Requisite variety of "voices" for psychosocial wholth: 6, 8, 12, 20, 30?

Memetic Analogue to the 20 Amino Acids as vital to psychosocial life? (Part #11)

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Solidarity and singularity: The introductory argument of the main paper was preoccupied with the dangerous limitations of the "us and them" dynamics in psychosocial life -- framed there from the perspective of "camp-us". This has been explicitly presented by Edward de Bono (I Am Right, You Are Wrong, 1991) in a study subtitled as From This to the New Renaissance: From Rock Logic to Water Logic. The dynamic is only too evident at the time of writing with the focus on solidarity in the face of threat, reinforced by repression, incarceration, flogging, capital punishment, and the like.

Curiously the quest for "solidarity" has been matched by recognition of the need for "liquidity" -- as became evident in the course of the ongoing global financial crisis. The quest could then be framed in Douglas Hofstadter's terms (Fluid Concepts and Creative Analogies, 1995).

Multiple "voices": The argument here can be taken further by using the factors elicited in the polyhedral mappings above as indicative of "voices" -- understood metaphorically as the voices in any instrumental, operatic or dramatic work. The difficulty faced by society is that solidarity is most readily expressed and understood through a single voice -- with any other then perceived as a challenging threat. This dynamic can be expressed in music and song -- and successfully reframed by use of a range of techniques. Clearly two voices do not necessarily make for the most attractive musical expression.

The central portion of the polyhedral map indicates how the number of voices might be increased, most evidently to 4 or 6. The manner in which these may work together is well illustrated by musical groups, whether in a chamber orchestra or a jazz group, or in small groups of singers. It is in this range that Edward de Bono stresses the need for a variety of ways of handling information, as he argues in several books (Six Thinking Hats, 1985; Six Action Shoes, 1991; Six Frames For Thinking About Information, 2008). However the core of the map points to other numbers, potentially indicative of a larger range of "voices", whether 8 or 12 -- or extending to 20 and 30 in some way.

Collective cognitive constraints: There is however a major constraint in the capacity to comprehend the subtleties of increasing complexity. This has been highlighted by 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), as discussed separately (Comprehension of Numbers Challenging Global Civilization: number games people play for survival, 2014). The latter notes other constraints which are variously evident in the polyhedral maps:

• "Spreadthink number": as identified by John N. Warfield (Spreadthink: Explaining ineffective groups, 1995). This reflects the the inability of groups to reach agreement on complex issue. This can be assumed to be 5.
• "Dunbar's number": as formulated by Robin Dunbar, This is a suggested cognitive limit to the number of people with whom one can maintain stable social relationships The commonly used value is 150.
• Span of control: The number of subordinates a leader can efficiently control or manage, currently understood as ranging up to 10.

Recognition in biology of the Hayflick limit, namely the number of times a normal human cell population will divide until cell division stops, merits consideration that there may well be a cognitive analogue of systemic significance. Such constraints feature in assessments of problematic-strategic complexity, as with the Situational Complexity Index (SCI) of the Institute for 21st Century Agoras.

Transcending constraints through interplay over time: The musical metaphor of voices is valuable in that it indicates that comprehension of greater variety is however possible through appreciation of the interplay of many more voices over time, namely through the manner in which they play off against each other in more complex music, notably in opera and other compositions, especially multi-part singing. This contrasts with the solidarity currently framed by defensive leaders as a matter of ensuring that everyone "sings from the same hymn sheet" -- or that the keynote of such leadership at this time should be presumptuously assumed to be unquestionably associated the sounding a mystical OM of cosmic unity as an expression of the highest values.

As an omnipresent factor in the polyhedral maps, a twofold dynamic clearly enables psychosocial space to be navigated. However current dynamics suggest that it tends to obscure the subtleties associated with the emergence of other factors. Given the importance of their role in global society, should the dynamics of any G20 or G30 group then be explored in terms of a higher order of complexity? But how? There is clearly a need to be able to disengage from factor-2 thinking under certain circumstances.

What might be the nature of an epic composition which would give fruitful expression to the variety of voices so problematically evident in society, as may be speculatively explored (A Singable Earth Charter, EU Constitution or Global Ethic? 2006). How many voices makes for fruitful global civilization -- and what extinction of voices constitutes its "deflowering" (Flowering of Civilization -- Deflowering of Culture: flow as a necessarily complex experiential dynamic, 2014).

Succinctly stated, the processes of requisite psychosocial variety need to be played out overtime to enable meaningful engagement with them. One indication in this respect is recognition of the number of dramatic plots which can be played out over time. A fictional plot is the sequence of interrelated events arranged to form a logical pattern and achieve an intended effect. The classic approach to organizing the dynamics of such plots is that of Georges Polti (The Thirty-Six Dramatic Situations, 1916) who endeavoured to categorize every dramatic situation that might occur in a story or performance -- building on the earlier work of Carlo Gozzi.

