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25 February 2009 | Draft

Engaging with Globality through Cognitive Circlets

2nd Dimension: Learning/Action cycles

-- / --

Dimension 2 of a four-fold exploration. Produced on the occasion of the "coronation" of Barack Obama (as president of the country from which insightful leadership is expected in response to global problems) and of the "crowning experience" of the Davos World Economic Forum (for the instigators and observers of the global credit crisis and its consequences). [Engaging with Globality -- Dimension 1: Cognitive Realignment; Dimension 2: Cognitive Circlets; Dimension 3: Cognitive Crowns; Dimension 4: Knowing Thyself]

Overview of Engaging with Globality

Dimension 1: Cognitive Realignment -- making points and aligning a target

Dimension 2: Cognitive Circlets -- learning/action cycles
Disconnected scales of scope
Symbols -- by-passing and focusing lengthy articulations
Cognitive torque and fruitful associations
Cognitive implications
Cognitive insights from mathematics
Resonances between power in practice and in imagination
Existential focus vs Radical reframing of "body of knowledge"
Cognitive challenge of 2-dimensionality and 3-dimensionality
Cognitive engagement with globality
Enabling designs of cognitive circlets and crowns
-- AQAL: "All Quadrants All Levels" | Mandelbrot set | Periodic table
-- Symmetrical polyhedra | -- Symmetry groups | Cognitive fusion
-- Cognitive work cycle and enantiodromia | Metabolic pathways | Global modelling
-- Basket weaving | Song cycles and epic poems | I Ching ***

Dimension 3: Cognitive Crowns -- all-encompassing, well-rounded experience

Dimension 4: Knowing Thyself -- embodying engagement with otherness

Annex A: Engaging with Globality through Playful Re-categorizing
Annex B: Global Governance via a Double-breasted Strange Attractor
Annex C: Engaging with Globality through Dynamic Complexity
Annex D: Intercourse with Globality through Enacting a Klein bottle



This is an exploration of the challenge of providing succinct integrative vehicles for significance, notably as this relates to any existential sense of coherence and identity. The focus in Dimension 1 and Dimension 2 is on the challenge more conventionally understood in terms of the knowledge management required by governance and the governors -- on behalf of the governed. This is developed in Dimension 3 with respect to those who are effectively "crowned". In Dimension 4 the inadequacies and impracticalities of such possibilities, hitherto considered realistic, are used to reframe the cognitive challenge for any individual obliged to order cognitive skills and accessible insights -- where such dependence on external authority is now clearly unrealistic. A summary of the 4-part argument is provided separately (Metaphorical Geometry in Quest of Globality, 2009).

In the light of Dimension 4, readers could consider avoiding the lengthy arguments of Dimensions 1-3 (regarding what is possible, but increasingly improbable) -- then focus only on the annexes of Dimension 4 for proactive viability and light relief, notably Annex B (Sustainable Governance via a Double-breasted Strange Attractor). Those annexes are premised on the assumption that sustainable governance is necessarily sexy -- and if it is not then it is unlikely to be sustainable.

The approach, especially in Dimension 1 and Dimension 2, is a development of arguments presented previously (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000) regarding cognitive survival devices in a fragmenting global society. It developed the following themes relevant to the argument here:

This argument also recognizes a degree of compatibility of such devices with widespread use of ornamental accessories, with or without symbolic and fashionable implications. These symbols may indeed be taken very seriously in traditional rituals (possibly dating from monarchical times) by institutions of governance, religions and sects with whom the powerful in the emerging global society tend to be associated and necessarily influential in any faith-based approach to its governance. The argument also relates to an earlier exploration of the need for mnemonic aids, which symbols may constitute (In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007).

As the sequel to this argument, in Dimension 4, the approach is reversed to present the role of cognitive circlets and crowns for the individual endeavouring to engage meaningfully and responsibly, and in an integrative manner, with globality -- independently of any reliance on distant coronations.

Disconnected scales of scope

There is necessarily a major challenge to ensuring any meaningful cognitive relationship between understanding :

Understanding associated with the scope of each tends to distort and over-simplify that associated with any other. Additionally each is to some degree fragmented and lacking in the functional integrity purportedly associated with it -- a consequence of the challenge to cognitive skills, especially memory, and notably as affected by distinct cognitive biases and styles of intelligence. The situation is complicated by the extent to which understanding of each kind is held to be "universal" and presented as such to others resistant to that claim. Consequently there is a recognition of "believers" and of those held to be "non-believers" -- and therefore problematic in some way.

The cognitive challenge, and its possible remedies. is usefully reflected in structures such as:

Such architectural closure is now replicated cognitively in gated communities -- in both cases emblematic of forms of cognitive closure and "circles of trust" offering a requisite sense of belonging and identity (Dynamically Gated Conceptual Communities: emergent patterns of isolation within knowledge society, 2004). It has been argued by Matt Frei (Taming the cyber beast, The Guardian, 24 January 2009) that:

The Bush White House circled the wagons and lived in a bubble; it turned loyalty into a test of service and largely disdained the clutter of opinions from the world outside...

