Aesthetic coherence essential to attraction of sustainability?

Interplay of Sustainable Development Goals through Rubik Cube Variations (Part #9)

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17 Symmetries of sustainability? The argument above was introduced with a discussion of "order in psychosocial space" -- and its implications for strategic design. This focus was the theme of an adaptation of Christopher Alexander's original study (5-fold Pattern Language, 1984). "Magic" could then be understood in terms of Alexander's quest as an environmental designer for the core attractor of a "place to be" -- then readily (and commonly) to be described as "magical". In the language of values, and of relevance to governance of sustainable global development, he framed this in terms of a "quality without a name":

There is a central quality which is the root criterion of life and spirit in a man, a town, a building, or a wilderness. This quality is objective and precise, but it cannot be named., The search, which we make for this quality, in our own lives, is the central search of any person, and the crux of any individual person's story. It is the search for those moments and situations when we are most alive (The Timeless Way of Building, 1979)

It is intriguing in relation to 17, that his study (as mentioned above) isolated only 15 "transformations" exemplified by the aesthetics of carpet design -- contrasting with other insights from archtectiural aesthetics. As argued separately, the quest for sustainable governance might indeed be framed in terms of the "magic carpet" metaphor (Magic Carpets as Psychoactive Systems Diagrams, 2010).

Architecture makes clear that any major construction of significance requires a preliminary design decision on proportion -- most notably in the case of cathedrals, temples and mosques. Such structures are an embodiment of patterns of numbers, as argued by Keith Critchlow (Keith Critchlow, Islamic Art and Architecture: system of geometric design. 1999). Curiously, with respect to 17, the point is made by the Islamic architecture of the Alhambra in Granada as a focus for the mathematician Marcus du Sautoy as Oxford Professor for Public Understanding of Science. This features in his book on Symmetry: a journey into the patterns of nature (2008) and in a TED talk (Symmetry, reality's riddle, 29 October 2009). He highlights the 17 symmetries of its decorations, offering the insight that: The language of group theory gives us the means to prove that 17 -- and no more -- different symmetry groups are possible on a two-dimensional wall. Taking the Alhambra as an inspiration, together with the variations of Bach, he has offered (with colleagues) a performance of 17 movements, 17 rooms, 17 patterns.

Implications of 20 and 37? The patterns of interaction of the numbers in relation to value-goals can be explored further following the recent importance speculatively attributed to the number 37, especially as the sum of 17 and 20 (Memetic Analogue to the 20 Amino Acids as vital to Psychosocial Life? Number 37 as indicative of fruitful pathways of transformation? 2015). Of particular relevance to the above argument is discussion there of Global strategic significance of 20-fold configurations, of Indicative examples of the recognized significance of 20-fold patterning, and In quest of number 37 through the pattern of spherical polyhedra.

God's number of 20: With respect to the minimal number of moves required to resolve a scrambled Rubik's Cube, it is then intriguing to take account of mathematical interest in that matter. As noted by Wikipedia with respect to optimal solutions for Rubik's Cube, There are two common ways to measure the length of a solution to Rubik's Cube. The first is to count the number of quarter turns. The second is to count the number of outer-layer twists, called "face turns". The maximum number of face turns needed to solve any instance of the Rubik's Cube is 20, and the maximum number of quarter turns is 26.These numbers are also the diameters of the corresponding Cayley graphs of the Rubik's Cube group. (Tomas Rokicki, et al., The Diameter of the Rubik's Cube Group Is Twenty, SIAM Journal on Discrete Mathematics, 2013; God's Number is 20, 14 August 2010). That diameter is known as "God's Number". There are many algorithms to solve scrambled Rubik's Cubes. An algorithm that solves a cube in the minimum number of moves is known as God's algorithm. Ironically it is to that capacity that cubing enthusiasts aspire.

It is very difficult to estimate the God's number of the Rubik's Revenge mainly because the centre piece of it isn't fixed because of which OLL and PLL parities occur. However it is estimated to be between 30 and 33 (Paolo Brolin Echeverria and Joakim Westermark, Benchmarking Rubik's Revenge Algorithms, 2013; Tomas Rokicki, 4x4x4 upper bounds: 57 OBTM confirmed; 56 SST and 53 BT calculated, Cube Archives, 3 Mary 2015; Bruce Norskog, God's algorithm calculations for the 4x4x4 "squares set", 4 March 2006; Bruce Norskog, The 4x4x4 can be solved in 79 moves (STM)).

