Challenges to Comprehension Implied by the Logo
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15 August 2016 | Draft

Con-quest Aesthetically Reframed via the Concordian Mandala

Inspired by implications of the systemantics of the Discordian Mandala

- / -

Requisite attributes of a mandala relating concord and discord?
Concordian Mandala as container for con-quest in a game-playing dynamic?
Checklist of words prefixed by "con" with frequency of usage
Potential systemic implications of configurations of mandala polygons
Systemic ordering of constructive and destructive value and functions
Use of Concordian Mandala for a 2D ordering of value polarities
Use of Concordian Mandala for a 3D ordering of value polarities


The focus here on the Concordian Mandala derives from previous interest in the surprising importance of "con" as a prefix, as variously discussed (New Paradigms via a Renewed Set of Prefixes? Dependence of international policy-making on an array of operational terms, 2003; Primary Global Reserve Currency: the Con? Cognitive implications of a prefix for sustainable confidelity, 2011). The argument of the latter notably framed the preoccupation with respect to building and sustaining confidence, namely the integrative function of "con".

As discussed, of particular interest in global discourse are the controversial implications of the prefix "con", as used with both integrative connotations and those of condemnation or opposition -- of contrariness and contradiction. An annex provided an extensive listing of a selection of the words with the prefix "con" (Embodiment of Identity in Conscious Creativity: challenge of encompassing "con", 2011). A second annex focused on the current strategic preoccupation with building and sustaining confidence (Exploration of Prefixes of Global Discourse: implications for sustainable confidelity, 2011).

A subsequent paper explored further the possibility of configuring the cognitive implications of the contrasting uses of "con" in a comprehensible, integrative pattern (Considerable Conglomeration of "Cons" of Global Concern: eightfold constraint on constructive conflict control? 2012). Using the site offering a listing of 1947 words starting with "con", that paper reproduced the list of 643 most common words (with the frequency of occurrence per million words given in parenthesis in each case).

In a period of remarkable global discord, the following speculative exploration is inspired by the so-called Discordian Mandala to which reference is made in the Wikipedia entry on Borromean rings (recognized to be of fundamental significance as the 3D logo of the International Mathematical Union). The mandala is described in the controversial Principia Discordia, elaborated by Greg Hill with Kerry Wendell, as the provocative doctrinal manifesto of Discordianism. It was originally published under the title Principia Discordia or How The West Was Lost (1965). The name was intended to signify The Principles of Strife.

The focus here is on the possibility of reframing the ingenious Discordian Mandala as a Concordian Mandala -- by interpreting the former through the variety of connotations of "con". Given the ambiguity of those connotations, the concern is whether their suitable juxtaposition is suggestive of a means of transcending the constraints of the simplistic binary implications of "dis" versus "con".

This speculative possibility merits a degree of attention -- given the unfruitful conventional approaches to concord and conflict at this time. Seemingly it is too confidently assumed and asserted that desirable concord can be best achieved and sustained through conquest and control -- an assertion with which many would concur. However confidence building is itself increasingly called into question through its association with the duplicity of confidence trickery.

The argument here is that the widespread enthusiasm for use of "con", with its ambiguous implications, could be usefully understood as framing a quest for an elusive dynamic condition -- an inherently mysterious concept. This reframes con-quest as a confluence of connotations transcending conflict and contradiction. Rather than this being simply an artifact of English, it could be considered a factor unconsciously favouring the popularity of that medium.

The possibility was introduced in a previous exploration of the requirements for an adequate cognitive "container" for such contrasting connotations (Evoking Castalia as Envisaged, Entoned and Embodied, 2016). With respect to its comprehensibility and memorability, particular emphasis was given to the aesthetic requirements of such a dynamic configuration. This was specifically explored with respect to figures of speech, rhyme and game-playing in contrast to those of reason -- metapoetics versus metalogic. The necessity of a dynamic approach therefore contrasts here with the conventions traditionally associated with a "cognitively static" mandala (or other static concept maps and mind maps).

The Discordian Mandala is assumed here to be a valuable catalyst for any such exploration -- given its explicit association with the discord characteristic of problematic psychosocial system dynamics. These can be usefully framed as "systemantics", variously documented by John Gall (2003, 1986, 1978) and separately summarized (Why Systems Fail and Problems Sprout Anew: commentary on the principles of 'Systemantics', 1980).

In conclusion, consideration is given to use of the Concordian Mandala to order the pattern of 45 value polarities resulting from the Human Values Project within the context of the Encyclopedia of World Problems and Human Potential.

We Shall have World Gov''ernment... by Conquest or Consent.
Declaration by James Warburg to U.S. Senate Committee on Foreign Relations, 17 February 1950
(see commentary by Global Research)

Requisite attributes of a mandala relating concord and discord?

The Discordian Mandala can be understood as depicting cycles that are moving not in union, but in resonance, such that even in the discord, there is balance and equilibrium. Detection of resonance offers one reason for an aesthetic emphasis in this argument. The point can be made otherwise through reference to the use of "conquest" in a romantic context, namely widespread appreciation of the possibility of "romantic conquest".

Whilst the deliberate provocation of Discordianism can be deprecated or considered irrelevant, the current incidence of discord and conflict give cause for great attention as an inspiration for so-called "new thinking". With respect to the latter, the point has been variously made (Edward de Bono, New Thinking for the New Millennium, 1990; Luc De Brabandere and Alan Iny, Thinking in New Boxes: a new paradigm for business creativity, 2013; Ton Jö''''''''rg, New Thinking in Complexity for the Social Sciences and Humanities: a generative, transdisciplinary approach, 2011; Kees Dorst, Frame Innovation: create new thinking by design, 2015).