Theories of variations: In the quest for "20 amino acid" memetic analogues, it is then arguably in musical terms that the case for requite variety may be better argued. The complex arguments of Hofstadter make extensive reference to the music of Johann Sebastian Bach, most notably the 30 Goldberg Variations. Are there insights of relevance to be gleaned from the musical theory of such variations? There are many studies of those variations, of which one brief but valuable overview is provided by the pianist and composer Tjako van Schie (J.S. Bach: the architect and servant of the spiritual). Other sets of musical variations have been composed (Joseph Haydn, 20 variations in G; Sergei Rachmaninoff, 20 Variations on a Theme of Corelli; Edward Elgar's 14 Enigma Variations).

The mystery of the core operations of the memetic analogue is: why 30, why 20, why 14? Why do such numbers "work"? Given the role of an orbifold in ordering musics (Dmitri Tymoczko, The Geometry of Musical Chords, Science, July 2007), it is intriguing that orbifolds have a recognized role with respect to what can be termed the "moonshine" connectivity of such subtle correspondences (Michael P. Tuite, Monstrous Moonshine from Orbifolds, 1992). Curiously the "theory of variations" is also a fundamental theme of mathematics -- although how this might inform the musical insight, or that of psychosocial life, remains to be highlighted (notably in the light of work on Hodge structures). There is clearly also some relevance to genetic variation with respect to the adequate variety of a gene pool -- and correspondingly to that of a meme pool.

Musical traditions: Of great potential value are the studies by the musicologist Ernest G. McClain (The Myth of Invariance: the origin of the Gods, Mathematics and Music from the Rg Veda to Plato, 1976; The Pythagorean Plato: prelude to the song itself, 1978). These were initially inspired by work on the tonal "languages" of the Rg Veda by Antonio de Nicolas, as reviewed by the latter (Meditations through the Rg Veda: a retrospective, Philosophy East and West, 1999), and discussed separately (Tonal patterns of Rg Veda poetry, 1984).

McClain's discussion of the "tone number field" and the "tonal mandala" is an inspiration to further research, especially in their relation to a polyhedral patterns framed by 2ⁿx3^px5^q < 60. He notably discusses how a tonal system is engendered by prime numbers 2, 3, 5, and 7. Consequently, as McClain notes, in commenting primarily on the musical implications of Plato's Laws with regard to the ideal city of Magnesia (his last and longest dialogue):

... we have a clue as to the identity of Plato's 37 guardians, 18 from the "parent city" and 19 "new arrivals," for new arrivals among Plato's products are those generated by 7. From our arithmetical analysis of all possible products of these four prime numbers we shall discover the identities of all 37 of Plato's guardians, group them into 10-man "wrestling teams," differentiate citizens into four "property classes," draw an accurate map of his circular territory whose twelve tribes must never, under any condition, move their "boundary markers," and even learn why his supposedly practicable city of Magnesia must have so many and such strong "nursemaids" for its integer children. We shall, in fact, find so much musical detail in Laws that we can never determine whether the slightest numerical element -- and everything in Magnesia is numbered exactly -- is free of musical implication (1978, p. 108, emphasis added)

McClain notes that reference is made over 50 times to the "37 guardians" in Laws. He argues that it is the musical dimension of Plato's Laws which has been ignored by Platonists in their focus on its sociopolitical implications.

Potentially more remarkable, and of considerable relevance at this time, is the extension by McClain of his approach to the foundations of Islam (Meditations Through the Quran: tonal images in an oral culture, 1981). This is of a sensitivity which has evoked the appreciation of Seyyed Hossein Nasr (Islamic Spirituality: Foundations, 1987) with respect to the application of harmonics to the study of the proportions of the Ka'ba, and to the inner dimensions of all known traditions of antiquity.

Using the mathematics of lattice arrays, McClain notes in particular an enigmatic reference to the "Nineteen Guardians of the fire" (Al-Muddaththir Verse No:31), which is the subject of continuing reflection (Anthony Wallace, The meaning of 74:30, The Hell Fire, The guardians on the Fire, and their number, Free-Minds, 2008). As before he uses primes to order tonal values and sets the resulting 37 tones elicited into the following lattice, in a detailed argument taking account of other number bases characteristic of those times (notably 60).

37 Tonal values in hexagonal lattice array (Reproduced from Ernest McClain, Meditations Through the Quran: tonal images in an oral culture, 1981, p. 95)

This is not the place to explore the potential implications of this approach to the underlying harmony between cultures. It does reinforce the merit of associating musical theory with mathematical theology (Mathematical Theology: Future Science of Confidence in Belief -- self-reflexive global reframing to enable faith-based governance, 2011). Given the fundamental importance of star configurations -- with which 37 is strangely associated (as noted above with respect to star numbers and centered hexagonal numbers) -- further possibilities can be considered (Middle East Peace Potential through Dynamics in Spherical Geometry: engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks, 2012).

It is appropriate to note that a new degree of legitimacy has been given to the distinctive meaning carried by sound through the use of sonification -- as promoted by the International Community for Auditory Display -- most notably in relation to pattern recognition in complex data streams engendered by major science projects.