A curious complement to "circling the wagons" against outsiders is now to be found in the emergent process in democratic societies of "corralling" or "kettling" protesters by the "forces of law and order" (Baton charges and kettling: police's G20 crowd control tactics under fire, The Guardian, 3 April 2009; Coralled and angry, G20 protesters switch focus of anger from bankers to police, The Guardian, 3 April 2009)

Symbols -- by-passing and focusing lengthy articulations

Narrative: Whatever the scope, there is a tendency to articulate understanding in the form of narrative and text. These modes may indeed rehearse the set of insights indicative of broader, deeper or more subtle understanding. Remembering the narrative may be a valued skill, as with story tellers.

Lists: An alternative to the continuity and integrity offered by any such narrative is a listing of the insights. Religion upholds sets of principles and injunctions in this way. Laws and regulations may be promulgated through such lists. In the form of "bullet points", the preoccupations deemed requisite to any strategy, or to the management of any enterprise, may be listed in Powerpoint style representations (as with this document). It is curious that much social organization is designed and managed through such "bullet point" lists and the appropriateness of doing so is seldom challenged (Enhancing Sustainable Development Strategies through Avoidance of Military Metaphors, 1998).

Network diagrams: More complex still is the representation of the elements as a network or a systems diagram -- even a mind map-- beyond the hierarchical limitations of nested lists; such linkage typically has implications for the reflection of the interconnectivity in organizational or technical operations.

Symbols: The cognitive content of lists may be rendered much more succinct and memorable by the representation of the elements as symbols. The use of sets of such symbols may in fact precede the verbal or textual articulation of the insight, or may be understood as mnemonic catalysts for such articulation. This is the case of the traditional symbols of many cultures, notably sets of gods forming a pantheon. It is however interesting that the content of some lists from early periods -- as with the Ten Commandments -- has not been represented by symbols.

Rosaries: The earlier paper (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000) noted how principles vital to understanding of the integrity of a pattern of belief were associated in many cultures with beads or symbols on some form of rosary. These provided a set of mnemonic triggers to recollect that pattern. Such devices are then to be understood as succinct carriers or holding frames. They provide a symbolic interface with that which is larger or more complex than can be coherently comprehended. The individual elements on any such necklace might then be understood as a set of cognitive "lenses" through which a larger context can be partially comprehended -- a form of "macroscope" (Joël de Rosnay, The Macroscope, 1979; Luc de Brabandère, Le Latéroscope: systèmes et créativité, 1989)

Identity: Necklaces, bracelets, anklets and belts may of course also be used to signify identification with a set of beliefs or understandings. They may be used to denote acquisition of understanding, notably as a mark of rank. They are a means of tribal identification in many cultures. More commonly they may also take the form of fashion accessories, expressive of other collective affiliations or associations. The distinct functions essential to integrated application of insight are best exemplified by the use by artisans of belts from which hang a set of tools. The use of key rings may also be understood symbolically and practically as holding access to a range of domains relevant to the exercise of an integrated set of functions.

Cognitive torque and its fruitful associations

The concern in the speculative exploration that follows is whether greater significance might be associated with such devices in practice, both in terms of their integrative capacity and the potential for psychoactive cognitive engagement. This necessarily goes beyond their mnemonic function and implies some form of existentially enhancing role. A potentially fruitful point of departure is the role of the torc as a more rigid form of necklace that has been the focus for symbolic and speculative treatment, as well as constituting a problematic symbol of high or low status -- even an indicator of property or enslavement in the latter case.

The torc (torq or torque) can be worn as an arm ring, a circular neck ring, or a form of necklace. Whereas a necklace or a rosary typically has a point of discontinuity, in the case of a torc it may be open-ended in that the ends do not meet -- the integrity being ensured by the rigidity of the material (typically metal). This is also true of the bracelet form or as a finger ring.

The significance of the torc may be understood through various fruitful associations:

Halo: as a halo (nimbus, aureole, glory, or gloriole), it is depicted as a ring of light that surrounds a person of spiritual significance, typically in religious art representing holy or sacred figures. So depicted, it may notably surround the head or be positioned as a ring above it. Rather than a ring, from some representations it is readily to be inferred that it is considered to be a sphere, namely a form of crown.

Mark of property and dominance:

Enabling "metapsychic powers": as enabling distinct "metapsychic" powers, notably as imaginatively explored in the science fiction series of Julian May (Saga of Pliocene Exile, notably The Golden Torc, 1982) where several torcs conferring such powers are distinguished: gold (ensuring complete operacy of those with latent powers), silver (ensuring control of the powers of the wearer by those wearing the golden form), grey (enabling only a degree of "farspeech" and ensuring control by those wearing the golden form). The series provided early imaginative support for understandings that now permeate online role-playing games and movie variants.

Signifying secular powers or bonds: as implying or conferring "powers" of some kind, if only in secular terms:

Of particular interest is the associated use of piercing, recalling the practices of indigenous peoples and the symbolism (of wholeness?) they may have attached to rings used in this way. However piercing also suggests an intuitive sense of the higher dimensionality that can only be reflected at lower dimensionality through such "cuts" (in psychoanalytic terms). On the other hand, disparaging references are made to being led by "a ring through the nose" -- as with a bull.

