Challenges to Comprehension Implied by the Logo
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26 May 2014 | Draft

The-O Ring and The Bull Ring as Spectacular Archetypes

Dramatic correlation of theatre, theory, theorem, theology, and theosophy

- / -

Metaphorical geometry as a cognitive vehicle
Mapping sets of theo-related cognitive functions: The-O Ring
Reframing a fundamental attractor as a target
Reframing a strategic attractor as a vortex involving a "cognitive twist"
Interestingness, suggestiveness, memorability and presentation
Theatre: spectator, spectacle of the feminine and the Bull Ring
Game-playing, bull-leaping and laurel wreaths
Engaging with a fundamentally integrative perspective
Nonsense commensurate with dysfunctionalities of "theo" variants

Part 2 of The-O ring: Theory, Theorem, Theology, Theosophy? a playful intercultural quest for fruitful complementarity (2014)


This is the concluding part of the argument that the prefix "theo" is effectively central to one of the most divisive debates in the current global civilization, namely that between science and religion. The argument addresses the question whether there is some connection between the etymology of "theorem" and words like "theology" or "theist". Beyond the obvious relationship of their prefixes, the issue is therefore whether and how Theorem, Theory, Theology, and Theosophy might indeed be related in some form of implicit cognitive "The-O ring" through a pattern of aesthetic correspondences.

A brief indication was given in the previous part of the distinctive nature of each and of the problems with which they are associated. The argument there was developed through the following sections:

The playfulness of this argument follows from previous recognition of its role in integrative insight (Humour and Play-Fullness: essential integrative processes in governance, religion and transdisciplinarity, 2005). Although playful, the suggestion here is that to ignore some such possibility is to court further disaster, already evident in the highly dysfunctional relationship between religion and science -- with all the consequences which they exacerbate, separately and in combination, denying any responsibility in the matter. The issue could be fruitfully explored in the terms of each, as argued separately, but that would seem to be unlikely (Mathematical Theology: future science of confidence in belief, 2011). This exploration could be considered a contribution to that possibility.

In methodological terms, the following argument could be considered an exploration of connectivity -- of the connectivity within the meta-pattern which supposedly connects. The four "theos" could each be understood as implying a particular form of connectivity and might even be distinguished by the connectivity which they consider "legitimate". Clearly this is also suggestive of how each might consider the other to be depending on an "illegitimate" form of connectivity.

The playful dimension is significant to the concluding argument here in that the etymology of "theo" is intimately related to "thea" (and theatre ). This fruitfully introduces the feminine dimension variously excluded from the preoccupation of the modalities with which with "theo" is associated. The concluding argument is usefully clarified using a variety of illustrations relating the theme to current global preoccupations. The emphasis here is on how dramatic incorporation of the feminine can enhance "interestingness, suggestiveness and memorability" of the "theo" modalities -- otherwise to be recognized as increasingly sterile, infertile and "unfit for purpose".

The argument as a whole might be caricatured by an adaptation of the title of a famed study of psychotherapy: We've Had a 1000 Years of Theo -- And the World's Getting Worse.

Metaphorical geometry as a cognitive vehicle

As noted above, in methodological terms, the following argument could be considered an exploration of connectivity -- of the connectivity within the meta-pattern which supposedly connects, as previously discussed (Walking Elven Pathways: enactivating the pattern that connects, 2006). The four "theos" each imply a particular form (or degree) of connectivity and might even be distinguished by the connectivity which they consider "legitimate" -- and consequently how they consider each other to be "illegitimate". The question is then the form through which connectivity can be provided or implied.

The question might be framed differently by recognizing that the "theos" have different degrees of preference for a "solid" argument, in contrast to one which might be more "flexible" (if not characterized by "liquidity"), or one which was "inspiring". This suggests that connectivity in argumentation might be fruitfully compared with the fundamental states of matter (solid, liquid, gas, plasma) and the nature of the bonding which distinguishes them. Understanding of the relationship between the forms of connectivity could then benefit from the manner in which states of matter are displayed together in a phase diagram capable of highlighting "critical points". Of some relevance, the phase diagram metaphor has been explored with respect to the distinction between data, information, knowledge and wisdom.

Different degrees of connectivity implied by phase diagram of states of matter
Typical phase diagram
(reproduced from Wikipedia)
Adaptation to theo* information (reproduced from
Patterns Essential to Individual and Global Health? 2010)

Comparing patterns of argumentation of the "theo" modalities to the "geometry" of states of matter also opens the way to exploring phase transitions between "theo" modes, the existence of possible correspondences to so-called non-classical states (glass, quasicrystals, magnetically ordered, quantum spin liquid, etc), low-temperature states (superfluids, etc), and high-energy states (see Wikipedia List of states of matter). How might this clarify the nature of inspiration, insight and "design concept" -- or the conditions of "pressure" and "heat" (metaphorically characteristic of argument) under which credible bonding of particular kinds could form, as suggested by the following table? Framed in this way, this notably highlights a degree of overlap between the "theos", especially in the light of the range of "states of matter"..

  Suggestive use of states of matter as metaphors of degrees of connectivity in argumentation (tentative)
  "solid" "liquid" "gas" "plasma"
"theorem" "axiomatic"      
"theory" "principles" credible applications hypothesis opinion, idea, possibility
"theology" "doctrinal principles" required belief revelation inspiration
"theosophy "experiential principles" credibility

Given the manner in which the "theo" modalities are challenged by humour, could this be understood in terms of phase transitions, especially in the light of efforts to reverse engineer human cognitive capacities (Matthew M. Hurley, et al. Inside Jokes: using humor to reverse engineer the mind, 2011)? The above presentation raises the question of how connectivity in argument described as "flaky" (unexpected, illogical, unreliable) is to be distinguished from what is otherwise valued (in chess) as "Knight's move thinking" (as discussed below).

The experience of certain forms, through the manner in which insight is carried by their geometry, offers a means of engaging with that integrity. Geometrical patterns, as experienced by the body in movement, offer an interface between ideographic and mythopoeic cognition -- as argued in the case of dance, especially in its ritual forms (Mark Johnson, The Body in the Mind: the bodily basis of meaning, imagination, and reason, 1987; Maxine Sheets-Johnstone, The Primacy of Movement, 1999). As an example, walking a labyrinth is valued for that reason.

More fundamentally, rather than geometry, this may be a question of number and its intimate experiential relation to time (Marie-Louise von Franz, Number and Time, 1974; George Lakoff and Rafael Nuñez, Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2001). For von Franz:

To sum up: numbers appear to represent both an attribute of matter and the unconscious foundation of our mental processes. For this reason, number forms, according to Jung, that particular element that unites the realms of matter and psyche. It is "real" in a double sense, as an archetypal image and as a qualitative manifestation of the realm of outer-world experience. Number thereby throws a bridge across the gap between the physically knowable and the imaginary. In this manner it operates as a still unexplored mid-point between myth (the psychic) and reality (the physical), at the same time both quantitative and qualitative, representational and unrepresentational. (pp. 52-53)

The geometry is experienced through modalities in addition to those of seeing, so fundamental to the association of the "theo" modalities with text in its many forms. This sense of the geometry, and the cognitive experience of its constraining force, is notably articulated by mathematician Ron Atkin (Multidimensional Man: can man live in three dimensions? 1981), as separately summarized (Comprehension: social organization determined by incommunicability of insights). The significance is evident in the efforts of environment designer Christopher Alexander (A Pattern Language, 1977; The Timeless Way of Building, 1979) and the cognitive equivalent it may imply (5-fold Pattern language, 1984).

Such arguments reinforce the implication that the four "theos" merit consideration as cognitive masks for modalities governed by number (and geometry). This frames the significance of a fifth modality, denoted here by "thea", potentially indicative of the emergent quintessence to which von Franz and Jung refer -- ironically a term now used by physics to refer a hypothetical form of dark energy, postulated to explain the accelerating universe. Of potential relevance is use of five by Peter Senge (The Fifth Discipline: the art and practice of the learning organization, 1990).

Introducing the feminine could be understood as a necessary methodological provocation. Put bluntly, none of the "theos" is able or motivated to engage with the sexual reality so familiar to ordinary mortals. This is despite the ambitions of each "theo" to be comprehensive in its worldview and its engagement with reality -- and to make claims in this regard, implying that other perspectives are irrelevant or erroneous.

This systemic "negligence" of " otherness" -- associated especially and symbolically with the feminine -- can be illustrated as follows:

None of the "theos" offers an experiential articulation of sexual attraction or intercourse -- fundamental to successful suggestibility in a market economy. This is most striking in the case of what mathematics might contribute to that understanding, as discussed separately (Reframing the Dynamics of Engaging with Otherness: triadic correspondences between Topology, Kama Sutra and I Ching, 2011).

More tragically, this is evident in any strategic discussion relating to population and resources (Formally ignoring a fundamental systemic process: the economy vs. the fucking? 2012), as discussed with respect to the Royal Society report on People and the Planet (2012). Those involved in such discussion reserve their engagement with sexual attraction and intercourse for shadowy "extracurricular" contexts to which reference can only be made through euphemism, if at all. This recalls the period in which participants at meetings of the World Health Organization debated the health dangers of smoking in smoke-filled rooms -- without for a moment recognizing the incongruity, the symbolic message, or the appropriateness.

If reports relating to global challenges, produced from any "theo" perspective, can be readily rated as essentially "unsexy", what does this imply for their capacity to engender interest and remedial action? It is ironic that the evolution of the four "theo" modalities has resulted in a form of cognitive "infertility" -- except in domains with which they are not preoccupied. The irony is all the greater in a period in which the infertility of human couples is a matter of increasing concern -- especially as a consequence of environmental factors variously exacerbated by the "theos".

It is from this perspective that "metaphorical geometry" is explored in the light of the "dimensions" which the feminine brings to any more inclusive engagement with reality by the "theo" modalities. This necessarily raises questions with regard to the connectivity of the argument. Is there a form of connectivity that is missing from the coherence which the "theos" variously purport to encompass -- effectively a missing link, in the light of the argument of Terrence Deacon (What's Missing from Theories of Information? 2010; Incomplete Nature: how mind emerged from matter, 2011)?

Curiously with respect to connectivity and coherence the "theos" have indeed been variously able to articulate understanding of patterns of connectivity unrelated to their particular logic. This is most evident in the case of musical and architectural harmony and associations within a poem. Such patterns may engender appreciation, even imposed as a norm, as with sacred music. However it has not been possible to generalize their relevance, whether to the coherence of the mindset of particular "theo" or to the challenges of wider society, as separately discussed (A Singable Earth Charter, EU Constitution or Global Ethic? 2006). Under the guise of "whatever works", this applies in particular to the credibility of connectivity associated with flirtation and to whatever it may lead. Use of spin and cosmetics offer examples of interesting case studies.

More generally, and less explicitly, the focus of any "theo" on explanation (in whatever terms) obscures other means of ensuring a degree of credible connectivity and coherence. This is most evident in design in its most general sense, but most clearly with respect to humour and story telling as framed by the Italian proverb: Si non è vero, è ben trovato (Even if it is not true, it is well conceived).

Framed in this way, there is a case for recognizing the inadequately explored role of correspondences of various kinds (Theories of Correspondences and potential equivalences between them in correlative thinking, 2007). Under what conditions is a degree of correspondence to be considered fruitful -- a question made evident by moonshine mathematics (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).