Holy grail of governance? The 17 value goals suggest that a higher degree of order is required than the fourfold (2x2) magic square highlighted by economics, Metaphorical use of "magic" suggests that the quest for their requiste interplay may as usefully be associated with the ultimate nexus of values associated with the quest for the holy grail (In Quest of Sustainability as Holy Grail of Global Governance, 2011; Interrelating Cognitive Catastrophes in a Grail-chalice Proto-model, 2006).

Poetics of policy-making for sustainability? Relatively little attention is typically accorded to poetry in relation to policy-making, despaite its potential, as argued separately (Poetry-making and Policy-making: arranging a marriage between Beauty and the Beast, 1993). Should it be expected that the coherence of a set of 17 sustainable development goals could -- and should -- be meaningfully rendered in poetic form?

The case for the use of poetry to render complexity comprehensible has been well-articulated by biologist/anthropologist Gregory Bateson:

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, Our Own Metaphor, 1972, pp. 288-9)

Given its declared importance for global civilization, arguably there is a case for poets to be challenged by the need for an epic to achieve widespread appreciation of sustainability and its goals -- as exemplified by the Mahabharata or the Kalevala. The value for memorability is relatively clear.

In contrast to the articulation of the 17 SDGs or the 8 MDGs by the United Nations, it is notewothy that the Chinese pattern of the BaGua, described above, is characterized by extensive poetic implications through the complementary ambiguities of the ideograms through which it is represented. This exentends to their calligraphy -- valued otherwise in that cultural tradition. Less clear evident to other cultures is the "story" which their connectivity implies -- and its extension into the detailed connectivity of the larger story of the I Ching.

In relation to the argument above, there is of course the creative possibility of associating poetic stanzas or themes with features of the cube -- the aesthetic challenge being then to form the poem as a whole through resolving the cube from its scrambled condition.

Sonification? Could the patterns inherent in the 17 value-goals lend themselves to similar articulation through sonification -- as argued more generally (A Singable Earth Charter, EU Constitution or Global Ethic? 2006).

Indications are offered by Michael Staff (Group theory 101: How to play a Rubik's Cube like a piano, TEDEd, 2 November 2015)

How indeed are people expected to "get their head's around" the cognitive requirements of global complexity -- and then to engage in "sharing values" -- other than through such mnemonic clues to "hands on" sustainable development? This frames the further reflection as to the extent to which one's own sustainable development merits consideration in these terms.

Coping strategies constrained by intellectual property? Curiously the appreciation of any works of artists, as envisaged above, is subject to questionable intellectual property constraints. Similar constraints are evident in the history of the development of Rubik's Cube (and its variants) -- framing an additional challenge constraining innovation potentially vital to sustainable development.

This is also the case with the conceptual frameworks and visual aids that can be associated with such devices. All of these tend to be subject to intellectual property constraints and rulings including Rubik's Cube itself, as indicated by a ruling of the Court of Justice of the European Union. (The Court sets aside the judgment of the General Court and annuls the EUIPO decision which confirmed registration of the shape of the Rubik's Cube as an EU trade mark. Press Release, 122/16, 10 November 2016).

If such devices prove to be vital l to sustainable development worldwide, how is access to them to be enabled rather than frustrated -- inhibiting their further development, as separately argued (Future Coping Strategies: beyond the constraints of proprietary metaphors, 1992).

"Mine" as fundamental to sustainability? Proprietary constraints suggest that, if only as a mnemonic or aesthetic curiosity, "mine" and its associations play a strange role in relation to the complex of sustainable development goals -- possibly illustrated by the following word-play:

• mine, as exemplifying possession, embodied in issues of intellectual property and copyright. Potentially this extends to use of UN iconogaphy (as above) in relation to the SDGs or the MDGs. It is very evident in relation to the creative development of Rubik's Cube and its variants -- whatever the application enavisaged. It is also evident in the strategic articulation of iconic leaders, possessively formulated as "My Way".
• mining, as exemplified by the mining industry (and mining the seas) in the quest for resources to sustain the lifestyle of humanity. It is hoped to extend this to mining asteroids and planets. In all such cases, forms of encroachment (rendering "mine") are extended through the staking of proprietary claims. This is evident even when natural resources are not explicitly involved, as in the case of territorial claims engendering conflict (Varieties of Encroachment, 2004).
• mining, as exemplified by analogy in the rapidly developing preoccupation with data mining, most notably extending to surveillance issues of security, irrespective of concerns with invasion of privacy. The data collected, whether secretly or otherwise, becomes the jealously guarded possession of the collector.
• mine, as exemplified in the widespread use of land mines and the associated development of improvised explosive devices (IEDs) -- with the concerns raised by minefields, especially when understood metaphorically in relation to psychosocial systems
• minding the environment, as the caretaker obligations of many sustainable development goals might be understood. This may be extended to reframing the past and selectively envisaging the future (Minding the Future: thought experiment on presenting new information, 1980). It can also be understood in the Buddhist sense of mindfulness.
• mind, as the possessive engagement of the mind with the environment, most notably as the effort to "grasp" its complexity in some way and render any explanation "mine" (Grasping for identity and the challenge of integrative knowledge, 1997; Beyond Harassment of Reality and Grasping Future Possibilities, 1996). The process of "cognitive grasping" can be contrasted with various senses of mindlessness, ranging from mindless indulgence to that articulated by Buddhism (Robert Sharf, Mindfulness and Mindlessness in early Chan, Philosophy East and West. 64, 2014)

