Challenges to Comprehension Implied by the Logo
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28 February 2009 | Draft

Engaging with Globality through Dynamic Complexity


-- / --

Annex C of Engaging with Globality through Knowing Thyself (2008), Dimension 4 of a four-fold exploration. [Engaging with Globality -- Dimension 1: Cognitive Realignment; Dimension 2: Cognitive Circlets; Dimension 3: Cognitive Crowns; Dimension 4: Knowing Thyself]
Overview of Engaging with Globality

Multi-global system?
"Bailouts" as "Pornbroking"?
Intimations of fruitful intercourse?
Geometry and topology of thinking and valuing
"Globalizing" the matrix
Closest packing of spheres
Institutional "pantheons"
"Sexual relations" within "pantheons"?
Internalizing a "dodekatheon" to inform the "dodecameral mind"
Communicating globality through paradoxical complementarity
Integrating "real" and "imaginary" through the plane of complexity



The following is one example of an exercise envisaged in Playfully engaging with globality through re-categorization and re-classification (in Dimension 4). The context for this exploration of a metaphor with sexual connotations is the subject of a series of comments provided separately as as Annex A (Engaging with Globality through Playful Re-categorizing):

Humour | Playful examples | Logical vs Aesthetic correspondences | Meaningful connectivity
Surfaces and orifices | Consumption and consumerism | "Knowing" another | Courtship | Kama Sutra

The cognitive implications of the metaphor are initially developed in Annex B (Global Governance via a Double-breasted Strange Attractor) and further developed in Annex D (Intercourse with Globality through Enacting a Klein bottle).

As noted in Annex A, this exploration is premised on the assumption that sustainable governance is necessarily sexy -- and if it is not then it is unlikely to be sustainable. By designing sex out of governance, sex has become identified with the problematic shadow of humanity.

Multi-global system?

The singularity of the planetary globe has long been considered unquestionable -- because of its unique spherical geography and the metaphors and symbolism that it inspires (including the logo of the UN). However this appealing simplicity has been undermined by:

As is recognized, these different "worlds" imply different worldviews but with little sense of the dynamics relating them together. Hence the potential learnings from breast dynamics in Annex B (Global Governance via a Double-breasted Strange Attractor), most notably with respect to:

"Bailouts" as "Pornbroking"?

Remedies to the current financial crisis -- framed as a "financial tsunami" beyond human responsibility -- have focused primarily on "bailouts" of targeted sectors as an appropriate metaphor for such a perfect storm (as discussed in Dimension 1). These are seen as providing the necessary "stimuli" to revive economic sectors -- "flagging" through no fault of their own (and irrespective of whether they had become "unfit for purpose").

Absent from this terminology, at least initially, has been the origin of the funds for the stimulation bailout -- or why such amounts were not more readily available for the "stimulus" of developing countries in dire need, in the interests of "global security".

But in effect governments have become pawnbrokers -- providing funds for devalued assets in the hope of their later recovery (Wall Street's Pawnbrokers, The Economist, 11 December 2008; Susan Guibert, Fed now financial market's "pawn broker", 18 March 2008; Marc Fleury, The pawnbroker of last resort, 11 March 2008). Or is it the taxpayer that has been transformed into a pawnbroker? (Ashley Seager, King promises taxpayers won't foot bill for 'pawnbroking operation', The Guardian, 21 April 2008). Margaret Thatcher's classic riposte to her use of this strategy was that indeed she was "selling the family silver" but that she was "selling it back to the family".

For when a corporation or government claims it is at risk of bankruptcy (or is so rated), as has been the case, a measure of relief may at least be sought from pawnbrokers -- even if pride would have them called by some other name (as has always been the case).

Building on the double-breasted playful exploration of Annex B, it is then appropriate to recall the 3-sphere symbol of a pawnbroker -- at least in those cultures at the centre of the financial diaster.

Symbol of pawnbroker or of pornbroker?