Much has however been made of the incidence of disagreement with respect to issues such as climate change. There has been little effort to study such disagreement with systems tools. Why not, if it is so fundamental? Are the tools adequate for the purpose, when disagreement is so rife within the sciences?

If the Principia Discordia was a provocative effort to frame the The Principles of Strife, a justification for the Discordian Mandala is nevertheless evident from the argument of Nicholas Rescher (The Strife of Systems: an essay on the grounds and implications of philosophical diversity, 1985):

For centuries, most philosophers who have reflected on the matter have been intimidated by the strife of systems. But the time has come to put this behind us -- not the strife, that is, which is ineliminable, but the felt need to somehow end it rather than simply accept it and take it in stride.

Structurally the Discordian Mandala (left-hand image below) is made of five interlaced irregular nonagons, fitted within an overall pentagon, as discussed separately (Cognitive Cycles Vital to Sustainable Self-Governance, 2009). No two nonagons are directly interlinked, but any three adjacent nonagons (for example, yellow, green and blue) are topologically in a Borromean ring configuration.

Discordian Mandala 5 Interlaced pentagons
Discordian Mandala

Interweaving: The Wikipedia commentary suggests the topologically-equivalent structure of 5 interlaced pentagons (on the right above) as being possibly easier to understand visually. Other suggested examples of linked structures with multiple Borromean ring configurations are shown below.

Borromean cross Borromean chain-mail

Writing at the time of the 2016 Olympic Games, the image on the left can be usefully contrasted with that of the Olympic symbol -- of lower complexity in that its elements do not form any set of Borromean rings.

Symbol of Olympic Games
Olympic symbol
Author: Pierre de Coubertin (public domain image via Wikimedia Commons)

Cross pattern: The "Borromean cross", contains four Borromean rings configurations such that no two circles are directly interlinked, and cutting the central loop frees the other four circles. As noted by Wikipedia, this could be interpreted as a Christian symbol, since it combines the cross with the Borromean rings (often used as a symbol of the Christian Trinity). However, a similar design (not Borromeanly-linked) is found as a Japanese mon in Handbook of Design and Motifs (1950), and may be occasionally used as a neo-pagan "five worlds" symbol.

Psychosocial implications: It is appropriate to note the contradictions traditionally associated with symbolic use of the pentagon as implied by its use in the Discordian Mandala, as discussed separately (Transforming from Paranoia through Metanoia and Hyponoia?, 2013). The contrast is evident in use of the following image promoted in religious contexts (possibly controversially). The Discordian Mandala, with its multiple Borromean rings, forms a Brunnian link in topological terms (namely removing any ring results in several unlinked rings).

Star pentagram

The cognitive implications of the Borromean knot (or ring), basic to the mandalat, are discussed separately in relation to the work of Jacques Lacan and Francisco Varela (Engendering holistic integration: Borromean knots and Klein bottles? 2010). The Borromean knot also figures -- as basic to the minimal stable concept -- in the work of Gordon Pask on his Interaction of Actors Theory, as extensively summarized by Nick Green (Interactions of Actors Theory, Kybernetes, 2004). Comments relevant to the above argument appear in a recent blog (Borromean Machine-Oriented Ontology, Strange Strangers, and Alien Phenomenology, LarvalSubjects, 24 July 2012).

Such imagery, and the associated arguments, are suggestive of the requisite complexity of any healthy dynamic interrelating paranoia with the other "noias". They are consistent with the self-reflexivity and paradox explored in the work of Douglas Hofstadter (I Am a Strange Loop, 2007) and its collective implication, discussed separately (Sustaining a Community of Strange Loops: comprehension and engagement through aesthetic ring transformation, 2010).

Concordian Mandala as container for con-quest in a game-playing dynamic?

In contrast with concord, it was previously argued that conquest could be suggestively (and provocatively) explored in terms of a quest for "con" -- as a confluence or configuration of the connotations of words with that prefix (Con-taining significance in the con-quest of the moment, 2016). That argument introduced the possibility of a Concordian Mandala through the dynamics of wordplay (Variety radically intoned through versification and wordplay, 2016).

Concordian Mandala
indication of a stage in the iterative adaptation
of the Discordian Mandala through a game-playing con-quest
Concordian Mandala

Challenges of the game: The introductory argument was framed in terms of playfully poetizing the quest for "con" through judicious attribution of terms (of which "con" is a prefix) to segments of the image above. In the quest for memorability of the pattern as a whole, con-testants in the game of con-quest are free to use any word-roots prefixed with "con-", as identified separately (Exploration of Prefixes of Global Discourse: implications for sustainable confidelity, 2011) and below:

Integrative implications: Whether in aesthetic or systemic terms, a prime consideration is the degree to which the resulting pattern is viable as a whole, perhaps in the light of the Viable System Model of cybernetics (as discussed further below). In that sense, does it embody requisite variety? Especially intriguing in restricting words to those prefixed by "con" is whether these enable such a coherent pattern to be constructed -- if only through the synonyms implied.

The outcome on each occasion effectively constitutes a "test" of the integrity engendered by "con". In the absence of any conventional conclusion, the process reinforces recognition of the elusive nature of "con" and its challenge to habitual modes of thinking and definition. In this sense, the playful allusions to the nature of "con" resembles those of traditional quest of alchemists for alkahest -- understood as the universal solvent capable of dissolving any container.

Symbolic container: Any periodic contest with the mandala thus explores the possible nature of such a container -- in dyamic cognitive terms, rather than in static physical terms.

The structure is sufficiently complex to be suggestive of a pattern that might be used to hold the complete set of Polti's 36 plots characteristic of human drama. These are presumably exemplified by the problematic dynamics of global governance -- effectively the pattern of narrative tunnels through which globality is variously imagined. The extent to which it achieves this may be indicative of its power as an attractor.