Rings as a mode of psychosocial organization: Widespreads reference is made to "rings", as in organized crime (drug rings, call-girl rings, criminal rings), and web rings. (including a Witches Circle Web Ring). A related variant is reference to a circle of contacts or a circle of friends, possibly reflected in circle, ring and round dances, including those of children (Ring a Ring o' Roses). .In the Wiccan tradition the construction of a ring is of ceremonial significance (R.J. Thompson, Drawing the Witch's Ring of Art, 28 January 2008)

Cognitive implications

Whilst the above uses of the torc -- in whatever form -- stress how the wearer is to be perceived by others and to distinguish the authority of the wearer in relation to them, they seemingly say relatively little about the cognitive significance to the wearer. There is an implication that in some cases, beyond any matter of authority, there is an unusual level of understanding and insight. This would be the preferred current implication with respect to the papal tiara or the collars of rank in freemasonry, although such an implication is now deprecated in relation to constitutional monarchs formerly claiming to rule by divine right (but with the continuing exception of those still held to be "living gods"). In such cases the understanding is typically held to be secret or beyond normal ken. The imaginative exploration of "metapsychic" powers, by Julian May and others, has merit in pointing to possibilities, however speculative.

The use of torcs in slavery and in bondage games offers another sense of the potential existential implications as experienced. Whether or not distinguished by use of torcs, strong arguments may be advanced for the continued existence of slavery in its traditional forms (E. Benjamin Skinner, A Crime So Monstrous: face-to-face with modern-day slavery, 2008). There are now alleged to be more slaves on the planet than at any time in human history. In addition there is the effective emergence of other forms of slavery, including phenomena associated with sexual slavery, wage slavery, white collar slavery or blue collar slavery (Jolly Roger, The New American Slavery, 2005).

Enslavement of any such kind suggests the value of recognizing what might be understood as "virtual torcs" by which people are "torqued" into some form of subservience. The intangible characteristic of such enforcement is presumably closely associated with structural violence as analyzed by Johan Galtung (Violence, Peace, and Peace Research, Journal of Peace Research, 1969). The term denotes a form of violence which corresponds with the systematic ways in which a given social structure or social institution kills people slowly by preventing them from meeting their basic needs. Examples include: institutionalized elitism, ethnocentrism, classism, racism, sexism, adultism, nationalism, heterosexism and ageism.

The analysis has been extended to include cultural violence (Johan Galtung, Cultural Violence, Journal of Peace Research, 1990) understood as any aspect of a culture that can be used to legitimize violence in its direct or structural form. Symbolic violence built into a culture in this way does not kill or maim like direct violence or the violence built into the structure -- however, it is used to legitimize either or both.

It is curious that the far more common use of the term "torque" in mechanics, notably as a verb, has associations to such intangible forms of violence. Thus to "impart torque" is to cause to twist, typically about an axis, fulcrum or pivot. Torque is then the moment of a force, namely the measure of a force's tendency to produce torsion and rotation about an axis. It is typically used to describe a rotational force down a shaft (for example a turning screw-driver), whereas "moment" is more often used to describe a bending force on a beam.

Such precise use in mechanics offers a template for understanding subtle psycho-social phenomena described by the term "twisted" (Twistedness in Psycho-social Systems: challenge to logic, morality, leadership and personal development, 2004; Engaging with Questions of Higher Order: cognitive vigilance required for higher degrees of twistedness, 2004). Put bluntly, this would appear to justify the subtle sense commonly described in urban jargon by the phrase "being shafted". This would accord with explorations of the experience, attributed notably to the enslaved, of "being torqued". It is also suggestive of insights relating to any "axis" around which people rotate or are expected to rotate.

Cognitive insights from mathematics

A very helpful bridge between the precision offered by a mathematical description and the cognitive implications (associated with torque) is to be found in the work of Ron Atkin (Combinatorial Connectivities in Social Systems: an application of simplicial complex structures to the study of large organizations, 1977; Multidimensional Man: can man live in three dimensional space? 1981). As summarized elsewhere (Social organization determined by incommunicability of insights), this highlights the way in which social action (of whatever kind) can be seen as traffic in an abstract geometry descriptive of cognitive relationships -- and specifically how this can be manipulated by ensuring the presence of "holes" in that space "around" which communication is forced to take place:

This traffic must naturally avoid the holes (because it is impossible for any such action to exist in a hole). The holes therefore appear strangely as objects in the structure, as far as the traffic is concerned. The difference is a logical one in that the word "q-hole" describes a static feature of the geometry, whilst the world "q-object" describes the experience of that hole by traffic which moves in that geometry....

This suggests new ways of comprehending the nature of a problem. As an "object" this phenomenon is an obstacle to communication and comprehension and obliges those confronted with it to go "around" in order to sense the higher dimensionality by which it is characterized. Communications "bounce off" such objects. As a "hole" this phenomenon engenders, or is engendered by, a pattern of communication. It appears to function both as "source" and "sink".

Atkin suggests that, in some way, which is not yet fully understood, object/holes act as sources of energy for the possible traffic around them. His use of q-analysis gives precision to the recognition that traffic of different degrees of content connectivity finds (or creates) its appropriate level in any psycho-social communication complex, presumably including a language:

Communicable insights are level-bound, especially where they are of high connectivity. In other words, at the level within which it is possible to communicate, problems cannot necessarily be anchored unambiguously into terms and definitions which "travel well"....

The relation between two personal or institutional structures, conceived as a multidimensional backcloth, carries whatever traffic that constitutes the communication between them. If this backcloth changes by becoming dimensionally smaller, then its geometry loses vertices and the consequent connectivity properties. This is first indicated by the failure of higher dimensional traffic which the geometry can no longer carry...

