Meta-pattern, Meta-poesis and Music

Global Insight from Crown Chakra Dynamics in 3D? (Part #13)

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Meta-pattern: Another approach to these questions is through the insight of Gregory Bateson, as a biologist/anthropologist, regarding some form of generative meta-pattern, as discussed by Richard J. Borden (Gregory Bateson's Search for "Patterns Which Connect" Ecology and Mind, Human Ecology Review, 23, 2017, 2. For Bateson:

The pattern which connects is a meta-pattern. It is a pattern of patterns. It is that meta-pattern which defines the vast generalization that, indeed, it is patterns which connect. (Mind and Nature: a necessary unity, 1979)

And it is from this perspective that he warns: Break the pattern which connects the items of learning and you necessarily destroy all quality (1979, pp. 8-11).

The cognitive engagement with such a meta-pattern invites speculative reflection (Walking Elven Pathways: enactivating the pattern that connects, 2006; Climbing Elven Stairways: DNA as a macroscopic metaphor of polarized psychodynamics, 2007; Hyperspace Clues to the Psychology of the Pattern that Connects, 2003).

Since the challenge of recognition of any such meta-pattern could readily be understood as engaging with "monstrous" sets of numbers, is this framing misleading if the issue is more appropriately understood as engaging with patterns through power laws and exponentiation -- as providing a sense of order?

Metapoetics as complement to metalogic? Given the appeal of aesthetic attractors, another approach is suggested by "poesis" -- especially given its significance for autopoesis. In explaining why "we are our own metaphor", Gregory Bateson pointed out to a conference on the effects of conscious purpose on human adptation that:

One reason why poetry is important for finding out about the world is because in poetry a set of relationships get mapped onto a level of diversity in us that we don't ordinarily have access to. We bring it out in poetry. We can give to each other in poetry the access to a set of relationships in the other person and in the world that we are not usually conscious of in ourselves. So we need poetry as knowledge about the world and about ourselves, because of this mapping from complexity to complexity. (Cited by Mary Catherine Bateson, pp. 288-9)

The challenge itself and any potential response can be fruitfully framed through poetry, most obviously that of W. B. Yeats exactly a century ago.

Challenging loss of strategic coherence

Turning and turning in the widening gyre The falcon cannot hear the falconer; Things fall apart; the centre cannot hold; Mere anarchy is loosed upon the world, The blood-dimmed tide is loosed, and everywhere The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.

W. B. Yeats, Second Coming (1920)

Requisite banners -- with a mnemonic device -- for navigating the measureless?
Kubla Khan	Excelsior
In Xanadu did Kubla Khan A stately pleasure-dome decree: Where Alph, the sacred river, ran Through caverns measureless to man Down to a sunless sea.	The shades of night were falling fast, As through an Alpine village passed A youth, who bore, 'mid snow and ice, A banner with the strange device, Excelsior!
Samuel Taylor Coleridge (1816)	Henry Wadsworth Longfellow (1841)

Curiously it can be argued that insights of a higher order can be embodied and appreciated through aphorisms -- as a necessarily succinct aesthetic form inviting a special form of cognitive engagement -- in contrast with systemic explanations of complex patterns (Andrew Hui, A Theory of the Aphorism, 2019; Victor S M De Guinzbourg, Wit and Wisdom of the United Nations: proverbs and apothegms on diplomacy, 1961). Haiku provide one example of this, notably appreciated by Dag Hammarskjold as an early UN Secretary-Genernal (Ensuring Strategic Resilience through Haiku Patterns, 2006). Recourse to "moonshine" as a descriptor by mathematicians, is indicative of this.

The issue is discussed separately in the light of meta-poetics as a complement to conventions of logic informing preoccupation with metalogic, (as the study of logical systems (Enabling memorability through poetic self-reflexivity: metapoetics, 2016). There is indeed an extensive literature on metapoetics, with a variety of emphases:

• insights "behind" particular modes of poetic expression, as effectively suggested by the title of various reviews (Graham Zanker, Metapoetics, or Leaving the Poetry Behind? The Classical Review, 1999; Christian P. Weber, Beyond the Poem: strategies of metapoetic reflection, Goethe Yearbook)
• approaches to defining poetics as indicated in the extensive listing under the title Metapoetics: Definitions of Poetics offered by Robert Sheppard (The Necessity of Poetics, 2000)
• poetry about poetry (especially particular poems and styles), as indicated in the extensive list by T. Nellen (Poems on Poems)
• identification and listing of poetic forms, as suggested by that of Robert Lee Brewer (List of 50 Poetic Forms for Poets, Writer's Digest, 4 August 2014). This suggests similar issues of classification to those highlighted above with respect to figures of speech.

