Polyhedral duality as a means of engaging otherwise with dualism: NATO's shadow?

Envisaging NATO Otherwise -- in 3D and 4D? (Part #6)

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In addition to the representations above, the basic form may be "unfolded" or "exploded" into its component tetrahedra, as illustrated in the animation on the left below.

Duality and double standards: More intriguing, as with any polyhedron, is the nature and significance of its polyhedral dual. This contrasting structure is indicated below, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. The dual is rotated on its own below -- and separately with the augmented tetrahedron embedded within it. Again, text and imagery could be added to the dual, in contrast to what might be associated with faces, vertices or lines of the base polyhedron.

Augmented tetrahedron and its dual
Tetra unfolding	Dual	Dual in rotation	Tetra with dual rotating
Images prepared using Stella Polyhedron Navigator

In a psychosocial system much challenged by duality and "otherness", what might be the significance of the interplay between the base polyhedron and its dual? What might any symbolic representation of this complex dynamic encompass? Arguably this offers a means of encompassing the tendency to double standards, as variously described (Enabling Suffering through Doublespeak and Doublethink, 2013; David Rohde, Ending NATO's Double Standard on International Justice, The Atlantic, 18 May 2012; Taras Kuzio, NATO's Double Standards: Why Montenegro but Not Ukraine? Atlantic Council, 31 May 2017; Double Standards? Nato's Afghan Errors, HonestReporting, 17 February 2010).

Challenging images of otherness: Such questions are especially pertinent in the case of NATO which is fundamentally structured and configured to respond to the threat of particular forms of otherness -- namely potential opponents and enemies. In any conventional depiction of NATO these threats are effectively extra-systemic, although essentially messy representations of them may be made as in the case of Afghanistan, as discussed separately (Cultivating Global Strategic Fantasies of Choice: learnings from Islamic Al-Qaida and the Republican Tea Party movement, 2010). This included the following image adapted from that by the PA Consulting Group and presented to the Office of the Joint Chiefs of Staff of the US of counterinsurgency (COIN). This takes the form of a map, notably publicized on behalf of McClatchy Newspapers by Dion Nissenbaum (The great Afghan spaghetti monster, Checkpoint Kabul, 20 December 2009; Graphic Shows Complexity of US Counterinsurgency in Afghanistan, The Huffington Post, 22 December 2009). Coincidentally this map was publicized over the web at the end of the 2009 Copenhagen climate change event.

To illustrate the possibilities (as in the above exercise), the "spaghetti map" was adapted (as reproduced below) to suggest the relevance of such a perspective to the climate change debate (Insights for the Future from the Change of Climate in Copenhagen, 2010). As with other enduring "wars", the need for another strategic approach is remarkably demonstrated by the decades-long conflict in Afghanistan (Transforming the Unsustainable Cost of General Education: strategic insights from Afghanistan, 2009; Review of the Range of Virtual Wars: strategic comparison with the global war against terrorism, 2005).).

Adaptation to climate change of a representation of counterinsurgency operations in Afghanistan (click on image for larger version)
Afghanistan COIN dynamic (clusters in original map)	Climate change COIN dynamic (clusters in adapted map)
Population/Popular support Infrastructure, Economy and Services Government Afghanistan Security Forces (ANSF) Insurgents Crime and Narcotics Coalition Forces and Actions Physical Environment	Population/Popular support Infrastructure, Economy and Services Governance Activist NGO Strategic Forces (ANSF) Dissenters ("Them") Crime and Distractions Initiatives of Coalition of the Willful ("US") Physical Environment

NATO's shadow? Any polyhedral dual, generated from a more complex polyhedral representation of NATO, then offers at least three distinct possibilities for exploration:

• dual as external opponent of NATO -- onto which the possibility of threat is projected. This is the issue of the engagement with "otherness", especially when it is framed as "evil" (In Saudi Speech, Trump Declares Absolute War Between Good and Evil, Anti-War, 21 May 2017).
• dual as external perception of NATO -- notably understood in terms of its problematic perception by others (of "its ugly face"), onto which they may project their own (mis)conceptions (Vladislav B. Sotirovic, The NATO's Violations of the "Just War" Principles in 1999, The Global Politics, 28 December 2016; US, NATO war crimes against thousands of Afghan civilians ignored, RT, 11 August 2014; Nato accused of war crimes in Libya. The Independent, 19 January 2012; Iraq, Libya, Syria: Extensive US-NATO War Crimes, 4th Media, 22 June 2013)
• dual as internal psychosocial collective shadow -- potentially to be understood in terms of unintegrated dimensions of NATO's structural modality and dynamics

Clearly there is an interplay between such understandings to be explored in the light of the insights of Carl Jung who argued: None of us stands outside humanity's black collective shadow (On the collective shadow and evil). Others write of its current implications (Paul Levy, Shadow Projection: the fuel of war, 2010; Mats Winther, Thanatos: a contribution to the understanding of the collective shadow, 2012; Nadine Kreisberger, Trump's election and what it reveals about our collective Shadow, 2016; Rosko Green, Trumpism: the collective shadow rises again, 24 December 2016).

Dynamics of engagement with the other: To give a degree of form to this shadow, through a process of "conjection" the possibility of geometric morphology may be used to transform the dual of the proposed NATO symbol through various procedures consistent with mathematical cartography. These are illustrated in the animations below. There is clearly some advantage to the colour contrast between the blue of the NATO symbol and the "threatening" red of the dual as it variously emerges. Are such emergent forms in red helpful in comprehension of what terrorism (ISIS, Al Qaida, etc) can be framed and understood in strategic terms from a NATO perspective? What are the possible cognitive analogues to these geometric transformations?

Morphing duals of augmented tetrahedron - A
By sizing	By truncation	By augmentation	By expansion
Images prepared using Stella Polyhedron Navigator

Morphing duals of augmented tetrahedron- B
By tilting quads	By tilting triangles	By tilting to compound	By tilting to rectify
Images prepared using Stella Polyhedron Navigator

The animations offer a sense of the struggle of NATO with its own shadow -- whether the shadow "within" or that projected without, as with the struggle with Islamic terrorism. Curiously this is consistent with the Islamic understanding of jihad as a continuing struggle, especially one with a praiseworthy aim. As noted by Wikipedia: Jihad can have many shades of meaning in an Islamic context, such as struggle against one's evil inclinations, or efforts toward the moral betterment of society. In classical Islamic law, the term refers to armed struggle against unbelievers, while modernist Islamic scholars generally equate military jihad with defensive warfare In Sufi and pious circles, spiritual and moral jihad has been traditionally distinguished under the term "greater jihad"

Such interpretations naturally find their analogues in the Christian understanding of crusade -- by which NATO is inspired to a greater degree -- and in the light of the traditional Christian response to Islam (Richard C. Csaplar, Jr, 1,400 Years of Christian/Islamic Struggle, CBN). However the sense of internal struggle has also figured in Christian mysticism (Neil Holman, The Struggles of a Christian, Bible Study, 21 December 2009; John Edmiston, The Christian's Struggle with Sin, Global Christians, 2010).

Of partiular interest for NATO are the institutional games in which it may engage as notably explored through a martial arts metaphor by Thierry Gaudin (Les katas institutionnels. Transnational Associations, 30, 1977) identified 21 tactical moves (katas) open to institutions, subsequently included in English translation as The Institutional Katas in an argument with regard to Game-playing in global governance? (Engaging an Opposing Ideology via Martial Arts Philosophy: reframing the challenge of Trump and Jihadism as worthy opponents, 2016). Of relevance in this respect is that the leader of the nation framed as the primary opponent of NATO is a martial arts black belt (Vladimir Putin Earns 9th Degree Black Belt In Taekwondo, Huffington Post, 16 November 2013). It is also the case that Donald Trump has been a major sponsor of mixed martial arts.

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