Meaningful configuration engendered only by tacit aesthetic entanglement

Concordian Mandala as a Symbolic Nexus (Part #3)

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The dynamic rendering of the mandala can, under certain conditions, be such that the 5 nonagons do not touch -- fulfilling the quest for a Borromean configuration. Other variations of the parameters may be such as to ensure they touch only occasionally, or that some always intersect. The argument here is that any such touching can be usefully reognized as a dysfunctional condition in which the processes associated with the distinct nonagons interfere with each other in some problematic manner.

The interest here is in a Borromean condition of the mandala in which the nonagons do not touch but are entangled through being looped together. It is in that condition that pentagonal configurations between the nonagons become especially apparent. The point to be stressed is that any pentagonal arrangement is an emergent perceptual effect for the observer. The nonagons are not connected in any such manner. There are no pentagons in the geometry of the set of nonagonal polygons. It is this particular arrangement that calls for further consideration.

Coherence through correspondence and proportion: The emergent pentagonal patterning suggests that the sense of order derives only from an aesthetic recognition of symmetry. It is not a feature of direct connectivity between the nonagons. Their relationship is then better understood in terms of correspondences. Understanding the latter has long been of interest to both the arts and the sciences (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007).

Rather than logical connectivity, the coherence then derives from an aesthetic harmony of perceptual symmetry and proportion rather than any conventional logic of unified systemic coherence.

With respect to the patterns in nature and architecture appreciated for their aesthetics, considerable attention has been given to the cognitive role of the golden ratio (phi). Of some relevance to this argument is its association with the regular pentagon and -- potentially -- as the growth factor in the golden spiral. (*** ching papers Fibonacci???) The Fibonacci spiral: an approximation of the golden spiral

• requisite cognitive twist / tilt to get non-touch
• ex not a contact -- confusion/conflation:
• affinity / mutuality
• mutual recognition
• implication rather than explication
• emergence of pentagons as integrating perceptual "illusion"/intangible -- pattern of symmetry
• equivalent in forms and patterns to the "poetic" beauty perceived in the distinctive characteristics and correspondences of numbers and constants -- beauty is truth

Interwoven threads: The nonagons can be usefully understood as "interweaving". The 5 9-phased threads pass over or under each other -- characteristic of what is recognized as warp and weft in weaving. Although that metaphor suggests that the threads touch, they are not connected as in a knot, nor do they intersect.

Rather than the conventional focus on connectivity, the weaving metaphor can be explored in terms of its significance for governance (Warp and Weft of Future Governance: ninefold interweaving of incommensurable threads of discourse, 2010; Warp and Weft: Governance through Alternation: world governance as a Gandhian challenge for the individual, 2002).

The weaving can also be usefully recognized in aesthetic patterns such as the Celtic Knot, or the so-called Endless Knot -- both valued for their symbolism. Although these terms use "knot", this refers to the pattern as a whole. As noted below, the threads of which they are composed are not knotted together. The mandala could then be considered a knot of this kind.

Bridging processes: An alternative metaphor is that for traffic, where there may be an overpass (a bridge) or an underpass (an arch). This metaphor is valuable because of the experiential engagement with either a bridge or an arch and the sense of separation offered in each case when traversed. This is a feature of traffic understood more generally (Being in the Flow on Strategic Highways and Byways: enabling sustainable self-governance through traffic signage, 2011). Whether as an arch or as pillars the experience may well characterize initiation rituals.

Fairly frequent use is made of the bridge metaphor to offer a particular sense of connectivity across what is otherwise perceived and experienced as an impassable gap. Of particular relevance to this argument is its use as the title of the Bridges Organization. This oversees the annual Bridges Conference on mathematical connections in art, music, architecture, education, and culture.

"Kiss-touch" connectivity: The tensegrity (tensional integrity) structures developed by Buckminster Fuller are of a form which is unique in addressing the challenge of using polarized (incompressible) elements. Without touching each other (as in conventional construction), these are configured and held in position by a continuous network of associative elements in tension. At most any "touching" is, as in geodesic domes, what was technically termed a "kiss touch" (by Fuller) -- being of no load bearing significance.

The last characteristic could be seen as a vital requirement in configuring polarized values, clashing cultures and other forms of binary thinking and relationship, into larger structures reconciling (but "respecting") their differences (From Networking to Tensegrity Organization, 1984). It thereby creates a free central space uncluttered by central "pillars" (as is normally the case). indicative of points of contact which do not affect each other through the transmission of stress or strain.