As a consequence of a failure to rise to the double-breasted opportunity, attention has been obliged to sink to the opportunities of a "lower sphere" -- which otherwise might have been associated with fruitful consummation through inter-bank lending (thereby forcing some losing competitors to consider relief from the pawnbroker).

Now however any possibility of such consummation is frustrated by the impotence of those who have so significantly failed to rise to the occasion. In this sense governments might be understood to have taken on the role of pornbrokers, especially in relation to the remedial measures they are obliged to take in regard to toxic debt ("dirty debt") -- the "hidden" bad or suspicious debt, which is poisoning the financial market. Or is it the taxpayer who has been forced into the role of pornbroker?

Curiously, in seeking "to motivate citizens to vote" in the EU Elections of 2009, the European weekly New Europe, has opened a contest inviting suggestions for an appropriate slogan in several categories. One category is:

Dirtiest Slogan: Because we know that it's often the dirtiest slogans which are most memorable -- and deserve honourable mention. Interpret "dirty" as you wish.

Intimations of fruitful intercourse?

Whereas the previous section is indicative of failed intercourse, there is a case for recognizing the extent to which a third sphere "above" the two discussed (in Annex B) is suggestive of fruitful consummation in the classical triangular symbolism -- implying a degree of sustainability. As indicated above, whereas its inversion is indicative of attention focused on a "lower sphere" through which such consummatiuon may be achieved in successful intercourse, that of the "lower sphere" is indicative of the emergence of a focus reflecting the consequence of any such interaction.

This undersatanding may be variously reflected in the following symbols discussed in Present Moment Research: exploration of nowness (Part 5 of Presenting the Future, 2005). These may also be variously indicative of the "triple crown cognition" (discussed in Dimension 3) -- recognizing that any such recognition of it implies a fourth perspective (a "fourth crown"?).

rings and knots
Phenomenological epoché
Traditional Celtic
knot pattern
Roerich Pax Cultura
Borromean rings Phenomenological epoché Traditional Celtic knot pattern Roerich Pact

Whereas the Borromean rings/knots are a focus of the psychoanalytic approach of Jacques Lacan, that of the phenomenological epoché has been a preoccupation of Francisco Varela (The Gesture of Awareness, 1999) [see also Claus Otto Scharmer. Three Gestures of Becoming Aware: Conversation with Francisco Varela January 12, 2000].

Varela proposes a 3-fold cycle at the core of the act of becoming aware in the moment:

Varela sees the phenomenological epoché as "the ensemble of these three organically linked phases", for the simple reason that the second and third are always reactivated by, and reactivate, the first. He provides a valuable discussion of the three interlinked cycles and the obstacles traditionally recognized to some of their processes.

Geometry and topology of thinking and valuing

Spherically symmetrical polyhedra and tensegrities: It is appropriate to note that a minimim of three interlocked cycles, as identified by Vareal (above), was the criterion for the emergence of a system in the ioneering work of R. Buckminster Fuller (Synergetics: explorations in the geometry of thinking, 1975/1979). This was discussed with respect to tensegirty in Annex B. A quite distinct approach is that of Arthur Young (Geometry of Meaning, 1976). Fuller offers extensive reflection on polyhedra as systems, and notably on spherically symmetrical polyhedra. In the above context those distinguished as "duals" are especially significant (as discussed in Annex B).

Further to that exploration of tensegity by Fuller, the value of a symmetrical polyhedral framework has been extensively explored in relation to governance (Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance, 2008; Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008). In the following images, dynamics are implied not only between the facets but in the possibility of flexibly transferring each particular polyhedron into other forms -- suggestive of unexplored relationships between facets.