Relevant to the method of this argument, and its exploitation of metaphor, Kenneth Boulding made the fruitful point that:

Our consciousness of the unity of the self in the middle of a vast complexity of images or material structures is at least a suitable metaphor for the unity of a group, organization, department, discipline, or science. If personification is only a metaphor, let us not despise metaphors - we might be one ourselves. (Ecodynamics; a new theory of societal evolution, 1978. p. 345)

Mapping of sets of theo-related cognitive functions: The-O Ring

Rather than attempting to explore further the tabular articulations, it appears more fruitful to consider how any articulation is mapped to facilitate comprehension, especially that of a higher order consistent with the complexity as it may be experienced and integrated. The use of geometry in this process has been argued separately (Geometry of Thinking for Sustainable Global Governance, 2009; Metaphorical Geometry in Quest of Globality -- in response to global governance challenges, 2009). It is consistent with the theoretical and symbolic understandings of the variants of "theo". The approach makes extensive use of mapping onto polyhedra as a way of embodying and implying integrity.

Polyhedral mapping: tetrahedron: A useful point of departure is to use the simplest polyhedron, the tetrahedron, as offering a surface for the four cognitive modalities on which attention has focused. The animation on the left below is one result. Of significance is the manner in which the polyhedron is contained and engendered by great circles -- a minimum of three of which are required. More are depicted in the image on the right. It is through the triangulation enabled by the minimum number of circles that the polyhedron "emerges" or is rendered sustainable. This has been extensively argued by Buckminster Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975), as separately discussed (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009; Triangulation of Incommensurable Concepts for Global Configuration, 2011). The cognitive implications have been discussed in relation to the challenge of otherness (Reframing the Dynamics of Engaging with Otherness, 2011).

The set of circles is suggestive of the non-linear multidimensionality of an "O-ring" through which the four "theo" variants are related, and by which they are integrated. Somewhat ironically they offer a sense of 3-in-1 and 1-in3 -- with the traditional challenge of its comprehension. Relevant to the cognitive challenge is that the great circles interlock precisely because they are of different orientation. Together they imply what is associated with a sphere and globality -- the degree of integration to which the various forms of "theo" aspire, explicitly or implicitly.

Animations of tetrahedron with great circles
(prepared with Stella Polyhedron Navigator)
Tetrahedron framed by 3 intersecting great circles
(click for animation)
Tetrahedron framed by multiple intersecting great circles
(click for animation)

Another way of considering this pattern is through images such as the following. The interlocked Borromean rings on the left are suggestive of the cognitive entanglement fruitfully associated with any understanding of the great circle interlocking. It is appropriate to note that a representations in two dimensions of that pattern of 3 rings is a classical image of the Christian Trinity. Associating the 4 "theos" with the vertices of the tetrahedron above, each expanded to the point of touching, offers a sense in which they may "pack" together within a spherical context (image on right, below).

Interlocking Borromean rings
(by Ron Bennett, image from Wikipedia)
Animation of 4 Theo modalities packed as spheres
(prepared with Stella Polyhedron Navigator)

Any such mapping readily suggests a static perspective which may well be completely inadequate. The circles through which the tetrahedron is constructed usefully imply a dynamic process for the emergence of the configuration -- and for sustaining it over time. This could be related to the arguments of George Lakoff and Rafael Nuñez (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2001) and Marie-Louise von Franz (Number and Time: reflections leading toward a unification of depth psychology and physics, 1974) -- recently figuring in a compilation by Alex Bellos (Alex Through the Looking Glass: how life reflects numbers and numbers reflect life, 2014). The sense of "getting somewhere" through any of the four modalities might be better framed by cyclic processes consistent with arguments for eternal return.

Cognitive nature of the interlocking threefold engendering the tetrahedral mapping of "theos"?: Failure to recognize "The-O Ring" could be considered as directly responsible for systemic neglect. In a separate discussion, inspired by the notorious "poem" on The Unknown of former US Secretary of Defense Donald Rumsfeld, sought to clarify the nature of this neglect (Unknown Undoing: challenge of incomprehensibility of systemic neglect (2008). Experimental use was made of classical Chinese coding patterns to clarify the relationship between a threefold set (knowing, feeling, acting), as presented in an annex at that time (Strategic Patterns in terms of Knowing, Feeling and Action, 2008).

This gave rise to the following table relating that threefold set to a fourfold set. The table has been adapted to associate the four "theos" with that fourfold pattern.

Association of generic conditions with classical Chinese binary codes
(amended from version in Strategic Patterns in terms of Knowing, Feeling and Action (2008)
which functions as a key to the various classical patterns of 64 hexagrams of the I Ching,
presented there: Fu Xi, Jing Fang, King Wen and Mawangdui -- with links to specific commentary)
binary coding
in hexagram
"theo" Knowing
(upper pair in hexagram)
(middle pair in hexagram)
(lower pair in hexagram)
"theorem" known
knowns (KK)
knowingly (FF)
knowingly (DD)
young yin "theory" known
unknowns (KU)

unknowingly (FU)

unknowingly (DU)
young yang "theology" unknown
knowns (UK)
knowingly (UF)
knowingly (UD)
old yin "theosophy" unknown
unknowns (*K)
unknowingly (*F)

The cells of the table have been shaded here to suggest degrees of overlap in significance relating to the distinct "theos".

In the light of the manner in which 3-fold and 4-fold category systems can be considered as interrelated, that exercise noted the complementary categorization of conditions of the Tao Te Ching, notably as experimentally related to another classic of that period, the T'ai Hsüan Ching (9-fold Magic Square Pattern of Tao Te Ching Insights: experimentally associated with the 81 insights of the T'ai Hsüan Ching, 2006). This gave rise there to an alternative pattern of strategies ordered in the light of the Tao Te Ching and T'ai Hsüan Ching with links to their commentaries. Rather than the binary coding system of the I Ching, giving rise to 64 hexagrams, it uses a ternary coding systems that gives rise to 81 tetragrams. This may be explored in the light of the keys offered experimentally by the following table.

Association of generic conditions with classical Chinese ternary codes
(amended as above to suggest relevance to the "theos")

"theo" Knowing
ternary coding  
(upper position
in tetragram)
"theorem" known
knowns (KK)
knowingly (FF)
knowingly (DD)
(third position
in tetragram)
"theory" known
unknowns (KU)

unknowingly (FU)

unknowingly (DU)
(second position
in tetragram)
"theology" unknown
knowns (UK)
knowingly (UF)
knowingly (UD)
(lower position
in tetragram)
"theosophy" unknown
unknowns (*K)
unknowingly (*F)

The cells of the table have been shaded here to suggest degrees of overlap in significance relating to the distinct "theos".

Polyhedral mapping: Szilassi: Of interest, when the 4 "theos" are mapped onto polyhedral faces, is the fact that all 4 faces of the tetrahedron are in contact with each other -- a feature unique amongst polyhedra, with the exception of the far more complex Szilassi polyhedron (one of the Stewart toroids).. With seven faces, the latter suggests the possibility of using it to map either:

These alternative patterns are presented in the images below.

Animations of the 7-faced Szilassi polyhedron
(prepared with Stella Polyhedron Navigator)
Version A
Cognitive modalities of "theo"
(theory, theorem, theology, theosophy)
Version B
Theology-related articulation as a template
(for theory, theorem, theology, theosophy)
The polyhedra above may be unfolded into net representations in 2D. Two such nets are required in each case, for the ""external" faces and for the "internal" faces. One option for the faces marked with "?" is the set knowing, feeling, action (discussed above).
"External" faces "External" faces
"Internal" faces "Internal" faces

The argument here is that the Szilassi polyhedron is suggestive of the requisite complexity through which a set of "theos" can be related -- the hexahedral face to which each is attributed sharing an edge with each of the 6 other faces in the configuration. As an unusual cognitive jigsaw puzzle, appropriately resistant to simplistic assumptions about how science and religion might be related, further insight may be obtained from the following animation. This shows how the polyhedron can be decomposed into the parts which are conventionally recognized -- and the challenge of comprehending how they might be drawn together into an integrative configuration.

Animation of folding and unfolding of Szilassi polyhedron
(prepared with Stella Polyhedron Navigator)
[See also the interactive Parameterized Szilassi Polyhedron
presented as a Wolfram Demonstration Project]

With respect to further development of this argument, it is appropriate to note that the Szilassi polyhedron has the topology of a torus -- with a central hole framed by the "inner" faces. It is therefore suggestive of a toroidal form to whatever can be associated cognitively with the O-ring, as indicated below.

Reframing a fundamental attractor as a target

Curiously the international community frames many strategic initiatives in terms of targets and goals. Most evident are the UN Millennium Development Goals (MDGs). A more recent articulation of the global challenge is that of Johan Rockstrom and Will Steffen (Planetary Boundaries: exploring the safe operating space for humanity, 2009). The conclusion was presented as a circular mapping which was then adapted by Kate Raworth (A Safe and Just Space for Humanity: can we live within the doughnut?, Oxfam, February 2012) presented on the left below.

Both mappings have been reframed into the image on the right below. This is discussed separately with respect to the feasibility of remedial strategies (Recognizing the Psychosocial Boundaries of Remedial Action: constraints on ensuring a safe operating space for humanity, 2009; Exploring the Hidden Mysteries of Oxfam's Doughnut: recognizing the systemic negligence of an Earth Summit, 2012).

Oxfam Doughnut
(from Kate Raworth,
A Safe and Just Space for Humanity:
can we live within the doughnut?
, 2012).

Nine remedial capacity boundaries
using the representational pattern
of the Planetary Boundaries (2009)
[click image for enlargement]

Earth-System remedial capacity   boundaries

With respect to this argument, it is the sense of goal and target that calls for further consideration. The question is how collective attention is focused on a "target" -- as implied by the image on the left below. A sense of how a "focus" may act to divert attention around it is provided by the image on the right.

Conventional representation of a "target"
-- a metaphor for collective endeavour

Mapping a neglected "global underground"
(from Mapping the Global Underground, 2010)
[click image for enlargement]

Reframing a strategic attractor as a vortex involving a "cognitive twist"

Mysterious nature of "holes": As separately discussed (Towards the Systematic Reframing of Incomprehension through Metaphor, 2012), a hole is the metaphor of choice for teaching the theory of general relativity. As a hypothetical topological feature of spacetime, for which there is no observational evidence, they predict the possibility of a "shortcut" through spacetime (Marcus Chown, Intergalactic subway: all aboard the wormhole express, New Scientist, 12 March 2012). Use of the comprehensible term "hole" inhibits recognition of the cognitive challenge of their multidimensional nature -- essentially unvisualisable and to that extent incomprehensible.

As a challenge in their own right for ontology and epistemology, bounding "nothingness" by "holes", invites richer insight (Roberto Casati and Achille C. Varzi, Holes and Other Superficialities, 1994; M. Bertamini and C. J. Croucher, The Shape of Holes, Cognition, 2003). As a metaphor, what then might a wormhole offer as an incomprehensible "shortcut" through communication space, in the light of the forms of (in)comprehension by which this is characterized -- and the probability that the nature of that shortcut would necessarily be incomprehensible within the framework of conventional experience? Holes are at the borderline of metaphysics, everyday geometry, and the theory of perception (as summarized in the entry on holes in the Stanford Encyclopedia of Philosophy). The confusing associations between hole, whole and holy follow from this -- further confounded by the unfathomable implications of budgetary holes.

