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21 August 2017 | Draft

Reframing the Square Wheels of Global Governance

Transcending vain hopes of squaring the circle in global decision-making

-- / --

Myth of the "round table"
Squaring the circle as an impossible aspiration?
Criticism of dependence of governance on square wheels
Improbable viability of square wheels
Circling the wagons of governance?
Governance "locomotion" enabled by loopwheels, telescopic spokes and multipedal legs?
Central pattern generators and higher order values?
Proprietary metaphors and "systemic blasphemy"?


There are many commentaries on the current inadequacy of governance, whether global, regional or national. As currently understood by those upheld as being insightful and skilled in matters of governance, it can be argued that society is proving to be increasingly ungovernable, if not inherently so (Ungovernability of Sustainable Global Democracy? 2011). Sustainable global governance as a goal merits recognition as an essentially elusive goal (In Quest of Sustainability as Holy Grail of Global Governance, 2013).

"Surreal" is a term increasingly used to give a sense of the complex of contradictions, paradoxes and tragically ridiculous dynamics of global civilization at this time, as experienced by many and discussed separately (Surreal nature of current global governance as experienced, 2016). Donald Trump is one amongst many that are embodying such dynamics in ways from which insights can hopefully be derived.

Some sense of the situation can be elicited from considering the aspirations to global governance as a form of delusion comparable to what has been associated down the centuries with squaring the circle -- and deprecated as such. With the circle as a two-dimensional projection of the globe, and the globe as a three-dimensional projection of some form of hyperdimensional heavenly consensus, the quest for such consensus on Earth can be compared with the delusion identified so controversially by Richard Dawkins (The God Delusion, 2006). The correspondence has been argued separately (The Consensus Delusion: mysterious attractor undermining global civilization as currently imagined, 2011).

The possibility that the vehicle of governance may currently be overly dependent on what are effectively "square wheels" may help to frame the challenge. This seemingly ridiculous concept might then offer a valuable means of eliciting fruitful thinking about the surreal nature of governance at this time. The challenge is of course exacerbated by the degree of systematic denial of any need to think otherwise by those most identified with the current pattern.

However, although seemingly ridiculous and unknown to most, vehicles with square wheels do exist and exhibit a degree of viability -- however questionable. Such limited viability can of course also be claimed of the institutions of governance -- however "unfit for purpose" they increasingly appear to be. Are they to be recognized as essentially "square pegs in round holes"? What might then be usefully recognized as "square wheels" in the case of those institutions and of the international community? Would such recognition offer an insight into the ridiculous condition in which society currently finds itself?

Curiously the vehicles of governance are indeed highly dependent on a pattern which takes square form. Most obvious are the statistical tables which serve as the primary guide to decision-making. However the pattern is more subtly present in the square and rectangular forms of the documents which are so fundamental to articulation of decision-making and the development and dissemination of strategic plans. It is with these that decision-makers aspire to viable global strategies capable of attracting a consensus -- or a viable majority. As with the rectangular computer screens which offer a window on reality for so many, why do these contrast so radically with the circular displays so vital to air traffic control -- an example, with radar screens, of a more rounded approach to governance?

One very modest corrective to this modality has been previously argued (Dynamic Transformation of Static Reporting of Global Processes: suggestions for process-oriented titles of global issue reports, 2013). A more radical approach has also been speculatively explored (Spherical Accounting: using geometry to embody developmental integrity, 2004).

The square may indeed correspond to a necessary mode of thinking in the world of grounded concrete reality -- locally. The question is how to engage with all that is implied by the cyclic and the circular with respect to integrative global governance and the dynamics of its complex cycles. In the vehicular metaphor of the "wheels of governance", what is the cognitive "transmission system" between the square and the round? How might "wheels within wheels" engage with the facility of the square?

The concern here is to challenge the "square modality" through insights to be drawn from the improbable viability of vehicles with square wheels -- otherwise understood, as argued here. Is there a possibility of enhancing "all-terrain" global viability by replacing such square wheels with a rounder form -- especially as their designs might be modified? Of related interest, might a new modality reduce the need for the corruption on which governance is currently so dependent (Sebastian Reyes, Greasing the Wheels: the secret benefits of corruption, Harvard Political Review, 8 December 2015)?

Myth of the "round table"

Round tables: Governance has long been inspired by the myth of the Round Table, the famed table in the Arthurian legend, around which King Arthur and his Knights congregated. Many gatherings down the centuries have sought to use this configuration in contrast to tables more readily and widely constructed in square or rectangular form. Wikipedia offers useful checklists of Famous gatherings around round tables, Organizations using round table in their names, and use of the term in Art, entertainment and the media -- noting the Microsoft RoundTable (a 360-degree video-conferencing device). The latter suggests the probability that the circular form will prove more viable with the coming deployment of immersive virtual reality environments. Do these all constitute an aspiration to more rounded forms of understanding and governance -- to "well-rounded governance"?

Curiously the problematic contrast between the square and the round is implied to some degree by the ambiguity of the term "circular table" -- given the most common forms of a table and reinforced by the widespread pattern of tabular presentations of information. The occasional use of so-called pie charts to render comprehensible such tables is strangely echoed by the form of faction seating maps used for debating chambers -- as described below.

Round table inspiration of "community": In the absence of effective global governance, there is a curious sense in which widespread reference to an "international community" -- especially as the focus of appeals for action -- could be considered to be implicitly inspired by the community of knights constituted by the Arthurian round table. The questionable existence of this ill-defined community is consistent with the problematic efficacy of global governance, as discussed separately (International Community as God or Sorcerer's Apprentice? Strategic chaos in the absence of an interlocking temporal pattern of longer-term cyclic processes, 2015).

To the extent that the existence of this community does indeed imply unconscious recognition of a "global round table", there is an ironic sense in which the form of that table, and its dynamics, could be understood as framing global governance in terms of a monocycle. Is the international community to be understood as some form of "big wheel"? Monocycle or not, the concern in this argument is whether that wheel is effectively "square" -- with a pretence of being round.

