- / -
This exploration was triggered by a 9-fold pattern and has exploited certain correspondences based upon it. This follows from earlier explorations of patterns of N-foldness (Representation, Comprehension and Communication of Sets: the role of number, 1978; Examples of Integrated, Multi-set Concept Schemes, 1984; Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1984).
Such explorations raise the question with respect to any recognition of a set of categories or remedial initiatives: why is a set of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or more, considered comprehensive and complete in a given case. Why 9 in this case? Should the 9 rather be 8 or 10? In any taxonomic initiative, what is the pressure to increase the number of categories ("split") or reduce them ("lump them together")? As was first said of the mini-skirt, a primary criterion of concern in determining the size of any set is whether it is "short enough to cover the subject and long enough to be interesting". Too small and it does not appropriately reflect variety and limits recognition of the pattern of significant relationships between the elements. Too large and it is a challenge to learning, comprehension and memory.
In a society increasingly sensitive to the design of communications for wider comprehension and use, contracting or expanding sets is associated as much with how categories best "fit" together for mnemonic purposes as to the nature of the "truth" they represent (In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007). In a knowledge-based society experiencing exponential growth in the quantity of information, the situation can only become more challenging (Emerging Memetic Singularity in the Global Knowledge Society, 2009).
The question here is how a 9-fold set might indeed contribute to understanding of remedial responses to both lifestyle diseases and to planetary crises (as suggested by the above-mentioned presentation on "planetary boundaries"). One much-explored response is through the integrative insights associated with the traditional enneagram to which reference was previously made in discussion of In quest of systemic functional connectivity (in Recognizing the Psychosocial Boundaries of Remedial Action: constraints on ensuring a safe operating space for humanity, 2009). Another concern is how any particular number of categories, such as 9, can be fruitfully related to any preferred sets of a smaller number -- possibly more easily comprehended -- or to a larger set implying a more fundamental form of healing.
"Healing" may then be partially associated with recognition of how the integration of the larger number of categories or processes is achieved through patterns with any smaller number. "Healing" is then understood as a form of "integration" -- with a balanced pattern of processes, in contrast to the "imbalance" typically associated with systemic ills. In the case of the individual, this view is consistent with many approaches to psychotherapy. The notion of 'goodness of fit', signifiant to design, may be of some relevance to healing.
A classic example is the case of the Lo Shu magic square, long-known in China, illustrated by the following example (from Wikipedia).
(columns, rows and diagonals all total to 15)
Ordering the elements of the nine numbers in this particular pattern offers a simple metaphor of a high degree of "healing". The approach underlies the satisfaction -- a form of "cognitive healing" -- widely achieved by many through sudoku, where 9 such sets may form part of a more challenging frame with 81 positions.
A widely known mechanical model of the challenge of such integration is offered by Rubik's Cube, a 3-D mechanical puzzle invented in 1974. Over 350 million have been sold worldwide. In its original version, each of the six faces is covered by 9 stickers, chosen among six distinct colours (traditionally white, red, blue, orange, green, and yellow). For the puzzle to be "solved" -- by adjusting the faces to which the stickers are applied -- each face must be transformed into a single colour. There are many variations (including virtual forms), notably with more than nine faces per cubic surface. Some versions been produced with markings on all of the squares, such as the Lo Shu magic square (above) or the four playing card suits: spades, hearts, diamonds, clubs (Playing Card IQ Cube, the Rubik's cube for card players). The possibility of Rethinking Rubik's Cube: a mnemonic device for ways of knowing and engagement? has previously been discussed within the context of Existential Embodiment of Externalities: radical cognitive engagement with environmental categories and disciplines (2009).
The latter discussion was notably concerned with Individual motivation: radical possibilities in response to global crisis in terms of:
Using metaphors as catalysts and vehicles, it suggested an Exploration of "inner games": polarization, agriculture, construction, mining of potential relevance both to individual healing and to a more fruitful cognitive engagement with the environment.
To the extent that lifestyle diseases are partly associated with urbanization, it is appropriate to note the role of the magic square in urban planning in Chinaas reviewed by Alfred Schinz (The Magic Square: cities in Ancient China, 1996).