However, if Fuller's "thinking" is to be understood in dynamic, process terms, then the degree to which separate domains touch is indicative of a potential cognitive transition point from one to another -- potentially vital for the cognitive coherence of the pattern as a whole. Thinking then "moves" into a different loop essential to sustaining the whole -- a feedback loop to be understood in terms of knowledge cybernetics (Maurice Yolles, Knowledge Cybernetics: a new metaphor for social collectives, Intellect, 3, 2006, 1).

This argument is a feature of various separate discussions (Transforming Static Websites into Mobile "Wizdomes" enabling change through intertwining dynamic and configurative metaphors, 2007; Engaging with Globality through Dynamic Complexity, 2009). The underlying tensegrity principles have notably been used to describe cellular architecture (Donald E. Ingber, The Architecture of Life, Scientific American, 278, January 1998).

With respect to Value polarities as archetypal bonds (2007), the symbolic subtlety of such a bond was illustrated by the following much appreciated image.

Creation of Man by Michelangelo (Sistine Chapel) as an indicative representation of the subtlest relationship bond (as discussed below with respect to the "kiss touch")

Of interest in the architecture of a geodesic dome, dependent on such a kiss-touch, is the emptiness of its centre -- with no supporting beam across it -- as has been appreciated in its symbolic value. This structural characteristic may be appropriately contrasted with the unfruitful "pillarization" of values and strategic intiatives, as with those of the European Community (as discussed in Challenge of "soullessness" -- beyond the "pillar-ization of Europe", 2004).

Requisite disconnectivity: There is of course widespread concern with the value of connectivity, assumed to be a prerequisite of harmonious global civilization. It is typically framed and promoted as fundamental in the quest for unity and unification in the sciences, the arts and religion. The focus of fundamental mathematics is primarily on connectivity although there is a degree of concern with disconnectivity (Xing-Ke Wang and Shang-Wang Tan. Ordering trees by algebraic connectivity Linear Algebra and its Applications, 2012).

Of some relevance to the development of this argument, as noted by Wolfram Mathworld:

Disconnectivities are mathematical entities which stand in the way of a space being contractible (i.e., shrunk to a point, where the shrinking takes place inside the space itself). When dealing with topological spaces, a disconnectivity is interpreted as a "hole" in the space. Disconnectivities in space are studied through the extension problem or the lifting problem. [see also disconnected space]

Disconnectivity in a wide variety of forms is conventionally regretted, if not deplored as being the antithesis of togetherness -- as epitomised by apartheid and alienation. Everything should supposedly be connected to everything.

Following the problematic religious practices of shunning, excommunication and disfellowship, it has become the focus of controversy in the case of disconnection as a practice in Scientology. This is the severance of all ties between a scientologist and any friend, colleague, or family member deemed to be antagonistic towards Scientology. Such disconnectivity could be explored in terms of confirmation bias -- perhaps to be understood as "conformation bias".

There is little recognition that requisite disconnectivity may be vital to connectivity of some "higher order" -- however that is to be understood. This is most obvious in electrical wiring and printed circuit boards where insulation between components is vital to the functioning of the whole. It is also evident in music. Appropiate disconnectvity is in fact vital to the operation of many systems in nature or in manufacturing processes. This is appreciated through recognition of the need for biodiversity, for example.

As a form of disconnection, far less understood are the implications of avoidance of issues and systemic neglect (Institutionalized Shunning of Overpopulation Challenge: incommunicability of fundamentally inconvenient truth, 2008; Vigorous Application of Derivative Thinking to Derivative Problems, 2013).

Potentially more challenging is the sense in which connectivity, as the cultivation of a form of universal intimacy conventionally understood, may effectively inhibit disconnectivity of another kind -- notably appreciated through the need for "space". This follows from provocative arguments that any "other" connected in this way is thereby reified to a degree in being disconnected as an "object" from the perceiver.

This disconnection can be explored in terms of extimacy (in contrast with intimacy) and the obverse (in contrast with reverse), as eloquently presented by Donald Kunze (Atlas of the Obverse, 2012). Extimacy (as defined by Jacques Lacan) is thus a poorly explored complement to intimacy, indicative of the existence, within the most intimate sphere of the I, of an "other", that which is external to the individual and with which the individual identifies.

The relation between obverse and reverse can be explored otherwise in terms of Chinese philosophy, as carefully clarified in relation to healing by Electra Peluffo (Cosmological Origins of the Obverse-Reverse Zang Fu Pairing in Chinese Medicine, Chinese Medicine, 2014, 5, 270 -276):

Chinese thought gives us a vision of the world based on the pairing among other concepts. And by using this word we want to describe becomingness or a process which starts from a duality in permanent interaction: opposition and complementariness as a result of a parallelism.