Comparable initiatives: As previously argued with respect to envisaging the glass bead game processes of an archetypal Castalia, rather than the univocal emphasis of the Eurovision song contest, the contest as a game constitutes a vast exercise in multivocal improvisation. The art involves the creative interplay of the variety of insights and functions with which "con" is associated, and by which it is transformed and modulated.

The contest could be compared to the periodic construction of an epic (like the Kalevala or the Mahabharata), or of a virtual temple (as with the periodic reconstruction of the Ise Grand Shrine in Japan). Through any game process the Concordian Mandala as a container for concord is constructed provisionally -- only to be recreated on a subsequent occasion.

This recalls the traditional Tibetan processes with respect to the Kalachakra Mandala, now cultivated through the International Kalachakra Network. Traditionally it has been constructed with coloured sand, and then destroyed (see Chart of the Elements in a Kalachakra Sand Mandala). Of particular relevance to this argument (as developed below) is the extensive investment in an interactive 3D variant of that mandala, accessible via the web.

Computer application: Of obvious interest is the implementation of the attribution of words (and other functionality) in an app which could be made widely available. This could including presentation of rhyming words (synonyms or antonyms) to enable selection -- as well as words with distinctive suffixes or prefixes. Aspects of this recall some computer implementations of Scrabble. One alternative is to offer clues to attributions to any segment, as is done with crossword design and dissemination.

The argument raises the question as to whether a variant of Scrabble could be based on rhyming of words in parallel columns/rows on the board. This clarifies the possibility within the mandala framework -- exploiting existing tools such as web-based rhyming dictionaries and their printed variants (Webster's Rhyming Dictionary, 2011; Sue Young, Scholastic Rhyming Dictionary, 2006).

Given the complementary argument for systemic correspondences, of further interest is whether checklists of these could be found in the spirit of general systems and pattern language research -- namely as "systemic rhyming".

Checklist of words prefixed by "con" with frequency of usage

Sources and clustering: The site offered a list of 1947 words starting with "con" (when accessed in 2012) for the earlier study (Considerable Conglomeration of "Cons" of Global Concern: eightfold constraint on constructive conflict control? 2012).

That site allows the words to be listed alphabetically, or by frequency of occurrence per million words. In that earlier document, these were clustered in three tables according to number of occurrences (More than 199; 50 to 199; Less than 50). A list of 643 most common words was presented there with the frequency of occurrence given in parenthesis in each case. The items from that source were however further clustered there by word root (eg "consider") and ordered by decreasing number of total occurrences per word root in the cluster (eg 902 for the "consider" cluster).

Clusters with less than 3 total occurrences were excluded from the main table. provides a further 1,304 less common words (presumably with occurrences less than 1 per million, which are then listed alphabetically on their site). It is unclear from what source the frequencies were derived and whether it has any English vs. American bias -- although this is irrelevant to the basic argument.

In those first tables (for greater than 49 occurrences), and purely for purposes of comparison, a count of Google search results for the root word is given (in millions). Note that these figures are purely indicative in that they derive from Google's use of stemming, which would tend to give unpredictable counts -- depending on the word stem used in the search, and Google's rules for interpretation of that root in any particular case, notably when ambiguity is possible. As a consequence, it is not clear what conclusions can be drawn from the comparison -- or any change implied for the ranking. A link was provided for convenience within each cluster to a definition of the term of highest frequency on the site of Clusters containing words of significant ambiguity were also flagged there.

The clustering by word root is of course tentative and could naturally be contested, especially since synonyms are not clustered together. This could significantly have changed the frequency ranking. Some clusters might also be usefully split.

Table legend: The following table (alphabetically ordered) endeavours to consolidate information from the previous exercises (adding details for the "total" and "Google" columns, but only for word-roots with more than 49 occurrences):