Hemicycles: Architecturally, with very few exceptions, use of the circle is currently "hidden" within use of the square -- as with national and international debating chambers. There are relatively few examples of the square being "hidden" within the circle -- as could be a valuable catalyst to the thinking required for sustainable global governance. Curiously the most obvious examples are provided by domed temples, cathedrals and mosques. Ironically, given their problematic role in global governance, these exceptions include St Peter's Basilica and the United States Capitol.

The latter includes hemicycles for the debates of Congress and the Senate -- as used by plenary assemblies of the United Nations. In the case of the European Council, its new Europa building in Brussels (of conventional rectangular architecture), "hides" within it a strikingly curved form -- colloquially named the Space Egg (Meet the "Space Egg", the EU's €321 million headquarters, Euronews, 8 December 2016). In legislatures, a hemicycle is a semicircular, or horseshoe-shaped, debating chamber (plenary chamber), where deputies (members) sit to discuss and pass legislation. A striking image is offered by that of the European Parliament in Strasbourg.

Hemicycles of the European Parliament
Strasbourg Brussels
Reproduced from Wikipedia

The hemicycle contrasts with variants on the rectangular form, especially exemplified by seating arrangements in which participants from the majority and the opposition are seated opposite each other (as in the Houses of Parliament, Westminster). The European Parliament seats 750 MEPs. That of Westminster seats 650 MPs.

There is little discussion of the patterns of communication which are enhanced or inhibited by such patterns, most notably as the number of participants increases -- and as implied by the possibility of communication within the hemicycles depicted above. The matter has been highlighted to a limited degree by the controversial declaration by the head of the EU's executive body after only a few dozen MEPs turned up to a debate (Jean-Claude Juncker criticises 'ridiculous' European parliament, The Guardian, 4 July 2017; EU's Juncker calls empty European Parliament 'ridiculous', BBC News, 4 July 2017).

As noted above, there is an issue with regard to "greasing the wheels" of governance (Nurul Aqilah Binto Zamri et al, Greasing the Wheels of the Worldwide Governance Indicators (WGI) through Smart Governance (SGM) in controlling Corruption, International Business Management, 9, 2015, 4). There is therefore considerable irony to that protest in the light of the controversial role of Jean-Claude Juncker, as newly appointed president of the European Commission just prior to the LuxLeaks disclosures in 2014. These revelations attracted international attention and comment about tax avoidance schemes in Luxembourg and elsewhere. This resulted in making available to the public tax rulings for over three hundred multinational companies based in Luxembourg. Juncker was Luxembourg's prime minister at the time when many of his country's tax-avoidance rules were enacted. The scandal contributed to the implementation of measures aiming at reducing tax dumping and regulating tax avoidance schemes beneficial to multinational companies.

Democracy: The issue is appropriately introduced by Saul Frampton (Agony in the Agora, Aeon, 7 August 2017). He argues that by nature, democracy is a contest between clashing political desires -- and specifically: That is why the public square matters so much:

After the collapse of the Mycenaean palace system around 1100 BCE, Greece experienced centuries of social and economic devastation.... Writing at the end of the period, the 8th-century poet Hesiod described the degeneration of the human race... down to his own violent "Age of Iron". He looked into the near future and saw children born grey, families at war with themselves, and society self-destructing. He concluded miserably: I wish that I had either died sooner or been born later.

Clearly these are words that might be used by many at this time. Frampton continues:

But it was at this moment that a new vision of society began to emerge....And at its heart is the birthplace of the Western intellectual and political tradition: the polis or Greek city-state... A polis was a self-governing city or town and its surrounding territory. In terms of size, it wasn't necessarily big: Aristotle said that all the citizens of a polis (i.e, men) should be able to be assembled by the voice of a single herald. Plato gave an ideal citizenry of 5,040. Some poleis were smaller, but few were much larger.

Such ideals would seem to be unrealistic in the present period. Frampton continues:

Research has shown that communities tend to "fissure" when they reach figures in the late 100s... Moreover, the evolutionary psychologist Robin Dunbar at the University of Oxford argues that such limitations are hard-wired. Scaling up from the size of primate brains, and primate groups sizes, he estimates that we can maintain meaningful relationships only with around 150 people - the average size of a village in the Doomsday book - with an upper limit of around 230.

This constraint has become known as Dunbar's number, a measurement of the "cognitive limit to the number of individuals with whom any one person can maintain stable relationships". Given the numbers of representatives gathered there, such a constraint is a challenge to current understanding of the effective operation of the debating chambers of regional or global governance, as discussed separately (Comprehension of Numbers Challenging Global Civilization, 2014).

Echo chambers? A key question, ignored in the announcement of Europe's "Space Egg", is the nature of the strategic and cognitive implications of this "new shape". Should it be recognized as a new "echo chamber" for groupthink -- a challenging metaphor used by a reviewer in The Economist:

The Western intelligentsia, snug in its echo-chamber, has done a dismal job of understanding what is going on, either dismissing populists as cranks or demonising them as racists. (A perfectly timed book on populism, 3 December 2016)

"Shape of the table"? A continuing them in responding to the challenge in governance of complex negotiations is specifically framed in terms of the shape of the table at which stakeholders in any potentially conflictual situation will be seated. To the extent that they necessarily represent different "sides", the table must necessarily reflect this -- even if the table is circular.

The implied geometry of the table can then be used to illustrate the dilemma of achieving well-rounded governance through a varying number of sides. This is further highlighted by the implication that all parties should be "on the same side". Some of the issues of the relationship between the square and the round are highlighted by the images below.

Nesting of regular polygons
Polygon inscription
(reproduced from Wikipedia)
Polygon circumscription
(animation developed from Wikipedia)
Nesting of regular polygons: Polygon inscription Nesting of regular polygons: Polygon inscription

The original static rendering of polygon circumscription has been animated experimentally (and arbitrarily) to suggest other dimensions to the challenge of comprehension. Note that the animation lends itself to various developments and technical improvements. In addition to the choice of direction of rotation (counterclockwise for red, odd-sided polygons; clockwise for blue, even-sided), line thickness is increased with the number of sides. Other effects suggestive of significance to comprehension could be offered by changes of relative rotation rate. (Speed of rotation can be controlled by right-click within the animation).