Juxtaposition of polyhedral representations of two sets of organizations (nongovenmental and UN agencies)
indicating possible geometric transformations of each to offer other insights
(extract from a poster In Quest of a Strategic Pattern Language, 2008 -- with commentary)
images generated and manipulated in Stella Polyhedron Navigator
Polyhedral configurations of organizations

This approach has been extended to the divisive challenge of human values (Coherent Value Frameworks: pillar-ization, polarization and polyhedral frames of reference, 2008) and especially with respect to the psychological engagement with sets of values (Topology of Valuing: psychodynamics of collective engagement with polyhedral value configurations, 2008). This highlights the need to shift beyond a purely "objective" relationship to what is indicated and configured by such structures (Embodying Values Dynamically through Alternation: integrating sets of polarized static values through indicative metaphor, 2008).

Juxtaposition of polyhedral representations of three international charters of human rights
indicating possible geometric transformations of each to offer other insights
(extract from a poster In Quest of a Strategic Pattern Language, 2008 -- with commentary)
images generated and manipulated in Stella Polyhedron Navigator
Polyhedral value sets

Cognitive dynamic implication: A "superficial" understanding of such static structures necessarily detracts from the dynamics implicit in them -- rendered more evident in the case of the tensegrities based upon such polyhedra. In a sense Fuller's subtitle (Geometry of Thinking) constitutes a cognitive trap of geometric explication in static form, obscuring the implication of the cognitive dynamic through which its form is traced (by the eye, etc).

What pattern does focused attention trace out and how is the focus and perspective shifted? Conversely there is of course a cognitive trap of engaging in the dynamic without re-membering the pattern or configuration thereby traced (a reason for the explorations of Dimension 2: Cognitive Circlets; Dimension 3: Cognitive Crowns). Similarly Young's title (Geometry of Meaning) obscures the dynamic through which "meaning" is given to something -- to "mean" it -- possibly later to be withdrawn. This includes the dynamic of "imbuing" with meaning as well as "deriving" meaning.

Beyond checklists of "targets": Given the fundamental importance of human needs in driving the operation of any financial system -- including the "greed is good" model of the one that proved itself to be dysfunctional in 2008 -- there is a strong case for exploring how to move beyond the articulation of needs in a checklist, or at best a matrix. This possibility has been explored with respect to polyhedra and tensegrities (Needs Communication: viable need patterns and their identification, 1980).

"Globalizing" the matrix

Further benefit may be derived from extending the exploration generically as suggested by the transformation of the ubiquitous matrix into a form of relevance to governance of sustainability (Spherical Configuration of Categories -- to reflect systemic patterns of environmental checks and balances, 1994; Spherical Configuration of Interlocking Roundtables Internet enhancement of global self-organization through patterns of dialogue, 1998; Spherical Accounting: using geometry to embody developmental integrity, 2004). In this context, the latter exploration might be usefully seen in relation to the many institutions that maintain "two sets of books" -- only one of which is presented to the tax authorities. Indeed the "double-breasted" financial system (discussed in Annex B) may also be seen in terms of the "formal" and the "informal" financial spheres.

This geometric generalization may offer even great possibilities to hold the dynamics of subjective engagement by confronting matreix and torus.

Screen shots of a dynamic virtual reality
model of intertwined tori

(click on each variant to access and manipulate in 3D;
in the free Cortona VRML viewer,
right click for preferences to switch from/to the "wireframe" presentation)
Red torus has a vortex (smoke ring) dynamic in the model;
Blue torus has a wheel-like dynamic in the model
Magic square
(illustrative extract from a 9x9 magic square in
9-fold Magic Square Pattern of Tao Te Ching Insights experimentally associated with the 81 insights of the T'ai Hsüan Ching, 2006; see also interactive variants in Strategic Patterns in terms of Knowing, Feeling and Action, 2008)
Interlocking tori Magic square extract from Tao Te Ching

In contrasting the two images above, it is appropriate to note that the 2 dimensions of the standard matrix are fundamental to the linear management characteristic of Dimension 1 ("making points and alingning a target") Typically, as in accounting. the focus is on the vertical total in a column -- leading to one and possibly more "bottom lines". Only secondarily, although vital to the viability of any corporate entity, is the manner in which the horizontal features of the matrix evolve -- typically over time. It is the relationship between the two which engenders the curves that are the theme of Dimension 2 -- especially when the budget "balances".