"Con-words" Total Google Implication? Use of the word-root with other prefixes
concatenate     -
conceal     -
conceit     deceit, receit
concentration 270 180 focus  
concept / conception / conceive 244 786 reflection, insight acception, contraception, deception, exception, inception, interception,misconception, perception, preception, proception, proprioception, reception, superconception, susception,
concern / concerning 490 418 potential danger decern, discern, excern
concert / concerted 67 1,200  
concession / concede     abscession, accession, decession, discession, incession, intercession, introcession, precession, procession, recession, retrocession, secession, succession
conciliation     domiciliation
concise / concision     abscise, circumcise, criticise, excise, incise, precise
conclave     enclave, exclave, inclave
conclusion / concluding 271 415 decision-making circumclusion, disclusion, exclusion, inclusion, interclusion, occlusion, preclusion, reclusion, seclusion
concoct     decoct, excoct, recoct
concomitant / concomitance     -
concord, concordance     accordance, discordance, recordance
concordat     -
concrete     accrete, decrete, discrete, excrete
concubine / concubinage     succubine
concupiscence     -
concur     excur, incur, intercur, occur, recur, reincur, transcur
concurrent     countercurrent, crosscurrent, decurrent, discurrent, excurrent, incurrent, intercurrent, occurrent, percurrent, recurrent, uncurrent, undercurrent,
concussion     discussion, excussion, percussion, recussion, repercussion, succussion
condemn / condemnation 58 45 blame-gaming  
condense / condensation     -
condescension / condescending      
condign     indign
condition / conditioning 511 2,020 dependencies dedition, edition, extradition, perdition, prodition, redition, sedition, tradition
condolence     indolence, redolence
condom     -
condone / condonation     -
conduct / conduction / conductor 192 510 conduit abduct, adduct, deduct, educt, induct, introduct,obduct, product, reduct, subduct, traduct
confabulate     -
confect / confection     affection, defection, disaffection, effection, infection, perfection, profection, refection
confederate / confederation     -
conference 252 970 dialogue circumference, deference, difference, inference, interference, preference, reference, transference
conferment / conferral     deferment, preferment, referment
confess / confession 54 59 truth-telling profess
confidence / confidelity 214 736 confidence diffidence
configuration / configure     defigure, disfigure, prefigure, refigure, transfigure
confine / confinement 68 22 restriction affine, define, diffine, prefine, redefine, refine, superfine
confirm / confirmation 198 697 "concrete proof" affirma
confiscate     -
conflagration     deflagration
conflation     inflation / reflation
conflict 159 347 afflict, inflict,
confluence     affluence, circumfluence, diffluence, effluence, fluence, influence, profluence, refluence, superfluence
conflux     afflux, deflux, efflux,influx, overflux, reflux, superflux, transflux
conform / conformity / conformance     biform, deform, efform, enform, inform, outform, perform, preform, reform, transform, unform, uniform, variform
confound     infound, profound, refound
confraternity     -
confront 73 68 truth-telling affront, effront
confusion 114 89 affusion, circumfusion, diffusion, effusion, fusion, infusion, interfusion, intrafusion, perfusion, profusion, refusion, suffusion, transfusion
confute     refute
congeal     -
congenial / congeniality     primigenial, primogenial, ungenial
congenital     -
congestion     digestion, disgestion, egestion, indigestion, ingestion, suggestion,
conglobation     -
conglomeration     agglomeration
conglutination     agglutination, deglutination
congregation / congregate     aggregation, disgregation, segregation
congress 121 477 aggress, digress, egress, ingress, progress, regress, transgress
congruence / congruity / congruent      
conjection / conjecture     abjection, adjection, dejection, disjection, ejection, injection, interjection, introjection, objection, projection, rejection,subjection, superinjection, trajection
conjecture     dejecture, projecture
conjoin / conjointly     adjoin, conjoin, disjoin, enjoin, injoin, interjoin, misjoin, rejoin, subjoin, underjoin, unjoin
conjugal     -
conjuration / conjuror     abjuration, adjuration, objuration
connect / connection 219 3,940 dependencies subnect
conniption     -
connivance / connive     -
connate / connature / connation     denature, ornature, transnature, unnature,
connoisseur     -
connotate / connotation     denotate
connubial     manubial, pronubial
conquest / conquer     request, inquest
consanguinous / consanguinity     ensanguine, exsanguine
conscience / conscientious 123 143 inscience, nescience, omniscience, prescience, unscience, overconscientious, unconscientious
conscious / consciousness lascious, luscious, multiscious, omniscious
conscribe / conscription     ascription, circumscription, description, inscription, prescription, proscription, rescription, subscription, superscription, transcription,
consecrate / consecration     desecrate, obsecrate, unconsecrate
consecutive     prosecutive, subsecutive
consension     dissension, presension
consensus / consensual 103 289 supersensual,
consent / consenting absent, assent, dissent, present, resent, unsent
consentient     assentient, cosentient, dissentient, insentient, presentient
consequence 192 152 outcomes subsequence
conservation / conserve 228 209 preservation, reservation
consider / consideration 902 893 systemic recognition desideration
consign / consignment     assign, cosign, countersign, design, ensign, obsign, resign, subsign, undersign
consignify / consignification     adsignify, presignify
consilience     dissilience, resilience, transilience
consimilitude     dissimilitude, verisimilitude,
consistence / consistency 195 188 composition absistence, insistence, overinsistence, persistence, resistence, subsistence,
consociation     association, dissociation
consolation / console / consoling     desolation, insolation, isolation
consolidate     -
consonance / consonant     assonance, dissonance, equisonance, resonance, unisonance,
consort / consorting     assort, besort, missort, resort
conspecific     nonspecific, subspecific, unspecific
conspicuous     perspicuous, transpicuous
conspiracy / conspiration     aspiration, inspiration, interspiration, perspiration, respiration, suspiration, transpiration,
constable     bistable, contrastable, instable, intastable, metastable, nonstable, prestable, unstable
constant / constance / constancy 92 445 predictability circumstant, distant, instant,restant, substant
constatation     -
constellate / constellation     -
consternation     prosternation
constitution / constituting 286 341 mandate, responsibility destitution, institution, prostitution, reinstitution, restitution, substitution
constrain / constraint / constraining 73 56 obstacles restraint
constrict / constriction / constringe     astriction, distriction, obstriction, presstriction, restriction
construct / construction 303 2,670 development,
"building the future"
destruct, instruct
construe     -
consubstantiate / consubstantiation     transubstantiate
consuetude     assuetude, desuetude, insuetude
consult / consultation 217 369 insult, result
consume / consumption     absumption, assumption, presumption, resumption, subsumption, transumption
consummate / consummation     missummation
contact 280 9,860 network intact
contagion / contagious     -
contain / container 400 1,040 attain, detain, distain, obtain, pertain, retain, sustain
contemper     attemper, destemper, distemper, mistemper, obtemper,untemper
contemporary / contemporaneity 65 639 cotemporary, extemporary
contempt / contemptuous     attempt, overtempt
content / contentment 178 6,910 satisfaction attent, detent, distent, extent, intent, ostent, portent, potent, retent, untent
contention / contentious     abstention, attention, detention, distention, intention, irretention, pretention, retention, sustention,
conterminous     -
contest 59 963 competitivity attest, detest, protest
context 200 656 intext, pretext
contiguity     -
continent / continence 59 289 abstinence, pertinence,
contingency / contingent     -
continuation / continuity / continuum 727 1,630 predictability  
contortion     detortion, distortion, extortion, intortion, retortion
contour     detour
contract 389 1,260 commitments attract, detract, distract, extract, protract, retract, subtract
contraction     abstraction, attraction, detraction, distraction, extraction, protraction, retraction, substraction, subtraction
contradiction 51 25 challenge  
contrast / contrasting 167 548 requisite variety  
contribution 311 583 support distribution, retribution,
contrition     attrition, detrition
control / controlling 811 3,700 governance, management  
controversy / controversial 64 179 conflict -
convenance     prevenance, provenance, souvenance
convene / convention / convent 149 597 circumvention, contravention, intervention, invention, obvention, prevention, subvention, supervention,
convenience     intervenience, prevenience, provenience
converge / convergence     devergence, divergence
conversance     -
conversation / converse 140 821 aversation, malversation, tergiversation, adverse, averse, controverse, diverse, everse, inverse, obverse, perverse, reverse, subverse, transverse, traverse, underverse, universe
conversion / convert 128 541 adversion, anteversion, aversion, contraversion, controversion, diversion, eversion, extraversion, extroversion, introversion, inversion, obversion, perversion, retroversion, reversion, subversion, transversion,
convert     revert, divert, subvert, invert, pervert
convey 56 83
convict / conviction 90 139 eviction, reviction
convince 86 118 "concrete proof" evince
convivial / comviviality      
convocation / convoke     advocation, avocation, devocation, equivocation, evocation, invocation, provocation, revocation, sevocation, univocation
convolution / convolute     advolution, circumvolution, devolution, evolution, intervolution, involution, revolution,