Overdefinition: As traditionally suggested within the Vedic philosophy of Neti Neti ("not this, not that"), and western classical recognition of the need for apophasis ("unsaying"), it would appear that "healing" might best be engendered by avoiding kataphatic closure on fixed definitions (Being What You Want: problematic kataphatic identity vs. potential of apophatic identity? 2008).
The dangers of premature closure -- in affirming "what is" -- might be understood as over-definition of "externalities". These could be considered as modelling errors of "subunderstanding", using the term of Magoroh Maruyama (Polyocular Vision or Subunderstanding, Organization Studies, 2004). Closure is likely to impose a degree of rigidity incompatible with the dynamics of a living system, whether an individual or the planetary environment (Hilary Lawson, Closure: a story of everything, 2001).
The nature of what tends to be lost through such conventional abstraction has been highlighted by Steven M. Rosen (Topologies of the Flesh: a multidimensional exploration of the lifeworld, 2006; Dimensions of Apeiron: a topological phenomenology of space, time, and individuation, Value Inquiry Book Series, 2004). He notes the manner in which the richness of psychosocial engagement with the world has been completely undermined by formal discourse -- an "eclipse of the lifeworld" in his terms. There is then every reason to suspect that this has problematic consequences for both the individual, in terms of lifestyle diseases, and for the planetary ecosystem. An essential dynamic is lost -- possibly involving vital feedback loops essential to health.
Embodiment: The question is therefore how to render explicit such paradoxical reflexivity and how cognitively to "embody" it in the light of the arguments of Francisco Varela (Laying Down a Path in Walking: essays on enactive cognition, 1997; The Embodied Mind: cognitive science and human experience, 1991) and George Lakoff and Mark Johnson (Philosophy In The Flesh: the embodied mind and its challenge to western thought, 1999). Such approaches have perhaps been most succinctly summarized by Jennifer Gidley (The Evolution of Consciousness as a Planetary Imperative: an integration of integral views. Integral Review, 5, 2007) to the effect that:
However, the growing awareness of a potential planetary crisis has highlighted the significance of finding new ways of thinking, if humankind is to move through our current complex challenges. This critical imperative appears to be mobilizing researchers from a wide range of disciplines to broaden the notion of evolution of consciousness beyond its biological bounds.
The case has also been argued as one of Being the Universe: a Metaphoric Frontier (1999).
'Embracing error": Donald N. Michael has appropriately argued with respect to both planning and learning, "On the requirement to embrace error", to the effect that:
More bluntly, future-responsive societal learning makes it necessary for individuals and organizations to embrace error. It is the only way to ensure a shared self-consciousness about limited theory on the nature of social dynamics, about limited data for testing theory, and hence about our limited ability to control our situation well enough to be successful more often than not (Learning to Plan and Planning to Learn, 1997)
It might then be suspected that any such "requirement to embrace error" merits consideration, if only tentatively or in alternation with other attitudes, as:
Although distinct, health-disease and wellness-illness are neither mutually exclusive nor polar opposites. Rather, they are one in the same process, acknowledging the changing person in the changing world. Wellness-illness is the human experience of actual or perceived function-dysfunction through the interaction of cognitive-affective dimensions. This experience arises out of intrapersonal, interpersonal, health-disease-related and extra-personal factors.
Military metaphors and conflict resolution: Military metaphors tend to be used (and recommended) in conventionally framing both the response to lifestyle diseases by individuals and to planetary problems by society -- as with the use of "fight" and "campaign" (Review of the Range of Virtual Wars, 2005). The appropriateness of such framing can however be challenged, as suggested above and previously (Missiles, Missives, Missions and Memetic Warfare: navigation of strategic interfaces in multidimensional knowledge space, 2001; Enhancing sustainable development strategies through avoidance of military metaphors, 1998).