In these terms, "cognitive torque" may be understood in terms of the experience of warped geometry:

This process of reducing communication expectations in order to continue to live within the new warped geometry is the classical problem of compromising. The feeling of "having to compromise" is a painful one. It is the feeling of stress induced by the warping of the communication geometry, namely the direct experience of a structurally induced force... It is the feeling associated with the distortion of an unsatisfactory translation between languages. This approach clearly provides a very precise approach to understanding more subtle forms of structural violence.

Atkin has applied this approach to an analysis of unemployment. Such considerations suggest the power of q-analysis in clarifying approaches to human and social development in general.

Reducing the dimensionality of the geometry on which a person (or group) is able to live is an impoverishment associated with repressive forces. Expanding the dimensionality induces positive, attractive forces through which a sense of development and enrichment is experienced. Q-analysis seems to be a valuable new language through which precision can be given to intuitive experiences and their communication, particularly since it provides an explicit measure of obstruction to change...

In the case of social development, it is probable that most continuing societal problems should be seen as holes/objects, especially given the well-established record of unfruitful action in response to them - however vigorous and dedicated. Typical examples are: peace/disarmament, development, human rights, environment, etc. Q-analysis could then provide understanding of why any action tends to be drawn into a vortex of futility, however much it satisfies short-term political needs for visible "positive" action. The participants in the action find themselves "circulating" around a central concern of which they are unable to obtain an overview due to the geometries of the overlapping conceptual and organizational structures through which they work (or which they somehow engender).

In the case of human development, Atkin shows how the individual can be defined in terms of a multidimensional geometry requiring a minimum of four levels. By relating this geometry to that of society, Atkin introduces an 8-level scheme within which the degree of integration (or eccentricity of communication) can be clarified in terms of developmental or anti-developmental forces.

In such a multidimensional geometry it is clear that, whether in the case of an individual, a group or society as a whole, it is not possible to eliminate "underdevelopment" as associated with low dimensionality. Such a geometry will necessarily continue to have traffic of very low-level connectivity co-present with that of increasingly higher level connectivity. The simplest illustration arises from the continuing birth of infants who will, when resources permit, continue to be educated through to the level of connectivity to which they can respond. But there will always be communication at both low and high-connectivity levels, especially about socio-political issues. The question is then how such learning communication between these different levels of connectivity can weave itself together within a social structure.

Resonances between power in practice and in imagination

Whilst the torque in any form is used as a visible mark of rank or insight (or the lack thereof), there are curious resonances between the imagined power of such distinction and imaginative interpretation of the cognitive implications of the symbols denoting it.

It might be argued that use of some form of circlet or torque is irrelevant to the dynamics of the real world, however much it is valued as a charming tradition or for the extreme economic and aesthetic value attributed to their bejewlled design. It remains a fact however that particular powers are associated with some wearers (or arrogated by them), as notably experienced by the wearers of lesser variants. The former are effectively capable of "warping" the experiential and cognitive geometry of the latter.

In both cases the torque may, if only potentially, be of greater significance virtually than in its tangible forms. Ironically, as mentioned above with respect to magical rings, considerable significance may in fact be attributed to imagined possibilities of a torque in speculative fiction and epic fantasies (appealing to the disempowered) than to their use as marks of rank (by the socially empowered). Nevertheless, at the time of writing, much is being made of the "coronation" of Barack Obama through which he will indeed be endowed with an array of powers which many of the disempowered (notably descendants of slaves) expect him to use to alleviate their condition.

Extreme tangible examples of torques, as noted, are the crowns of royalty, the papal tiara, mayoral chains, and the collars of freemasonry. In each case, using Atkin's approach, power may be used by the wearer to "warp" the experiential geometry of the relatively disempowered. The distinctions of freemasonry, emphasized by symbolic jewels, even suggest a way of thinking about the relative cognitive warping within any body of freemasons in the light of Atkin's analysis of the possibility of communicating insights otherwise held to be secret. This would be true to a lesser degree with respect to the bejewelled collars of orders of knighthood.

Given the significance attached to cut jewels in the design of some torques, it is appropriate to explore how their faceting may point to integrative understandings of dialogue of different quality -- whether or not they enable such communication is some special way (Patterning Archetypal Templates of Emergent Order: implications of diamond faceting for enlightening dialogue, 2002).

Existential focus vs Radical reframing of "body of knowledge"

In what follows, circlets and torques are explored as a form of cognitive interface -- for the wearer -- between:

For the individual faced with the knowable universe in this way, and potentially disempowered by its dimensions and dynamics, there is a legitimate protective need to emulate pioneers in "circling the wagons" -- in this case the cognitive wagons. Whether as bracelet, necklace, tiara or torque, any circlet then echoes traditional cognitive arrangements exemplified by:

Cognitive challenge of 2-dimensionality and 3-dimensionality

The cognitive challenge is even clearer when the person has responsibility for collective action in response to the challenging complexities of the knowable universe. The cognitive elements are then reflected in tangibles exemplified by:

The high-pressure nature of such contexts is exemplified by the challenge for the driver of any vehicle operating at speed and expected to respond in the shortest possible time (as a matter of life or death) to conditions represented by an array of dials and indicators. The question is how can knowledge be appropriately communicated under such conditions, especially when the driver needs to be empowered to integrate that which is being offered through the separate indicators. This is the challenge of cognitive fusion which is the focus of military research in support of fighter pilots.

