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l June 2015 | Draft

Correlating a Requisite Diversity of Metaphorical Patterns

Entuning the dynamic of cognitive eases and diseases

-- / --

Systemic organization of diseases and eases?
Relevance of weather metaphors to existential unease
Psychosocial unease and cognitive weather
Crises framed by weather metaphors
Cognitive implication in a Chinese system articulated through weather-related metaphors
Interpretations of patterns of empowering and disempowering conditions
Path-ology: eliciting dynamic patterns of empowering and disempowering conditions
Beyond dispute in 5-dimensional space: Pentagramma Mirificum?


This is an exploration of a methodological possibility of dynamically interweaving disparate threads which might thereby offer integrative insight. This follows from an earlier discussion (Interweaving Thematic Threads and Learning Pathways, 2010). Threads considered are:

The central focus is on the varieties of psychosocial unease and how engagement with them might be more fruitfully articulated through weather as a metaphor -- given the extent to which weather metaphors are used to frame social crises. There is a familiarity and coherence to weather which suggests that its patterns may offer ready access to greater experiential insight than is offered by more conventional models. It could be considered extraordinary that a term like "depression" is used to explain both weather and economic phenomena at a time when it is also recognized as an increasingly widespread form of individual unease and personal agony..

The question is whether there is a recognizable pattern of any value to such connectivity -- and for whom. The question might itself be framed through a metaphor of animal movement and how it is enabled or constrained in a natural environment. The organization of knowledge is readily compared to tree structures (Humberto Maturana and Francisco Varela, The Tree of Knowledge: the biological roots of human understanding, 1992). Understood as information silos, what kind of movement between such "trees" is possible and by whom? Clearly some apes can travel easily by swinging from tree to tree. For others movement is constrained to branches of individual trees, with aversion to the risk of going to ground level in order to climb another. For birds there is much less constraint on connectivity. Ground dwellers are faced with different kinds of constraint, notably when faced with water barriers to movement, unless able to swim.

The issue can also be explored through correspondences as enabling cognitive transitions, as clarified separately (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007). This has been highlighted in the case of so-called moonshine mathematics associated with symmetry group theory -- now extended with regard to a mysterious connection between number theory, algebra and string theory (Erica Klarreich, Mathematicians Chase Moonshine's Shadow, Scientific American, 7 April 2015). In the case of symmetry, this focused on the existence of a mysterious entity called the monster group, a gargantuan algebraic object that, mathematicians believed, captured a new kind of symmetry. The concern here is whether such insights have as yet unexplored psychosocial implications (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007). The question to be asked is what kinds of connectivity are deprecated using single terrain modalities -- in the absence of an all-terrain cognitive vehicle or pentathlon-enabled skills? How does such cultivated inhibition fail those facing despair and a sense of meaninglessness?

Although such incredible complexity could be set aside as unnecessarily abstruse, the need to engage with it is evident in the increasing recognition of so-called wicked problems. These exemplify the challenge of connectivity across multiple conventional domains and knowledge trees. Curiously the point is made by extension of small world theory to the global problematique. Not only is everyone connected to anyone through six intermediaries, but so too are the problems of society (Duncan J. Watts, Six Degrees: the science of a connected age, 2004; Albert-László Barabási, Linked: how everything is connected to everything else and what it means for business, science, and everyday life, 2003). It is in this sense that the insights into "cognitive weather" and "experiential weather" , offered by personal recognition of its complexity, suggest ways of engaging otherwise with any change in the global climate -- whether in physical or metaphorical terms.

There is therefore a case for recognizing the exploration of such "cognitive metabolic pathways" as constituting a discipline which might be appropriately named "path-ology" -- namely the study of experiential "snakes and ladders" as this may relate to the many forms of unease in a period of questionable public hope-mongering.

Systemic organization of diseases and eases?

It is remarkable that so much is made of the Diagnostic and Statistical Manual of Mental Disorders (DSM) as a categorization of individual diseases -- whether in appreciation or criticism thereof. There is little comparable effort to distinguish the characteristics of "eases" as might be implied by such detailed recognition of "dis-eases". A case has even been made that any use of "dis-ease" is an indicator of quackery (Disease, "dis-ease", what's the difference? ScienceBlogs, 19 March 2013). Curiously the implication is that "health" is not to be interpreted in terms of "healths", which could presumably be usefully understood as multiple -- whatever the degree of (dis)harmony between them. This recalls the adage: the operation was a success but the patient died.

Similar examples are evident in the case of intelligence for which only minimal distinction is made in terms of multiple intelligences (Howard Gardner, Frames of Mind: the theory of multiple intelligences, 1983). Ignorance offers a more striking example in that little explicit distinction is made of "ignorances" -- presumably remedied by the implications of specific knowledge qualifications ("knowledges"?), ignoring the ignorances thereby left unidentified. Are there indeed different "healths" -- like different intelligences -- calling for a "theory of multiple healths"? Could an equivalent to the DSM be derived in terms of memetic diseases (Memetic and Information Diseases in a Knowledge Society: speculations towards the development of cures and preventive measures, 2008)?