The frequency of occurrence of certain terms prefixed by "con" suggests that the more frequent are associated with more essential patterns of systemic understanding -- of how things work and of how to navigate through life. Those of lesser frequency could then be understood as secondary insights, whether or not they are associated with subtler insights into such navigation.

Any such distinctions suggest the value of contrasting functions framed by "con-words" in terms of how essential these are to degrees of understanding of systemic function. Can the operation of psychosocial systems be understood with a smaller set of such terms -- and what inadequacies become apparent through failure to use a larger set? More questionable is what system functions are not recognized through the emphasis accorded to "con-words", as might be suggested by insights from other languags?

Potential systemic implications of configurations of mandala polygons

Nesting: Offering the opportunity of further reflection is the possibility of nesting the Discordian/Concordian Mandala as shown below.

Nesting of Mandala

Pentagonal pattern: In highlighting the emergent pentagons, the mandala of nonagons can be further explored in terms of its use in two classical health patterns based on use of the pentagram in Western and Eastern cultures, as discussed previously (Memorable dynamics of living and dying: Hygeia and Wu Xing, 2014; Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012):

Hugieia 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

Given the depiction above of 5 interlaced pentagons as being topologically equivalent to the depiction of the Discordian Mandala, the 5 pentagons in the Concordian Mandala can be juxtapositioned in various ways which are potentially of further interest, as illustrated by the following animation.

Configuration of 5 interlaced pentagons
(provisional animation:
overlapping not yet coloured correctly)

Pentagramma Mirificum: Anticipating the discussion below of a 3D variant of the mandala, any quest for a configuration beyond discord can be usefully inspired by the discovery of the geometry of the so-called Pentagramma Mirificum. This originally proved to be fundamental to navigation of the globe, as separately discussed (Global Psychosocial Implication in the Pentagramma Mirificum: Clues from spherical geometry to "getting around" and circumnavigating imaginatively, 2015; Beyond dispute in 5-dimensional space: Pentagramma Mirificum? 2015)

Pentagramma Mirificum -- a non-regular spherical pentagon
As sketched by John Napier Gauss's sketch of Napier's Adaptation to Wu Xing pattern
Pentagramma Mirificum by Napier Gauss Pentagramma Mirifium

(Correlating a Requisite Diversity of Metaphorical Patterns: entuning the dynamic of cognitive eases and diseases, 2015) ****

Nonagonal pattern: The pattern of 5 nonagons in the mandala suggests consideration of the mandala in terms of the extensive literature reflecting on the system dynamics framed by the enneagram (A. G. E. Blake, The Intelligent Enneagram, 1996). Such consideration can be extended by the possibilities for its representation in 3D, as discussed separately (Correspondences between Traditional Constellations and Pattern Languages: requisite simplexity for sustainable comprehension of complexity, 2014).

Given that the mandala is composed of 5 nonagons, rather than pentagons, it is also of interest to consider the possibility of an analogous animation -- which may only be possible in 3D.

Especially intriguing is the manner in which their representation in the mandala can be better understood if each nonagon is tilted in 3D such that one edge is in a higher position, and another in a lower position. The 5 higher and 5 lower edges then form two distinct pentagons (by implication) -- one forming the external pentagon and one forming the internal pentagon, with thicker and thinner sides respectively. In 3D the mandala would then frame a kind of bowl in which the nonagons are regular (equal sided) rather than irregular as in the 2D image.

Systemic ordering of constructive and destructive values and functions

The assumption is that the clustering of terms prefixed by "con" merits consideration in systemic terms, especially given the relative ranking of the number of occurrences in each cluster. Higher level clusters of systemic significance could be made, as indicated in the eightfold pattern of clusters presented previously (Considerable Conglomeration of "Cons" of Global Concern: eightfold constraint on constructive conflict control? 2012). The question is then how many would be significance from a cybernetic perspective -- perhaps in the light of the Viable System Model.

One approach taken took the following form, as presented previously (Exploration of Prefixes of Global Discourse: implications for sustainable confidelity, 2011).