Solidarity? With respect to the concern with unquestionable solidarity, how is the "theme" on which any variation is performed to be compared with any sense of the art of variation by "unthemed" voices. One questionable framing is offered by Stephen Hough (On the art of variation: why Paganini's theme is so popular, The Guardian, 5 July 2013):

If sonata form is about theprocess of reaching adestination, variation formismore abouttaking pleasure in the journey itself. While sonata form explores material through argument - contrasting ideasthrashed out and eventually synthesised - variation form is more about one unopposed idea being explored, mined, twisted and turned inamonologue of elaboration.

A contrasting perspective is offered by the avant-garde composer, Vinko Globokar, articulates guidelines for improvisation by a group of instrumentalists (Drama and Correspondences, Harmonia Mundi, 1973). Correspondences are based on the principle of mutual psychological reactions and attempts to "join" the four participants with each other and to make them increasingly dependent on each other. He distinguishes four levels:

(a) The musical material is entirely fixed, but the choice of instruments is left open.

(b) 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').

(c) The composed material is completely substituted by the description of the possibility arising from the reactions of the performers to their neighbours.

(d) 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.

Subtlety and exclusivism: Such thinking is effectively the antithesis of the "camp-us" approach criticized in the main paper. Unfortunately, whilst there is much to be learned from music and multi-part singing, it is curious to note the manner in which "camp-us" mindsets emerge amongst musical elites with respect to the subtleties of multiple variations and voices. In a sense the more complex patterns suggested by the polyhedral relationships are upheld as "hidden" and accessible only to the few. In his commentary, Tjako van Schie quotes the pianist Dirk Schäfer on Bach:

The more perfect the work, the less the quantity of those to whom it reveals itself completely. In despite of exhibitions, reviews, yes seeming popularisations the Art Work is and remains the property of solitude. A perfect contrapuntist certainly shall be able to analyze Bachs works technically and, being musically talented, also musically. But Bach is more than a miraculous contrapuntist. He is deeply devoted, not according to a certain formula... but devoted 'in the spirit'...

Hofstadter cites a related argument by Albert Schweitzer:

Many performers have been performing Bach for years without experiencing for themselves the deepening that Bach is capable of brining out in any true artist. Most of our singers are far too caught up in technique to sing Bach correctly. Only a very small number of them can reproduce the spirit of his music; the rest are incapable of penetrating into the Master's spiritual world. They do not feel what Bach us trying to say, and therefore cannot transmit it to anyone else. Worst of all, they consider themselves to be outstanding Bach interpreters, and have no awareness of what it is they lack. (cited in I Am a Strange Loop, 2007, p. 351)

The implied elitism is then readily to be perceived as yet another variant of "camp-us" sensibility. Jacques Attali has argued that the modern period is currently living out the mode of organization characterized by classical music and has yet to organize psychosocial life in a manner which transcends its constraints (Noise: The Political Economy of Music, 1985).

The insight from the polyhedral maps is that it is necessary to disengage from factor-2 thinking ("I am right; you are wrong") in order to recognize and navigate the more elusive pattern of other pathways (Walking Elven Pathways: enactivating the pattern that connects, 2006; Climbing Elven Stairways: DNA as a macroscopic metaphor of polarized psychodynamics, 2007).

Multifold cognition? The issue at the polyhedral core, on which this quest for "20 amino acids" has focused, is how to think about the interplay between the various number-associated processes. In memetic terms the "acids" might be usefully understood as mindsets, processes or styles. The indications cited above from combinatorics regarding a "12-fold way" and a "20-fold way" merit exploration in relation to proposals for a "30-fold way" by Michael Lugo (The Thirtyfold Way, God Plays Dice, November 2007). They contrast with arguments for a Third Way in politics. This then appears simplistic by comparison -- notably in the light of various arguments for a Buddhist Eightfold Way, an Eightfold Way in Particle Physics, or the Eightfold Path of Policy Analysis.

Also of relevance, as noted, is the extensive discussion of 30-fold syntegration from a cybernetic perspective (Stafford Beer, Beyond Dispute: The Invention of Team Syntegrity, 1994; J. Truss, et al., The Coherent Architecture of Team Syntegrity: from small to mega forms, 2000). The challenge lies in the nature of "beyond" if it is questionably assumed to be comprehensible only to the few, as may be speculatively explored (Engaging with Insight of a Higher Order: reconciling complexity and simplexity through memorable metaphor, 2014).

The argument here is that, as fruitfully understood through musical voices, the "wholth" vital to psychosocial life has something to do with emergence associated with whatever is associated with the interplay of the number-associated organizing principles (Wholth as Sustaining Dynamic of Health and Wealth: cognitive dynamics sustaining the meta-pattern that connects, 2013). The interplay suggests that such wholth may involve a dynamic understanding of personal identity as discussed separately (Emergence of Homo undulans -- through a "grokking" dynamic? 2013; Encountering Otherness as a Waveform: in the light of a wave theory of being, 2013) in the light of the argument of Daniel Dervin (Creativity and Culture: a psychoanalytic study of the creative process in the arts, sciences, and culture, 1990).

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