How do "holes" function as attractors -- especially with respect to the fascination of sexuality and intercourse? Appropriate to the manner in which the feminine may be "negatively" framed, Casati has elaborated what might be understood as a complementary study (Shadows: Unlocking Their Secrets, from Plato to Our Time, 2004). Such considerations can also be related to the significance of "nothing" at the present time, especially in terms of what people are offered for their future and can hope to anticipate (Emerging Significance of Nothing, 2012).

Integral spiral dynamics: A widely appreciated combination of fourfold integration is that associated with the AQAL 4-quadrant configuration (on the left below) and development through the complementary experiential quadrants by a spiral dynamic (as suggested by the schematic on the right below). AQAL theory is fundamental to the integral movement, as inspired and articulated by Ken Wilber, which constitutes an interface between transpersonal psychology, ontology, epistemology, and methodology. Spiral dynamics is a dynamic model of human development and of meme-carrying systems as introduced Don Beck and Chris Cowan (Spiral Dynamics, 1996). There are numerous complex images of both AQAL and spiral dynamics (accessible on the web) -- alone and in relation to one another -- most seemingly subject to questionable intellectual property restrictions (governing the competitive presentation and promotion of these models). As with any motivation to copyright a religious symbol, such restrictions are an interesting challenge for social change (Future Coping Strategies: beyond the constraints of proprietary metaphors, 1992).

Schematic illustrating the AQAL system Schematic suggestive of the Spiral Dynamics seystem

The images together suggest the developmental convergence on a particular kind of "target" -- but with little indication in the images of what happens when the "target" is achieved as a "goal". There is of course some implication that the target is better understood as a form of portal or doorway -- a "hole", potentially more consistent with the configuration of a torus. The images usefully raise the challenge of how the "theos" might be related to the AQAL quadrants and how "The O-ring" encircling them is recognized, given progressive experiential learning through spiral dynamics.

Toroidal thinking? As an attractor for strategic initiative, there is a sense in which any target functions as a form of vortex -- suggested to some degree by the images above. Any use of "target" then mistakenly renders static what is fundamentally a dynamic -- as implied by any quest for sustainability, namely a sustainable dynamic. Furthermore, if "target" is to be used as a strategic metaphor, it is useful to recognize that whatever is targetted may not be as static as might be preferred, as argued with respect to use of military metaphors (Enhancing Sustainable Development Strategies through Avoidance of Military Metaphors, 1998).

The dynamics may be explored through representations based on a torus. One approach is through the strategic game-playing associated with so-called Knight's move thinking, as partially indicated by the image on the left below (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011; Swastika as Dynamic Pattern Underlying Psychosocial Power Processes: implicate order of Knight's move game-playing sustaining creativity, exploitation and impunity, 2012). It is appropriate to note that although "Knight's move thinking" is appreciated in game-playing (as in chess), it is specifically deprecated as a thought disorder -- the move of the knight in chess is then used as a metaphor for the unexpected, and illogical, connections between ideas (irrespective of the success to which these may lead).

Another approach is through recognition that the associated complexity is better understood through the dynamic of two intertwined tori, as indicated by the image on the right below (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: Transforming a matrix classification onto intertwined tori, 2006).

Knight's move thinking mapped onto a torus

Intertwined tori

Requisite "cognitive twist"? As noted earlier with respect to the tabular and cubic arrays, both any O-ring or torus readily imply a comprehensible simplicity -- a dangerously oversimplistic form of closure. They obscure the cognitive challenges implied by the contrasting orientations which engender the tetrahedron. It is in this sense that a more complex mapping surface is more appropriate. This is suggested by the twist in a Möbius strip (on the right below). Mapping the "theos" onto a torus -- emphasizing the mnemonic suffix (discussed in the first part of the paper) -- offers the suggestion that any "portal" through the central hole in the torus (indicative of the O-ring) may be effectively blocked by an "article", usefully to be seen as a cognitive mindset common to the "theo" modalities in their engagement with reality. The definite article -- "the" -- is the most frequent word in English.

Suggestive toroidal configuration of "theos"
sensation, intuition, thinking, feeling

Möbius strip
(image reproduced from Wikipedia)

The twist in the Möbius strip may be used as a means of mapping the relationship between the four "theos", as suggested by the images below. These necessarily imply a form of O-ring.

Möbius strips used to map relationships between two sets of "theos"

Embodying complexity?
This approach map be taken further by combining the two images above, increasing the implied complexity of the implicit O-ring. The image on the right derives from a discussion of the possibility of mapping strategic challenges onto a form of complex plane as suggested by mathematics (Imagining the Real Challenge and Realizing the Imaginal Pathway of Sustainable Transformation, 2007).

Interrelation of 2 Möbius strips as an appropriately
complex configuration of the 4 "theos"
Interrelating problematique, resolutique, "imaginatique" and "irresolutique" in terms of real and imaginary

Dynamics of BaGua and Knight's move: A further possible development (of the image on the left above) is to associate a configuration of 4 Möbius strips (in the image on the left below) to incorporate insights deriving from the BaGua pattern of "theos" (as discussed in the first part of the paper). The challenge cognitive (dis)connectivity of the BaGua pattern could be seen as reflected in the (dis)connectivity of Knight's move thinking, as represented in the animation on the right below, and separately discussed (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2007)

Representation of BaGua
embodied within four interwoven Möbius strips
("Earlier Heaven" arrangement )
Animation of 8 of the Knight's moves in chess
(suggestive of the dynamics of both the blame game
and Knights of the Round Table)

Octopedal insight? Of possible relevance to the challenge implied by the schematic of cognitive functions on the left, is current work in artificial intelligence on how to design an octopod -- notably the issue of how it avoids typing itself in knots (Nir Nesher, et al, Self-Recognition Mechanism between Skin and Suckers Prevents Octopus Arms from Interfering with Each Other, Current Biology, 2014; Katherine Harmon Courage, How to Build a Robot Octopus, Scientific American, October 2013).

From an implicit ring to implicit globality: Further to the point made above, the question is how to enable comprehensibility of ever higher dimensionality -- without reinforcing simplistic comprehension at any stage. The images above use the Möbius strip (singly or in configuration) to imply a subtle form of O-ring. This might be more fruitfully understood as implying a spherical/global form related in complex ways to a toroid. These possibilities can be further suggested by the following animations -- reminiscent to some degree of the dynamics of intercourse, through the "O-ring" in quest of the "egg", thereby engendered -- as discussed separately (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011)

"Degeneration" of a torus into a sphere
(animation reproduced from Wikipedia)
Clifford torus
(animation reproduced from Wikipedia)

The above animations are indicative of the challenge of thinking about the relation between externality/explicate/objectivity and internality/implicate/subjectivity as may be associated with "theo-science" (theory/theorem) and "theo-belief" (theology/theosophy). This relation can be variously discussed (Psychosocial Implication of Without Within, 2013; ¡¡¿ Defining the objective ∞ Refining the subjective ?!: Explaining reality ∞ Embodying realization, 2011).

Interestingness, suggestiveness, memorability and presentation

As a form of presentation, a key question with respect to the "theo" modalities is whether their presentation together meets requirements of interestingness and memorability -- irrespective of the challenge they may independently face (as noted above). What might ensure that their configuration was not "boring"?

Interestingness: The "mappings" above are one approach to the issue. "Interest" is clearly a driving force, as argued separately (Investing Attention Essential to Viable Growth: radical self-reflexive reappropriation of financial skills and insights, 2014). As noted there, although experientially obvious, the nature of the interest-generating dynamic may elude conventional description. How is a potential investor "turned on"? The possibility has been speculative explored separately (Global Governance via a Double-breasted Strange Attractor: cognitive implication in a dynamic sexual metaphor, 2009). Potentially highly relevant is the nature of the boredom-generating dynamic which triggers "turning off" and disinvestment (Lars Svendsen and John Irons, A Philosophy of Boredom, 2005). Taken together, the two dynamics are significant in defining direction of movement in cyberspace (and the noosphere).

That earlier discussion noted a degree of focus on the unusual term "interestingness", most notably as highlighted with respect to the preoccupations of advertisers and the focus on artificial intelligence by Douglas Lenat. Strangely the term now figures in a US patent application (Interestingness Ranking of Media Objects). With respect to an early paper, now a sociology cult classic, by Murray S. Davis (That's Interesting: towards a phenomenology of sociology and a sociology of phenomenology, Philosophy of Social Sciences, 1971), Oliver Burkeman (This column will change your life: interestingness v truth, The Guardian, 5 April 2014) notes:

What is it, Davis asks, that makes certain thinkers - Marx, Freud, Nietzsche - legendary? It has long been thought that a theorist is considered great because his theories are true, he writes, but this is false. A theorist is considered great, not because his theories are true, but because they are interesting. Even in the world of academia, most people aren't motivated by the truth. What they want, above all, is not to be bored. ...We live in the Era of Interestingness: attention is money, and purveyors of the interesting can make millions from Twitter feeds of amazing facts - even if they're not always true facts - or from books or blogs offering intriguingly counterintuitive perspectives... Moreover, Davis argues, there are only a handful of main ways for an idea to be interesting. To grab people's attention, you should argue that something we think of as bad is good, or vice versa; that some apparently individual phenomenon is really collective; that several seemingly disparate things are actually part of the same thing; and a few others....

In his paper, Davis included The Index of the Interesting. The question of relevance here is what would make a configuration of "theo" modalities interesting -- rather than a trigger for boredom? Irrespective of their relative interest individually -- itself questionable globally -- how might their interestingness together be enhanced and rendered sustainable? The question is especially relevant to the extent that the various modalities reinforce challenges of governance relating to sustainability -- including the issue of whether appropriate governance is viable as currently understood (Ungovernability of Sustainable Global Democracy ? Towards engaging appropriately with time, 2011).

Interesting patterns: One possible exercise, following the above mappings, is to consider more generally how a pattern of four modalities might be configured to enhance the interestingness of the resulting pattern of connectivity. Initially the possibility could be considered from a formal perspective in the light of representations of distinctions made in set theory, most notably through Venn diagrams and Borromean rings. Use of configurations of Borromean rings follows from the discussion above regarding the interlocking great circles engendering a tetrahedron. The contrasting schematics raise the issue as to whether meaning is then to be "carried" within the areas created by the rings, or through the rings (dynamically around them). As noted above, the latter perspective is addressed by Ron Atkin (Multidimensional Man: can man live in three dimensions? 1981). Are the "theo" processes to be considered space-related or time-related?

Borromean ring
Venn diagram
(reproduced from Wikipedia)
Borromean ring

The dynamic around three rings is explored as the époché by Francisco Varela -- adapting Husserl's concept (Rachel Zahn. Francisco Varela and The Gesture of Awareness: a new direction in cognitive science and its relevance to the Alexander Technique. 2005). This involves stopping the flow of habitual thoughts and belief structures long enough to perceive the phenomena of the present moment through a three step formula for becoming consciously aware: suspension, redirection, and letting go -- as illustrated by the following schematic (on the left) with its own formal equivalences of potential significance.

Varela's argument is especially valuable in giving focus to the future in the moment, as may be variously explored (Present Moment Research: exploration of nowness, 2001; Now as the Ultimate Cognitive Strange Attractor: a continuing invitation "down the rabbit hole"? 2014)

Phenomenological epoché
Traditional Celtic
knot pattern
Roerich Pax Cultura
Celtic knot pattern

Relationships between sets: One useful development of the argument is through the symbolic language of sets (or algebra of sets) as may be partially explicated by Venn diagrams. The alternatives are usually presented using two overlapping circles, possibly placed within a framing (contextual) rectangle. In the following images, the two overlapping circles are set within a third (contextual) circle.

