European Parliament as a viable system: enneagram embedded within icosahedron?

Experimental Visualization of Dynamics of the European Parliament in 3D (Part #4)

Viable system: This argument follows from the work of Stafford Beer as a management cybernetician, especially known for his role in the development of a viable system model (Brain of the Firm, 1972). This raises the provocative question as the extent to which the European Parliament is a "viable system". His reference to the brain metaphor in relation to institutions raises the further provocative question as to how the "brain of Europe" is to be understood at this time -- potentially in relation to any global brain in the emerging knowledge-based society.

Curiously references to "European brain" are primarily by artists or with respect to brain research by European neurologists, notably funded by the European Commission, as with the Human Brain Project. The European Brain Council funded by the European Parliament invites the question as to the extent to which the European Parliament can itself be understood to "have a brain" -- especially in the light of its far greater preoccupations with a "brain drain" (How To Solve Europe's Brain Drain Problem, Foreign Affairs, 5 January 2016; Brain drain tearing Europe apart, Express, 8 October 2017)?

Is the complex of European institutions now to be understood as "brainless" -- or is the Joint Research Centre to be understood as constituting its "cerebral" locus -- with CORDIS serving as a form of "spinal cord"? Curiously the JRC website notes that it contributes to only 9 of the 10 political priorities for 2015-2019 of the European Commission, but not to that of Democratic Change: making the EU more transparent and democratically accountable.

In the case of the European Parliament alone, it is noteworthy that it is endowed with a European Parliament Think Tank, presumably to be understood as functioning as its "brain". However, although the public is invited to ask questions of it in the expectation of an answer from its experts, the website does not appear to have any facility for acquiring input from the public -- which may be otherwise informed. Has it been designed as a "brain" to provide output without any need for input from the public -- anticipating one of the fears with regard to artificial intelligence, of which such a "tank" is effectively a precursor? This could be seen as symptomatic of the disconnect to which eurosceptics so frequnetly allude. The tank metaphor is perhaps especially unfortunate in its implication of the brain being heavily "armoured" as a protection against the public, as separately challenged ("Tank-thoughts" from "Think-tanks": metaphors constraining development of global governance, 2003).

How might the functioning of a "European brain" be understood from an institutional perspective in the cybernetic context of the future? The coordination of the European intelligence services would be but one aspect of this, as would the Supreme Headquarters Allied Powers Europe (SHAPE). Rather than imagining it to be physically localized it could be more appropriately understood as decentralized, as with the understandings of the distributed nature of any global brain. In that sense it could also be understood as outsourced by Europe to a degree, as with the FuturICT Knowledge Accelerator in which the EU has been expected to invest heavily over an extensive period.

It is curiously symptomatic that the European Parliament has a formally instituted Spokesperson's Service in order to communicate with the wider world, but (as with other institutions) there is no fomally instituted "Listeningperson's Service". This reinforces the view of the wider public that instutions of governance may indeed "listen" (surreptitiously via surveillance processes) but they are effectively unable to "hear". The challenge in both cases is processing a flood of information -- beyond ignoring it, or responding in an automated manner, such as to be able to claim the adequacy of such commnication.

Representing the EU institutional complex: Central to this argument is the organization of the European Parliament into 9 political groupings in practice and how this might be understood to relate to the 12-fold symbolism expressed through the Flag of Europe and otherwise, as noted above. This focus avoids consideration of the institutional complex of the EU's principal decision-making bodies within which the European Parliament is itself embedded.

Being 7-fold, as defined by the Treaty on European Union (2007), the contextual complex raises considerable problems regarding how its coherence is to be represented, especially for popular comprehension. Although unrelated to the following polyhedral argument, it is of some interest that perhaps the only polyhedron on which the 7 institutions can be appropriately represented in 3D is the Szilassi polyhedron. It is unique in that each of the 7 faces of this polyhedron shares an edge with each other face -- potentially appropriate to a representation of the interrelationship between those institutions. Its 21 edges are of 12 distinct types. Topologically it is a torus, each of its faces being hexagonal.

Indicative mapping of the EU's principal decision-making bodies onto a Szilassi polyhedron
Rotation (paired sides similarly coloured)	12 types of the 21 edges (highlighted by colour)	Unfolding of 2 nets of polyhedron (flat on left; folded on right)


Produced using Stella Polyhedron Navigator

Related applications of the Szilassi polyhedron of potential relevance are considered separately (Mapping of WH-questions with question-pairs onto the Szilassi polyhedron, 2014; Dynamics of discord anticipating the dynamics of concord, 2018).