Echoes of this challenge are to be found in:

The examples above are indicative of a progression from an essentially 2D configuration of elements in a circlet of distinct cognitive devices through to a 3D configuration (as explored in Dimension 3 on Cognitive Crowns). It is of course the case that the "2D" forms imply integrative cognition in "3D" and beyond. However it is only in the "helmets" that there is any 3D correspondence to the design of a crown and the insight it supposedly symbolizes.

This raises the intriguing question of the nature of the cognitive interaction with the knowable universe that is supposedly enabled by a crown or implied by its symbolism -- beyond that enabled by a circlet or other torque. Ironically this question is especially pertinent at the time of writing, with the "coronation" of Barack Obama and his acclamation as the most powerful person in the world -- effectively the cognitive Top Gun, beyond whom the cognitive buck does not pass. Given the universally acknowledged complexity of his challenge, how are his cognitive facilities to be appropriately configured, and suitably enhanced, to be commensurate with that challenge?

Whilst Obama will necessarily make use of the White House Situation Room, how does he embody the "King Arthur cognition" necessary for any transcendence of the problematic, conventional, 2-dimensional dynamics of the cabinet roundtable? (cf Pattern of Meeting Participant Roles: shadowy 'roundtable' hidden within every meeting, 1993).

Does the challenge resemble that of a juggler keeping a set of hoops rotating at various orientations? How does he ensure the appropriate interlocking of the 2D cognitive circlets of his team gathered at that roundtable? How might their interrelationships sustain a cognitive dynamic, through some form of self-organization, that enables the emergence of a higher order of cognitive integration which any crown supposedly symbolizes.

How will this interlocking "bend" cognitive space to enable new forms of strategy -- hopefully characterized by wisdom?

Cognitive engagement with globality

Common to the personal sense of identity and to the sense of a wider knowable universe (as contrasting themes of the previous section), is some sense of "globality":

The challenge in both cases is that of how to engage meaningfully with globality and a sense of wholeness. The challenge for the private individual mirrors that of anyone who is "crowned" with responsibilities for global leadership. It might even be assumed that, unless such integrative engagement is rendered meaningful to the disempowered, any strategy by the empowered will necessarily be experienced as "warping" and doing violence to their space.

Enabling designs of cognitive circlets and crowns

Beyond the examples indicated above, there is a case for imaginative exploration of possibilities for designs that might enhance integrative cognitive capacity -- if only as mnemonic aids, as argued elsewhere (In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007). Such exploration is necessarily speculative, recognizing however that it is to some degree the imaginative engagement through metaphor with any design that significantly enables such capacity (Metaphors as Transdisciplinary Vehicles of the Future, 1991). It is increasingly the case that what can be imagined in this way can be replicated in virtual environments, both as a representation but -- more significantly -- as a means of interfacing with knowledge resources on the web. Imagination is the constraint. The enabling technology is in many respects in advance of what imagination is currently requiring.

Design clues might then include (in no particular order):

Passing patterns: As indicated in Dimension 1, it is astounding that greater sophistication is applied to the analysis of patterns of interaction in various sports -- passing patterns -- than is applied to the patterns of dialogue at vital strategic gatherings (Jochen Voss, The Mathematical Theory of Juggling, 2007; Ben Beever, Guide to Juggling Patterns; Mark Weston, Passing Patterns, 2006; Athalie Redwood-Brown, Passing patterns before and after goal scoring in FA Premier League Soccer, International Journal of Performance Analysis in Sport, 2008; Association for Soccer Education and Teaching, Passing Patterns and Small Sided Games, 2008; Alan Reifman, Network Analysis of Basketball Passing Patterns II, 2006; Patrick Riley, Coaching: Learning and Using Environment and Agent Models for Advice, 2005). The approach has been adapted to message passing in complex organizational networks. The situation is all the more curious given the widespread metaphoric use of "ball" in strategic dialogue -- as in the "ball is in their court".

Given the constant pressure for higher quality performance in such contexts, how is the quality of dialogue regarding the current crisis to be evaluated? The movement of a ball, or a set of clubs, has long been tracked and visualized to improve performance (Daniel A. Reed, Matthew J. Gardner and Evgenia Smirni, Performance Visualization: 2-D, 3-D, and Beyond). How is it that no effort is made to do so for strategic dialogue -- especially widely publicized panel sessions? In whose interest is it to avoid doing so?

OODA loop: This loop or cycle orders the sequence: Observe, Orient, Decide and Act. In response to the potential "targets" (the theme of Dimension 1), it is notably applied to the combat operations process, often at strategic level in both the military and commercial operations (Daniel Ford, When Sun-tzu met Clausewitz: John Boyd, the OODA Loop, and the invasion of Iraq). It was created by military strategist and USAF Colonel John Boyd. As such it focuses on strategic military requirements but has been adapted for business and public sector operational continuity planning. It is compared with the Plan Do Check Act (PDCA) cycle (otherwise known as the Shewhart cycle, the Deming Cycle, the Deming Wheel, or Plan-Do-Study-Act), which focuses on the operational or tactical level of projects.