The symbolic connotation of a "matrix" is of course of fundamental symbolic significance as being the framework from which novelty emerges -- a context within which something else originates, develops, or is contained, as with the womb. Such a symbolic connotation highlights the recognition that for such a matrix to "work", and "give birth", it needs to acquire curvature beyond the linearity of the grid -- it need to be able to enfold. Implicit enfolding is recognized, for example, where a matrix acwquies the structure of a "magic square" -- sudoku-like -- such that columns, rows and diagonals "fold together" through another dimension of signikficance. Recognition of such a "pattern which connects" offers a way beyond the sterile limitations of conventional accounting -- pointing to the possibility of "bottom lines" of a higher order.

The interlocking tori on the left introduce a degree of interactivity which can be fruitfully interpreted in terms of its cognitive implications (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006). It may also be understood as a generic cognitive model of intercourse, even sexual intecourse. It also offers one indication of the interlocking of the circlets (discussed in Dimension 2) in any cognitive crown (discussed in Dimension 3).

Interlocking circlets

Closest packing of spheres

A major theme in Fuller's discussion of the Geometry of Thinking is the range of possibilities for the closest packing of spheres -- and its implications for the configuration of the result. These implications have been highlighted by Keith Critchlow (Order in Space: a design source book, 1969; Islamic Patterns, 1976), especially in terms of the implications for distinct spherically symmetrical polyhedra -- variously approximating a sphere.

A key issue in "closest packing" is the extent to which such spheres touch and whether a configuration can be transformed to enable the insertion of a central sphere touched by all of them. With respect to the "multi-global system" discussed here, the issue is the manner in which such spheres (of influence) touch one another through feedback loops in any larger system -- of necessarily greater globality -- whose emergence such touchings thereby ensure. Within a sexual metaphor, how do such lesser spheres get close and intimate?

Symbolically this is significant as a static configuration. Fuller uses the term "kiss touch" with respect to the architecture of tensegrities -- indicative of points of contact which do not affect each other through the transmission of stress or strain. However, if Fuller's "thinking" is to be understood in dynamic, process terms, then the degree to which particular spheres touch is indicative of a potential cognitive transition point from one sphere to another -- potentially vital for the cognitive coherence of the pattern as a whole. Thinking then "moves" into a different loop essential to sustaining the whole -- a feedback loop to be understood in terms of knowledge cybernetics ***.

Symbolically such interlocking is intuitively appreciated through Celtic knots, four-leaved clover, and their enactment in some traditional dance patterns. These might however be understood as intuitive exercises in embodying or echoing the manner in which sets of cybernetic feedback loops work in ordering and ensuring the transfer of information between distinct domains whose integrative functioning is essential for the viability of those domains together.

In that sense, Fuller's assertion that polyhedra are systems applies to an even higher degree with respect to polyhedral spheres in closest packing. In effect the pattern of their touchings is indicative of system maps -- analogous to the many interrelated cycles of metabolic pathways in biological cells.

Archimedean polyhedra
Successive truncations of octahedron
2, 3, 4-fold symmetry
Successive truncations of icosahedron
2, 3, 5-fold symmetry
  1. truncated octahedron (14 polygons: 4 / 6 sided)
  2. cuboctahedron / vector equilibrium (14: 3 / 4)
  3. truncated cuboctahedron (26: 4 / 6 / 8)
  4. snub cube (38: 3 / 4)
  5. rhombicuboctahedron (26: 3 / 4)
  6. truncated cube / hexahedron(14: 3 / 8)
  1. truncated icosahedron (32 polygons: 5 / 6 sided)
  2. icosidodecahedron (32: 3 / 5)
  3. truncated icosidodecahedron (62: 4 / 5 / 10)
  4. snub dodecahedron (92: 3 / 5)
  5. rhombicosidodecahedron (62: 3 / 4 / 5)
  6. truncated dodecahedron (32: 3 / 10)
truncated tetrahedron (8 polygons: 3 / 6 sided)
Arrangement of the 12 Archimedean polyhedra in their most regular pattern, a cuboctahedron, around a truncated tetrahedron (adapted from Keith Critchlow, Order in Space, 1969, p. 39). Arrows indicate the succession of truncations from 1 to 6 in each case. (Clicking on a polyhedron links to a spinning image)
truncated dodecahedron icosidodecahedron truncated icosidodecahedron truncated octahedron rhombicosidodecahedron rhombicuboctahedron truncated tetrahedron truncated cuboctahedron truncated icosahedron cuboctahedron truncated cube snub cube