Another exercise in mapping the EU instititional complex is presented as an annex (Coherent Representation of the European Union by Numbers and Geometry: mapping structural elements and principles onto icosahedron and dodecahedron, 2019).

Icosahedron: One justification for this exploration is the recognition by Stafford Beer of the association between the 9-fold enneagram and the 12-fold icosahedron as being central to his investigation of the possibility of handling disagreement otherwise (Beyond Dispute: the invention of team syntegrity, 1994). Beer describes these insights as emerging from collaboration with Joseph Truss, who had brought the existence of the embedded enneagram to his attention, as articulated in a chapter on The Dynamics of Icosahedral Space (Beyond Dispute, 1994, pp. 196-209). For Beer:

But it is a matter of great interest that in the whole of the literature... the enneagram occurs as a plane figure. Nowhere had there been the slightest hint that a three-dimensional manifestation existed... No wonder the search took so long, given that the diagram was discovered spread across four vertical planes... The icosahedron is the actual origin of the enneagram... (p. 206)

In the quest for richer and more meaningful ways to map the features of the European Parliament in the light of Beer's studies, it is appropriate to note that the properties of the icosahedron central to his modelling efforts are characterized by both 12 vertices and 30 edges -- the latter being of potential value in any mapping of the circa 28 EU member countries. With respect to comprehension of how the European Parliament might "work", the 20 faces of the icosahedron invite further reflection in terms of another unquestioned collection of strategic sets (Requisite 20-fold Articulation of Operative Insights? Checklist of web resources on 20 strategies, rules, methods and insights, 2018).

Pentagonal stars: Whilst the EU option for 12-foldness is explained to some degree above, more mysterious is the derivation of the pentagonal form of the 12 stars. One approach is to consider their relationship to birds and their capacity for flight, as separately argued (Star symbols as schematic birds?; Star rotation: achieving and sustaining controlled flight? 2018)

Implications of a star might be clarified by the geometry of the icosahedron, as it may be analyzed and presented visually in terms of its stellation diagram and faceting diagram -- as illustrated below. A faceting of a polyhedron is one which shares the same vertices, but has different faces connecting them; faceting is the dual process to stellation, the former keeps the vertices while the latter keeps the facial planes.

Geometrical clues to the origin of the pentagonal stars in the Flag of Europe
Faceting diagram for icosahedron	9-fold Stellation diagram for icosahedron	Pentagonal prism with faceting diagram	Pentagonal stephanoid by faceting pentagonal prism ,


Produced using Stella Polyhedron Navigator

The depiction of the pentagonal prism followed from the role it plays in the extensively patented lens systems of the widely known Pentax cameras, enabling management of light and imagery under a variety of circumstances. It has 7 faces, 15 edges and 10 vertices, properties of interest to the development of the following argument; its faceting diagram is 9-fold. From the prism, the pentagonal stephanoid -- a crown polyhedron -- can be derived by a faceting process. This is a toroidal polyhedron, of which one perspective is of a pentagonal star with a central hole. Given the use of pentagonal prisms in cameras, it is metaphorically suggestive of the role the 12-stars of Europe might be expected to play. In building the animated 3D models of the 12 stars, as shown below, use was made of the dual of the pentagonal prism, namely the pentagonal bipyramid (7 vertices, 15 edges, 10 faces).

The 7-fold argument with respect to the Szilassi polyhedron above, can be explored further when 6 Szilassi polyhedra are linked into a circular "crown" via a Schatz linkage enabling the inversion of the ring, as illustrated separately (Association of the Szilassi polyhedron with cube inversion; Dynamics of discord anticipating the dynamics of concord, 2018). Relevant to any such discussion, given the long-standing symbolic importance attached to a crown, is its potential cognitive implications (Engaging with Globality through Cognitive Crowns -- 3rd Dimension: All-encompassing, well-rounded experience, 2009).

There is a curious historical irony to the discoveries in Europe of an artefact from the Roman Empire. Known as a Roman dodecahedron, its function in that civilization has not yet been determined. With 20 vertices, as the geometric dual of the icosahedron, its potential relevance to enabling comprehension of coherence is discussed separately (Roman dodecahedron, Chinese puzzle balls and Rubik's Cube?, 2018).