These points frame the issue of the significance of "ease", given the current widespread emphasis on the tangibles of quantitative easing. Nothing is said of "qualitative easing". The latter might however be considered appropriate, given the abuses associated with the quantitative variant and the disastrous conditions that many face, as argued separately (From Quantitative Easing (QE) to Moral Easing (ME): a stimulus package to avert moral bankruptcy? 2010). It is especially significant that quantitative easing is enabled by fiat -- as fiat money -- raising the question as to whether the qualitative variant could be similarly enabled. The role of exemplars in this respect contrasts usefully with that of various forms of moral directive and fatwa.

The argument can be taken further in the light of the widespread preoccupation with "healing", accompanied by relatively little matching concern for "illing" -- except in terms of side-effects. Whilst "ease" is adapted to "easing" in quantitative terms, there is a lack of concern with "diseasing". The reverse is evident in recognition of "easement" (with respect to tangibles), in that there is a lack of focus on widespread forms of "diseasement" (especially in the case of intangibles). The period is witness to an easing of pain through medication and psychotropic drugs -- to alleviate the unease leading to ever greater incidence of suicide..

There is a desperate quest for wholeness, wellness and wellbeing as an undifferentiated condition of integration -- but one that is undermined by processes enabling illness and being-ill (Juliet Michaelson, In Defence of Wellbeing, Open Democracy, 21 May 2015). In terms of intangibles this may be challenged as the quest for happiness for commercial purposes (William Davies, The Happiness Industry: how the government and big business sold us well-being, 2015). There is however little recognition of the "sadness industry", represented by emotional blackmail in funding appeals and disaster tourism. The point is well-made by James Hillman and Michael Ventura (We've Had a Hundred Years of Psychotherapy -- And the World's Getting Worse, 1992).

Missing is any systemic framework through which the variety of eases and diseases can be fruitfully interrelated, notably in terms of the transitions between them. A relevant metaphor is the traditional board game of snakes and ladders, through which transition from forms of empowerment to those of disempowerment (or vice versa) can be understood in dynamic terms. It has evoked mathematical analysis as an absorbing Markov chain.

As noted by Wikipedia, that game is a central metaphor of Salman Rushdie's Midnight's Children (1981). The narrator describes the game as follows:

All games have morals; and the game of Snakes and Ladders captures, as no other activity can hope to do, the eternal truth that for every ladder you hope to climb, a snake is waiting just around the corner, and for every snake a ladder will compensate. But it's more than that; no mere carrot-and-stick affair; because implicit in the game is unchanging twoness of things, the duality of up against down, good against evil; the solid rationality of ladders balances the occult sinuosities of the serpent; in the opposition of staircase and cobra we can see, metaphorically, all conceivable oppositions, Alpha against Omega, father against mother.

Relevance of weather metaphors to existential unease

Models and metaphors: There is considerable debate about "climate change", paralleled by recognition of need for a "change of climate" -- metaphorically understood (Climate Change as a Metaphor of Social Change, 2008; Climate of Change Misrepresented as Climate Change: insights from metaphorical confusion, 2008). It is appropriate to recognize the contrast between understanding of "climate" (as a global technical and strategic focus) and understanding of "weather" (as people experience it locally and personally).

Curiously this contrast is partially highlighted by Paul Krugman in a discussion of Metaphors and Models (The Fall and Rise of Development Economics (2012, and elsewhere titled as The Rise and Fall of Development Economics):

The objective of the most basic physics is a complete description of what happens. In principle and apparently in practice, quantum mechanics gives a complete account of what goes on inside, say, a hydrogen atom. But most things we want to analyze, even in physical science, cannot be dealt with at that level of completeness. The only exact model of the global weather system is that system itself. Any model of that system is therefore to some degree a falsification: it leaves out some (many) aspects of reality. How, then, does the meteorological researcher decide what to put into his model? And how does he decide whether his model is a good one? The answer to the first question is that the choice of model represents a mixture of judgment and compromise. The model must be something you know how to make -- that is, you are constrained by your modeling techniques. And the model must be something you can construct given your resources -- time, money, and patience are not unlimited. There may be a wide variety of models possible given those constraints; which one or ones you choose actually to build depends on educated guessing....

Krugman then cites Dave Fultz, widely admired for his pioneering work on laboratory models of the general circulation of the atmosphere (through understanding of the patterns formed by rotating fluids in response to various mechanical and thermal forces):

Dave Fultz was a meteorological theorist at the University of Chicago, who asked the following question: what factors are essential to generating the complexity of actual weather? Is it a process that depends on the full complexity of the world -- the interaction of ocean currents and the atmosphere, the locations of mountain ranges, the alternation of the seasons, and so on -- or does the basic pattern of weather, for all its complexity, have simple roots? He was able to show the essential simplicity of the weather's causes with a "model" that consisted of a dishpan filled with water, placed on a slowly rotating turntable, with an electric heating element bent around the outside of the pan. ....