Institutional "pantheons"

"Globality" in this exploration has been understood generically in terms of its integrative potential -- whether it is to be understood as divinity in the singular, as a set of globalities offering access to an integrative system (as in the case of pantheons), or even as the "market is God" from a secular "faith-based" perspective (Harvey Cox, The Market as God, Atlantic Monthly, March 1999; Laurent Chenot, Are Markets Our God? The Harbus: Harvard Business School, April 2002). It is also appropriate to recall the extent to which pantheons have been elaborated in other cultures (notably the Hindu pantheon) to perform similarly integrative, value-related functions -- all meriting a degree of attention, if only as a communication interface. As such, the dynamics of pantheons are elaborate systems diagrams holding insights of potential relevance to contemporary governance.

As the framework from which European thinking emerged -- as the basis of the mindset of the United Nations, the European Union, and the international community -- the cultures of Greece and Rome merit attention with regard to the respect in which they held their pantheons -- each of 12 principle gods and goddesses.

Greek and Roman Pantheons
12 Corresponding Gods and Goddesses "Close to the Olympians"
Greek (Olympians; Dodekatheon) Roman (selection)
Zeus Jupiter

Bia - Personification of violence.
Cratos - Personification of power.
Eris - Goddess of dscord.
Eros - God of lust and desire.
Morpheus - God of dreams.
Muses - Nine ladies of science and arts.
Nemesis - Goddess of retribution
Nike - Goddess of victory.
Pan - God of the wild,
Paean - Universal healer.
Zelus - Emulation.

Poseidon Neptune
Apollo Apollo
Ares Mars
Hephaestus Vulcan
Hermes Mercury
Hera Juno
Demeter Ceres
Hestia Vesta
Aphrodite Venus
Artemis Diana
Athena Minerva

Representations of the the Specialized Agencies of the United Nations, often specifically associated with such dieties through their iconography, might fruitfully be configured together as a single polyhedron. There is no iconography of the UN system as an integrative whole. The same might be said of other key sets of of global fora. To what extent do such configurations suggest the possibility of systemic Rosetta Stones?

"Sexual relations" within "pantheons"?

It was stated above that this exploration is premised on the assumption that sustainable governance is necessarily sexy -- and if it is not then it is unlikely to be sustainable.

Sexual relations -- symbolizing systemic intercourse -- were a major factor in understanding the dynamics of those pantheons, notably the credibility in which they were popularly held. Thereafter such dynamics were considered irrelevant -- with each deity appreciated for his or her distinct function, but not as together forming a dynamic system through which the world was ordered. To the extent that the logos or nomenclature of variuous specializaed agencies of the United Nations even make use of the iconography of those deities, there is no sense in which this implies any need to look attentively at the quality of the relations between them -- often much to be deplored.

The argument here is four-fold:

It is in these senses that vital systemic insights have been designed out of contemporary governance and its "plans" in response to the challenges of sustainability. The drama of the "science vs. religion" / "intelligent design" debate, in societies upholding faith-based governance to an unusual degree, is to be seen as being in extreme danger of "throwing the baby out with the bathwater". This is due to failure to encompass the subtleties in question -- whilst bemoaning the complexity of the challenges of governance and the failure to engage voters appropriately.