There is the intriguing possibility that the skills long-developed for conflict resolution, peace and reconciliation could be adapted to the "military" response to both lifestyle diseases and to the problems against which any collectivity campaigns. The generic challenge in all three cases (violence, lifestyle diseases and other problems) is one of engaging with "otherness" -- potentially to be exemplified by any future contact with extraterrestrials ("Human Intercourse", "Intercourse with Nature" and "Intercourse with the Other", 2007 ; War against Terra, 2002). Of particular interest would be the application of the philosophy of the eastern "martial arts" to such reframing (Ensuring Strategic Resilience through Haiku Patterns: reframing the scope of the "martial arts" in response to strategic threats, 2006).
The extension of the classical logical dilemma to the quadrilemma reframes a constraining polarity: whether as wellness/disease for the individual or as crisis/non-crisis for the planet. Kinhide Mushakoji (Global Issues and Interparadigmatic Dialogue, 1988) has drawn attention to the relevance of the quadrilemma. This may be exemplifiedin the form:
|Distinction by de Bono||logic/truth||health/viability||judgement/evaluation||knowledge/certainty||states of matter|
|'water logic'||A and not-A
true and false
|both health and illness
both sustainable and unsustainable
|guilty and not-guilty
success and failure
|known and unknown
certainty and uncertainty
|neither A nor not-A
neither true nor false
|neither health nor illness
neither sustainable nor unsustainable
|neither guilty nor not-guilty
neither success nor failure
|neither known nor unknown
neither certainty nor uncertainty
The first two conditions (rows) correspond to the conventional binary logic -- famously given prominence in US foreign policy relating to terrorism by the declaration "You're either with us or against us", as previously discussed (Us and Them: relating to challenging others, 2009). Whether an individual is held to be suffering from a lifestyle disease may however also merit appreciation in terms of the last two conditions. This may be equally true of the health of planetary ecosystems. The distinction made by Edward de Bono between "rock logic" and "water logic" may be understood as between the first two conditions (together) and the last two (I Am Right, You Are Wrong: from this to the New Renaissance -- From Rock Logic to Water Logic, 1990).
With respect to this distinction, there is a charming degree of irony to the fact that inscribed on the gravestone of the poetic exponent of the last two conditions, namely John Keats, is the phrase: Here lies One Whose Name was writ in Water (at his request). As Keats pus it: A man's life is a continual allegory - and very few eyes can see the mystery of his life - a life like the scriptures, figurative.
A finer distinction might regroup the categories to distinguish "air logic" and "fire logic". The notorious poem of Donald Rumsfeld (The Unknown, 2002) drew attention to the distinctions with regard to the "known unknowns" from a strategic perspective, as discussed previously (Unknown Undoing: challenge of incomprehensibility of systemic neglect, 2008). It is of course Keats who articulated the aesthetic importance of negative capability: that is when man is capable of being in uncertainties, Mysteries, doubts without any irritable reaching after fact and reason.
The question is how such subtlety might be associated with more appropriate responses to individual health and planetary ills. With respect to the latter, it has notably been reported by Deutsche Welle (February 2010) with respect to the UN Climate Change Conference that:
Professor Adil Najam from Boston University, one of the authors of IPCC´s Fourth World Climate Report, the authors of which were awarded the Nobel Peace Price in 2007 along with Al Gore, said that Copenhagen was not a success and not a failure....
Individuals are perhaps most aware of this level of ambiguity in interpersonal relationships (eg she loves me; she loves me not; she loves me and she loves me not; she neither loves me nor does she not). Typically these conditions are recognized at various times in the dynamics of that relationship. In that sense, assessment of the relationship alternates between four conditions and may only be sustainable because of its resilience in being able to do so. In relation to the environment, people expect to engage -- effectively to "dance cognitively" -- between the extremes of rocky-flat, wet-dry, windy-still, and hot-cold. This capacity is the essence of resilience and the appreciation of nature in all its forms, especially by deep ecologists.