Squaring the circle as an impossible aspiration?

The entry on squaring the circle in Wikipedia usefully clarifies the mathematical aspiration over centuries to construct a square with the same area as a given circle by using only a finite number of steps aided by a compass and straightedge. It was only in 1882, that this was proven to be impossible when the constant pi (p) on which the circle is based was proven to be transcendental, rather than an algebraic irrational number. In contrast, approximate squaring to any given non-perfect accuracy, is possible in a finite number of steps, since there are rational numbers arbitrarily close to p.

As a consequence, the expression "squaring the circle" is sometimes used as a metaphor for trying to do the impossible. There is however the possibility of approximating to the ideal through iterative use of the square. Wikipedia offers a summary of modern approximative constructions. The question is how, metaphorically or otherwise, this might relate to the integrative aspirations for global governance.

Poetic articulation: The insights of poets with regard to squaring the circle, as offered by Wikipedia, merit consideration with respect to those aspirations:

(Dante Alighieri, 1320)

(Alexander Pope, 1742)
As the geometer his mind applies
To square the circle, nor for all his wit
Finds the right formula, howe'er he tries
[Canto XXXIII]

Mad Mathesis alone was unconfined,
Too mad for mere material chains to bind,
Now to pure space lifts her ecstatic stare,
Now, running round the circle, finds it square.

Reproduced from Wikipedia

Freemasonry? Given the widely documented role of Freemasonry in relation to governance (irrespective of the suspicions of conspiracy theorists), it is intriguing how the key symbolism of that world view specifically emphasizes the square and the compasses, often embedded within a circle (below left). Considerable emphasis is placed on the implications of the phrase being on the square -- a phrase variously adopted outside that context as an indication of morality. Its use offers a curious contrast to current recognition in many contexts of the need to "grease the wheels" of governance through some form of corruption (as noted above).

Echoing the round table, the circle is depicted otherwise in the so-called Camp symbol (below right), as discussed separately (Speculation on Potential Symbolic Relevance of the Concordian Mandala, 2016). The Camp symbol of the Ancient and Accepted Scottish Rite of Freemasonry is a nonagon enclosing a heptagon, within whose lines is a pentagon which encloses a triangle in the center of which is a circle. This is curiously reminiscent of the pattern of circumscription of regular polygons as depicted above.

Symbols of Freemasonry
Square and compasses Camp symbol
Symbol of Freemasonry: Square and compasses Symbol of Freemasonry: Camp symbol
Reproduced from Wikipedia Variously presented by Eric Ginette
(The Long Journey of the Masonic Camp, The Northern Light, August 2015).

Potentially relevant to this argument, The Masonic Roundtable is an activity of the International Order of Freemasonry for Men and Women.

Surrealism? As suggested in an earlier argument (Surreal nature of current global governance as experienced, 2016), the impossibility of the aspiration to global governance as currently framed is now highlighted by references to the surreal nature of governance at this time. This corresponds strangely to aspirations to squaring the circle. Originally understood as a movement to "resolve the previously contradictory conditions of dream and reality", it could be said that surrealism has become a defining characteristic of international politics, if only to some degree (as argued on a website Surrealism in Politics).

Especially interesting are the media echoing that perspective:

In that vein, as queried by Christopher Fear, do academic discussions of political theory belong to the world of make-believe? (Down the rabbit hole, Prospect: Harvard University Press, 1 October 2013). From a perspective of international relations theory, for Victoria Lennox, as a graduating student:

Although particular theoretical paradigms within IR emphasise specific characteristics of global governance, no single paradigm has been capable of fully capturing the complexity of global governance. Resultantly, the conceptualisation of global governance requires a combination of particular aspects of realism, institutionalism, constructivism, and pluralism, that embraces and goes beyond Rosenau's conception of global order to enhance the comprehensiveness and sophistication of the conceptualisation of global governance by infusing it with meaning and value. (Conceptualising Global Governance in International Relations, E-International Relations, 3 October 2008)

Consistent with its origins, the engagement with the surreal is evident both in the arts and in the special effects of popular entertainment and marketing. In the following exploration of its relation to hyperreality, it is also evident in the unconstrained use of hyperbole and spin in many domains, most notably politics.

Criticism of dependence of governance on square wheels

It could be considered surprising that Wikipedia should have an entry on such a "ridiculous" form of technology as the square wheel. There it is simply described as a wheel that, instead of being circular, has the shape of a square. The discussion of that technology is preceded by the comment: While literal square wheels exist, a more common use is as a metaphor meaning feeling bad and naive.

There are many images on the web caricaturing the use of square-wheeled vehicles as exemplifying a fundamentally inappropriate approach to governance. The following is an addition to those depictions based on an adaptation of the innovative design by Buckminster Fuller of the Dymaxion Car (1933). Use of the image is especially valuable since Fuller associated the word Dymaxion with much of his work, a portmanteau of the words dynamic, maximum, and tension, to summarize his goal to do more with less -- specifically in relation to more appropriate global governance of resources. The adaptation here substitutes square wheels as suggestive of the tabular statistical mindset indicated above as especially constraining on governance at this time -- however much it aspires to being global in design, and claims so to be.

Square-wheeled Dymaxion Car?
Square-wheeled Dymaxion Car?
Adaptation of an image of the Dymaxion Car in Wikipedia

Criticism of governance: The metaphor has been used in criticizing various governance situations, notably in relation to reinventing the wheel:

A UK government spokesman is cited as declaring: Square wheels are ineffective, and do nothing to support the UK's drive to greater productivity (Michael Baxter, UK government heralds end of stone age for internet on public transport, FreshBusinessThinking, 22 November 2016).

Improbable viability of square wheels

Despite their improbability, a description of square wheels is offered by Wikipedia, distinguishing between real wheels of that shape and the more common use of the term as a metaphor of a problematic condition -- equivalent to that of a square peg in a round hole. Several distinct experiments with square wheel are variously demonstrating their viability.