Of course the drama of the relationships between the gods is explored in epic works of culture -- as with The Ring Cycle by Richard Wagner (to which reference was made in Dimension 1). It is valued for its aesthetics but seemingly without any learnings for governance. Where are the contemporary epics to hold and commemorate such systemic insights for all? Or is this function to be seen as implicit in blockbuster fantasy movies and their symbolism -- or their online interactive gaming analogues? (cf Imaginal Education: game playing, science fiction, language, art and world-making, 2003).

Of particular interest is the manner in which globality can be understood both as a "hole" and an "object" as reviewed from a mathematical perspective by Ron Atkin (Multidimensional Man: can man live in three dimensional space? 1981). As "object" it may be understood as the focus of criticism of "sex objects" by feminist scholars. As "hole" it is intimately related cognitively to the experiential significance of intercourse, as discussed further in Annex D (Intercourse with Globality through Enacting a Klein bottle)

A remarkable mystery for contemporary culture is how sexual attractors "work", given their fundamental importance for the dynamics of civilization and for the problems they engender. Whether it be in terms of "greed" or "lust", the systemic mapping offered by pantheons offers a complementary means of comprehending the challenge of governance. Hence the potential significance on such a map of "deities" that are perceived as "close to Olympians", notably Eros as the God of lust and desire.

Internalizing a "dodekatheon" to inform the "dodecameral mind"

This argument has been developed in Union of Intelligible Associations: remembering dynamic identity through a dodecameral mind (2005) from which the above image on close packaing has been reproduced. It could be argued that the distinct polygonal patterns, so integrated, could potentially correspond to the distinct approaches of the only comparable institutional system at the global level, namely the system of UN Specialized Agencies -- as argued in Spherical Configuration of Categories (1994). An exploration of the polyhedral representation of a set of such agencies is provided above.

Much is made of the bicameral mind and the two hemispheres of the brain. Contemporary governance, through designing out sexuality, is effectively functioning with one hemisphere -- however much the operations of the other are drawn into secondary, "under the table" roles, and especially "spin".

A dodekatheon, with its sets of "sexually" interrelated "gods" and "goddesses" -- in the sense they they engage in effective intercourse -- highlights the potential of the cognitive internalization of such a dodekatheon (presumably an insight from epics such as Wagner's Ring Cycle). The dynamics of the bicameral mind, with all the problems of polarization with which it associated, is thereby set within the richer dynamic context of a dodecameral mind.

Comprehension of the dynamic relationships in the dodecameral mind (by analogy to the metabolic pathways of the cell or the transformation pathways of the I Ching) may then be enabled by:

Symbolically, and in principle cognitively and functionally, the 12-fold pattern corresponds to the archetypal 12 seats at the Arthiran roundtable, presumably with each occupant being "matched" or "marked" by an "opponent" of the opposite chirality.

Of particular interest are the issues arising from the 26 polyhedra that might be variously associated with globality represented by deities:

Of course, in terms of "correspondences" (as discussed in Playfully engaging with globality through re-categorizing and re-classifying categories), this set of 26 is suggestive of the 26 dimensions supposedly fundamental to the orgsanization of the universe -- in one of the current versions of string theory.

Communicating a sense of globality through paradoxical complementarity

Radically contrasting alternatives, highlighted as the double-breasted challenge of global governance in Annex B, may be seen as paradoxical complements in the cognitive spirit pioneered by modern physics. Any such complementarity may also be expressed in terms of the media through which the challenges, options and intentions of governance are currently expressed -- or opposed.

Complementary media for communicating engagement of governance with globality
Images, Flags, Sound
Strategic Challenge of Polysensorial Knowledge
United Nations Charter: "We the Peoples..."
Universal Declaration of Human Rights
Earth Charter, Global Ethic
Agenda 21
Slogans ("Health for All by the Year 2000")
Tales told and sung (at one's mother's breasts) International treaties and conventions
A Singable Earth Charter, EU Constitution or Global Ethic? (2006)
(as a cognitive "bra" to hold such complements together?)