The argument here is that there is scope for exploring beyond simplistic understandings of what "is", whether from a scientific or other perspective. The emphasis here is on the contrasting qualities of knowing and engagement with categories. What "is", however this is asserted to be so, might then be understood as having the quality of "rock logic" in contrast with what it is asserted "not to be", namely "not-A" as contrasted with "A" in the table above). The certainty of both what "is" or "is not" is then to be contrasted with the uncertainties (a la Rumsfeld) between what might "both be and not be" or might "neither be nor not be". The suggestion is that these distinctions are reminiscent or echoed by the quality of the encounter with earth, air, fire and water -- then to be understood as mnemonic cues or metaphors. Contemporary tendencies to deprecate such distinctions is indicative of a form of cognitive entrapment -- typically in rock logic.
Cognitively there is a danger of entrapment either in the formal discourse that "eclipses the lifeworld" (as noted by Rosen) or in an associative discourse which lacks a structure amenable to the existing methodologies and disciplines on which governance depends. For some mathematicians, there may indeed be an elusive poetry to numbers (Sarah Glaz and JoAnne Growney, Strange Attractors: poems of love and mathematics, 2008). Such comprehension is however only accessible to the few. Projecting integrative meaning -- vital to "health" -- into patterns of numbers, however rich and elegant to the eye, is problematic for most, whatever their satisfaction with pattern completion in sudoku (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008). The matter has been fruitfully discussed by Marie-Louise von Franz (Number and Time, 1974)
Dependence on numbers -- notably by administrative "bean counters" -- is intimately related to the danger of falling victim to the formal discourse challenged (above) by various authors. There is every probability that "health" is associated with a more appropriate relation to the "lifeworld", however that is to be understood. Indeed, in the case of lifestyle diseases, it is this relation which has been severely undermined, as is recognized in their definition. Curiously the definitional focus on the disassociation from nature in the lifestyle excesses of industrialized societies obscures the dysfunctional relationship to the environment in the case of the impoverished in developing countries. They might be appropriately understood to be vulnerable to "lifestyles diseases of deficiency" rather than of excess. It is regrettable that the term should have been appropriated to imply that "lifestyle" is a condition characteristic of the relatively privileged, especially when the quality of life 'pre-development' has been recognized to be superior to that 'post-development' in many instances.
Arguably the ills of the planet as a whole arise from a similar disassociation from the lifeworld on the part of human society. This may to some degree be recognized through the increasing emphasis of government on narrative, photo opportunities and spin. Laurence Gonzales demonstrates that modern man has fallen into a pattern of creating scripts for his daily life that prevent him from thinking critically about his surroundings (Everyday Survival: why smart people do stupid things, 2008). Appropriately his study is itself praised for its narrative style.
Of interest therefore is the possibility of some form of hybrid cognitive device, perhaps a "metaphorical formalization", to serve as a kind of "cognitive prosthetic". This could catalyze and enable a healing process. It would be characterized by both the relational formalization of mathematics and the metaphoric richness with which people so readily engage. In the healing process it would effectively assist in "re-membering" -- a "mnemonic catalyst" as mentioned above. Curiously the patterns and processes of the environment offer a rich source of metaphors to this end -- if not the richest.
The challenge is appropriately and fruitfully to "bond" metaphors cognitively to a formal structure. Aspects of this challenge have been explored previously (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009; Geometry, Topology and Dynamics of Identity: cognitive implication in fundamental strategic questions and dilemmas, 2009; Metaphorical Geometry in Quest of Globality in response to global governance challenges, 2009; Topology of Valuing: psychodynamics of collective engagement with polyhedral value configurations, 2008).
It is too readily assumed that the patterns appropriate to the healthy integration of individual or planetary systems, and of both together, are relatively simple and comprehensible. It is therefore useful to note the extreme forms of beauty and elegance detected by mathematicians in the most profound forms of symmetry held to be fundmental to the organization of the universe. Examples include the Gosset 421 polytope (an' 8-dimensional semiregular uniform polytope composed of 17,280 7-simplex and 2,160 7-orthoplex facets') and the Fischer-Griess Monster a group of finite order ('a giant snowflake in 196,884 dimensions composed of more elements than there are supposedly to be elementary particles in the universe, namely approximately 8 x 1053 '). Known as the 'Monster', for mathematicians it might ironically be considered the essence of 'Beauty'. The significance of the Monster is briefly well-summarized by Marcus du Sautoy (Finding Moonshine, 2007; Patterns that Hold Secrets to the Universe). The clues to its existence gave rise to a literature on 'monstrous moonshine'. It is certainly monstrous in the challenge it constitutes to comprehension -- evoking a sense of deep 'unease', perhaps to be associated with 'disease'.