Speeding: A TV presentation by the MythBusters experimented with modifying vehicles with square tires, determining that, with speed, a truck fitted with square wheels can deliver a relatively smooth ride (Mythbusters: Square Wheels, YouTube, 15 April 2012). Although of least relevance to the argument here, it could be interpreted as implying that even if governance is operating as a "square peg", done speedily enough it is viable to a degree. Characteristic of "just in time" governance, whether such speed is desirable with respect to longer-term issues is cause for reflection.

Skateboarding: Square wheels have been demonstrated to offer skateboards more control and grip (Francie Diep, Reinvented Wheel Is A Square, Popular Science, 10 June 2013; Megan Garber, This Guy Reinvented the Wheel ... by Turning It Into a Cube (Seriously). The Atlantic, 10 June 2013)

Weight shifting: A patent application has been made seemingly jointly by Global Composites, Inc. and Distributed Robotics LLC regarding a new method of locomotion that may prove useful in many scales of operation. (Stephen Derby, Square Wheel Car Propels Itself by Shifting Weight -- Possible MEMS Locomotion, PRWEB, 2 December 2005). While the title suggests a very narrow topic, there are claimed to be many interesting variations that arose during the development of this patent pending device -- the application of which includes robots, micro machines, novelty toys, and others.

Catenary vehicles: Of greatest relevance to the argument here is the range of experiments with the design and operation of square wheeled vehicles which enable a smooth ride on a catenary roadway. As noted by Allan Mills (Non-circular wheels: Reuleaux and squares, Physics Education, 46, 2011, 2):

Circular wheels are so familiar on vehicles of all types that it is seldom realized that alternatives do exist. This short non-mathematical article describes Reuleaux and square wheels that, rolling along appropriate tracks, can maintain a moving platform at a constant height. Easily made working models lend themselves to demonstrations at science fairs and open days.

In 1997 Macalester College mathematics professor Stan Wagon constructed the first prototype of a catenary tricycle. An improved model made out of modern materials was built when the original vehicle wore out in 2004, as variously described (Ivars Peterson Riding on Square Wheels, Science News, 30 March 2004; Andrew Bradshaw, Square-Wheeled Tricycle, YouTube, 22 October 2007).

An accessible description of the technicalities and model-building guidelines is provided in the Square Wheels (Exploratorium Science Snackbook, 2002; Square Wheels, Science Snacks), based on an earlier articulation by Jeffrey Regester (A Long and Bumpy Road, The Physics Teacher, 35, 232, April 1997). The most useful overview of the matter of relevance to this argument is that provided in a slide presentation by Stacy Hoehn Fonstad (Smooth Rides on Square Wheels, Vanderbilt University, 4 October 2011).

Illustration of principle of square wheel operation
(according to Stacy Hoehn Fonstad)
Illustration of principle of square wheel operation
Bumpy: As the square wheel rolls across a flat surface, the center of the square changes elevation.
Illustration of principle of square wheel operation
Smooth: To compensate for these elevation changes and to smooth the ride, the road's surface needs to be uneven
Illustration of principle of square wheel operation
Roadway: A series of these "bumps" forms a road on which a square can roll smoothly.

The question is then how this might apply to the wheels of governance -- if the vehicle of governance is required to move smoothly along a "bumpy" road, perhaps characterized by cycles, with the requisite resilience to navigate the adaptive cycle (Daniel Christian Wahl, The adaptive cycle and panarchy as dynamic maps for resilience thinking, Medium, 15 April 2017).

Circling the wagons of governance?

In contrast with the mythical possibilities of a round table gathering, and the aspirations these evoke, a far more concrete recognition of the value of a circle is evident in the phrase circling the wagons -- otherwise known as forming a wagon fort. This is a mobile fortification made of wagons arranged into a rectangle, a circle or other shape and possibly joined with each other to form an improvised military camp (Gregory; Michno and Susan Michno, Circle the Wagons!: attacks on wagon trains in history and Hollywood films, McFarland, 2008).

Variously used as a metaphor, "circling the wagons" can be readily applied to governance in terms of its strategic and institutional implications. In the case of the United Nations, for example, its "wagons" could be understood as the set of its Specialized Agencies. Configured in a circle, these then constitute a global system of defence against the problems of society.

However this configuration is at the present time as much an ideal as that of the round table at which their representatives may come to be seated in the process of global decision-making. The implication of the mobility is however valuable, whereas the appropriateness of the implied fortress mentality is inherently questionable (Fortress mentality on EU migration creates xenophobia, warns Italian PM, The Guardian, 20 January 2015; Environmental insecurity and fortress mentality, International Affairs, 90, 2014, 4; Fortress mentality, The Economist, 15 September 2016).

Inspired by the improbable possibility of square wheels, the concern here is whether the understanding implied by "circling the wagons" can be transformed into a new understanding of the "wheels of governance" and how these might give it "all-terrain" capability, rather than being dependent on previously prepared roads.

The metaphor can be explored through the following images. That on the left is indicative of a successful circling of the institutional wagons of global governance (FAO, UNESCO, WHO, ILO, etc). Each is variously equipped with the statistical tables understood as providing the vital insights through which governance is enabled. That pattern could be rotated (as with the animation on the right) to suggest how each comes in contact with the road travelled by the vehicle of global governance -- other such wheels supporting the vehicle could feature in an animation.

The animation on the right suggests how the distinctive agencies (as "boots") might successively encounter the terrain as the vehicle progressed -- offering another sense of "boots on the ground". Both images are inadequate in that they avoid any sense of the kind of "bumpy" terrain which an all-terrain vehicle might be expected to traverse -- as illustrated by the square wheels above.

Schematics indicative of "circling the wagons"
UN Agencies filtering reality through tables Agencies engaging with reality as boots
Schematic indicative of 'circling the wagons': UN Agencies Schematic indicative of 'circling the wagons': Agencies engaging with reality as boots;

Stacy Hoehn Fonstad, in the presentation above, makes it clear that the same procedure used for "square wheels" will work for any regular polygon (except for a triangle). As the number of sides of the polygon increases, the bumps on the catenary road will necessarily become flatter and flatter. Given some other wheel shape, the argument there focuses on de terming the shape of the corresponding road.