1.0 Structure / Order / Pattern

1.1 Boundednes / Integrity / Identity
1.2 Complementarity

2.0 Time  
3.0 Focus / Concern / Commitment

3.1 Intimacy / Entanglement
3.2 Empathy / Feeling

4.0 Agreement / Disagreement

4.1 Pattern / Norm
4.2 Visibility / Salience / Trickery / Subterfuge
4.3 Judgement / Opinion / Belief
4.4 Discourse
4.5 Deprive / Attribute

5.0 Engender

5.1 Influence
5.2 Outcome
5.3 Collapse / Fusion

6.0 Implication / Meaning

6.1 Knowledge

The Concordian Mandala suggests that these previous experiments could be fruitfully challenged in order to achieve a higher order of systemic integrity in the light of its 9-fold and 5-fold patterning.

Use of Concordian Mandala for a 2D ordering of value polarities

Given the 5x9 pattern of pentagons and nonagons, there is therefore a case for exploring the use of the Concordian Mandala as a means of framing a previous 5x9 clustering of value polarities. This pattern of 45 categories resulted from the Human Values Project within the context of the online Encyclopedia of World Problems and Human Potential.

The project undertook a very extensive review of "constructive" and "destructive" value-charged terms in English. To handle synonyms these were initially ordered as value polarities (synonym/antonym) guided by the ordering of Roget's Thesaurus. These words were used as a basis for relating values to perceived world problems (destructive values) and to proposed organizational strategies (constructive values) in the Encyclopedia.

Subsequently the value polarities were themselves clustered into a 5x9 pattern reproduced in the table below. An analysis of the original data corresponding to each cell is presented in separately in the commentary (see Figure 5 and Figure 6).

Clustering of value polarities (constructive-destructive)
Cluster type names are only indicative. Value polarities are detailed separately
Relative motion*complex 
Absolute properties*complex  
Relative properties*comp. 
Intellectual faculties*. 
Discriminative affection*complex  
  "Yellow" "Green" "Blue" "Red" "Purple"

Clearly the terms heading cells in each 9-fold column of the table can be allocated to a nonagon in the Concordian Mandala. Provisionally this could take the form indicated below.This allocation assumes that attributions to elements in a given nonagon could be subsequently adjusted in relation to those in another -- in the light of parallelism reflective of the 5-fold rows in the table. It should of course be stressed that the terms by which the cells were each named in the original exercise are arbitrary indications of generic notions for which adequate terms may well be elusive.

Attribution of value-polarity clusters to Concordian Mandala
(uncompleted preliminary exercise)

Questionable result: The process of attribution involved proceeding down the preceding table in which the columns (left-to-right) were considered to be associated with nonagons (coloured successively in the mandala as yellow, green, blue, red, purple). The requirement was that elements in each row (assumed to be associated with pentagonal parallels) should be in different colours (namely corresponding to different nonagons).

It became apparent that in the later stages of that process it bore a strong resemblance to the challenge of Rubik's Cube in that some earlier attributions required reallocation in order to position some later attributions appropriately. Further effort is clearly required with the possibility that all the attributions cannot be successfully made -- as indicated by unattributed segments of the mandala and a few terms from the table which have not been appropriately allocated to the image. Does the Borromean ring interlacing of the mandala preclude complete attribution from a table as attempted here?

Whether or not any such attribution is possible, the exercise highlights the need for a higher and more coherent order of integration for value polarities. The incoherence of widespread reference to "human values", as noted in the original Human Values Project, remains to be addressed in a global civilization that continues to appeal to such values.

Potential articulation: The words attributed to the mandala in the image above, as derived from the table cell headings, could readily be understood as too abstract. This in contrast to the articulation in the detailed processes of the project results from which they derived.

Several possibilities could be considered using web technology. The distinct elements of the image could offer mouseover pop-ups with greater detail of lower abstraction -- or could provide links to such details.

Another approach would be to make use of the value polarities in the table cells, perhaps attributing them to parallel versions of the mandala, especially if these were distinguished in terms of concord and discord. Missing is further considerations of the extent to which functions described by terms prefixed by "con" (or "dis") could then be highlighted.

Implications of a contrasting values quest? In contrast to the concern here with "ConQuest", a more recent formulation of the challenge of values has been made in a Club of Rome partnership with the Alliance for Religions and Conservation (Martin Palmer and Karl Wagner, "ValuesQuest": the search for values that will make a world of difference, 2013). As described on the ValuesQuest web page:

In March 2013 a partnership between ARC and the Club of Rome launched ValuesQuest, a radical programme of social, cultural and philosophical enquiry aimed at uncovering and challenging the values underpinning contemporary European society. The aim of ValuesQuest is to identify those values that would be needed for ensuring a safe, just and sustainable world for the future, drawing together contributions from (and discussions between) the worlds of the creative arts, psychotherapy and spirituality as well as politics and social theory. [emphasis added]

The initative could well be understood as deliberately embodying a fruitful paradox through seeking to make "a world of difference" through a radical quest for a particular set of values. This is perhaps exemplifed by the deliberate use of "radical" in a period when any form of radicalism is widely deprecated in the most extreme terms, as separately discussed (Radical Innovators Beware -- in the arts, sciences and philosophy: terrifying implications of radical new deradicalisation initiative in France, 2016). As a project with a European focus, is ValuesQuest liable to be subject to the surveillance and scrutiny of the EU Radicalisation Awareness Network (RAN)?

Unfortunately, as with many projects questing for a particular set of transformative values, the ValuesQuest project seems to fail to recognize that it is not new values that need to be discovered -- as a set of magical "silver bullets". Rather the need is for new ways of thinking systemically about sets of values that have long been articulated and variously upheld as a problematic basis for ConFlict and ConQuest. What may be required is a new ConFiguration of existing values -- whether or not this is to be understood and deprecated as "radical".