By contrast it is surprising to note that obverse and reverse are most frequently cited in western literature in relation to the two faces of coins. The particular relevance is that this is with respect to the primary token of mutual confidence -- the coin.

These various associations suggest that, in the quest for for unifying insight, the universal and the universe might be more meaningfully explored through a curious form of cognitive resonance between reverse and obverse. The health metaphor thus offers a way of reframing this quest (Remedies to Global Crisis: "Allopathic" or "Homeopathic"? Metaphorical complementarity of "conventional" and "alternative" models, 2009).

Preoccupation with diversity as a requisite complement to unity may be a form of distraction when some kind of contraction is essential. The may become evident through the inadequacy of "multiverse" as the new complement to universe (Transcending both scientific and poetic comprehension of multiverse, 2012).

Separation of "powers" and resources: Understanding of requisite separation and disconnection is widely recognized in terms of seemingly disparate domains. Constitutional law takes careful account of the need for separation of powers. Typically the state is divided into branches, each with separate and independent powers and areas of responsibility so that the powers of one branch are not in conflict with the powers associated with the other branches. Responsibilities are divided to limit any one branch from exercising the core functions of another. The intent is to prevent the concentration of power and provide for checks and balances. Typical branches include: executive, legislative, judicial, auditory, electoral, and prosecutory. Importance may also be attached to the separation of church and state -- "church" being understood as religion of any kind.

Particular attention may be given in system design to the isolation of resources, most notably to ensure that such systems fail safe in the event of any failure or as the result of any attack -- preventing any cumulative domino effect. Redundncy may then be values. Such separation is a vital preoccupation when exposed to any form of cyber-attack on information systems.

Understood in terms of any form of covert operation, requisite separation is clearly a valuable strategy for both cartels and organized crime. Arguably any covert collaboration between major corporations, may depend on such separation as a means of avoiding exposure to public criticism and investigation -- despite the connectivity offered by "old boy networks" and interlocking directorates (see Wikipedia List of people on multiple governing boards). Such possibilities enable plausible deniability ensuring that no concrete evidence of involvement can be legally proven (especially when covered by non-disclosure agreements or superinjunctions). This is especially important when there is recourse to so-called "dirty tricks".

Such protective measures have however been of considerable importance in the design of intelligence networks to ensure that detection of one cell does not jeopardise the continued operation of other cells and their personnel. Use may be made of a cutout -- a mutually trusted intermediary, method or channel of communication -- to facilitate the exchange of information between agents. Cutouts usually only know the source and destination of the information to be transmitted, but are unaware of the identities of any other persons involved in the espionage process. A captured cutout cannot therefore be used to identify members of an espionage cell.

Tacit bonds and soft power: A contrast can be recognized between well-defined and undefined contacts in a variety of domains:

• clear-cut definitive linkage characteristic of the obligations entailed by "hard power" can be usefully contrasted with tacit links better recognized in terms of so-called "soft power". This is the ability to attract and co-opt, influencing the preferences of others noncoercively -- ensuring change through relatively less transparent channels.
• chemistry offers the contrast between inorganic and organic bonds, potentially valuable as a metaphor -- especially in terms of "resonance"
• in interpersonal relationships, a distinction can be made between contractually defined bonds and those framed by such terms as fraternity, community, mutuality and affinity

The distinction invites the kind of encoding offered in Chinese culture by the distinction between yang and yin. This in turn highlights the unresolved dynamics between male and female, and the masculine exclusivity implied by fraternal bonding.

Requisite variety: As increasingly acknowledged with respect to biodiversity, the design considerations are of more general relevance from a cybernetic perspective in terms of requisite variety. Far less attention has been devoted to the requisite degree of socio-diversity (Sabine U. O'Hara, Valuing socio-diversity, International Journal of Social Economics, 22, 1995; P. Dansereau, Biodiversity, ecodiversity, sociodiversity: three aspects of diversity, Aspen Bibliography, 1997, 1535).

More controversially this may be recognized to be of relevance to the requisite variety of modes of intelligence, as argued by Edward de Bono (Six Thinking Hats, 1985; Six Action Shoes, 1991), or with respect to the 9 team roles identified by Meredith Belbin (Belbin Team Inventory).

Missing from such consideration is a means of creatively reframing the highly controversial issues associated with the perceived need for separation by gender (men, women, transgender, etc), ethnicity and race, culture and education, and otherwise -- as is so vigorously (and violently) argued in various contexts (Cultivating the Myth of Human Equality: ignoring complicity in the contradictions thereby engendered, 2016).

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