The challenge for all-terrain governance is the reverse, namely to be able to adjust the shape of the wheels according to the shape of the road. This is the concluding question of that presentation: Given a road shape, can we find a wheel that will ride smoothly over that road? The issue is that the path to be followed may have a variety of configurations -- as illustrated by the development of wheeled vehicles for exploration of other planets.

With the wheel understood as a polygon, whether square or otherwise, the issue then becomes how a polygon might change its shape in response to terrain. One simple illustration of this possibility is indicated below, on the assumption that the wheel might be 12-sided -- namely a dodecagon, using a form with properties favoured in the articulation of strategies (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011). In the absence of an animation, the deformation of the polygon is suggested by the use of telescopic joints.

Schematics indicative of all-terrain governance -- using telescopic joints
Traversing a bump Traversing a hole
Schematic indicative of all-terrain governance -- using telescopic joints Schematic indicative of all-terrain governance -- using telescopic joints

Given that "all-terrain" may imply more than three dimensions -- with the complexity currently attributed to the challenges of governance -- there is a case for extending the metaphor through use of polyhedra. With the example of the cubic wheels, cited above as being of interest to skateboarders, consideration could be given to the transformations between spherically symmetrical polyhedra, as previously explored with the use of animations in 3D (Psychosocial Implication in Polyhedral Animations in 3D: patterns of change suggested by nesting, packing, and transforming symmetrical polyhedra, 2015; Five-fold ordering of strategic engagement with time, 2015).

Governance "locomotion" enabled by loopwheels, telescopic spokes and multipedal legs?

Technomimicry? Although innovation in governance is typically claimed to enable change and movement, as noted above the ideal is primarily associated with the static notion of "table" -- with the Holy Grail of governance framed by the processes associated with the Arthurian round table. Use of "wheel" is primarily used with respect to the complexity of the "inner wheels" of governance.

Following the inspiration to technological development of biomimicry, notably for flight and robotics, there is therefore a case for extending this transposition of insight through technomimicry -- as it might apply to governance (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011; Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014).

With respect to this argument, introduced by the impossibility of squaring the circle, it is appropriate to note the study by Barry Cox and Stan Wagon (Mechanical Circle-squaring, College Mathematics Journal, 40, 2009, September, pp. 238-247), presented otherwise as Drilling for polygons (American Mathematical Monthly, 119, 2012, pp. 300-312). The technique for the seemingly improbable drilling of square holes raises questions as to what possibilities this approach might suggest for governance? One lead is offered by the sense of drilling down in its relationship to data mining.

Concern has long been expressed at the lag between the creativity facilitated in academia and its application to technological development "in the real world". An analogous concern could be expressed regarding the proven technological developments and the lag in adapting that thinking to psychosocial systems. Such developments are then to be understood as a rich source of metaphor offering guidance to psychosocial development -- specifically with respect to governance, according to the argument developed here.

Wheel design: With governance understood in terms of wheel-enabled locomotion, it is therefore appropriate to explore innovations in wheel design for clues to models of value to governance. A set of possibilities is summarized by Minds Eye Design (7 Incredible Wheel Designs You Have to See to Believe, YouTube, 3 August 2017). Two of these are of immediate relevance to the argument here:

Animation indicative of loopwheel principle
Loppwheel animation
Animation adapted with permission from Loopwheels from
So How Does It Work: absorbing vibrations and smoothing roads

Telescopic spokes: The argument above for an understanding of telescopic spokes in any use of the wheel metaphor in governance merits consideration in the light of patents with respect to such redesign of spokes -- many dating from the early decades of the century past:

Spring and telescopic wheel designs
"Resilient wheel" (1908) "Spring wheel" (1910) "Spring telescopic-spoke wheel" (1913)
Spring and telescopic wheel design: Resilient wheel Spring and telescopic wheel design: Spring wheel Spring and telescopic wheel design: Spring telescopic-spoke wheel
US Patent 950761 A, 30 December 1908 US Patent 1090797 A, 27 July 1910 US Patent 1145775 A, 27 August 1913

In a period in which much is made of the need for resilience in governance, it is somewhat ironic that one of the earliest such innovations was termed the "resilient wheel". Proposed in 1908, this is arguably an indication of the degree of lag in adapting insights from technology to governance.

Given the ideal of a 12-fold round table, it is also of interest that the first two proposals indicated above envisaged 12 telescopic spokes.

Multipedal robots: Whilst much is currently made of the potential future implications of artificial intelligence to governance -- given the increasing dependence on information systems -- little attention has been given to the metaphors offered by robotics for governance. In metaphorical terms, the institutions of governance can be readily understood as "robots" of a kind -- beyond their deprecation as "robotic". They are groupware-based, rather than hardware-based -- anticipating the emergence of the intelligence-based systems now framed in terms of "artificial intelligence".

There is therefore a case for exploring developments in robot locomotion as a source of insight into the "locomotion" of government institutions, separately and collectively, as vehicles of change. Examples of recent innovations offering such inspiration are provided by the following:

Of particular relevance to governance is the concern with multipedal robots as a means of anticipating a response to failure of any "leg". Clearly a concern in governance is the possibility of the failure of any institution, or division thereof, on which the viability of the system as a whole is dependent. A "multipedal" approach is then consistent with the Precautionary Principle and the need for a systemic understanding of potential failure (Variety of System Failures Engendered by Negligent Distinctions, 2016).

Given the need for "locomotion" in governance, if there is to be an adequate response to popular appeals for "change" and "movement", an appropriate question is the number of "legs" required to enable such movement and guarantee stability in the process. It is appropriate, if somewhat ironic, to consider the need for different "gaits" in governance as a consequence of contextual challenges and in the event of partial failure.

Given the extensive understanding of the locomotion of animals in nature, developments have focused on quadripedal robots (with inspiration from mammals) and hexapedal robots (with inspiration from insects).