Values as psychosocial "flowers"? The relevance is clarified otherwise through aesthetic configurations of flowers and their petals, with which values have been so strongly associated traditionally -- as with mandalas. The association has been extensively explored by Keith Critchlow (The Hidden Geometry of Flowers: living rhythms, form and number, 2011; Islamic Patterns: an analytical and cosmological approach, 1999). Cut flowers are curiously valued as a means of enhancing conference venues, as discussed separately (Flowering of Civilization -- Deflowering of Culture: flow as a necessarily complex experiential dynamic, 2014; Taryn Simon, Finding Flower Power, On a World Stage, The Wall Street Journal, 16 February 2016).

The association with values has been explored even more explicitly and poignantly by Ann Elias (War and the Visual Language of Flowers: an antipodean perspective. War, Literature and the Arts, 2008; Exquisite Corpse: Flowers and the First World War. International Journal of the Humanities, 2007). The association is widely cultivated through the presentation of flowers on significant occasions and especially through the philosophy of ikebana.

There is therefore a huge metaphorical irony to the fact that the preservation of such valued symbols for their appreciation and study over time is conventionally achieved by pressing dessicated flowers -- into 2D. Any implications for the appreciation and study of values thus calls for careful attention. Clearly what is preserved in this way is only a distant indication of what is appreciated in flowers, whose primary expression is in 3D -- if not 4D. Should conventional reference to values be called into question from some such perspective, especially in the light of use of cut flowers for the period of a conference or ceremony?

There is the further implication that over time (namely in 4D) flowers grow and fade -- requiring that that cycle be re-engendered in some way to ensure their conservation. Is this also the case with respect to values -- as suggested by the rituals of mandala recreation and temple reconstruction mentioned above?

Use of Concordian Mandala for a 3D ordering of value polarities

Relationship to icosahedron: The relationship between 9-fold and 5-fold configurations also lends itself to exploration in terms of the icosahedron, The latter has triangular faces but can be understood as the interlacing of 12 pentagonal patterns (each composed of 5 triangles). The icosahedron is of particular interest as the focus for the management cybernetics of Stafford Beer in articulating the group integration process trade marked as syntegration (Beyond Dispute: the invention of team syntegrity, 1994). One review of this process, using electronic protocols, is provided by Paula Boyle and Peter Lloyd (Web-Weaving, 2007). This follows from earlier experiments organized by Stafford Beer and Gordon Pask, as separately described (Metaconferencing: discovering people / viewpoint networks in conferences, 1980).

Further insight is also to be derived from Stafford Beer's recognition of the association between the enneagram and the icosahedron, which he describes as emerging from collaboration with Joseph Truss -- in a chapter on The Dynamics of Icosahedral Space (Beer, 1994, pp. 196-209):

But it is a matter of great interest that in the whole of the literature... the enneagram occurs as a plane figure. Nowhere had there been the slightest hint that a three-dimensional manifestation existed... No wonder the search took so long, given that the diagram was discovered spread across four vertical planes... The icosahedron is the actual origin of the enneagram... (p. 206)

As Beer notes with respect to detection of the enneagram "hanging" within the icosahedron:

Consider: if it can be detected when the icosahedron stands on one vertex, it must be detectable when the model stands on any vertex. Moreover, if it is present when these two poles are aligned, it must be present when any two poles are aligned. Thus it comes about that points 4 and 5 on the enneagram refer to any side [meaning edge] of the icosahedron -- which therefore enfolds 30 three-dimensional, four planar, enneagrams... The icosahedral model conceived as a spinning sphere could be regarded as "an interpenetration of phi-ness"... an interpenetration of three-dimensional four-planar enneagrams... (p. 206-207).

A representation of the enneagram embedding is discussed separately (Representation of Creative Processes through Dynamics in Three Dimensions: global insight from spherical reframing of mandalas, the zodiac and the enneagram, 2014). This includes the following

9-fold enneagram embedded within an icosahedron
with addition of an indicative central sphere (constructed by manual modification of a virtual reality model of
the icosahedron generated by Stella Polyhedron Navigator software)
View of enneagram associated with only
one pattern of vertices of icosahedron
(view in 3D with virtual reality plugin)
View of enneagram from left image
with the icosahedron framework hidden
(view in 3D with virtual reality plugin)
Note the colour coding and positioning of the icosahedral vertices -- which offer guidance when rotating the above models in virtual reality in order to render visible the enneagram pattern. Green-Magenta links of the enneagram are the only links embodied within icosahedral edges (on the left), where they are invisible. Three of the 12 vertices, positioned on the vertical axis (of the image on the right), do not form part of the 9-fold enneagram pattern (Red, Cyan and Black). The various possibilities for rotating the models in three dimensions affect the proportions of the enneagram as portrayed and the relative visibility of the Cyan and Black vertices.

The earlier discussion offers additional visual renderings. Beer remarks with respect to mentation, both in individuals and groups, and the role of an information set (an " infoset"):

It is at least possible that the multiple enneagrammatic structure, reverberating as it does, provides a complex of linkages to constitute such a "corporate brain" that would then give rise to its own [infosettic] consciousness. (p. 208)

Icosahedral analogue? Clearly such an argument could well apply to the Concordian Mandala. This suggests the merit of seeking a polyhedral analogue to the icosahedron in 3D -- potentially one of greater complexity. This is consistent with the interest noted above in a 3D variant of the Kalachakra Mandala.

This 3D approach is further justified by the visual "deficiences" of the standard rendering of the Discordian Mandala (most notably the variable lie width). This suggests that the nonagons should indeed be tilted between the (proximate) surrounding pentagonal configuration and the (distant) pentagonal confiuration in the centre. The changing width of the lines of a given nonagon is consisistent with this assumption. The question is then whether the 5 nonagons could be arrayed across such an implied polyhedron within which they are effectively embedded.

