Four-dimensional requisite for a time-bound global civilization?

Enhancing Strategic Discourse Systematically using Climate Metaphors (Part #5)

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Shape of society? Considerable resources are devoted by astrophysicists to the challenge of determining the shape of the universe. It is however curious that, for a global civilization in crisis, little attention is given to what might be understood as the "shape of global society" -- a shape which might enable more fruitful understanding of differences in perspective. What indeed is the form of the container in which we "live and move and have our being"? In the case of the global structure of the universe, debate currently focuses on

• whether the universe is infinite or finite in extent
• whether the geometry of the global universe is flat, positively curved, or negatively curved
• whether the topology is simply connected like a sphere or multiply connected, like a torus

Appropriate to this argument is the extent to which shapes favoured as containers of identity are 2D polygons (hexagon, pentagon, and various stars -- Star of David, Star of Islam, as noted above). It could be argued that some flags depict multiple stars, but without any sense of the 3D polyhedron any given set would form from the set of such figures. In that sense, as discussed below, what is the shape of the European Community with its focus on 12 stars, or the USA with its 50 stars? What indeed might be the shape of the elusive international community now upheld as being so vital to global governance?

As with the universe, if the global structure of society is to be understood in topological terms as "multiply connected" (like a torus), this would call into question the prevalent assumption of conceiving it to be "simply connected" (like a sphere). Multiple connectivity could be consistent with current explorations of small world theory. With respect to use here of the drilled truncated cube as a polyhedral mapping surface, its specifically toroidal nature is noteworthy. How might the relation between sphere and torus then need to be understood, given the subtle comprehensibility of the following transformation? (Topological Clues to a Memorable 12-fold Systemic Pattern, 2011)

Recognizing cognitive and strategic relationships between sphere and doughnut
Sphere-Torus transformation (reproduced from Wikipedia)	Earth understood as a hollow torus (cutaway projection of globe onto torus)	Oxfam Doughnut by Kate Raworth (A Safe and Just Space for Humanity: can we live within the doughnut?, 2012).

As asked, argued and illustrated from a physics perspective by Anders Sandberg: What would the Earth be like if it was the shape of a donut? (Andart, February 2014). More relevant to this argument are the cognitive implications, most notably suggested by Oxfam, as depicted in the right-hand image above and discussed separately in relation to remedial strategies (Exploring the Hidden Mysteries of Oxfam's Doughnut: recognizing the systemic negligence of an Earth Summit, 2012; Recognizing the Psychosocial Boundaries of Remedial Action: constraints on ensuring a safe operating space for humanity, 2009). Especially intriguing are the implications of the central hole in contrast to the integrity associated with that of a sphere. Is there a "hole" in global civilization of particular functional significance of which concern with the ozone hole is merely symptomatically indicative (Cognitive Mystery of Holes,Lacunae and Incompleteness, 2014).

Pseudoscience? As a container, how is any sense of closure of global society to be understood in terms of boundedness (Hilary Lawson, Closure: A Story of Everything, 2001)? Given the enthusiasm of physics for sets of "dimensions" from 11 to 26 as necessary to the explanation of reality, how many dimensions might then be appropriate to explaining society? More challenging is the arrogant implication for governance that, as recently argued: We are the most powerful species in the known universe, and with great power comes great responsibility (The Human Universe: should we take responsibility for the cosmos? New Scientist, 29 April 2015). HQ of the universe? Ironically arrogance is not a concept meaningful to science, despite the strange resemblance it bears to gravity -- itself a continuing mystery to science.

With the age of the universe now estimated at some 14 billions of years, it is curious that humanity has seemingly such a limited understanding of time, especially as it relates to governance and the foreseeable changes to its own global environment over the coming decades. Is that understanding of commensurate complexity to the challenges, in the light of arguments summarized by Robin Le Poidevin (The Experience and Perception of Time. The Stanford Encyclopedia of Philosophy, 2015; Travels in Four Dimensions: the enigmas of space and time, 2003). As might be expected, contrasting views are presented in a compilation from an anthropological perspective (Wendy James and David Mills, The Qualities of Time: anthropological approaches, 2005). It is in this complex of assertions, enigmas and denials that the current assumption regarding the fourth-dimensionality of time merits continuing consideration (William J. Friedman, About Time: Inventing the Fourth Dimension, 1990).

Given the preceding points made with regard to the memorable patterning insights offered by the I Ching, some preliminary clarification is required with regard to the interest engendered in the past by the controversial arguments promoted by Terence McKenna (Derivation of the Timewave from the King Wen Sequence of Hexagrams). These purported to predict, in the light of mathematical analysis, the ebb and flow of novelty in the universe as an inherent quality of time (John Sheliak, A Mathematical and Philosophical Re-Examination of the Foundations of TimeWave Zero and Novelty Theory). The arguments evoked considerable interest with respect to 2012 eschatological beliefs -- which ironically now take non-religious forms.

Whilst this focus is now readily deprecated as pseudoscience, as with the predictive value of the I Ching more generally, such definitive judgement distracts from a degree of human incompetence in the face of emerging crises -- and from the incapacity to engage more effectively with time in that regard. The demand of science to rely on a worldview calling for 11 to 26 incomprehensible dimensions might then be more appropriately understood as exemplifying pseudoscience -- if, as science claims, the need is for a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

It is readily forgotten that the pattern of hexagrams and their relationships derives directly from the binary coding system so valued by science. The issue here is how that pattern offers a memorable framework through which to engage more effectively with time and the diversity of conditions which could be usefully recognized as the qualities of time -- distinctions currently beyond the capacity of science.