Complementary musical modes for communicating engagement with globality
Eurovision Song Contest Winner (Athens, 2006) EU anthem (Beethoven's Ode to Joy)
Lordi 2006 Anthem
If aesthetic harmony (notably musical lyrics) offers a way forward, possibilities might include:
A Singable Earth Charter, EU Constitution or Global Ethic?
All Blacks of Davos vs All Greens of Porto Alegre: reframing global strategic discord through polyphony?
Reframing the EU Reform Process -- through Song: responding to the Irish challenge to the Lisbon Treaty
Poetic Engagement with Afghanistan, Caucasus and Iran: an unexplored strategic opportunity?

Integrating "real" and "imaginary" through the plane of complexity

The "complements" highlighted in the images above, and in Annex B, point to the need to incorporate insights from the explorations of chaos theory and the dynamics of complex systems which have so long been the focus of the Santa Fe Institute. It is remarkable how little insight of this kind has been relfected in the remedial responses to the failure of the finanancial system -- even though much use was made of them in designing both the stock trading strategies and the derivatives which brought about its collapse.

It might be said that, seemingly at least, the complexity sciences have not risen to the occasion in enabling the financial system to "rise again" from its ashes. Potentially of greater interest, to the extent that the financial superbubble was based on inflated hopes and the continuing practice of hope-mongering, the complexity sciences -- with their understanding of the secrets of strange attractors -- do not seem to have been applied to values beyond the economic (Human Values as Strange Attractors Coevolution of classes of governance principles, 1993). Most unfortunately, they would seem to have proven themselves to be more part of the problem than of the solution.

Any attraction to globality -- whether in the form of conceptual integration, psychological integration, engagement with deity, or the epiphany of sexual consummation -- would seem to need to benefit from insight into the nature of strange attractors. Of particular interest is the ability to work with the relationship between "real " and "imaginary" -- as least as it is understood mathematically.

In Annex B, it was suggested that some such relationship was fundamental to the decision-making response to alternatives -- as represented by "two breasts" and the choice of which is to be a source of nourishment. This of course has its parallel in the governance by governing party or opposition -- as a perceived source of nourishment for the people.

The images below offer two insights into the relationship between "real" and "imaginary". That on the right is a rendering of the famed Mandelbrot set of mathematics of the complex plane -- indicating the fractal boundary between chaos and order. Given the challenges to global governance, this might be assumed to be of the highest relevance to strategies for the immediate future.

The image on the left responds in part to the challenge (partially articulated by the Club of Rome) of interrelating the world resolutique with the world problematique (Ken Bausch, Problematique and the Club of Rome). To that binary understanding has been added in the image, the complementary challenge of the imaginatique and the irresolutique (the game-playing most characteristic of strategic initiatives).

Any such representing of complexity, encomapssing "real" and "imaginary" dimensions, pose a fundamental problem of comprehension. This is the theme of this exploration of engaging with globality. Arguably there is a case for enriching the dimensionality of both images with a third axis -- to reflect known (effective comprehension) and unknown (effective ignorance). Implications have been discussed in Unknown Undoing: challenge of incomprehensibility of systemic neglect (2008). A number of efforts have been made to render fractals in three dimensions (Melinda Green, Visualizing the 4D Mandelbrot/Julia Set; Skytopia, The Mystery of the REAL, 3D Mandelbrot Fractal)

Integrating "real" and "imaginary"
Imagining the Real Challenge
and Realizing the Imaginal Pathway of Sustainable Transformation
Sustainability through the Dynamics of Strategic Dilemmas
in the light of the coherence and visual form of the Mandelbrot set
Imagining the Real Challenge Mandelbrot set vetical

The possibility of further insight into cognitive implication in globality, from geometry and topology, is explored in Annex D (Intercourse with Globality through Enacting a Klein bottle). The "cognitive process" implied is intercourse, generically understood ("Human Intercourse" "Intercourse with Nature" and "Intercourse with the Other", 2007). Intercourse with globality takes place through the narrow opening between the real and the imaginary -- and, through any fruitful consummation, may engender new globality.

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