Of interest is whether the visual possibilities -- as indications of connectivity -- then exhaust those required by the formalism of the language of sets. To the standard explications (in each case in the following table) are added possible ways of interpreting the relationships between "theo" modalities -- each "theo" being considered as a set in its own right.

Symbolic language of sets (preliminary)
describing relationships between sets A and B (inner circles) and universal set U (outer circle)
NB: when A and B do not overlap, they would be termed disjoint sets -- as is common with the "theos" in practice
set union (A union B)
A ? B
everything that is in
either A or B
(A union B)
- (A instersect B)
everything in A or B,
but not in both

(A intersect B)
A n B
only what is in both
sets A and B
relative complement of A in B
AC n B
everything in A, except
for anything in B
(difference of two sets)
theology ? theosophy?
theory ? theorem?
theo-science ? theo-belief?
  theology n theosophy?
theory n theorem?
theo-sciencen theo-belief?
theology - theosophy?
theory - theorem?
theo-science - theo-belief?
not (A union B)
¬ (A ? B)
everything outside
A and B
  not (A intersect B)
¬ (A n B)
everything outside of
overlap between A and B

absolute complement of A in U
not (theology ? theosophy)?
not (theory ? theorem)?
not (theo-science ? theo-belief)?
  not (theology n theosophy)?
not (theory n theorem)?
not (theo-science n theo-belief)?

Also of potential interest: an empty set (namely one with no elements), and a universal set (everything). This language could be used to indicate what is variously included or excluded from the perspective of any of the "theos", or any combination of them. Most intriguing is what they collectively include (if anything), and what they collectively exclude.

The use of three circles might be considered adequate for the discussion of possible relationships between three "theos". It is clearly problematic to represent a fourth within that convention -- other than by implying its total inclusion (or exclusion) by an other. This would then reflect a condition under which one was subsumed by another.

Interweaving "theo" modalities in patterns: Beyond the conventional depictions of set relationships through Venn diagrams, the argument can be taken further through the following experiments in relating four or more domains -- with the implication of their being bound together by a "Theo-O ring" (as argued above).

Configurations of 5 rings in 2 dimensions
4 theos "packed within" an O-ring
(recalling seed pod configurations)
4 theos "threaded on" an O-ring
(recalling prayer bead circlets)
4 theos overlapping
(recalling the Venn format)
3 theos overlapping
(framed by a fourth)
3 theos overlapping
(a fourth set within)
2 theos overlapping within a third
(a fourth set within)

Given the earlier 3D image of a tetrahedral closest-packing of 4 spheres, each indicative of a particular "theo", the images above might be reviewed as a 2D plan view of some such configuration. Each might also be considered as a view by refraction through a form of lens (constituted by one "theo") of the others.

Suggestiveness and memorability through the vesica piscis / vagina / vulva
: The image on the lower far right is in fact that of the famed vesica piscis (or mandorla) -- but embedded within a circle and with a circle embedded within its central portion. The vesica piscis is a shape that is the intersection of two circles with the same radius, intersecting in such a way that the center of each circle lies on the perimeter of the other. The form is held to be of considerable significance in various mystical traditions (associated with two of the "theos"). Numerous available images are indicative of the associated speculation. The form is also of mathematical and architectural interest.

Perhaps appropriately, considerable controversy (as with that regarding the Wikipedia entry) is associated with traditional (and recent) specific references to the resemblance between the form of the vesica piscis, the vagina and the vulva. The resemblance (through either term, however inappropriate anatomically) is variously upheld as indicative of the fundamental role of that organ in procreation and in the origin of human life. The existence of these cross-cultural inferences, the symbolism, and the controversy, are however indications of "interestingness" -- as well as "suggestiveness" and "memorability" -- as required by any more fruitful configuration of the "four theos".

Exploiting the Venn diagram style above, the possibility of alternative weightings to the elements of that image can be considered, as with the outer images below. Those options can be combined dynamically with 6 other variants, as suggested by the animation in the central image below.

Vesica piscis -- Pattern A Animation between 8 patterns Vesica piscis -- Pattern B

Is the relationship between the four "theos" best understood dynamically? Can it only be adequately comprehended in these terms? Is the meaning to be derived from them dependent primarily on the alternation between the cognitive functions -- recalling the requirements for the locomotion of any quadriped?

Embedding a circle, within the classical form as depicted, could be understood as reconciling controversy regarding "vulva vs. vagina" -- with the added advantage of emphasizing the cognitively mysterious role of a "hole", as mentioned above with respect to discussion by Roberto Casati (1994). Irrespective of the controversy, the geometrical form -- as a focus of speculation and fantasy -- is clearly an idealization of the anatomical form. As embodied in female anatomy, given the unquestionable attraction of the form and its associated dynamic (to the male-dominated theo-mentality), it clearly constitutes a suggestive "spectacle" for memorable "play" (the theme of a later section).

There is a curious irony to the traditional associations to the form as engendering mystical veneration. Seemingly distinct from the veneration in which the vulva may be held, the prefix "venera" derives from the Latin venereus (from vener-, venus love, sexual desire) -- hence its significance in relation to sexual indulgence and venereal disease (contracted as a result of sexual intercourse). A further irony is offered by Venera, the Russian series of "space probes" to gather data from Venus (between 1961 and 1984) -- Venera being the Russian name for Venus, the Roman goddess of love, namesake of the planet. It is of course phonetically amusing that "Venn" diagrams contribute to clarifying the matter.

Dimensions and dynamics: The argument above implies a degree of progression in dimensionality and consequently a challenge to representation and comprehensibility. From a mathematical perspective these are not especially significant. Although the point is well-illustrated by representation of 4 sets as a Venn diagram, the constraints are usefully discussed by Tony Phillips (Topology of Venn Diagrams, AMS, June 2005). Experimental 5-set, 6-set and 7-set Venn diagram representations are available. Although "interesting", they are not of immediate interest to this argument -- because of the challenge of memorability and suggestiveness. Possibilities in 3D, as discussed by Phillips, are similarly less immediately useful.

The point to be stressed is that the issue here is not one of Venn diagrams per se, rather it is how to benefit from these patterns of significance in order to enhance memorability and suggestiveness. These would appear to depend partly on centro-symmetrical configuration in 2D as explored in the tables above. Clearly these depart from Venn diagram conventions when a fourth circle is introduced centrally (as above). However the logic of the introduction of such additional frames of significance can be better understood if the "dimension" they represent is understood in terms of time -- hence the value of an animation in which the significance of the "dimension" is carried by the dynamic. The significance of the vesica piscis is then notably associated with the implied dynamic in intercourse -- whether physical or metaphorical -- as a "fourth dimensional experience" with a very particular focus.

The tabular representation of the conventional language of sets (above) -- framed in each case by a circular "universe" -- also merits consideration as a set of patterns. This raises the question as to how many patterns can be fruitfully recognized and represented by such means -- as embodiments of the formal mathematical notation. Which cannot? Could that set of patterns then be fruitfully formed into a periodic table of some kind? From a mathematical perspective this recalls the extensive literature on tilings and tesselations, although here it is not a question of whether the patterns fit together (as in the tiling problem), but rather whether, considered independently, they "fit" into a periodic table.

Somewhat relevant to the possibility is a related problem with respect to polyhedra (Sándor Kabai, et al, Clusters Produced by Placing Rhombic Triacontahedra at the Vertices of Polyhedra, The Mathematica Journal, 2012). Would the emergence of "interestingness" then become apparent within the table? How would the suggestiveness of the vesica piscis emerge?

A notable possibility is that the visual patterns could be complemented by another semi-visual visual approach, namely the configuration of 8 trigrams and 64 hexagrams of the I Ching. These can be considered in relation to the archetypal morphologies of René Thom (Structural Stability and Morphogenesis, 1972). More provocative is whether both can be related to the topological configurations of the 64 sexual acts encoded by the Kama Sutra, as separately discussed (Reframing the Dynamics of Engaging with Otherness: triadic correspondences between Topology, Kama Sutra and I Ching, 2011). As discussed there, Thom' s illustrations are especially suggestive.

Locus of principal changes of topological type
(reproduced from René Thom, Structural Stability and Morphogenesis, 1972)
1. curve with cusp pointing downward
2. appearance of new point at origin, where lip formation begins --
3. this grows... .
4. pierces the cusp..
5. and crosses it form the phallic mushroom... characteristic of the parabolic umbilic...
6. the cusp meets the lower branch of the lip in a hyperbolic umbilic...
7. and then the two branches cross to form a curvilnear triangle piercing laterally a convex curve
8. the triangle shrinks, first touching the curve
9. and then shrinking inside it
10. to form a hypercycloid with three cusps, and finally vanishes in an elliptic umbilic..
11. reappearing immediately with the same orientation
12. its lower cusp meets the curve
13. and pierces it
14. the curve and upper edge of the triangle touch in beak-to-beak singularity, which separates
15. producing two symmetric swallowtails, reabsorbed into the curve
16. leading to the original configuration

This is indicative of the possibility of a periodic table of "intercourse with otherness" -- with an emphasis on dynamics. Rendering time central to representation, through animation and its embodiment, may then be recognized as fruitful ( The Isdom of the Wisdom Society: embodying time as the heartland of humanity, 2003; Strategic Embodiment of Time: configuring questions fundamental to change, 2010). The graphic framed by each square in the schematic has been placed within a circular frame in a "sexy" animation at the end of this section.

Further questions: As a potentially suggestive animation, functioning as a motivating attractor, further questions could be considered:

The-O Ring and the psychoactive: Implicit in the above argument is an appreciation of the extent to which "The-O Ring" in its present form fails to be psychoactive to an increasing proportion of the population. Hence the quest for the psychoactive in other domains -- most obviously in drugs and various forms of gaming, and notably enabled by a variety of (interactive) media experiences.

It is clear that the psychoactive has much to do with imagination and its cultivation -- and how an imaginative experience can be sustained. The "theo" modalities are very constrained in their capacity to respond to such a demand. They may well be perceived as "dead" by those in quest of what is "alive". Any conventional "theo" denial of this could be framed by a question, as separately argued (Being neither Dead nor Alive : but how to know now? 2014). Intriguingly, the response might be framed dynamically, using an animation such as that above -- with its implications for the potential loss of attraction in any relationship, exemplified by experience of the sexually "dead".

Less provocatively, is psychoactivity to be usefully explored in terms of a sense of humour? Are the "theo" modalities -- with respect to their own methodology -- to be recognized as completely lacking in any sense of humour (however much they may claim to cultivate it "on the side")? The question is explored separately, notably with respect to religion and spiritual development and to philosophy (Recognized Role of Humour, 2005). In that respect are the "theo" modalities per se to be understood in terms of the Asperger Syndrome spectrum -- given the manner in which they are challenged by nonliteral language?

In the terms of Christopher Alexander, is there a case for imagining the design of psychoactive carpets (Magic Carpets as Psychoactive System Diagrams, 2010)? The case for imagination can of course be extended to governance (Imagining Attractive Global Governance: questioning possibilities and constraints of well-boundedness, 2013; Tentative adaptation of Alexander's 15 transformations to the psychosocial realm, 2010). With respect to the latter, should the "carpet" be understood as representing -- and interrelating -- a fundamental set of patterns, much as is done in experimental representations of the periodic table of chemical elements?

