Musical implications of orbifolds for comprehension of questioning dynamics

Now as the Ultimate Cognitive Strange Attractor (Part #8)

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The Heawood graph is a basic feature in discussion of the subtleties of orbifolds (for "orbit-manifold") in the mathematical disciplines of topology, geometry, and geometric group theory. 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, notably by Dmitri Tymoczko (The Geometry of Musical Chords, Science, 2006; A Geometry of Music, 2011). Given the above argument, the abstract is suggestive of the possibility that the distinctive cognitive feel for the WH question-pairs might be associated with chords:

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.

Engagement with music in the moment might be understood as the "art of now" -- a theme otherwise variously discussed (Jay Dixit, The Art of Now: six steps to living in the moment, Psychology Today, 1 November 2008). Music activates integrative associations and correspondences in the moment across the variety of modes of cognition. In framing "now", the "dimension" associated with any question-pair as a polarity might then be explored in terms of basic musical theory (Polarities as Pluckable Tensed Strings: hypercomprehension through harmonics of value-based choice-making, 2006).

A related study of potential relevance is that of Guerino Mazzola (The Topos of Music: geometric logic of concepts, theory, and performance, 2002). In eliciting a sense of "now", of particular concern is whether and how the "music" is capable of sustaining interest. The question could be considered a musical metaphor of the challenge of sustaining the sustainability which is the quest of global governance -- especially its cognitive sustainability. This is significant given the risk of its obsolescence, meaning how innovative concepts undergo a career of stages or phases, a life-cycle in other words -- as noted by Johan Galtung with respect to "concept careers" within the UN system (Processes in the UN system, 1980). Ironically the issue also relates to traditional implications of heavenly music and its eternal nature -- the music of immortality?

Given the widespread popular appeal of music to all sectors of society, the vulnerability of the current global civilization to catastrophic (over)simplification (discussed in the main paper), merits discussion in musical terms. Music and poetry offer means of encompassing complexity, as argued by Gregory Bateson in explaining why "we are our own metaphor" to a conference on the effects of conscious purpose on human adaptation:

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're 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. (Mary Catherine Bateson. Our Own Metaphor, 1972, pp. 288-289)

Some possibilities have been discussed separately:

• Being a Poem in the Making: engendering a multiverse through musing, 2012
• A Singable Earth Charter, EU Constitution or Global Ethic? 2006)
• Poetic Engagement with Afghanistan, Caucasus and Iran: an unexplored strategic opportunity? 2009
• Poetry-making and Policy-making: arranging a marriage between Beauty and the Beast, 1993

However both music and poetry also lend themselves to over-simplification inappropriate to the cognitive challenges of the time. Hyothetically, what factors ensure that "heavenly music" -- the music of the spheres -- does not become boring in an eternal context?

With respect to a poetic approach to the set of questions, they have been famously memorialized for children by Rudyard Kipling in the following poem -- by implication in relation to combat in the Afghanistan arena. The decision-making emphasis of "Which" is notably absent.

Kipling's poem, more specifically regarding Afghanistan (The Young British Soldier, 1895), has recently been rewritten in the light of experience there (Ryan Kisiel, "When you're lying alone in your Afghan bivvy...": British soldier re-writes Rudyard Kipling poem in damning attack on conditions, Mail Online, 4 August 2009).

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