Especially helpful in distinguishing the emphasis here are the introductory distinctions made by Huda J. Fakhreddine (Defining Metapoesis in the Abbasid Age, Journal of Arabic Literature, 2011):

Meta-poetry -- poetry about poetry -- is often motivated by poets' preoccupation with their medium and their constant need to examine and justify using it. This is why many meta-poetic compositions often voice the anxieties of a poet towards his/her role and place in a tradition....

However, meta-poetry is not restricted to twentieth-century Modernism and can sometimes be much more than merely addressing poetry and poetics as themes in the poem. This is why it is important here to make the distinction between thematic meta-poetry, i.e. poems whose subject or theme is poetry (poetry about poetry), and a different, harder to define meta-poetry that can be deeper and much more critical in nature although it might not be signaled or marked as clearly as the former. I choose to call this second type referential or contextual metapoesis to reflect a consciousness apparent in the manner in which a poet responds to or engages poetic references, and the context of critical ideas and frameworks in which the poet writes. [emphasis added]

This understanding can be used to clarify the engagement of an audience exposed to poetic improvisation, as with the Basque folk art of bertsolaritza. Fakhreddin comments further:

Contextual metapoesis also requires a specifically alert and expectant audience. Consequently, a major shift in focus occurs in such meta-poetic compositions. The medium of the poem becomes an end and a statement in itself, regardless of the subject matter. This is why for the purposes of this paper, I will define metapoesis as a poet's creative reproduction of, or response to, his poetic heritage. It is a creative state in which a poet's self-awareness as participant in a project for poetic change is evident. However, he is constantly looking over his shoulder to see how his predecessors have done things, not to imitate them or necessarily break away from them but mainly to signal references; references against which his contributions become more obvious and meaningful. (pp. 205-206)

Another desciptions is offered by Hubert Dreyfus and Sean Dorrance Kelly in  concluding that embracing a "meta-poietic" mindset is the best, if not the only, method to authenticate meaning in our secular times:

Meta-poiesis, as one might call it, steers between the twin dangers of the secular age: it resists nihilism by reappropriating the sacred phenomenon of physis, but cultivates the skill to resist physis in its abhorrent, fanatical form. Living well in our secular, nihilistic age, therefore, requires the higher-order skill of recognizing when to rise up as one with the ecstatic crowd and when to turn heel and walk rapidly away. (All Things Shining, 2011)

Memorability, aphorisms and logos: The relevance to this argument can be expressed otherwise through the challenge of memorability in the face of engagement with complexity. Clearly the more complex the explanation -- whether in the case of the monster group or the crown chakra, for example -- the greater the challenge to memorability and communicability. This may apply both to the young in the earlier stages of learning and to older generations as their capacities diminish -- even though they may continue to have a role in articulating the challenges of governance.

Memorability could be understood as a response to the question: how are complex patterns to be re-membered? It is intriguing to note that one of the mathematicians most associated with the monster group is also responsible for developing both the Conway polyhedron notation and the Conway knot notation. The first could be seen as a means of ordering patterns of integration, with the latter an ordering of complexity -- epitomized by the Gordian knot for governance (Engaging globally with knots and riddles -- Gordian and otherwise. 2018). It is however even more intriguing to note that the issue of comprehensibility is a factor in neither -- although both may be understood as a matter of learning and insight. Do power laws offer clues to both memeorability and comprehensibility? Is biomimetics indeed a clue to memorability?

Curiously the polyhedron notation helps to frame the question of memorability otherwise -- through its use of a biological metaphor, namely a "seed" (as highlighted below left). In contrast to the indication of generation of forms by Conway operations on polyhedra, the speculative map on the right explores the numeric relations between the characteristics of a set of polyhedra, notably through the prime number factors associated with their product, as discussed separately (Memetic Analogue to the 20 Amino Acids as vital to Psychosocial Life? 2015). Of some relevance in relation to the primes evident in the monster group, of the complete set of the first 12 primes (2, 3, 5, 7, 11, 13, 17, 19, 23 29, 31 and 37), the first four are especially evident with respect to the tetrahedral pattern of Platonic polyhedra. Only 29 is not immediately evident, although 17 is seemingly relatively rare.

Creation of 12 forms from a cube by 3 operations (indicative of Conway operations on a polyhedral "seed")	Relationships between spherically symmetrical polyhedra (regular and semiregular; prime number factors in square brackets)
Tomruen at English Wikipedia / Public domain;	Preparation discussed separately

Arguably the fundamental challenge of memorability and communicability is one of designing the most efficient packaging -- as remarkably achieved by seeds. This is obvious in the case of a seed (pod). It has acquired importance for humanity in terms of seed banks and the need foreseen by science fiction for packing the totality of human culture into some form of container for the future, or to accompany migrants to distant planets. Packaging could be recognized as the skill so effectively employed by mnemonists, as explored by Frances Yates (The Art of Memory, 1966).