Distinguishing psychoactive design criteria: The argument could be usefully summarized by a table of the following kind, highlighting the enduring "focus" suggested by the bottom row -- perhaps exemplified by animation of the vesica piscis.

Criteria for transformative forms of presentation
  interestingness memorability
suggestiveness sustainability
("back for more")
mapping complexity
(as a network)
high, but
only briefly
somewhat, but the map
rather than the content
(too complex)
(centro) symmetric
(patterned complexity)
briefly maybe, but the pattern
rather than the content
(except as mandala?)
(but possibly)

maybe, but the animation
rather than the content

(too gadgety)
dynamic animation
("mechanical focus")
possible maybe, but the animation
rather than the content
(too gadgety)
dynamic animation
("biological focus ")
high? high? "sexy" (as sought
by advertisers)

Theatre: spectator, spectacle of the feminine and the Bull Ring

As noted above, despite the manner in which the variants of "theo" appear to be unrelated to "thea", the relationship is an intimate one with various facets. This is evident from the etymology, the status of "thea" as the feminine form of "theo" in the original Greek context, together with the implications of "thea" in the etymology of theatre -- at least.

The manner in which the feminine is designed out of the four conventional cognitive modalities of "theo" may well be rated as extraordinary by the future. This is especially the case when so much global scandal surrounds revelations of inappropriate sexual interactions involving the highest (male) leadership -- the exemplars of theo.

This is remarkably exemplified in the case of a managing director of the International Monetary Fund, framed as a future president of France (Pre-Judging an Institution's Implicit Strategy by the Director's Private Behaviour: remarkable parallels in the case of the IMF and Dominique Strauss-Kahn, 2011). Strangely this followed years of critical reference to the IMF as "raping" countries through its structural adjustment process (Institutional "rape" as systemic equivalent to individual rape? 2011).

Rather than the feminine alone, it is the dynamic of the interaction between male and female which is so profoundly fundamental as an attractor -- whether for a spectator or for the unconstrained reproduction of the species (at whatever cost to the environment and global civilization). The point can be variously argued (Scientific Gerrymandering of Boundaries of Overpopulation Debate Review of The Royal Society report -- People and the Planet, 2012; Formally ignoring a fundamental systemic process: the economy vs. the fucking? 2012).

With respect to the metaphysics of representation, in discussing the relation between philosophy and aesthetics Philippe Lacoue-Labarthe (Typography: Mimesis, Philosophy, Politics, 1998) recalls Heidegger's mistrust of the theoretical, citing him as follows:

The word 'theory' stems from the Greek verb theorein. The noun belonging to it is theoria. Peculiar to these words is a lofty and mysterious meaning. The verb theorein grew out of the coalescing of two root words, thea and horao. Thea ( cf. 'theater') is the outward look, the aspect, in which something sbows itself, the outward appearance in which it offer itself. Plato names this aspect in which what presences shows what it is, eidos. To have seen this aspect, eidenai, is to know [wissen]. The second root word in theorein, horao, means: to look at something attentively, to look it over, to view it closely. Thus it follows that theorein is thean horan, to look attentively on the outward appearance wherein what presences becomes visible and, through such seeing, to linger with it ... [But] the Greeks, who in a unique way thought out of their language. i.e., received from it their human existence, were also able to hear something else in the word theoria, and this in accordance with the supreme rank that theoria occupies within the Greek bios. When differently stressed, the two root words thea and orao can read thea and ora. Thea is goddess. It is as a goddess that Aletheia, the unconcealmcnt from out of which and in which that which presences presences, appears to the early thinker Parmenides. (page 93, footnote 80)

These points suggest that the variants of "theo" are variously associated with engaging as spectators in some form of play or game. These may have cognitive implications in addition to the descriptive. It suggests a degree of faith in a "story" and fascination with it.

For David Loy(Indra's Postmodern Net, Philosophy East and West, 43, 1993, 3):

Johan Huizinga's classic study Home Ludens shows how many aspects of human culture originate in play and how they have lost that quality over time. A good example is mythopoesis, where Huizinga applies the allegorical nature of personification to religion. "it is impossible, in my view, to make any sharp distinction between poetic personification in allegory and the conception of celestial -- or infernal -- beings in theology." This suggests that our conceptions of deity, ritual, and dogma were originally more spontaneous experiences and expressions which were later taken dogmatically as they became understood as the means to attain salvation from this vale of tears. That would be consistent with the general tendency whereby playful, unselfconscious elements tend over time to become formalized and then petrified, until their crust is broken through by the irruption of something new. For Derrida as well, "the divine has been ruined by God," and "the death of God will ensure our salvation because the death of God alone can reawaken the divine." (p. 499)

With their systematic practice of dissociation from the experiential dynamics of sexual reality, two extremes can then be usefully considered. With respect to Heidegger's reference to aletheia, both may be understood in terms of "unclosedness", "unconcealedness", "disclosure" or "truth" -- by which it may be variously translated. Its literal meaning is "the state of not being hidden; the state of being evident", also implying sincerity and the factuality or reality. As is recognized in the case of both theatre and humour, they offer the ability to express and experience the unsaid -- what cannot otherwise be rendered explicit (Global Strategic Implications of the "Unsaid": from myth-making towards a "wisdom society", 2003). The extremes can then be explored (as follows) in terms of the spectacle of the feminine and that of the bull.

Spectacle of the feminine: It could be said that the challenge posed by the feminine, amongst the masculine implications of the variants of "theo", plays out in the spectacle that they engender -- framed by the feminine in various ways as an inspiration to both speculation and contemplation, however controversial. The reinforcement of censorship in that regard is strikingly illustrated by the notorious erotic novel with a title potentially relevant to this argument (Anne Desclos, Story of O, 1954).

The challenge of the feminine is more obvious through the form of any arena or ring in which the spectacle is presented, or the proscenium arch under which it is staged. This could even be understood as positioning the "theo" modalities as "voyeurs".

Irrespective of anatomical technicalities and terminology, it is in this sense that the feminine can even be said to transcend in some way the plane of reality in which the variants of "theo" engage -- an argument made otherwise by Elise Boulding (The Underside of History: a view of women through time, 1976). There is a strange ambiguity to the omniabsence of the vagina from the formal discourse within the "theo" modalities -- complemented by its omnipresence in the living reality for many -- indeed an underside to match the overside (Epistemological Challenge of Cognitive Body Odour: exploring the underside of dialogue, 2006). As suggested by the polyhedral mappings (above), the circular form with which the feminine is associated is relatively invisible from the surfaces to which those modalities are attributed.

The interplay offered by theatrical presentation, its sexual connotations, and the cognitive implications of the spectator/voyeur of reality can be usefully highlighted by the strong sensitivities to harassment (Beyond Harassment of Reality and Grasping Future Possibilities: learnings from sexual harassment as a metaphor, 1996).

The theme has been evoked in worldwide presentations of Eve Ensler's Vagina Monologues. The matter has been considered otherwise by Emma Rees (The Vagina: a literary and cultural history, 2013), as described in the following terms:

From South Park to Kathy Acker, and from Lars Von Trier to Sex and the City, women s sexual organs are demonized. Rees traces the fascinating evolution of this demonization, considering how calling the c-word obscene both legitimates and perpetuates the fractured identities of women globally. Rees demonstrates how writers, artists, and filmmakers contend with the dilemma of the vagina's puzzlingly covert visibility .

In our postmodern, porn-obsessed culture, vaginas appear to be everywhere, literally or symbolically but, crucially, they are as silenced as they are objectified. The Vagina: A Literary and Cultural History examines the paradox of female genitalia through five fields of artistic expression: literature, film, TV, visual, and performance art.

There is a peculiar paradox unlike any other regarding female genitalia. Rees focuses on this paradox of what is termed the covert visibility of the vagina and on its monstrous manifestations. That is, what happens when the female body refuses to be pathologized, eroticized, or rendered subordinate to the will or intention of another? Common, and often offensive, slang terms for the vagina can be seen as an attempt to divert attention away from the reality of women's lived sexual experiences such that we don't look at the vagina itself. Slang offers a convenient distraction to something so taboo.

There is no lack of recognition of the vagina as an architectural metaphor (Kelsey Campbell-Dollaghan, A Brief History of Buildings That Look Like Vaginas, Gizmodo, 21 November 2013). This currently extends to controversies regarding the design of a football stadium of global relevance (Tomas Jivanda, The Accidental Vagina Stadium: design for Qatar's first 2022 World Cup purpose-built stadium released, The Independent, 18 November 2013; Holly Baxter, Qatar's accidental vagina stadium is most gratifying, The Guardian, 18 November 2013).

Curiously one of the most basic options of stage design is improbably termed the thrust stage -- with the stage surrounded on three sides by the audience. A number of authors and playwrights have explored the metaphorical relation between the design of the theatre proscenium and the vagina -- with deliberately challenging enactions of the vagina and direct exposure to it.

In recognizing the attention of postmodern theory to the role of theatre, Mark Pizzato (Edges of Loss: from modern drama to postmodern theory, 1998) sees it as revealing an obsession with the destruction of social institutions and the "universal truths" of modernism. Theater is understood as a marginal form revealing the unstable edges of community and the ways such community is imagined and staged, notably in terms of a nostalgia for a lost ritual "womb" (in Nietzsche's proto-postmodern views of ancient tragedy).

In Pizzato's discussion of Antonin Artaud's Womb in Derridean Re-presentation:

Artaud (as Derrida performs him) must inhabit the structure of the Oedipus myth in his attempt to reverse and demolish Western theological theater. Yet he also strives to go outside the logos-law of tragic stage space.... Thus, while Derrida, like Artaud (and Nietsche), "refuses to subsume Life to Being"... he also risks repeating Leibniz's failure to see the theological, logocentric, universalizing tendencies of the East as well as the West... Artaud's search for the Other within (through pantheological rebellion) against the Western phallogocentric stage appears in his plan for a play, The Philosopher's Stone, published in 1929. The set Artaud describes, out of conventional theatrical materials, presents a cavelike opening or vulva within the proscenium frame... This is not just a theater within a theater, but a choral, uterine edge -- a vulval signifier shaped out of the inner proscenium curtain. This (ideo)graphic set as a womb comes ritually alive through a perverse Oedipal triangle... (pp. 85-86)

A metaphorical proscenium/vagina figures in a famed play by Federico García Lorca, Asi que Pasen Cinco Años, as noted by Farris Anderson (The Theatrical Design of Lorca's Asi que Pasen Cinco Años, Journal of Spanish Studies: Twentieth Century, 7, 1979, 3, pp. 249-278). For Nicola Pitchford (Tactical Readings: feminist postmodernism in the novels of Kathy Acker and Angela Carter, 2002):

This vastly hyperbolic description of a sexual region that can "not admit the possibility" of connection to a body associates the pornographic image with society's most elevated institutions: the viewer (who is the imagined lover) enters the woman as a conquering hero entering a "triumphal arch"; he passes under the "coat of arms" that legitimates his nobility, through "red and purple crenellations," the colors and the fortress of royalty, to survey his kingdom within. The vaginal "proscenium" is the site of the elaborate staging of male power. (p. 173)

Are such descriptors aesthetically reminiscent of the orgasmic celebration of male beatification enabled by theology, as so recently disseminated globally -- to honour individuals who were significant in avoiding the pattern of systematic sexual abuse by the clergy for which they were responsible over decades? (UN Committee Against Torture criticises Vatican handling of sex abuse, The Guardian, 23 May 2014; UN denounces Vatican over child abuse and demands immediate action, The Guardian, 5 February 2014).