In the quest for such a polyhedron, initial clues are provided by polyhedra offering a proximate (larger) pentagonal form and a distant (smaller) pentagonal form. Other clues are offered by the number of vertices or sides. Especially intriguing is the possibility that the embedding may only be achieved through two sets of 5 nonagons, namely 90 sides or vertices -- with 10 implied pentagons.

This would then suggest that separate mapping templates could be used for a "discordian" and a "concordian" ordering of value polarities. This would be consistent with one sense of traditional mandalas in which both are essentially illusory -- as conventionally understood.

Polyhedra suggestive of the possibility of embedding 5 regular nonagons
(potentially as 2 complementary sets of 5)
Truncated icosahedron
(90 edges of 2 types)
Drilled truncated icosahedron
(90 vertices of 15 types)
Images generated by Stella Polyhedron Navigator software

Initial efforts to construct the mandala in 3D using virtual reality software were only partially successful, due primarily to the relative incompetence of the author. A degree of greater skill would enable the possibility to be explored more appropriately -- notably in relation to Borromean ring interlocking with regular nonagons. Some preliminary results are indicated by the following images.

Concordian / Discordian Mandala in 3D
(stages in preliminary experiment -- "work in progress")

In considering this 3D mandala as an integrative mapping surface in relation to the 2D approach, of particular interest is the extent to which the pentagonal features (as yet not evident in the right hand image above) are emergent effects of perspective and therefore of cognition. With respect to the table above, it is these 9 sets of intangibles (indicated by pentagons) which are primarily associated with the rows of that table, whereas the more tangible systemic linkages are associated with the 5 columns of that table (indicated by nonagons).

The global interlocking of the nonagons is usefully consistent with considerations of quantum entanglement, whether with respect to the subtlety of human values or the complexity of so-called wicked problems. The challenge to comprehension necessarily calls on an aesthetic dimension, even one of mythopoeic nature, as envisaged by J. R. R. Tolkien as author of the epic tale The Lord of the Rings (1954). This has proven to be of exceptional global appeal, as discussed separately (Relevance of Mythopoeic Insights to Global Challenges, 2009).

Comprehension of the configuration of the Concordian Mandala could then be allusively compared to that tale -- described as governed by a complex "metric", with the scenario classically synthesized in poetic form:

Three Rings for the Elven-kings under the sky,
Seven for the Dwarf-lords in their halls of stone,
Nine for Mortal Men doomed to die,
One for the Dark Lord on his dark throne
In the Land of Mordor where the Shadows lie.
One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them
In the Land of Mordor where the Shadows lie.

As might be expected, there is indeed confusion to the configuration with which the concept of concord may be associated.

An entry in the Unionpedia: the concept map on Borromean rings and Three Rings notes that The Three Rings are fictional artifacts in Tolkien's legendarium (as indicated in the poem above). Although others have recognized this association, most remarkable is the mathematical work extending Borromean and Brunnian rings to new higher order versions, as explicated with numerous images (citing Tolkien) by Nils A. Baas (New States of Matter Suggested by New Topological Structures, International Journal of General Systems, 2012). This notes that in recent years some strange and counterintuitive states of matter have been observed in cold gases and nuclear systems.

The question to be asked is whether "strange and counterintuitive" insights are now urgently required with respect to viable configurations of human values variously conducive to concord and discord. Does Tolkien's intuited set of 20-plus rings lend itself to understanding otherwise, especially given the possible configuration of a "9-ringed" mandala -- for Mortal Men doomed to die?

Given the appeal of his speculative spirit, is discord to be understood as a strange form of "dis-ease" calling for more appropriate framing by metaphor (Memetic and Information Diseases in a Knowledge Society, 2008)? Is his set of rings somehow consonant with a yet-to-be-recognized set of metabolic pathways, mysteriously configured such as to sustain life (Memetic Analogue to the 20 Amino Acids as vital to Psychosocial Life? 2015). How might a Concordian/Discordian mandala be consistent with:

One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them


Nils A. Baas:

Stafford Beer. Beyond Dispute: the invention of team syntegrity. Wiley, 1994

A. G. E. Blake. The Intelligent Enneagram. Shambhala Books, 1996

Paula Boyle and Peter Lloyd. Web-Weaving. Taylor and Francis, 2007

Derek Cabrera and Laura Cabrera. Systems Thinking Made Simple: new hope for solving wicked problems. Odyssean, 2015

Keith Critchlow:

Edward de Bono. New Thinking for the New Millennium. Penguin, 1990

Luc De Brabandere and Alan Iny. Thinking in New Boxes: a new paradigm for business creativity. Random House, 2013

Kees Dorst. Frame Innovation: create new thinking by design. MIT Press, 2015 [contents]

Ann Elias:

John Gall:

Cecilia Heyes and Uta Frith (Eds.). New Thinking: the evolution of human cognition. Philosophical Transactions B, 367, 2012, 1599 [contents]

Ton Jörg. New Thinking in Complexity for the Social Sciences and Humanities: a generative, transdisciplinary approach. Springer Science and Business Media, 2011

Jeffrey C. King, Scott Soames and Jeff Speaks. New Thinking about Propositions. Oxford University Press, 2016 [review]

A. Leonard. Team Syntegrity: a new methodology for group work. European Management Journal, 14, 1996, 4, pp. 407-413.

Martin Palmer and Karl Wagner:

Marc Prensky. Before Bringing in New Tools, You Must First Bring in New Thinking. Amplify, June 2012 [text]

Nicholas Rescher:

Theodore Schick and Lewis Vaughn. How to Think About Weird Things: critical thinking for a New Age. McGraw-Hill Education, 2013

Joseph Truss, C. Cullen and A. Leonard. The Coherent Architecture of Team Syntegrity: from small to mega-forms. Team Syntegrity Inc. [text]

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