Clearly there is extensive interest in humanoid robots and their bipedal locomotion. It is therefore curiously ironic that governance is obviously challenged by the coordination of the two "feet" typical of the conventional political extremes -- "left" and "right" -- if not by a multipedal situation as a consequence of a greater number of political factions. Of interest, therefore, is whether studies of robot movement offer insights to reframe understanding of possibilities for governance challenged by issues of coordination -- readily recognized as resulting in spastic movement, deprecated as characteristic of governance. Given the role of biomimicry with respect to development of airplanes, helicopters and drones, the potential implications for the challenges of extremes to governance merit consideration (Counteracting Extremes Enabling Normal Flying: insights for global governance from birds on the wing and the dodo, 2015).

Central pattern generators and higher order values?

As a consequence of insights into pattern language from the perspective of various disciplines, reference is increasingly made to the range of patterns appropriate for consideration in governance. Central pattern generators are biological neural networks that produce rhythmic patterned outputs without sensory feedback. As noted by Gerasimos G. Rigatos (Advanced Models of Neural Networks: nonlinear dynamics and stochasticity in biological neurons, Springer, 2014, p. 84):

Dynamical models of coupled neural oscillators can serve as Central Pattern Generators (CPGs). This means that they stand for higher level control elements in a multi-layered control scheme which provide the activation frequency and rhythm for controllers operating at the lower level, e.g. controllers that provide motion to robot's joints. CPG methods have been used to control various kinds of robots, such as crawling robots and legged robots and various modes of locomotion such as basic gait control, gait transitions control, dynamic adaptive locomotion control, etc. CPG models have been u.sed with hexapod and octopod robots inspired by insect locomotion. CPGs have been also used for controlling swimming robots, such as lamprey robots. Quadruped walking robots controlled with the use of CPGs have been studied.... Models of CPGs are also increasingly used for the control of biped locomotion in humanoid robots.

Three-fold patterns: The loopwheel design (noted above) calls for speculative reflection on the possibility of an analogous pattern with respect to governance, perhaps to be understood as an "inner wheel" or "governor". This possibility merits reflection in the light of the oldest, and perhaps most fundamental, insights into the configuration of such an inner wheel. In that sense the loopwheel pattern can be compared with variants of the triskelion or triskele. As noted in the Wikipedia description, the spiral design can be based on interlocking Archimedean spirals, or represent three bent human legs. As indicated there, variants have been used in Europe from Neolithic times, in Celtic culture, and in the Mediterranean region from classical Greek times. Variants are noted in Asian cultures. It features in Christian church architecture. Curiously it is also a symbol favoured by the controversial BDSM community.

For the purpose of this argument two variants of the triskelion are presented below in animations to evoke reflection on the significance of such an underlying "central" dynamic in governance.

Rotational wheel-like animations of the triskelion
Rotational wheel-like animation of the triskelion Rotational wheel-like animation of the triskelion
Rotations generated from images in Wikipedia

The triskelion has been compared in previous arguments to the significance of such a pattern in the higher order insights associated with trinitarian principles or deities, notably with the pattern fundamental to some understandings of governance: liberty, equality, fraternity (Imagining Order as Hypercomputing: operating an information engine through meta-analogy, 2014; Holiness framed by a triangulated configuration of holes, 2014). The animations, with their "spring", "leg" and "shock absorbing" implications (as clarified by the loopwheel design), suggest a dynamic absent from imagery tending to reinforce the static, structural patterns of conventional governance.

Borromean rings Phenomenological epoché Christian Trinity
Borromean rings Phenomenological epoché Christian Trinity
Notable for their topological implications As explored by Francisco Varela Reproduced from Wikipedia

The fundamental cognitive significance of such triadic patterns is evident in the semiotic triangle of meaning of Charles Ogden, and the triangulated Oedipus complex of Jacques Lacan, as separately discussed and interrelated using animations (Interrelating disparate threefold cognitive patterns as a polyhedron, 2017).

3D Configuration on tetrahedron of triadic articulations
(screen shots of unfolding-refolding animations )
4 "Cognitive" triangles (GIF animation) 4 "Symbolic" triangles (GIF animation)
Configuration on tetrahedron of triadic articulations  (folded) Configuration on tetrahedron of triadic articulations (unfolding)
Images prepared using Stella Polyhedron Navigator

Given the directionality possible in any rotational dynamic, it is also of interest to explore counter-rotation of the earlier three-fold symbols, as in the animations below. Although constructed to offer "closing" and "opening" animations, on inspection the two variants alternate between these conditions and therefore should not be distinguished except to make that evident.

Counter-rotation of three-fold symbols
Triskelion A ("opening") Triskelion A ("closing") Triskelion B ("opening") Triskelion B ("closing")
Counter-rotation of three-fold symbols Counter-rotation of three-fold symbols Counter-rotation of three-fold symbols Counter-rotation of three-fold symbols

Of particular interest is the manner in which the animations "engender" a fourth "implicit" position through their vertical reversal in the counter-rotational cycle. The relevance to value-based governance merits reflection in the light of the Axiom of Maria, notably appreciated from the perspectives of Carl Jung and Marie-Louise von Franz.

Given the challenge of "otherness" for governance, such triadic patterns justify even more speculative exploration (Reframing the Dynamics of Engaging with Otherness: triadic correspondences between Topology, Kama Sutra and I Ching, 2011).

Four-fold patterns: Similar significance can potentially be derived from four-fold patterns of which the most controversial is the swastika, given the contrasting interpretations of it and its symbolic implications for recent history (Swastika as Dynamic Pattern Underlying Psychosocial Power Processes: implicate order of Knight's move game-playing sustaining creativity, exploitation and impunity, 2012).

As noted, and illustrated there with animations, the swastika offers an encoding of the dynamics of the nonlinear Knight's move of chess and is therefore intimately related to creativity and strategic surprise. It is for this reason that the Knight is part of the emblem for the US Psyops as a traditional symbol of "special operations" -- signifying the ability to influence all types of warfare. Appropriately it is discussed by Wikipedia in relation to various positional plays in the game of go. This is framed as the most challenging strategy game and the ultimate test of artificial intelligence, as exemplified by the recent, widely-publicised victories of AlphaGo.