In this light, given the sidedness of arguments regarding climate change -- and a quest for consensus reminiscent of that of the vain quest for unity of science -- it would be helpful if the subtle n-dimensional insights of physics could be applied to improvement of strategic discourse within the immediate global context of humanity.

Static flat world and perspective sides? As indicated above, there is a curious assumption that there are typically only two sides to an argument, or to a difference of opinion -- with the other readily framed as nonsensical (Alan Sokal and Jean Bricmont, Fashionable Nonsense: postmodern intellectuals' abuse of science, 1998). There is the further assumption that one side (the right one) should have no relation to the other -- the "underside", only too readily associated with wrongness and evil. The assumption may be presented metaphorically in terms of the right end and the wrong one -- as when the other is understood to have "the wrong end of the stick". This suggests an even more linear framing than that based on sides -- perhaps to be understood as "endedness"..

There may of course be many sides, just as there may be many factions in a democratic system -- however much each regrets the existence of the other. Little effort is made to configure the multiplicity of sides as a polyhedron as would then be appropriate -- a terahedron for 4 sides or a dodecahedron for 12 sides. Curiously this is despite the enthusiasm for 12-foldness in social undertakings -- including roundtables -- as separately indicated (Checklist of 12-fold Principles, Plans, Symbols and Concepts, 2011; Implication of the 12 Knights in any Strategic Round Table, 2014). Typically, even declarations of fundamental strategic principles are presented as lists of points -- without aspiring to any higher pattern of order reflective of the functional connectivity between them.

Whilst understandings of globality may be readily associated with a sphere -- echoing the form of the planet -- that sphere is strangely assumed to be static, even flat in the eyes of award-winning author Thomas L. Friedman (The World Is Flat, 2005), as separately discussed (Irresponsible Dependence on a Flat Earth Mentality -- in response to global governance challenges, 2008).

In topological terms, this geometry figures curiously in the expectation of arguments for adherence to a "global plan" -- possibly even of divine inspiration (Adhering to God's Plan in a Global Society: serious problems framed by the Pope from a transfinite perspective, 2014). A "plan", framing a "raft of proposals", is readily upheld as a modern magic carpet through which the impossible may be achieved -- with the expectation that only the misguided will not strive to be "on board". Unfortunately a plan is also the epitome of sidedness, necessarily having a relatively invisible underside -- from which improbable surprises emerge, as explored by Nassim Nicholas Taleb (The Black Swan: the impact of the highly improbable, 2007).

Dynamics over time: The above argument suggests that if a representation of 3D globality is portrayed in 2D, such a depiction is inadequate for comprehension of the subtleties of a 3D world. Similarly, for a global civilization evolving over time, any assumption that it can be adequately portrayed in 3D is dangerously inadequate for comprehension of the subtleties of a 4D civilization.

The concern here is the manner in which globality is also readily assumed to be peculiarly static, as separately argued (Dynamic Transformation of Static Reporting of Global Processes: suggestions for process-oriented titles of global issue reports, 2013).

Given that there are many issues which necessitate comprehension with respect to their evolution over time -- such as climate change, overpopulation, environmental degradation and resource overshoot -- there is a case for examining how such comprehension is to be enabled. It is difficult enough to project 3-dimensional understanding into 2 dimensions to enable documents to be printed. Web technology does however increasingly enable representation in 3 dimensions. Much is currently made of the possibility of 3D printing -- although there is little call for such representation in matters of governance, however much it may be vital to military undertakings.

From 3D to 4D? In the light of such analogies, the challenges of a global civilization in crisis may therefore call for new capacities to represent and comprehend 4-dimensional patterns -- beyond the use of equations readily adapted to thousands of dimensions, but incomprehensible in consequence. How are 4 dimensions to be rendered memorable, if they are indeed of relevance to governance? Expressed otherwise, if the "ordinary" language of conventional international governance is demonstrably inadequate to the challenges, what images might best trigger reflection on the "extrsordinary" patterns -- only too readily assumed to be irrelevant?

How might a global civilization be understood as travelling through time, namely navigating the adaptive cycle of resilience , in the light of the arguments of Thomas Homer-Dixon (The Upside of Down: catastrophe, creativity, and the renewal of vivilization, 2006)?

The question is especially relevant to any strategic decision, given the consequences it is expected to have over time -- as well as the unexpected surprises. These take on unusual significance now that the cloak of secrecy and stealth is being systematicallty cultivated, most obviously with respect to negotiations, as in stealthily Imposing TTIP-TPP-TISA as the caliphate of normality? (2015), or conventions of a similar nature (Global Strategic Implications of the "Unsaid", 2003).

Use of I Ching transformations as an example: If the I Ching, as the Book of Changes, offers a comprehensive indication of the set of possible changes of "climate" over time (as a consequence of a strategic decision), this suggests that these might best be portrayed through some kind of emulation of 4D. As indicated above, with each of the 64 conditions potentially transforming into each other, consideration could be given to 64x6 transformations (namely 384). Since the transformations are in both directions, these might also be considered as only 192 bidirectional pathways.

384 transformations between 64 Hexagrams of I Ching
Screen shot of animation of inner circle of trigrams relative to outer circle	Screen shot of 192 2-way pathways force-directed layout animation

If the mapping challenge is switched to the 384 transformations between the 64 conditions, the following forms merit consideration.

Prism-expanded rhombicosidodecahedron (animation)	Topo small stellated dodecahedron
of 200 faces (18 types), 384 edges (32 types), 176 vertices (16 types)	of 204 faces (5 types), 660 edges (11 types), 384 vertices (8 types)

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