The question this raises is whether comprehension of this 'monstrous beauty' provides a vital key to 'health' -- as the ultimate form of beauty (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007). Might it indeed involve processes highlighted in myths regarding the archetypal encounter between Beauty and the Beast? (Poetry-making and Policy-making: arranging a Marriage between Beauty and the Beast, 1993).
|Tyger, tyger, burning bright
In the forests of the night,
What immortal hand or eye
Dare frame thy fearful symmetry?
(William Blake, 1757-1827. The Tyger)
The panoply of organic molecules essential to life, based on the "benzene molecule", suggests the possibility of a "metaphoric chemistry" of some kind -- of relevance to quality of life. This might be analogous to the resonant structure of the benzene molecule -- essential to the constitution of living organisms -- perhaps even a form of "alchemy". This might be understood as a connective device for a variety of (complementary) metaphors such that each might take precedence under certain circumstances. The contrast between such metaphoric "organic chemistry" and a corresponding "inorganic chemistry" might be seen as equivalent to that between de Bono's "rock logic" and "water logic" -- both of course being essential to daily life as it is known.
Of great interest in this respect are the long-articulated and much-respected systems of the 64 hexagrams of the I Ching and the 81 tetragrams of the Tao Te Ching and the Tai Hsuan Ching. With the elements of each a metaphor is traditionally associated -- better to be understood as "cognitively bonded". Such metaphors have been the subject of extensive reflection and commentary. Arguably such hexagrams may be considered as a kind of cognitive analogue to the hexagonal pattern of the benzene molecule -- notably in the light of the alternation by which the latter is characterized as a resonance hybrid fundamental to life of any kind (Patterns of Alternation: cycles of dissonance and resonance, 1995). The representation of the benzene molecule is of course a conventional formalization of a dynamic articulated through molecular orbital theory. This makes apparent that the benzene molecule is not as it is simplistically represented for human comprehension.
The six lines of an I Ching hexagram are made up of two trigrams. In Chinese culture, the set of 8 trigrams are conventionally widely represented in a BaGua circular configuration (often surrounding a "BaGua mirror") and held as such to carry some fundamental philosophical insights (cf Stepping into, or through, the Mirror: embodying alternative scenario patterns, 2008). That pattern is also related to the numeric arrangement of the Lo Shu magic square (above, and included in the representation below) and to the practice of feng shui. That practice points to valued traditional understandings of an interface between individual health and a "healthy" environment. References are indeed increasingly made to the use of feng shui in response to lifestyle diseases -- perhaps a case for further investigation, given the predictions of increase in such diseases and the challenge they seemingly pose.
Typical schematic representations of 8-fold Ba Gua (Pa Kua) Mirror
The possibility of a methodology characterized by a tentative dynamic (as suggested above) can be usefully framed in terms of playfullness, as previously argued (Playfully Changing the Prevailing Climate of Opinion: climate change as focal metaphor of effective global governance, 2005). This dimension is notably evident in engagement with Rubik's cube and sudoku to achieve a "solution" -- and especially in sustaining interest in repeated pursuit of such a quest. The argument here is that the continuing quest for a desirable outcome through such a process can contribute insights into that of achieving and sustaining "health". Arguably there is a correspondence between "health" as "balance" and any "solution" as a pattern of "symmetry" -- especially when understood as the creative process of "patterning" balance and symmetry rather than any single static outcome. The oscillating bonds of the benzene molecule as a resonance hybrid might then even be understood as "playful".
From the perspective of recreational mathematics the approach is effectively one of playing with patterns of numbers. The 3x3 framework (above) can be used to highlight this. It suggests the question: what might be a balanced "healthy" pattern and how many constituents might be required to represent it meaningfully in the light of understandings of requisite variety.
|Indication of patterns of symmetry on 9|
|4 or 5||5 or 4||8 and 1|