The concern with respect to global governance is whether insights can be memorably packaged, especially in a context of potential civilizational collapse (Societal Learning and the Erosion of Collective Memory, 1980). Given the emphasis on comprehension and memorability implied by the challenge of the crown chakra, of interest is the power law role in recent research into learning decay, memorability and forgetting (John T. Wixted and Shana K. Carpenter, The Wickelgren Power Law and the Ebbinghaus Savings Function, Association for Psychological Science, 18, 2007, 2; Aditya Khosla, et al, Memorability of Image Regions, Proceedings of the 25th International Conference on Neural Information Processing Systems, 1, 2012; Michael J. Kahana, et al, Note on the power law of forgetting). The issue is related to the power law of practice in learning.

Logos and emblems could be considered the epitome of integrative long-term memorability, especially in their heraldic form. They are the means by which followers are led to "battle" -- or remembrance of it. In the latter respect, especially curious is the considerable value attached to flowers (Ann Elias:, War and the Visual Language of Flowers: an antipodean perspective, War, Literature and the Arts, 20, 2008, 1-2). The role of flowers as a key to memorability in the face of complexity can be argued more generally (Flowering of Civilization -- Deflowering of Culture: flow as a necessarily complex experiential dynamic, 2014). Especially relevant with respect to this argument is the articulation offered by Keith Critchlow (The Hidden Geometry of Flowers: living rhythms, form and number, 2011).

Hence the case for exploring more engaging forms, or run the risk of their manipulative imposition, as in the case of the swastika (Eliciting Insight from Mandala-style Logos in 3D, 2020; Quantum Wampum Essential to Navigating Ragnarok, 2014; Swastika as Dynamic Pattern Underlying Psychosocial Power Processes, 2012). In this respect it is striking to recognize the potential relationship between logos, symbolically understood, and logos philosophically understood -- highlighted by the contrasting studies by the topologist René Thom (Structural Stability and Morphogenesis, 1972; Apologie du logos, 1990).

Music: It is remarkable to note the strange attraction of music in a global civilization torn both by disasters and by conflicting visions and insights. More curious are the numerous clues offered by music to memorability and integrative comprehension -- in a culture striving desperately for "harmony". Sonification is valued as a means of pattern recognition in complex data streams engendered by major science projects, as promoted by the International Community for Auditory Display (Sonification of Twitter Leadership at the G20, 2017). Considerable symbolic importance is associated with music in the formalities of governance through ritual  performance of national anthems. Strangely, although characteristically, this does not extend to any appreciation of music in enabling more effective engagement with the governance of complexity, as can be variously argued:

• A Singable Earth Charter, EU Constitution or Global Ethic? (2006)
• Aesthetics of Governance in the Year 2490 (1990)
• Reversing the Anthem of Europe to Signal Distress (2016)
• Envisaging a Comprehensible Global Brain -- as a Playful Organ (2019)

More remarkable are the insights potentially offered by musicologists into complexity and its comprehension, as suggested by the work of:

• Dmitri Tymoczko:
  • A Geometry of Music: harmony and counterpoint in the extended common practice (2011)
  • The Generalized Tonnetz (Journal of Music Theory, 56, 2012, 1)
• Ernest McClain:
  • Myth of Invariance: the origins of the gods, mathematics and music from the Rg Veda to Plato (Nicolas-Hays 1976);
  • The Pythagorean Plato: prelude to the song itself (Nicolas-Hays 1978);
  • Meditations Through the Quran: tonal images in an oral culture (Nicolas-Hays 1981),
  • Music and Deep Memory: speculations in ancient mathematics, tuning, and tradition (2018)

In relation to the monster group, it is intriguing to note McClain's use of the mathematics of lattice arrays, primes and their exponents to order tonal values in a detailed argument taking account of other number bases characteristic of other cultures (image on left). Does such exponentiation suggest a future possibility of comprehending the array of the sporadic simple groups, whether constituting the monster group or not, of which the image (below center) reflects current insight? Showing how they fit together, the diagram is based on that by Mark Ronan (Symmetry and the Monster, 2006).

Tonal values in hexagonal lattice array	Array of sporadic simple groups	The Logic Alphabet Tesseract
Reproduced from Ernest McClain, Meditations Through the Quran: tonal images in an oral culture, 1981, p. 95)	By en:User:Drschawrz - [File:Finitesubgroups.svg], CC BY-SA 3.0, Link	Diagram by Warren Tschantz (reproduced from the Institute of Figuring) .