Are the implications of the vagina to be explored as a fundamental challenge to globalization, as separately discussed (Engendering Invagination and Gastrulation of Globalization: reconstructive insights from the sciences and the humanities, 2010)?

Spectacle of the bull; A fruitful contrast to preoccupations with the vagina is the significance associated with the role of the bull in various forms of spectacle, dating back to a tradition of bull worship as a primary symbol of fertility -- including that of bull-leaping. The bull was central in many ways to the period with which the Olympic deities were associated -- even to the Olympic Games in their original form. For Michael Rice (The Power of the Bull, 2014):

Everyone has heard of the Minotaur in the labyrinth on Crete and many know that the Greek gods would adopt the guise of a bull to seduce mortal women. But what lies behind these legends? The Power of the Bull discusses mankind's enduring obsession with bulls. The bull is an almost universal symbol throughout Indo-European cultures. Bull cults proliferated in the Middle East and in many parts of North Africa, and one cult, Mithraism, was the greatest rival to Christianity in the Roman Empire. The Cults are divergent yet have certain core elements in common. Michael Rice argues that the ancient bulls were the supreme sacrificial animal. An examination of evidence from earliest prehistory onwards reveals the bull to be a symbol of political authority, sexual potency, economic wealth and vast subterranean powers. In some areas representations of the bull have varied little from earliest times, in others it has changed vastly over centuries. This volume provides a well-illustrated and accessible analysis of the exceptionally rich artistic inheritance associated with the bull.

This engagement with the bull continues to this day in some Mediterranean cultures through bull-fighting and forms of bull-leaping. Most curiously "bull" continues to figure uniquely and plentifully in English jargon regarding the inadequacy of arguments presented through all modalities of "theo" and within them (Dilemma intrinsic to modern usage of "bull", 2009). This is a reaction to recognition of "spin". It is in this sense that "bull-fighting" can be fruitfully explored as a relevant metaphor (Viable Global Governance through Bullfighting: challenge of transcendence, 2009; Transformation of Global Governance through Bullfighting: visual symbols and geometric metaphors, 2009).

As a bull/cow the significance can be traced back further into the earliest Indo-Aryan creation myths of the Rg Veda regarding Vishvarupa, as clarified by Maria M . Colavito (The Heresy of Oedipus and the Mind /Mind Split: a study of the biocultural origins of civilization, 1995). Vishvarupa is considered the supreme form of Vishnu, the whole universe being understood as contained within him and originating from him. In discussing bulls as masculine prototypes, Colavito indicates that:

We have seen from the... myth of creation that there appears to be several references to bulls, not all necessarily representing the same act; a similar situation in the way bulls were portrayed in the Oedipus cycle, namely in varying ways. What we can begin to notice by looking further at the Indo-European myth is that the images of bulls are consistently dissimilar in the same way that the bulls in the Oedipus myth cycle are. In other words the acts of bulls are varied, but these varied acts are consistent among the myth systems. The only time that a problem arises with interpretation of these prototypes is when one views them by ideographic "seeing" and not by mythopoeic "seeing"... the way the seers see (mythopoetically, as One) and the way other mortals see (ideographically, as disparate entities)... when the story was transported via the Phoenicians, the ideographic story became THE story; the mythopoeic fell by the wayside into the realm of the unknown... (pp. 124-125).

These indications point to the difficulties with the argumentation process of the "theo" modalities. The underlying integrity is readily lost through ideographic description. Hence the value of the truth implied by participative spectacle whether with respect to the vagina or the bull. Ironically efforts have been made to complement the Vagina Monologues with Penis Monologues.

This argument can be taken further through the associations of the arena ring with that of a bull. It is in this sense that the form of the vagina as a ring, the bull ring, and the form of bull horns, all carry significance at a level underlying conventional modes of seeing -- a different order of truth (to which reference is made with respect to the experience of any spectacle).

Potentially more significant is the manner in such which forms embody the dynamics of a cycle, eluding simple seeing and requiring experiential proprioception through multiple modalities (Strategic Challenge of Polysensorial Knowledge bringing the "elephant" into "focus", 2008). This extends to that of any globality cycles may then frame -- and the generative response to the potential of an egg or the globe.

With respect to common reference to the lack of ability to see beyond the end of one's nose, there is a significant irony with regard to any ring in the nose of a bull. Can the bull see the ring, irrespective of whether it can feel it -- especially when pulled by it? Does this apply in some respect to "The-O ring" discussed above? Can those modalities "see the ring" at the end of their noses?

More provocatively, can the bull only see the ring when it drinks from a pool in which it is mirrored? Such recognition would require ability to pass the mirror test, namely for the bull to be able to recognize itself in the reflection. Seemingly it continues to be debatable whether recognition of one's mirror image implies self-awareness (Jens B. Asendorpf, et al., Self-Awareness and Other-Awareness II: mirror self-recognition, social contingency awareness, and synchronic imitation, Developmental Psychology, 1996). As discussed above, are the "theo" modalities to be understood as appropriately self-reflexive and self-aware -- in the light of how they may be perceived by the future?

Conference arena as combination of O-ring and Bull ring?: A conference arena, as with the European Parliament, can be readily depicted in physical terms as a form of ring, as with the image on the left (below). Implied in that arrangement is the composition, typically of political parties or other factions, as with the central image. Both these images are essentially static and give little sense of the dynamics. Although impressive in principle, this impression is severely undermined by the level of absenteeism -- indicative of lack of interestingness reinforcing the democratic deficit (currently highlighted by European elections). Missing is any means of representing the dynamics, as might suggested by use of the animation on the right.

Ways of seeing a plenary conference arena
Physical layout Pie chart of composition Sexually dynamic process?

A conference arena is readily appreciated as a place of drama, even deprecated as "theatre". The "horse trading" dynamics may well be comparable with those of a stock exchange -- readily described as a bull pit (Martin Schwartz, Pit Bull: lessons from Wall Street's champion day trader, 1999). In the light of the vaginal architectural traces evident at some conference arenas, there is a case for exploring the extent to which participation at a conference is an unconscious collective effort to return to the womb.

Use of "congress" as an alternative term, with its sexual connotations, also suggests careful consideration of other features of the process. Does prominent placement of a singular podium for a keynote speaker offer associations to clitoral stimulation -- potentially to engender a form of "collective orgasm"? Can varieties of orgasm then be usefully distinguished as leading to dissemination of the conference outcome? Given the constraints on creativity at such events, is there a case for exploring the implications of contraceptive devices and chastity belts in relation to such arenas? Given enthusiasm for "roundtable", what of the silence imposed on such arenas when its knights go questing elsewhere (Implication of the 12 Knights in any Strategic Round Table, 2014)?

Aside from implicit presence of the feminine in design options, typically missing from conventional descriptions of these processes has been the explicit involvement of women (Women and the Underside of Meetings: symptoms of denial in considering strategic options, 2009). This is primarily evident to a degree in formal "receptions" on the occasion of the event. However providing "entertainment" has long been a recognized feature of business meetings -- as a means of facilitating the conclusion of a deal. Far less evident is the degree to which such interaction may be inherent in the attraction of any international conference. A major restraint on better understanding of the wider system (within which the formal conference is set) is that it is in no one's interest to report on the matter -- most notably journalists at risk of losing their access rights to future events. This extends to an appreciation of the extent of use of sexual metaphor by participants in describing the interaction between the parties (Backside to the Future: coherence and conflation of dominant strategic metaphors, 2003)

Interweaving the functions of O-ring and Bull ring, are conferences to be fruitfully understood as the institutionalization of dalliance -- whatever its connotation? The lack of information (and the collective investment in denial) is relevant to current debate regarding the full cost of the monthly movement of MEPs from Brussels to Strasbourg -- costing taxpayers some 180 million euros per year, whilst debating public austerity (The farce of the EU travelling circus, The Daily Telegraph, 14 January 2014; Euro Shuffle: MEPs s Rebel Against Monthly Move to Strasbourg, Spiegel Online, 19 November 2013).

Missing from any analysis, as a factor in resistance to any change, is the effect on "extracurricular activity" at each location -- and on the various "service industries". Potentially more fruitful is the emergence of insight into how conferences really "work" in their more inclusive sense.

Game-playing, bull-leaping and laurel wreaths

The images and animations above suggest an extraordinary symbolic interplay between integrative significance, associated with the ring and the sphere, and the cognitive modalities from which the feminine is so strangely excluded -- although so intimately present through the problematically participative role of those modalities as spectators of theatre on a global scale.

Game-playing: This follows strangely from the mythical game-playing of the gods, now rehearsed globally through heavy investment in the Olympic Games and their global appreciation. This is echoed strangely by continuing practice of the so-called Great Game, now framed by a new Noopolitik (Playing the Great Game with Intelligence: Authority versus the People, 2013). Curiously many forms of popular games and wars "of the gods" now feature as the central theme of much-appreciated fantasy gaming -- a modern form of imaginal education.

The Olympiad theme is also sustained through a pattern of International Science Olympiads -- of which the oldest is the annual International Mathematical Olympiad (IMO). Highly appropriate to the geometric imagery of the argument above is its logo (on left below). Similarly relevant, with respect to the pattern of interlocking circles (discussed above), are the Borromean rings interlocking in 3D (on right below).

Logo of the International Mathematical Olympiad
(reproduced from Wikipedia; see IMO animation)
Logo of International Mathematical Union
(see Wolfram Mathematica animation)

Whereas the earliest origins of the Olympic Games in Minoan Crete featured bulls (and bull-leaping), and later variants featured nude athletes, the modern Olympic Games feature surrogates of various kinds -- consistent with a pattern of cognitive avoidance -- exemplified by the separation of male and female, whatever their relative size or strength. The surrogates include track and field sports and gymnastics within a closed stadium, as well as shooting sports. Strangely reminiscent of the skills of bull-leaping -- from which it can be understood to have developed -- the gymnastics include uneven bars, balance beam, vault. pommel horse, still rings, parallel bars, and the high bar. Shooting naturally involves a target -- with the aspiration to score a "bull's eye".

Although there are science olympiads, there are none for the belief systems sustained by theology and theosophy. What would an International Theological Olympiad look like -- and how might it differ from the Parliament of the World's Religions? Curiously in the case of both the sciences and the belief systems, with their explicit recognition of the "fields" of their respective disciplines, a variety of "field sports" could be considered recognizable as the arenas provided by international conferences.

The choice of the logos above is especially intriguing as indicative of a fundamental appreciation of a form of circular interlocking relevant to the cognitive complexity by which the tetrahedron is engendered (as noted above). However, in terms of the cognitive significance of a spectacle and the intimacy of participation in it, as argued above, the complex of circles -- the O-ring -- can be understood as combining the role of an attractor, the form of the vagina (as a target), a game-playing arena, and the fertile potential for renewal through an egg. Beyond framing the tetrahedron, the complex might then be understood as defining a multidimensional global form with which the powerful attraction of an egg is associated (Complexification of globalization and toroidal transformation, 2010). This attraction combines that of a sense of integrity and consummation in the moment.

Bull horns and laurel wreaths: Especially relevant to this argument, through the functional trace back to bull-leaping, is the manner in which the configuration of some gymnastic challenges echoes the cognitive skills required in the past -- and the engagement with risk. The challenge could be said to have been dubiously and unconsciously transmogrified -- even neutered. This is strangely evident in the manner of response to the "horns of dilemma" -- presented as a Wikipedia essay introduced by reference to dilemma, as being Greek for "two premises" and likened to the front end of an angry and charging bull. The essay is illustrated by the following image (on the left).