AQAL: "All Quadrants All Levels": This is a theory developed by Ken Wilber and promoted by the Integral Movement. The concentric circles, divided into four quadrants, together offer one of the most sophisticated maps of cognitive engagement with the world -- a map which is in part the product of the subtleties of meditative experience and a guide to them. Its schematic geometry might however be understood as the basis for the design of circlets, especially given the colour coding already used to distinguish cognitive conditions associated with the map. An understanding of the "jewels" distinguishing such conditions within the Integral Movement is indicated by the poetic summary of a discussion about satsang by Corey W. deVos (General Discussion: Brahman is the World, 5 November 2008) in the following terms: "The melodies of timeless thought ribbon through our minds, threading our souls together into the living jewelry of consciousness..."

The relevance of this approach to governance has been notably explored by Steve McIntosh (Integral Consciousness and the Future of Evolution: how the integral worldview  is transforming politics, culture and spirituality, 2007). Announcements regarding the State of the World Forum (Washington DC, 2009) indicate that its dynamics are to be regulated by this approach, irrespective of ongoing reservations about it (Self-reflexive Challenges of Integrative Futures, 2008).

The AQAL system is integrated with a theory of developmental Spiral Dynamics. From a design perspective, this too could be made the basis of a circlet or bracelet. More intriguing is the possibility that AQAL (through such a spiral) offers a schematic for a form of crown (as discussed in Dimension 2), with a spiral component to its design. The basic AQAL schematic is effectively a projection into two dimensions of what is to be experienced in three (or more). Crowns of such design, whatever their symbolic significance, are notably to be seen in South-East Asian cultures.

Mandelbrot set: Discovered by mathematician Benoît Mandelbrot, this is a set of points in the complex plane, the boundary of which forms a fractal that may be represented and explored in striking ways. The Buddhabrot is a special rendering of the Mandelbrot set (discovered by Melinda Green) which, when traditionally oriented, resembles to some extent certain depictions of the Buddha. As the basis for the design of any crown, the set in fact includes features commonly labelled as crowns. The association of the set with understandings of complexity suggests that it might be used for purposes of cognitive organization -- thereby giving significance in practice to the symbolic form of a crown in which significance is normally only implied. The strategic significance has been explored at greater length elsewhere (Sustainability through the Dynamics of Strategic Dilemmas -- in the light of the coherence and visual form of the Mandelbrot set, 2005; Psycho-social Significance of the Mandelbrot Set: a sustainable boundary between chaos and order, 2005).

Periodic table: The periodic organization of chemical elements (and their isotopes) has long constituted a challenge to insightful design. Many approaches have been considered. As noted above, such periodicity has been an inspiration to the classification of knowledge, notably for access via the web (Functional Classification in an Integrative Matrix of Human Preoccupations, 1982). This was partly inspired by an effort to generalize the original table by Edward Haskell (Generalization of the Structure of Mendeleev's Periodic Table), which appeared in a book of which he was the principal editor (Full Circle: The Moral Force of Unified Science is an attempt at the unification of human knowledge, 1972). Such possibilities might be extended to address the strategic challenge of interrelating the belief systems currently fragmenting any integrative approach (Tuning a Periodic Table of Religions, Epistemologies and Spirituality -- including the sciences and other belief systems, 2007). Clearly any such "table" lends itself to representation as a circlet, if only for mnemonic purposes. Given the many design alternatives that have been considered, the question is whether it can be usefully configured as a crown that could be cognitively "worn" -- notably in a virtual environment.

Symmetrical polyhedra: From a design perspective, such polyhedra offer the most direct inspiration for the design of any crown -- just as symmetrical polygons may be the basis for simpler circlets. Polygons have long been fundamental to representation of the pattern of cognitive relationships with the world, notably in the various traditions of magic. They are effectively an articulation of the notion of "circling the cognitive wagons". They may figure as options for data representation in spreadsheet applications such as Microsoft Excel. The case for representation of strategically significant knowledge and functions in polyhedral form has been argued elsewhere (Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance, 2008; Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008). The argument has been extended to human values (Coherent Value Frameworks: pillar-ization, polarization and polyhedral frames of reference, 2008; Topology of Valuing: psychodynamics of collective engagement with polyhedral value configurations, 2008). Of particular relevance to the range of design possibilities is the software facilitation offered by Stella Polyhedron Navigator as discussed elsewhere (Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008). This is a particular example of the kind of tool required to enable global cognition (Envisaging the Art of Navigating Conceptual Complexity: in search of software combining artistic and conceptual insights, 1995).

Symmetry groups: In abstract algebra the symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation. Mathematically it is a generalization into many dimensions of the characteristics notably associated with polygons and polyhedra. Such symmetry is fundamental to any understanding of order, especially higher degrees of order that are typically beyond ordinary comprehension. Considerable importance is for example attached by mathematicians to the classification of finite simple groups and to the discovery of groups such as as the Fischer-Griess Monster -- a 196884-dimensional object -- believed to be fundamental to understanding of the structure of the universe. Similar importance is attached to discovery of the E8 Lie group -- a 248-dimensional object -- part of a family of closely related structures derived from Lie algebras. It is of significance in theoretical physics, in particular in string theory and supergravity. It is the basis of the radical unified field theory of Antony Garrett Lisi (An Exceptionally Simple Theory of Everything, 2007). The challenge of such comprehensive understandings of order lies in both their relative incomprehensibility and in their significance to the psycho-social realm in which people "live and move and have their being" -- and which is the preoccupation of sustainable governance. Whilst the efforts to represent the E8 Lie group (on the web for example) make clear its "beauty" (perhaps as the basis for a cognitive crown), it is unclear how these incredible objects relate to the disharmony which reigns in global society and in the lives of individuals. These issues and possibilities are explored elsewhere (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007; Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008).

