier Heaven (Fuxi) pattern of transformations	Anti-clockwise over Later Heaven (King Wen) pattern	Clockwise over Earlier Heaven (Fuxi) pattern

  
  Any resonance within the BaGua patterns is of particular interest in that each of the 8 trigrams is associated metaphorically with a climate-related natural phenomenon, as discussed separately (Cognitive implication in a Chinese system articulated through weather-related metaphors, 2015; Enhancing Strategic Discourse Systematically using Climate Metaphors: widespread comprehension of system dynamics in weather patterns as a resource, 2015; Weather Metaphors as Whether Metaphors, 2015).
  
  
• 9-voice resonance (nonuple / enneagram): As noted above, the enneagram is a notable feature of a particular school of thought which associates modes of thought and personality characteristics with the vertices of a variant of the 9-pointed star. A detailed mathematical description is provided by Harvey Heinz (Order-8 Magic Stars, 2003). Of relevance to bonding explorations, a more rigorous interactive approach to the 9 pointed star is offered under a pseudonym in the GeoGebra environment. Understood in terms of pillars, examples include: Stephen Sideroff (Nine Pillars of Resilience and Success, 2015), Gunnar Sevelius (Nine Pillars of History, 2010), and the Nine Pillars of Conservatism of the European Young Conservatives.

  Especially relevant to the argument here for increasing the mnemonic characteristics of symbols, musical notes are associated with those vertices -- as presented in an animation in the enneagram entry in Wikipedia. That image is adapted in the following simplistic animation which points to the possibility of associating bonding relationships with complex patterns of memorable chordal relationships through sonification.

  Animation of 9-fold bonding pattern

  Adapted from Wikipedia

  In the mathematical disciplines of topology, geometry, and geometric group theory, the Heawood graph is a basic feature in discussion of the subtleties of orbifolds (for "orbit-manifold"). An orbifold is a generalization of a manifold. It is a topological space (an "underlying space") with an orbifold structure. Seemingly incomprehensible to most, orbifolds have been applied to music theory. As discussed separately (Musical implications of orbifolds for comprehension of questioning dynamics, 2014), there is the possibility that the distinctive cognitive feel for logical distinctions and connectivity might be associated with chords -- in the light of the work of Dmitri Tymoczko (The Geometry of Musical Chords, Science, 2006; A Geometry of Music, 2011):

  A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.

  Another approach to a 9-fold pattern of voices is through the variety of key roles appropriate to the coherence of a fictional plot, as argued by Robert Wood (How Many Characters Should A Novel Have? Standout Books, 14 January 2014). Such a set of systemic roles is discussed with respect to one such classic (Enrolling Winnie-the-Pooh's Companions in Climate Change Discourse: key roles in the environmental psychodrama of Hundred Acre Wood, 2019). As noted there, the set then invites comparison with the nine Team Roles identified by Meredith Belbin from the manner in which members of teams interacted during business games run at Henley Management College (Management Teams, 1981). This gave rise to the Belbin Team Inventory (also called the Belbin Self-Perception Inventory), since developed to identify preference for nine Team Roles: Plant, Resource Investigator, Co-ordinator, Shaper, Monitor Evaluator, Teamworker, Implementer, Completer Finisher, and Specialist.
  
  That comparison noted the irony of the 9-fold pattern of political groups within the European Parliament -- readily to be recognized as 9 contrasting voices.

A 12-fold patterning of voices is also suggested by the circle of fifths, namely the relationship among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys.

A quite distinct approach to the experience of resonance is suggested by patterns of movement in dance. This would be consistent with the arguments of Mark Johnson (The Meaning of the Body: aesthetics of human understanding, 2007) with respect to the role of aesthetics in understanding. Cognitively, the emphasis is then placed on an understanding "through" the body and its dynamics by both Johnson and by Maxine Sheets-Johnson (The Primacy of Movement, 1999). Arguably forms of resonance of different complexity are experienced in 2-person dances, 3-person dances (such as the Triangle Dance), or 4-person dances, and possibly more.

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