The current game-playing within various arenas -- O-rings in their own right, with their various targets -- can then be understood as having "de-horned" the dangers of dilemmas in favour of enabling an "o'er leaping" of threat in the present moment -- as suggested by Shakespeare (But here, upon this bank and shoal of time. We'd jump the life to come). This might even be considered a central characteristic of political decision-making (Vigorous Application of Derivative Thinking to Derivative Problems, 2013).

Bull horns indicative of the horns of a dilemma
(reproduced from Wikipedia)
Laurel wreath
(reproduced from Wikipedia)

More curious is the manner in which victorious Olympic athletes were originally rewarded with laurel wreaths for their gymnastic achievements. This followed from depictions of the head gear of deities. In Imperial Rome they were symbols of martial victory, crowning a successful commander during his triumph. Their depiction in ancient times was a horseshoe shape, whereas modern versions are usually complete rings -- and, with respect to success in any field, are only awarded metaphorically. Such an award is currently evident in the form of the laureates of Nobel Prizes and Gandhi Peace Awards -- perhaps to be understood as recognition of excellence in "cognitive gymnastics". Many now hope to "rest upon their laurels".

It could be considered remarkable that the original laurel wreath echoed the visual form of the bull's horns -- and the existential challenge they represented. Their form and symbolism also frames the male target of sexual intercourse within a typical "missionary configuration" of female legs during that process -- as explicitly described by the French phrase: une partie de jambes en l'air. The question is even asked: Pourquoi les hommes sont prêt a tout pour une partie de jambes en l'air?.

Sexual intercourse in the missionary position
(depicted by édouard-Henri Avril, reproduced from Wikipedia)

The laurel wreath, in its horseshoe form, is central to the logos of many international organizations, most notably the United Nations and its agencies. Strangely relevant to this argument, it frames a circle, symbolizing the planetary globe. This offers a complex of associations through bull-fighting, intercourse, targetting the quest for an "egg" through which humanity can be sustained -- together with "development", and the "structural adjustment" for which the IMF is renowned (as noted above). Are UN processes to be understood in terms of une partie de jambes en l'air?

This "story" can be explored through a set of images, as undertaken separately (Transformation of Global Governance through Bullfighting: visual symbols and geometric metaphors, 2009). Some of these are presented and commented below. As indicated by the first, it is within this ring that the matador confronts the bull, as with any confrontation with otherness or between polar opposites (right/wrong, positive/negative, female/male, etc). Contrasting colours are used to indicate such incommensurable differences.

Bull and Matador encounter (phase 1) Bull and Matador encounter (phase 2 Bull and Matador encounter (phase 3)

As a result of a simplifying "executive" decision, the emergent order on its own, readily lends itself to the simplistic representation of other panels -- with a consequent difficulty in encompassing the "excised" complexity implicit in the representation.

Bull and Matador encounter (later phase) Bull and Matador encounter (later phase) Bull and Matador (later phase)
The challenge of any "other" (epitomized by the bull) having been overcome, the victor (the matador) now "rests on the laurels" -- emblematic of that victory. Differences have been eliminated, or can be ignored, as a result of that achievement -- or so it may be assumed. Harmony is implied. From a global perspective, the laurel branches now frame an understanding of globality and integrity. Global differences are assumed to have been indistinguishably harmonized in an ordered world of higher values. Underlying discordant dynamics can be ignored -- having been cut out as a disassociation from the Dionysian -- identifying Zeus with Apollonian values. The ends of the laurel branches are opened to "release" global understanding in both its planetary and integrative senses. It can now be understood as finite but unbounded rather than constrained by a grid. As such it is now associated symbolically with a range of Sun god symbolism.

The images above raise the provocative question as to whether the break in the laurel wreath implies an inability to recognize any complex cycle and to address strategic issues which take cyclic form (Web resources on "breaking the cycle", 2002). Is the use of the laurel wreath in UN logos an indication of the extent to which a process of "resting upon laurels" has been institutionalized?

Reverting to strategic dilemma, as implied by the form of the bull's horns (as echoed by the laurel wreath), is there a fundamental inability to "grasp the bull by the horns" -- as suggested, for example, by David Alexander (Grasp this Bull by the Horns! Making our energy and environment plans, Planet Thoughts)?

Transgender spectacle? In the period in which this text was written, the world has been exposed to a striking confrontation of images disseminated globally by the media. On the the one hand this has taken the form of enhanced exposure to declarations of politicians variously imbued by the theo modalities -- notably in anticipation of a critical European election. On the other, and improbably, the 2014 European Song Contest engendered and crowned Conchita Wurst, a transgender person, dressed as a female and with a substantial beard.

Commentary makes it abundantly clear that the declarations of politicians are uninteresting and unmemorable -- especially to the young, expected to exacerbate the democratic deficit. By contrast, approval of the singer reflects recognition of interestingness, suggestiveness and memorability -- especially for the young.

It remains to be discovered what insights emerge from this development -- most notably with respect to the binary thinking so characteristic of the theo modalities (Transcending Simplistic Binary Contractual Relationships, 2012; Marrying an Other whatever the Form: reframing and extending the understanding of marriage, 2013).

Engaging with a fundamentally integrative perspective

Ensuring connectivity: Curiously the reference above to grasping the bull "by the horns" is suggestive of the sense in which it is human cognitive capacity which is required to make the integrative connection between the "horns" -- to ensure the vital connectivity in Bateson's meta-pattern -- the "pattern that connects", as noted above (Hyperspace Clues to the Psychology of the Pattern that Connects, 2003). Inability in this respect can be recognized in the universal proclivity for the "positive" -- designing out the "negative" by every means, with the associated remarkable inability of the "theo" modalities to process disagreement of any kind.

This "disconnect" ignores every insight from physics, and most obviously from the electrical circuit design through which light is generated and motors of every kind are driven. It is little wonder that the current global system does not "work" -- other than by "fits and starts". More symbolically, it is unable to ensure the "circulation of the light" (Circulation of the Light: essential metaphor of global sustainability? 2010). More obviously it highlights the challenging process of recycling, namely dealing with what remains (Reintegration of a Remaindered World: cognitive recycling of objects of systemic neglect, 2011). This is evident in the symbolism of the broken laurel leaf, and in avoiding any risk associated with "grasping the bull by the horns". More problematic in relation to the symbolism of Olympic game-playing is the necessary focus on the many losers engendered by it -- ignored in celebration of the winners.

As with the distracting role of slang in relation to the vagina and the use of "bull" (mentioned above), cyclic incompletion is especially evident with respect to human biological processes. Ironically this has been made especially evident with the global focus on Facebook -- ignoring what might be fruitfully associated with Arsebook (variously proposed), however much the former may carry intimate images more appropriate to the latter. Again however the compensation for this neglect is evident in slang at every level of society (Backside to the Future: coherence and conflation of dominant strategic metaphors -- Worshipping the Golden Ass, 2003). Curiously, in contrast to the vagina, widespread use of "arsehole" is consistent with unconscious recognition of a fundamental absence which is a theme of this argument.

Instinctual "bull response" in an unconscious civilization? The possible nature of an immense cognitive "hole" -- far "beneath" the conventional thought processes characterizing society, relationships and communication -- was the theme of separate exploration (Unthought as Cognitive Foundation of Global Civilization, 2012), with a section on Existential implications -- of a "hole" in conventional reality?. The approach was partly inspired by the work of John Ralston Saul (The Unconscious Civilization,1995), partly by that of Maurice Merleau-Ponty (The Phenomenology of Perception, 1945), and partly by that of Carl Jung on the collective unconscious. As argued by Saul, the paradox of our situation is that knowledge has not made us conscious. Instead, we have sought refuge in a world of illusion where language is cut off from reality.

As framed by this argument, that "hole" could be curiously associated with "The-O Ring" whose nature and existence is so elusive to conventional comprehension. The elusiveness could be described as a form of "Theo-O Ring blindness" by analogy with dyslexia -- possibly understood in terms of loop blindness or cycle insensitivity, or actively reinforcing them. The challenge in this respect has been separately articulated (Encycling Problematic Wickedness for Potential Humanity, 2014).

Of interest is how an unconscious civilization would respond instinctively to some kind of intuitive recognition of the existence of such a "hole". Curiously the most evident response is through several interrelated extremes:

These unconscious factors may be articulated in terms of asserting and acquiring a right to a "seat at the table". The table may itself be understood as indicative of an intuitive sense of the nature of "The-O Ring" -- potentially to be recognized in terms of the subtle dynamics of the archetypal "roundtable", as widely and variously valued (Implication of the 12 Knights in any Strategic Round Table: each circulating globally in quest of sustainability and immortality, 2014). Achieving a seat at the UN Security Council, or in other arenas, can be understood in this light.

Symbolic rings as attractors: Contrasting with the previous point, there is no lack of recognition of rings as much-valued attractors -- if only with respect to an engagement ring. Less evident is the drama required to render their fundamental significance meaningful. What is the meaning embodied in that experience? What drama might render comprehensible the nature of "The-O Ring"?

Striking examples of ring-focused dramas, which have long captured the imagination, are those of Richard Wagner (The Ring of the Nibelung) and of J. R. R. Tolkien (The Lord of the Rings). Their themes have been variously compared (Barnaby Thieme, Rings of Power: Wagner and Tolkien, Mesocosm, 23 December 2012; Alex Ross, The Ring and the Rings: Wagner vs. Tolkien, The New Yorker, 22 December 2003).

O-ring transcendence? Strangely it is now physicists who refer to the mythological Ouroboros -- the ultimate O-ring -- as discussed separately, and from which the image on the left is reproduced (Transcending both scientific and poetic comprehension of multiverse, 2012).

Again, however, such depiction raises questions about how to engage with, and comprehend, any dynamic implied by that ring -- as tentatively discussed in the contextual article (Being a Poem in the Making: engendering a multiverse through musing, 2012). As indicated there, theoretical physicist, Chris Clarke (Weaving the Cosmos: science, religion and ecology, 2010) comments on the adaptation below of the traditional image of the Ouroboros by Joel Primack to depict objects of steadily increasing size from the very smallest to the cosmos as a whole. Necessarily extending to the multiverse, as further developed by mathematical astrophysicist Bernard Carr (The Anthropic Principle Revisited, 2007), the symbol offers a means of holding the sense of observer-participancy presented by astrophysicist John Wheeler -- namely the sense in which the Universe is observing itself (cf. Brian D. Josephson, Biological Observer-Participation and Wheeler's 'Law without Law', 2011).

Ouroboros symbol
presented as a scale for size of physical objects

Adapted from Nancy Ellen Abrams and Joel R. Primack
(The View From the Center of the Universe, 2007)
Circular configuration of 64 hexagrams
and their relationships

(reproduced from
Transformation Metaphors, 1997)
Ouroboros symbol presented as a scale for the size of physical objects Logo of Laetus in Praesens

Another depiction is offered by the image on the right above, namely that of a circular configuration of the 64 hexagrams of the I Ching and the transformational relationships between the conditions of change they represent (as discussed separately). Appropriately perhaps the emergent pattern is strongly reminiscent of a formal representation of the vagina -- especially if the action of the transformational relationships is understood dynamically as corresponding to muscle action during labour.