Cognitive fusion: With respect to the military context, as noted above, consideration has been given to the integration of two technologies, temporal event correlation and case-based reasoning (G. Jakobson, L. Lewis and J. Buford, An Approach to Integrated Cognitive Fusion, 2004). This forms part of a more general concern with "information fusion" which is the focus of a journal (Information Fusion: an international journal on multi-sensor, multi-source information fusion) and of the International Society of Information Fusion, with its own fusion conference series and its Journal of Advances in Information Fusion. In the spectrum data, information, knowledge, wisdom, this explores considerations that might be considered a precursor to knowledge fusion (cf Richard Scherl, Introduction to Knowledge Fusion and Representation, 2004). This has been defined by Anthony Hunter (Fusion Rule Technology: a knowledge fusion framework for structured reports, 2006) as:

The question is the extent to which the "information" or "knowledge" focus bridges the gap to psychoactive engagement with that knowledge, even to its embodiment following the arguments of such as George Lakoff and Mark Johnson (Philosophy In The Flesh: the embodied mind and its challenge to western thought, 1999). This is the challenge speculatively addressed in the exploration of Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8) by exploiting the unusual cognitive challenges of the ITER nuclear fusion reactor. For such cognitive fusion, the unusual questions of complementarity and self-reflexivity, dematerialization and virtualization, coactive contextual relations, and the role of myth and symbol making were specifically addressed. How might the design of any such cognitive reactor be understood as a crown, recognizing the dynamic thereby introduced to what is otherwise understood as a static configuration? Given the role of the torus in such fusion reactors, the possibility of a toroidal aspect to the crown design merits exploration, if only as interlocking cognitive circlets (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006).

Cognitive work cycle and enantiodromia: Implicit in any sustainable strategy of cognitive organization is a dynamic sustained by learning/action cycles, as notably explored by Arthur M. Young (Geometry of Meaning, 1978) as discussed elsewhere (Characteristics of phases in 12-phase learning-action cycle, 1998). Democracy itself is supposedly sustained by some such dynamic. This points towards an understanding of any circlets as distinct cybernetic loops (possibly interlocking as a cognitive "crown"), necessary to the integrity of the system with which governance is engaged. The radical learning within such cycles may be fruitfully understood in terms of enantiodromia (Psychosocial Energy from Polarization within a Cyclic Pattern of Enantiodromia, 2007). The combination of continuity and apparent discontinuity in such cycles is usefully represented by the apparent paradox of the Möbius strip (Psychosocial Work Cycle: beyond the plane of Möbius, 2007). Circlets can of course be designed in the form of such strips which may be necessary to embody the discontinuities between different epistemological domains (Interrelating Metaphors -- to enable a cycle of transformation between epistemological modes, 2007). More intriguing is the possibility of integrating such strips to form a crown appropriately embodying paradox. Möbius Strips of different chirality can be used to form a Klein bottle -- perhaps an interesting design metaphor for any cognitive crown.

Metabolic pathways: These are successions of chemical reactions occurring within a cell, often regulated by a cycle where one of the products in the cycle starts the reaction again, such as the Krebs Cycle. Erich Jantsch (The Self-Organizing Universe; scientific and human implications of the emerging paradigm of evolution, 1980), in his wide-ranging synthesis of self-organizing systems and their implications for policy-making and human development, draws attention to metabolic transformation cycles such as the carbon cycle. The map of metabolic pathways could prove to be a very provocative challenge to organizational sociologists of the future (Doutor Pedro Silva, A general overview of the major metabolic pathways, 2002). More generally, WikiPathways: pathways for the people has been established to facilitate the contribution and maintenance of biological pathway information in an open, collaborative platform. From a general systems perspective, the set of interconnected metabolic cycles and pathways may well exemplify the kinds of transformation pathways which need to be identified for organizations. The set of cycles is a challenge to comprehend as a whole -- ironically even those operating within the human cell. Mnemonic assistance to students is however currently provided by a set of songs (Harold Baum, The Biochemists' Songbook, 1995). The design argument here raises the question of whether the cycles can be understood as circlets, interlocking to constitute a larger system. There is clearly the possibility of then configuring the set of circlets as a form of "crown" -- which could be "worn" in a virtual environment enabling interaction with information on each. This would enhance the current pathway browsing facility in list form.

Global modelling: The metabolic pathways example points the way to engaging with a range of systems of strategic relevance, irrespective of the challenges of cognitive fusion noted above. Of particular interest are the patterns of feedback loops resulting from studies of system dynamics, developed by Jay Forrester, notably as they informed the report to the Club of Rome on The Limits to Growth (1972, 2004). This approach has been complemented by that taken in compiling profiles of thousands of perceived world problems and advocated remedial strategies, and interrelating them in networks of aggravating or alleviating relationships (Assessment: Global modelling perspective Encyclopedia of World Problems and Human Potential, 1995). Experiments have been undertaken in detecting loops within such networks and representing them as 3D constructs in virtual reality, notably by projecting them onto polyhedra. As with metabolic pathways, such loops could be reframed as cognitive circlets and their interlocking relationships configured into "crowns" to be "worn" -- if only as a "crown of thorns" in the case of problem circlets.