In support of this argument in relation to the wheel metaphor, the right and left-facing forms of the swastika are presented in rotation in the contrasting counter-rotating animations below. These are presented with the counter-rotating variants of the four-fold lauburu, previously discussed (Improvisation in Multivocal Poetic Discourse: Basque lauburu and bertsolaritza as catalysts of global significance, 2016).

Animations of counter-rotation as suggestive of a "central pattern generator"
Swastika ("closing") Lauburu ("closing") Swastika ("opening")
Swastika animation Lauburu animation

The patterns generated are partially a consequence of the relative degree of shading of the two counter-rotating forms in each case. The relative speeds of rotation could also be changed.

The swastika patterns are presented on a 3x3 grid which serves to illustrate the possible Knight's moves in chess (as previously illustrated). Use of the grid here challenges the problematic tabular pattern of "square wheels" caricatured above. It is intriguing that counter-rotation of the swastika introduces a more fruitful manner of engaging with the binary controversies with which it is so commonly associated.

More complex implications of the animation of the lauburu pattern are discussed separately (Paradoxical container for the uncontainable: prescriptive constraints on creativity, 2016).

Requisite "counter-rotation" as fundamental to viable governance? It could be argued that conventional governance derives its inspirations from static symbols, whether three-fold of four-fold. There is thus a curious contrast between the static nature of any round table and the implication that the "wheels" of governance actually rotate in some way. With respect to rotation it is however especially significant to note the problem to which rotation in one direction only may give rise in any vehicle which is expected to "fly". This is notably evident in the case of multi-engine propeller-driven aircraft requiring counter-rotating propellers (spinning in opposite directions) or single engine aircraft using coaxial contra-rotating propellers, as distinguished in the animations below'

Principles of counter-rotation as necessary for governance?
Counter-rotating propellers Contra-rotating propellers
Counter-rotating propellers: Principles of counter-rotation as necessary for governance? Counter-rotating propellers: Principles of counter-rotation as necessary for governance?
Reproduced from Wikipedia; made by Michael Frey - Own work, CC BY-SA 4.0, Link

The issue of counter-rotation is especially evident in the case of the helicopter. Most helicopters have a single main rotor, but the torque (or twisting force) created as the engine turns the rotor causes the body of the helicopter to turn in the opposite direction to the rotor (by conservation of angular momentum). To eliminate this effect, some sort of anti-torque control must be used, which typically takes the form of a second propeller. These are highly suggestive of metaphors to counteract any analogue to torque in governance as a consequence of unidirectional efforts to achieve "lift-off". There are several common configurations that use the counter-rotating effect to achieve this, as noted by Wikipedia:

Using the phenomenon of torque, counter-rotation is a feature of the reaction wheels used in spacecraft to maintain position; their failure is thus potentially a cause of mission failure. With the rapid development of drones and space technology, it could be assumed that some of the principles are of relevance to governance. "Spaceship Earth" has been variously promoted as an evocative metaphor for governorship and navigation. Is there a need for "reaction wheels" on Spaceship Earth? There is some irony to the extensive use of "governor" in the control of the speed of an engine, especially since extensive use is made of economic "engine" (Governor Control, 2009).

Whilst the notion of "torque" does not appear to have been considered in relation to global governance, there are indications of its use with respect to strategic management in other contexts (Matthew Harvey, Strategic Torque: social media in higher education. CAUDIT). Of relevance to the following discussion on proprietary metaphors, Business Torque Systems is a registered trademark, as with the marketing agency Torque Global. One rare trace of torque with respect to global governance is its use as a verb (Michael G. Schecter, Our Global Neighborhood) :

In many ways the same point is evident in ... [mainstream] frustration with international economic institutional reform.... the reasons for their frustration, and ultimately for the inadequacy of their policy recommendations, comes from their approach. That approach accepts the international political economy, including the global distribution of power that it implies, as givens and tries to torque institutions in ways to make them responsive to the needs identified by those in powerful positions in that current system. Had they been able to think beyond the current system, which they knew was undergoing massive structural transformations as they were meeting, and tried to envisage what institutional remedies might be most desirable from the vantage point of currently disadvantaged and largely silenced voices, they might actually have come up with a widely different set of proposals, including some that point in the direction of remedies around which large numbers might mobilize. (In: Martin Hewson and Timothy J. Sinclair (Eds.), Approaches to Global Governance Theory, SUNY Press, 1999, pp. 248) [emphasis added]

The equivalent to torque in psychosocial systems may perhaps be better recognized through some aspects of "spin" -- or "arm twisting". Some use of the metaphor is recognized as "political torque" (PM Justin Trudeau says he is aiming to counter the 'political torque and misinformation' on the federal government's controversial carbon-pricing plan, Saskatoon Star Phoenix, 14 October 2016).

With the long association between the flight of birds as an inspiration to that of aircraft design, the point can be argued otherwise with respect to the function of bird wings (Counteracting Extremes Enabling Normal Flying: insights for global governance from birds on the wing and the dodo, 2015). The dysfunctional dynamics between "left" and "right" in politics may well be implicit in the neglected implications of the directionality of reading (Unquestioned Bias in Governance from Direction of Reading? Political implications of reading from left-to-right, right-to-left, or top-down, 2016).

It would appear that development of technology can be usefully understood as prefiguring or heralding applications in psychosocial systems -- as intuitively recognized in central symbols. As noted above, helicopter development has offered clues in this respect, most notably through the work of Arthur Young, as separately discussed (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011). Also of interest are the seminal insights of Nikola Tesla with respect to the rotation of a magnetic field (Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014).

The association between the rotation of the fundamental symbols above and the use of propellers, raises the interesting question for governance of the necessary rate of their rotation to achieve "propulsion" -- possibly to enable "lift-off". Technology has also found it necessary to devote considerable resources to propeller blade design and the possibility of their adjustment in controlled flight.

