Beyond the superficial: engaging other sides as the hidden challenge of sustainability

Interplay of Sustainable Development Goals through Rubik Cube Variations (Part #6)

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Comprehending the hidden: A polyhedron like a cube offers the particular advantage that much of the structure is hidden from any given perspective -- as with any effort to perceive the planetary globe as a whole. This characteristic echos the case made with regard to an empty centre -- possibly understood as a hole in cognitive terms. There is necessarily always something missing from global comprehension. The point is usefully made with respect to the UN art installation depicted above. The other side(s) cannot be seen in the absence of some other operation -- waking around, etc.

Given the commentary it has long evoked, the point is also clarified by the polyhedron in the engraving by Albrecht Durer's Melencolia I (as mentioned above and depicted below). The question has long been what was the actual form of that polyhedron, and the implications to be drawn from that. One strong assumption is that it is a complex of 6 pentagons associated with 2 triangles, as shown in the two images on the right.

Clarifying the challenge of the "hidden" of relevance to a global perspective on SDGs
UN art installation (detail of image above)	Dürer's polyhedron (detail of engraving)	Dürer's polyhedron (corresponding construction)	Dürer's polyhedron (rotated)

Illusion of 2D "comprehension" of coherence: It is readily assumed that a "flat" array in 2D -- a map -- addresses the challenge of comprehension of global coherence. The point is partially made by unfolding the Durer polyhedron as in the image on the left (below). Such a presentation offers an illusion of clarity and comprehension regarding the nature of the structure. The nature of the illusion in the quest for strategic integration is evident to a degree from the dynamics of folding and unfolding the flattened array in the animation on the right (below). How that coherence is to be comprehended and enabled in practice is the case for any array of sustainable development goals.

Given any focus on a particular set of value-goals, as might correspond to the mandate of a particular UN Specialized Agency, what is partially or completely "hidden" from that focus and what implication does it have for a coherent understanding of the whole? More specifically, and of greater significance, is whether and how "sustainability" is dependent on the coherent relationship between facets variously hidden from each other. A polyhedron, as with Rubik-style cubes, is helpful in rendering this challenge more explicit.

Clarification of assumed Dürer construction
Representation of unfolded polyhedron	Animation of polyhedron (un)folding
Images prepared using Stella Polyhedron Navigator

Lure of the mysterious: In emphasizing the attractive power of "magic" for many, the associated role of the "hidden" merits particular recognition. The challenge to enhancing the attraction of an array of sustainable development goals is how to indicate the significance of what is hidden and potentially emergent -- the hidden magic of that condition.

Why is sustainability less attractive to the popular imagination than the mysterious fictional focus given to the yearning for the "lost"? This is most obvious in the tales of the quest for lost treasure, lost knowledge, secret codes, or the Holy Grail -- exemplified by the cult following elicited by the novels of Dan Brown (The Da Vinci Code, 2004; The Lost Symbol, 2009).

Millennium Development Goals: One approach might then be to have 8 surfaces with icons on one side of a cube matched by 8 with icons on the opposite side. This could serve to encompass conceptually the highly probable problematic opposition to the original 8 goals -- themselves perceived as opposed by those of "problematic deposition". Each opposing side is then effectively a "shadow" of the other -- whether in a psychological sense or in that of ball-games when players on one side are expected to "shadow" or mark the players corresponding to them on the opposing side.

Whilst this approach takes account of two sets of 8 MDGs (on a single dimension), the issue is then what significance might be usefully attributed to the other two sets of 8+8 sides -- retaining the emptiness of the central square in each case. A valuable clue is offered by the colouring of Rubik's Cube. Six colours are necessarily required; one for each surface of the cube as a whole. Of interest is the use of the primary colours Red, Green and Blue -- potentially to be matched by Yellow, Mauve and Cyan.

A further clue is provided by the widely popular science fiction movie regarding strategic decision-making, namely The Matrix (1999), as discussed separately (Psychosocial Transformation by "Pill Pushing"? Model-making, strategic advocacy and the myth of the "red pill", 2017). This notably features a choice framed in binary terms between the Red Pill and the Blue Pill, namely a choice between enabling knowledge, freedom and the sometimes painful recognition of reality -- in contrast with a blue pill, typically deprecated as reinforcing more-of-the-same, namely falsehood, security and blissful ignorance of illusion (Jenny C. Yip, Red Pill or Blue Pill? What You Don't Know May Hurt You! Psychology Today, 6 September 2012). The Red Pill can also be understood as associated with radical strategies, however these are appreciated or deprecated.

Arguably the binary nature of the choice obscures the possibility of a hypothetical Third Way -- or even a Middle Way. This can be usefully associated with the colour Green. The three primary colours, Red, Green and Blue can then be understood as opposed or shadowed by problematic perspectives -- from which they themselves would be appreciated as problematic (as noted above). The colours Yellow, Mauve and Cyan can be used to hold these understandings. Each side thus frames itself as "positive" and its opposite as "negative" -- as with the sides in any ball-game and the views vigorously held in that regard.