There is an interesting sense in which the appropriation of the Ouroboros by astrophysicists, and a mapping of the classical Chinese worldview, could be explored in terms of the design challenges of the toroidal nuclear fusion reactor with which potential future energy resources are associated (Enactivating a Cognitive Fusion Reactor Imaginal Transformation of Energy Resourcing (ITER-8), 2008).

It is in this sense that transformation of the aesthetics of the "play" within the ring merit consideration (Sustaining a Community of Strange Loops: comprehension and engagement through aesthetic ring transformation, 2010). The civilizational threat of the dysfunctional interplay of the four-fold "theo" could even merit consideration in terms of the drama of the Four Horsemen of the Apocalypse, as separately explored (Beware of Legality, Accountability, Marketability, Security! Be where the Four Hoarsemen of the Apocalypse are not? 2012)

Selected images of the Yi-globe of József Drasny
(reproduced with permission from The Image of the Cosmos in the I Ching: the Yi-globe, 2007)

Yi-globe of József Drasny Yi-globe of József Drasny

Global cognitive healing? The argument above has distinguished five modalities denoted by theory, theorem, theology, theosophy and theatre. Various ways of considering their relationship have been explored. The challenge can be reframed through another metaphor, namely that of healing -- especially in the quest for what might be understood as "cognitive hygiene" or "conceptual hygiene", capable of encompassing and sustaining global governance. Any such possibility could be formulated in terms of a quest for mnemonic clues, as discussed previously (In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007).

Expressed differently, does the problematic nature of the relationship within and between the five clusters constitute a global public health problem worthy of the preoccupation of global institutions concerned with "health" -- such as the World Health Organization? Does the conflict engendered within and between clusters constitute a challenge to global "health" given the suffering and death it can engender? To what extent are "health" systems currently adapted or indifferent to issues of global cognitive health framed in this way? Beyond "hygiene", does the integrative challenge imply the need for a form of "healing"?

Practitioners of the various "theo" modalities -- whatever their eminence -- have a remarkable tendency to die following a period of senility. There is therefore clearly a case for exploring understandings of healing dynamics with a more open mind -- in the quest for better metaphors through which to engage in this process (Metaphors To Die By: correspondences between a collapsing civilization and a dying person, 2013)

A valuable clue to the nature of this cognitive healing process is provided by schematics which have been at the origin of consideration of healthy 5-fold dynamics in both the Greek culture (which gave rise to a sense of hygiene through the goddess Hygeia), and through the Chinese Wu Xing cycle

Hygieia Pentagram of Pythagoreans
Chinese 5-phase Wu Xing cycle
Hugieia Pentagram of Pythagoreans Chinese 5-phase Wu Xing cycle
Reproduced from Hygiea entry in Wikipedia
(G. J. Allman Greek Geometry From Thales to Euclid, 1889, p.26) with labels added
Adapted from Wu Xing entry in Wikipedia
Interaction arrows:
black=generating; white= overcoming

Their significance, and the correspondences between them, have been extensively discussed separately (Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012; Potentially health developmental integrity from 5-fold symmetry, 2012). The question is whether such cyclic 5-foldness offers insights for the integrative, cyclic interrelationship of the cognitive modalities of this argument. The schematics below suggest how they might be configured -- with the strong possibility that the attributions (and directionality of arrows) alternate within each configuration -- forming a cognitive "resonance hybrid"..

Indicative attribution of the* modalities
in a pentagram cycle
Indicative attribution of the* modalities
in a pyramidal configuration

In the separate discussion of the Hygeia / Wu Xing "healing" cycles, further possibilities of cognitive integration are considered in separate sections (Cognitive health as a sustainable cycle of self-reflexivity, Mnemonic possibilities towards cognitive health, Health and sustainability misleadingly framed as target acquisition, Frames of reference and conceptual revolution, Magnum Opus: cyclic transformation of Qi / Chi?).

It would seem that fundamental to such exploration is the nature of connectivity in terms of the credibility of various understandings of correspondences (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007). This has been recently highlighted with respect to so-called monstrous moonshine mathematics through which the so-called Monster Symmetry Group was discovered -- known by that name because of its very high dimensionality. Its integrative significance is discussed separately (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007). With such understanding, aesthetic correspondences deriving from patterns significant to the different senses may offer fruitful clues to further integration.

A valuable contribution to the possibility of 5-fold correspondences is the above-mentioned study of Maria M . Colavito (The Heresy of Oedipus and the Mind /Mind Split: a study of the biocultural origins of civilization, 1995). This explores a biocultural paradigm transcending the nature/nurture (evolution/environment) controversy by recognizing the neuro-biological origins of human development and by delineating exactly how and when sociological influences can and cannot affect those neuro-biological invariants. For Colavito:

It is composed of five proto-cultural models ("biocultures") which correspond to the five evolutionary centers of our neurological structures. Each bioculture then is formed by the cultural manifestation of the primacy of certain neurological traits over others, eventually (through the habitual repetition of the primacy of certain neurological links at the expense of others), these individual traits become societal ones.... The sociological evidence is founded primarily upon sociolinguistic grounds, by analyzing the relationships between the literary remnants of certain cultures and their corresponding social, political, and religious structures.

Nonsense commensurate with dysfunctionalities of "theo" variants

A number of authors have articulated what is now a matter of daily reality for many (Comprehension of ignorance, nonsense and craziness. 2011). They include Charles Handy (The Age of Unreason, 1991; The Age of Paradox, 1995) Michael Foley (The Age of Absurdity: why modern life makes it hard to be happy, 2011), Paul Feyerabend (Farewell to Reason, 1987), and Brent C. Sleasman (Albert Camus's Philosophy of Communication: making sense in an Age of Absurdity, 2011).

It is in this spirit that the above "argument" can be taken further.

Kenneth Boulding was wont to conclude the discussion of the complexities of an international conference -- plays in their own right -- through composition of a poem reflecting its processes and preoccupations. This offered a striking contrast to the theo modalities exemplified by such events -- especially given his notable speech impediment. The poem introduced an aesthetic connectivity typically designed out of the conference content and processes -- or marginalized into receptions and entertainment whose cognitive significance could be ignored.

As a piece of relevant nonsense, given the Greek etymological associations explored here, it is appropriate to recall that the famed futurist and Cold War strategist, Hermann Kahn was co-founder of the Hudson Institute at Croton-on-Hudson -- improbably recalling the homebase of Pythagoras, as one of the earliest of "model-builders" (based at Croton in Sicily). More improbably, Croton-on-Hudson was also the base of the World Modelling Association -- grouping the top models employed to display their looks in the promotion of commercial products. Kahn was an early exemplar of global model-building -- and was himself a model -- for Dr Strangelove or: How I Learned to Stop Worrying and Love the Bomb (1964).

It was Kahn who facilitated reflection on the "unthinkable" in relation to the strategic doctrine of "Mutual Assured Destruction" (Thinking about the Unthinkable, 1962; Thinking about the Unthinkable in the 1980s, 1984). Curiously common to both "models" was the manner in which they offered a comprehensibly simplistic enshrinement of ideals -- thereby precluding considerations of the challenges of more complex realities.

Of course the Hudson River is also the location of the headquarters of the United Nations with its laurel-wreathed logos. In terms of the bull metaphor, sadly the UN has been emasculated since its Secretary-General framed the Iraq intervention as illegal. This disempowerment seems to have been further reinforced by highly controversial invasive surveillance (Alleged Breach of UN Treaty Obligations by US: press coverage and commentary following WikiLeaks cable dissemination, 2010).

Thus framed, the Brooklyn accent, native to the location facing the United Nations across the river, can be used to offer a twist to the above argument in a world tormented both by the cognitive drone conditioned by the "theo" modalities and by the increasingly fatal use of invasive drones.

Ode to the Theo Drone: De-O and De-US
(inspired by one of the many improbable variants of the Brooklyn National Anthem)

De spring is sprung, de grass is riz
I wonder where de boidies is?
De boid is on de wing, but dat's absoid,
De wing is on de boid

De grass is riz de trees is green
And in de moitle tree a boid is seen.
A boid is seen and also hoid
And also felt. He dropped a toid.
Dis gets woise
And so de boid what did doit
Has got to die and dat's a coit
I gets me gat intent on moider
Detoimined dis won't get no foider
Oh boy! Oh boy! Am I pertoibed

I lifts me gat de boidie choips
I gotta give de squoit de woiks
But in the moitle tree above
There sits a little toitle dove
Remember moitle?
I've got me shooter primed but now
2 boids are sitting on de bough
And so, I cannot shoot de dove
Because de spring's de time for love

The commonly recognized first verse (above) points helpfully to the surreal relationship between the explicit "wings" (of which the "vanes" of the Möbius strip below are suggestive) and the implicit "boid" which they engender and transport. The emergence of explicate and implicate are a matter of dependent origination or dependent co-arising as featured in Buddhist philosophy (Pratityasamutpada).

The challenge of course is how to recognize the need for a "ring" and how then to discover it -- as teasingly intimated by one of the Poems Every Child Should Know -- implying a dynamic outcome in a strange light.

The Owl and the Pussy-Cat
by Edward Lear (renowned for his various works of nonsense)
The Owl and the Pussy-Cat went to sea
In a beautiful pea-green boat,
They took some honey, and plenty of money,
Wrapped up in a five pound-note.
The Owl looked up to the stars above,
And sang to a small guitar,
'O lovely Pussy! O Pussy, my love,
What a beautiful Pussy you are,
You are,
You are!
What a beautiful Pussy you are.'
Pussy said to the Owl, 'You elegant fowl,
How charmingly sweet you sing.
O let us be married, too long have we tarried,
But what shall we do for a ring?'
They sailed away for a year and a day,
To the land where the Bong-tree grows,
And there in the wood a Piggy-wig stood,
With a ring in the end of his nose,
His nose,
His nose!
With a ring in the end of his nose.
'Dear Pig, are you willing, to sell for one shilling
Your ring?' Said the Piggy, 'I will.'
So they took it away, and were married next day,
By the Turkey who lives on the hill.
They dined on mince, and slices of quince,
Which they ate with a runcible spoon;
And hand in hand, on the edge of the sand,
They danced by the light of the moon,
The moon,
The moon!
They danced by the light of the moon.

Aside from more obvious sexual connotations, one remarkable no-nonsense commentary on the possible hidden significance of the poem is offered by David Cowles (Owl and Pussycat, Aletheia, 26 March 2014). With respect to the ring he wonders:

Could it be that the ring was actually a Möbius strip, a one sided, 2 dimensional object? A Möbius strip is 'non-orientable', a topology in which there is no fixed beginning or end and no fixed orientation. Many eschatological cosmologies, for example Dante's in the Divine Comedy, include a non-orientable topology. A Möbius strip has the unique property that allows you to travel around it continuously, always coming back to the starting point; however, each time you return to the starting point, your orientation is reversed.

As concluding "nonsense", it is appropriate to note the value that continues to be attached in unsuspected ways to bull/cow/ox and an associated ring. The image on the left below depicts a phase in the classic sequence of Zen Ox-herding Pictures, or Ten Bulls -- with implications separately discussed (Commentary on the Integration of perceived Problems). The image on the right of a famed goddess of ancient Egypt is augmented by a suggestive animation, discussed separately (Embodiment of Identity in Conscious Creativity, 2011) . Hathor remains significant to the current symbolism of freemasonry.

One phase in the classical
Zen Ten-Bull sequence
Animation using an Egyptian deity,
the cow goddess Hathor --
a suggestive vehicle for transcendent insight?


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