Of further interest is the nature of any transition in psychosocial systems between 2-fold, 3-fold, 4-fold, or N-fold patterns, as provocatively implied by Hindu and Buddhist insights into the system of chakras, or the principles of transmission systems. This may refer simply to the gearbox that uses gears and gear trains to provide speed and torque conversions from a rotating power source to another device.

The rotation of the symbols, together with the spiral design of propellers, suggests the possibility of exploring the implication for governance of the dynamics of such symbols in 3D rather than 2D. With a pair of counter-rotating symbols, animations could be readily produced with each reducing in size alternatively -- to disappear into the centre or emerge from it. An exercise in presenting the lauburu in 3D, for example, is illustrated separately with animations (Psycho-social Hyperbubbling: beyond one-bubble credibility and despair? 2017). Global governance as conventionally imagined can readily be understood in terms of aspirations to a single "bubble".

Proprietary metaphors and "systemic blasphemy"?

Missing from the argument developed above is the role played by understandings of intellectual property -- especially as it may apply restrictively to an even greater degree in the future. This is evident with respect to any technological innovation in relation to wheels and how they might be "reframed". This is already obvious in the case of applications for patents with respect to square wheels for skateboards and for robotics (as mentioned above).

Of far greater relevance to global governance is the sense in which metaphors of relevance to wheel design acquire a proprietary dimension. This is notably evident in the case of concepts and processes which are developed and franchised by management consultants and the like, as argued separately (Future Coping Strategies: beyond the constraints of proprietary metaphors, 1992).

A striking example is provided by the innovation proposed as a formal model by management cybernetician Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994). This has resulted in the development of the Syntegration process. As noted by Wikipedia, "Syntegrity", "Team Syntegrity", and "Syntegration" are all registered trademarks. To the extent that the associated insights are of vital significance to global governance, such trademarking necessarily restricts the development of those insights according to the open source modality which has proven to be such a catalyst for the development of information technology. It is therefore highly ironic that the the term "square wheels" should itself have been trademarked, restricting the mention of insights and imagery from that source to enrich this argument.

The related issues merit further consideration in that the governance ideal of a "round table" -- as inspired by the Arthurian legend (and mentioned above) -- is embodied in initiatives whose names may be variously subject to legal restrictions, as with RoundTable International, The ideal may be exploited otherwise for purposes of entertainment, as with books and movies it has inspired, however these may avoid legal restrictions or engender others. An amusing example in relation to the above argument is an animated series (Arthur! and the Square Knights of the Round Table).

A fundamental question is therefore how use of any radical new technical "design" of relevance to governance might be subject to intellectual property restrictions -- inhibiting its use and effectively holding the world to ransom if it is of value to remedial initiatives. Succinctly stated, to what extent is the metaphor inspired by patented technology itself subject to intellectual copyright?

With some considerable irony, the point may be made otherwise by considering the governance functions embodied in the 12-fold Greek and Roman pantheons -- the Dodekatheon and the Dii Consentes. Western civilization has systematically exploited their individual and collective significance by appropriating the names of the deities as registered trademarks -- in all probability more widely recognized than their esteemed originals or the vital functions they represent:

The process extends to many minor deities in those pantheons -- of which a striking example is provided by Nike. Also striking is the manner in which the significance of many deities has been restrictively associated with initiatives of the United Nations, as in the case of Ceres. A similar process is evident in relation to Hindu and other pantheons.

There is a curious possibility that such exploitation of symbols of high cultural value for commercial purposes merits exploration as a form of "systemic blasphemy" or "functional blasphemy".

In a period in which there is great sensitivity to wearing (or bearing) religious symbols in a secular context, the case of Hermès (whether or not it is accented) merits particular consideration in relation to the degree of controversy associated with hiding of the face with the burkha (Burkha as Metaphorical Mirror for Imperious Culture? 2009). There is a strange degree of irony to the opposite obsession with selective exposure of the face, as currently exemplified by Facebook, cosmetics, and facial profiling (Facism as Superficial Intercultural Extremism: burkha, toplessness, sunglasses, beards, and flu masks, 2009; Challenges to Facist Identity and Facial Identification, 2009).

Whilst readily held to be ridiculous in the case of deities considered "dead" or irrelevant, the significance of the issue -- and its potential relevance to global governance -- becomes more apparent when considering the possibility of trademarking symbols of current religious significance, notably for the Abrahamic religions. The case of "Jesus" provides an example (Rebecca Leber, Meet The Corporation That Trademarked 'Jesus', ThinkProgress, 26 February 2013). Given exploitation of the Arthurian round table, could the same be imagined with respect to that of the "Last Supper"? What role does cultural property then play in restricting or enabling global governance?

There is a further irony to metaphorical use of "wheel" in relation to governance, in that not only may the design of the wheel be a matter of intellectual property. Such a restriction may also apply to any "road" on which the wheel is imagined to travel -- as with any vehicle of governance. This is evident in the manner in which political parties and religions, if not disciplines in general, may possessively frame their "way" -- echoing legal issues in relation to use of roadways and rights of access. This is clearest in the case of strategies defined in documents (typically books) which are themselves subject to copyright and available only through a relatively costly commercial transaction -- as may be the case for many reports of significance to global governance. The ironies of the metaphor may also be recognized in the manner in which tire tread patterns (ensuring roadway grip) are themselves patented.

Does controversy in relation to "blasphemy" imply an understanding of "appropriateness" which merits particular consideration in relation to the quality of thinking and comprehension of global governance (Comprehension of Appropriateness, 1986) ?


Stafford Beer. Beyond Dispute: the invention of team syntegrity. John Wiley, 1994

Saul Frampton. Agony in the Agora. Aeon, 7 August 2017 [text]

Sebastian Reyes. Greasing the Wheels: the secret benefits of corruption. Harvard Political Review, 8 December 2015 [text]

Gerasimos G. Rigatos. Advanced Models of Neural Networks: nonlinear dynamics and stochasticity in biological neurons. Springer, 2014

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