These dimensions play out in the institutional engagement with those sustainable development strategies corresponding to their particular mandates -- and in the proposals made by other bodies and individuals in that regard. Institutions are typically extremely possessive and the quest for sustainability could well be "undermined" by "turf wars".

Fivefold iconic implications of the 17th SDG? The 17th Sustainable Development Goal is: Partnership for the Goals. This is understood as strengthening the means of implementation and revitalizing the global partnership for sustainable development, as framed by the 16 goals discussed above. The fivefold rendering of the iconography (image on left below), whatever the reason for that choice, merits comparison with other traditonal fivefold iconography with related concerns (however implicit) -- and potentially in contrast with those of The Pentagon

Iconography of 17th UN SDG	Hugieia Pentagram of Pythagoreans	Chinese 5-phase Wu Xing cycle
Reproduced from Global Goals for Sustainable Development	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

The question of how the fivefold rendering might relate to the 16 goals could be variously explored. The Pythagorean framework (above centre) comes from the origin of the subsequent sense of hygiene which figures in the international iconography relating to health -- with sustainable development perhaps usefully to be understood as a sense of planetary health. The Wu Xing cycle (above right) is fundamental to traditional Chinese thinking on patterns of flow in the environment as generally understood.

These framewoks are dicussed separately in relation to the so-called Pentagramma Mirificum of navigational mathematics (Global Psychosocial Implication in the Pentagramma Mirificum: clues from spherical geometry to "getting around" and circumnavigating imaginatively, 2015; Beyond dispute in 5-dimensional space: Pentagramma Mirificum? 2015). These drew attention to the curious parallel with respect to health and healing between the pentagonal Wu Xing pattern, as a fundamental Chinese concept, and the Pythagorean symbol of the Hygiea, also compared separately (Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012; Potentially healthy developmental integrity from 5-fold symmetry, 2012).

The introductory paper explored a mapping of the Interplay of 17 value-goals -- integrating opposing "hemispheres of the global brain". They were rendered as axes across a 4-Frequency tetrahedral geodesic sphere (Refining the Value of Sustainable Development Goals: in quest of the systemic coherence of global attractors, 2017). Nine of these axes passed through the centre of that polyhedron. The question could then be how the fivefold set of circles in the UN iconography might relate to that configuration -- if the concern is understanding the systemic integration of those value-goals. One approach is to explore the great circles within that 3D sphere. The images below indicate how the 5 great circles circles of the UN iconography obscure recognition of an additional 2 great circles characteristic of the systemic integrity of the pattern of 17 value-goals mapped into that 3D configuration. This reinforces the argument that a 3D rendering (at least) is necessary for comprehension of systemic integrity.

Screen shots of 4-Frequency tetrahedral geodesic sphere (faces transparent) Illustrating how the perspective chosen renders some of the 7 great circles visible only as a line
Great circles (3-fold axis, with partials)	Great circles only (3-fold axis, showing 7)	Great circles only (2-fold axis, showing 5)	Great circles only (2-fold axis, showing 4)
Images prepared using Stella Polyhedron Navigator

An earlier argument explored the coherence associatd with 5 interlocking cycles of nonagons (Concordian Mandala as a Symbolic Nexus: insights from dynamics of a pentagonal configuration of nonagons in 3D, 2016). As illustrated below, a subsequent study provided an animation of 5 such interlocking 9-fold helical cycles (Visualization in 3D of Dynamics of Toroidal Helical Coils -- in quest of optimum designs for a Concordian Mandala, 2016).

Screen shots of illustrative animation of possible dynamics of 5 coil configuration of partnership among 16 UN Sustainable Development Goals (Variants: interactive X3D or VRML; videos: MP4 or MOV)
"Top view"	"Side view"
Animation prepared using X3D Edit

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