Basket weaving: The traditional process of weaving vegetable fibers into a basket offers many design indications regarding the manner in which circlets could be interlinked to form a crown. The implications with regard to comprehension have been discussed elsewhere (The Future of Comprehension: conceptual birdcages and functional basket-weaving, 1980). There is of course considerable symbolism associated with basket construction, presumably with cognitive implications. This points to the merits of using such constructs to communicate complex patterns.

Song cycles and epic poems: These have long been used as a means of holding and communicating complex patterns of information, notably to enable coherent and appropriate action. Arguably melodies might be understood as circlets in this design argument. A famed example is of course the Ring Cycle of Richard Wagner. The suggested comparison (in Dimension 1) of the Davos Forum with Neuschwanstein -- dedicated to Richard Wagner (and appropriately decorated) -- becomes especially relevant to the chalenge of circlets. The drama of that cycle -- regarding a magic ring that grants the power to rule the world -- could be fruitfully adapted to the governance aspirations of the Masters of the Universe for which Davos had been a focus.

The innovative initiative of Franz Josef Radermacher (FAW - Institute for Applied Knowledge Processing, Ulm), in association with the Global Marshall Plan Initiative, illustrates the possibility of a step in a complementary direction. The 12 songs of The Globalization Saga: Balance or Destruction (2004) are presented as a CD accompaniment to a book.

Given the universal engagement with music -- in contrast to text -- there is a strong case for exploring new possibilities of embodying strategically meaningful information in music, song and poetry in which it can be appropriately configured to render larger and more complex patterns accessible -- as a "crown". The possibilities have been explored elsewhere (A Singable Earth Charter, EU Constitution or Global Ethic? 2006; Poetry-making and Policy-making, 1993). Given the importance of song and music to individual and collective identity within society, a case may also be made for recognizing how the cyclic organization of harmony sustains such identity (Emergence of Cyclical Psycho-social Identity Sustainability -- as "psyclically" defined, 2007).

BaGua and I Ching circular configurations: The significance of these arrangement, especially in Chinese culture and its understanding of the challenges of the governance of change, is discussed elsewhere -- notably in relation to configurations of policies (Towards Another Order of Sustainable Policy Cycles: insights from the Chinese Book of Changes, 1990; Documents relating to Patterns of I Ching / Tao te Ching; Challenges to Comprehension Implied by the Logo of Laetus in Praesens, 2007; Animation of Classical BaGua Arrangements: a dynamic representation of Neti Neti, 2008). Of particular interest are the mnemonic implications through the poetic use of metaphor.

Chladni patterns: The psychosocial implications of this phenomenon are reviewed elsewhere (Chladni Patterns: examples of integrated, multi-set concept schemes, 1984) raising the possibility of "cognitive chladnic patterns" (Polarities as Pluckable Tensed Strings: hypercomprehension through harmonics of value-based choice-making, 2006)

Adaptive cycle: The phases of this cycle, as presented by the Resilience Alliance, are considered vital to the precautionary strategic importance of resilience in ecosystems -- has recently been stressed in the synthesis by Thomas Homer-Dixon (The Upside of Down: catastrophe, creativity, and the renewal of civilization, 2006). The development of the concept is summarized by Aura Reggiani, Thomas De Graaff and Peter Nijkamp (Resilience: an evolutionary approach to spatial economic systems, Networks and Spatial Economics, June 2002).

Crop rotation: This is widespread farming prtactice of growing a series of dissimilar types of crops in the same area in sequential seasons for various benefits such as to avoid the build up of pathogens and pests that often occurs when one species is continuously cropped. As such it constitutes a powerful metaphor for many of the cyclic preoccupations highlighted here (Sustainable Cycles of Policies: crop rotation as a metaphor, 1988).

Organizational "rings": As mentioned aboved, in contrast both to the hierarchical focus of Dimension 1, and to partially ordered networks, widespreads reference is made to "rings", as in organized crime (drug rings, call-girl rings, criminal rings, carousel fraud), and web rings. A circle of contacts or a circle of friends offer other variants. Carousel fraud is usefully understood as part of a class of more complex transactional rings (possibly more appropriately considered in Dimension 3) where the exchanges enabling the existence of the ring to be inferred can only be detected using more complex analysis (as with software such as Netmap).

Circle of aesthetic associations: Whether simplistically in the form of a musical "round", or through architectural features which take the eye through a circuit, or through the structures developed in other arts, such circles (or cycles) offer a cognitive sense of completion.

A relevant perspective from Chinese culture regarding Dimension 2?
The Pivot of Chuang-tzu

Tao is obscured when men understand only one of a pair of opposites, or concentrate only on a partial aspect of being. Then clear expression also becomes muddled by mere wordplay, affirming this one aspect and denying the rest....

What use is this struggle to set up "No" against "Yes," and "Yes" against "No"? Better to abandon this hopeless effort and seek true light! .... But disputants continue to affirm and deny the same things they have always affirmed and denied, ignoring the new aspects of reality presented by the change in conditions....

When the wise man grasps this pivot, he is in the center of the circle, and there he stands while "Yes" and "No" pursue each other around the circumference.

The pivot of Tao passes through the center where all affirmations and denials converge. He who grasps the pivot is at the still-point from which all movements and oppositions can be seen in their right relationship....

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