Potentially of far greater simplicity, the dynamics of oppositional logic is indicated by the polyhedral array (above right) of the 16 possible binary Boolean operations -- the logic alphabet by Shea Zellweger in a four-dimensional cube (Oppositional Logic as Comprehensible Key to Sustainable Democracy: configuring patterns of anti-otherness, 2018; Neglected recognition of logical patterns -- especially of opposition, 2017; Alessio Moretti, The Geometry of Logical Opposition, 2009).

In terms of the language of "monstrous moonshine", this could be considered a "baby monster" fundamental to the problematic nature of discourse in a global civilization currently vitiated by fake news. There is, for example, the delightful possibility that its 30 conjugacy classes offer a degree of correspondence to the 30 edges of the icosahedron determined from a magement cybernetics perspective to be a means of transcrending unproductive discourse (Stafford Beer, Beyond Dispute: the invention of team syntegrity, 1994; Joseph Truss, et al., The Coherent Architecture of Team Syntegrity: from small to mega forms, 2000). How might those dynamics be rendered comprehensible through music, given the four-dimensional implications of the logical tesseract?

There is a charming irony to the traditional tales of the manner in which archetypal monsters have been "tamed" or "pacified" by music, especially given the many references to it as a "monster" (Monster or Machine? A Profile of the Coronavirus at 6 Months, The New York Times, 2 June 2020). Speculation in that mode is to be recognized in the recent sonification of COVID-19 (Vineeth Venugopal, Scientists have turned the structure of the coronavirus into music, Science, 3 April 2020; Markus J. Buehler, Nanomechanical sonification of the 2019-nCoV coronavirus spike protein through a materiomusical approach, arxiv, 2003).

Understanding mathematics as a quest for meta-patterns, it can be readily imagined that their association with primes and groups will eventually engender a new understanding of order -- as with discovery of the supersingular primes of moonshine theory, through which the monster group was recognized (Marcus du Sautoy, The Music of the Primes:Â searching to solve the greatest mystery in mathematics, 2003). This potentiality can be more speedily enabled by noting the potential correspondences among recognizably fundamental patterns across the disciplines. Given as yet unexplained preferences for sets of strategies numerically reflective of their characteristics, the dodecahedron and its dual are tantalizingly suggestive as comprehensible holding patterns for:

• 15-foldness: the supersingular primes (as a set of great circles or golden rectangles)
• 20-foldness: sporadic groups, crown chakra rings, amino acides vital to life
• 30-foldness: dispute dynamics, conjugacy classes

Arguably conflicts around the globe are exacerbated by misguided attachment to contrasting forms of cognitive geometry (Middle East Peace Potential through Dynamics in Spherical Geometry, 2012). This has been reinforced by theological negligence in failing to explore the mathematical theology on which preferred symbols are based (Mathematical Theology: Future Science of Confidence in Belief, 2011).

There is a considerable degree of irony to the traditional terminology of angelology regarding the distinctions to be made in assiduously numbered angelic hierarchies  -- to the extent that this terminology has been variously borrowed in relation to the current distinctions of global governance. Thrones, Principalities, Dominions and Powers are notably distinguished. In a contect tortured by "wicked problems", with "evil" as an explanation of last resort, a case can be made for exploring such numbering as patterns articulated in terms of powers (Engaging with Hyperreality through Demonique and Angelique? Mnemonic clues to global governance from mathematical theology and hyperbolic tessellation, 2016).

Playfullness and game-playing? Future recognition of a meta-pattern, and of any pattern language by which global goverance might be appropriately informed, would appear to call for human cultivation of pattern recognition beyond any dependence on artificial intelligence in that respect (Patterning Intuition with the Fifth Discipline, 2019).

The crown chakra is one such pattern. The crown chakra is especially valuable as a cognitive challenge in that it is associated with a contemplative discipline. Typical of such disciplines is the manner in which closure is called into question -- in contrast to the quest for a "solution", an "explanation" or a "description", conventionally held to be the most appropriate guarantor of human mastery of reality. To a remarkable degree this attitude resembles that developed in playfullness and game-playing, notably as celebrated in the classic by Hermann Hesse (The Glass Bead Game, 1943), as discussed separately (Evoking Castalia as Envisaged, Entoned and Embodied: the great game informed by the bertsolaritza cultural process? 2016; Humour and Play-Fullness: essential integrative processes in governance, religion and transdisciplinarity, 2005).

Rather than "containing" and "taming" complexity (and truth) as this implies, the more fruitful engagement may be quite otherwise -- through recognition of the premature nature of closure and the cognitive boundaries it imnplies (Engaging with Elusive Connectivity and Coherence: global comprehension as a mistaken quest for closure, 2018). Indicative in this respect to the Zen Buddhist attitude of shoshin, in which engagement is primarily characterized by lack of preconception (Christian Jarrett, How to foster "shoshin", Psyche, 17 May 2020).

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