The 8 Millennium Development Goals then lend themselves to:

Sustainable Development Goals: Such use of colours for a 3x3x3 cubic arrangement of MDGs can of course be applied to a 4x4x4 arrangment of SDGs. How many strategic "colours" are required for sustainability? Using the 6 colours above, a very preliminary experiment resulted in the following. Design choices endeavoured to highlight not only the opposition indicated by use of an opposing (complementary RGB colour) but also the systemic "magic" within the 4x4 pattern of the magic square noted above. Whether or not the pattern of numbers had any significant relation to the numbering of the SDGs, the patterns totalling to 17 within the above table served to highlght that further inquiry might elicit the existence of connectvity which has not seemingly been indicated to date. On that basis it was decided to distinguish:

• on the red and cyan faces of the cube: the 4 circles in the quadrants, each totalling to 34.
• on the green and mauve faces: the 4 sets of relationships denoted by arrows, with each arrow indicating a relationship totalling to 17 (and the symmetrical pairs totalling to 34)
• on the blue and yellow faces: the central square of 4 cells, together totally to 34 (as indicated by a circle), but with arrows indicating relationships each totalling to 17

If only mnemonically, these are the linkages which hold the pattern of 16 SDGs together as an integrative systemic whole -- namely the linkages implied by the 17th SDG: Partnerships for the Goals

The model shown below could of course be improved in various ways. No effort has been made to address the issue of the relevant orientation of the icons on the faces, or of the faces in relation to one another. The lower-left image can of course be used to provide a set of stickers which could be applied to any 4x4x4 Rubik's Revenge Cube (a tabbed version can be used to cut-out and construct the model)

Indicative allocation of a 4x4 pattern of 16 SDGs to a 4x4x4 cube (with indication of systemic patterning in the light of the magic square allocation of SDGs)
Cube presented with all sides	Cube presented with one side rendered transparent
Animtions prepared using Stella Polyhedron Navigator

Unfolded cube of 16 SDG attributions	Animation of (un)folding of cube of 16 SDG attributions
Images prepared using Stella Polyhedron Navigator

Directionality framed by a 3D cube: It is of course the case that politics has been traditionally defined in terms of the left-right spectrum -- originally derived from the allocation of seats in the French parliamentary assembly. Within this frame there are necessarily only two "sides" to any strategic argument. The possible (or necessary) existence of any other "sides" is considered meaningless in practice -- whatever token reference is made to the diversity of democratic expression.

It is in this sense that a cube offers a pattern of directions consistent with a three-dimensional understanding of reality:

• left-right, as it currently predominates to the effective exclusion of other dimensions. It is on this dimension that extremism is now defined
• front-back, as is evident in the distinction between "front benchers" and "back-benchers" in any assembly, with the latter readily ignored as effectively irrelevant to the real business of government. This dimension is associated with perception of those who are "in" in contrast to those who are "out"
• up-down, as is evident in any hierarchical organization, with those in power at the "top", and those of whom only token account is taken at the "bottom". The dimension is especially evident when politics is somehow associated with religion and its exclusive claim to articulate the values of "heaven" for the benefit of those of lesser distinction enjoined to "believe" (for their own good).

Clearly the three distinct dimensions can be readily collapsed into a single dimension (any of the above) which is then a focus of psychosocial dynamics.

The question is how greater meaning can be given to such multi-dimensionality without (and with) the bias of the special value with which a given direction may be associated -- according to its salience and (in)visibility, as discussed further below.

6-fold directional framework: A valuable insight into the variety of perspectives required for sustainability has been offered in a series of studies by Edward de Bono (Six Frames For Thinking About Information, 2008). The latter is a generalization of arguments presented in books more widely distributed (Six Thinking Hats, 1985); Six Action Shoes. 1991; Six Value Medals, 2005). It could be claimed that his concern with the MDGs is framed by another study (New Thinking for the New Millennium, 1999). The visual depictions of the 6 direction in each case are relevant to more extensive interpretation of Rubik's Cube as a mapping device

Current example: The need to take account of an attribution of the above kind is highlighted at the time of writing by the dramatic transformation of the French political scene. Traditional parties have been very significantly marginalized by the public in favour of a new party headed by Emmanuel Macron. An unusual feature of this party is the exclusion from office of those subject to any form of legal investigation, irrespective of the outcome of such proceedings. It aspires to being recognized as a "good guy government" (despite being uniquely distinguished by a majority of women). However one obvious weakness is that it is a minority government brought into power by only 42% of the electorate. The issue then becomes what "colours" and "sides" of public opinion have been effectively "hidden" and how will they manifest over the period of the mandate of the government? Will the Macron regime be found to be essentially "superficial"?

Early criticism has already been voiced in France with regard to the requisite diversity in any democratic process -- especially when faced with the democratic deficit of historic abstention. How is diversity to be integrated into a democratic process when its governance is held to be dependent on a majority with a very particular perspective? As with the debate in other countries, this frames the question as to whether democracy is sustainably governable, as currently conceived (Ungovernability of Sustainable Global Democracy ? Towards engaging appropriately with time, 2011).

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