In fact, we are all builders and purveyors of unrealistic simplifications. Some of us are self-aware: we use our models as metaphors. Others, including people who are indisputably brilliant and seemingly sophisticated, are sleepwalkers: they unconsciously use metaphors as models.

What to do when the models are experienced as inadequate for engagement with reality?

Psychosocial unease and cognitive weather

The concern for many is the weather they experience -- especially when it is unusual and extreme. The focus of global debate on climate may well be an unrecognized device for avoiding attention to the personal experience of what it may imply. Failure to attend to this dimension in a period of increasing psychosocial unease could be seen in the light of Krugman's own concern in relation to the recent global financial crisis (How Did Economists Get It So Wrong? The New York Times, 2 September 2009).

With respect to psychosocial unease there is a curious sense of preoccupation with one's own "cognitive weather" -- and with how better to engage with it. A term of concern is being "under the weather". Evident changes to the "psychosocial climate" -- as a theme of social commentary -- furnish parallels readily described through weather metaphors.

Climate change is readily characterized as exposure to increasingly unseasonal weather -- to abnormal weather conditions. An equivalent change is evident in psychosocial terms, then characterized by extremes of cognitive weather -- termed social unrest.

It is somewhat ironic that the "dishpan" dynamic of Fultz's experiment (as mentioned above) reflects the complexity of cognitive weather -- at least to some degree. Ironically everybody is then appropriately to be considered as a dishpan in cognitive terms.

Weather classification? Given the focus on climate change, it might be expected that there is universal clarity with regard to the distinction of varieties of weather. However it would appear that any exploration of "varieties of weather", as might be experienced by an individual, is confused with "varieties of climate". As noted by Wikipedia, "climate" is indeed understood to be distinct from "weather", in that weather only describes the short-term conditions of variables in a given region. Individual experience is strangely entrapped in the short-term with the relation to the longer-term constituting a somewhat complex challenge: anticipation, memory, fear, and the like.

A region's climate is generated by the climate system, which has five components: atmosphere, hydrosphere, cryosphere, lithosphere, and biosphere. The difference between climate and weather is usefully summarized by the popular phrase: Climate is what you expect, weather is what you get. This could be fruitfully understood as a valuable qualification on consideration of global climate in contrast with the weather as individually experienced. It is also a reflection on the value of meteorological forecasting and the distinctions it makes. A corresponding phrase might take the form of: Remedial action is what you expect from global strategic plans, unforeseen problems are what you get.

There is a curious disconnect between the various ways of classifying climate into similar regimes and the distinctions made which are meaningful to individual experience -- especially when exposed to severe weather phenomena, or to extreme weather (usefully distinguished by Wikipedia). The Bergeron classification is the most widely accepted form of air mass classification and uses a combination of three letters. In the Spatial Synoptic Classification system (ssC) there are six categories. In discussion of it, six weather types are proposed by Scott C. Sheridan (The Redevelopment of a Weather-Type Classification Scheme for North America. International Journal of Climatology, 2002): dry polar (DP); dry moderate (DM); dry tropical (DT); moist polar (MP); moist moderate (MM); moist tropical (MT). These could be considered seriously unrelated to weather as experienced.

The most widespread system used to classify the climates of places is the Köppen Climate Classification System. This is an empirical system based on observable features. The first level recognizes from 5 to 9 major climatic types with each group being designated by a capital letter. Numbers vary due to modifications and extensions to the system in the light of new proposals and recognition of deficiencies

Köppen-Geiger climate classification

Other systems are either "genetic" classification systems (based on the causes of the climate like solar radiation, air masses, pressure systems, etc) or "applied" classification systems created for, or as an outgrowth of, a particular climate-associated problem. (e.g., Trewartha climate classification based on potential evapotranspiration).

A recognized shortcoming of these classification schemes is that they produce distinct boundaries between the zones they define, rather than the gradual transition of climate properties more common in nature. The local experience of weather is indeed especially sensitive to such transitions. Of some relevance is reference to "subjective" in the analysis of so-called "Lamb Weather Types" by Hubert Lamb (Phil Jones, The Development of Lamb Weather Types: from subjective analysis of weather charts to objective approaches using reanalyses, 2013)

Such classification initiatives recall the early stages in the emergence of the tabular periodic classification of chemical elements, especially issues regarding the number of groups and distinctions within groups.

Crises framed by weather metaphors

There are detailed studies of the extent to which weather metaphors are used to frame crises (Maria Enriqueta Cortes de los Rios, Cognitive Devices to Communicate the Economic Crisis: an analysis through covers of The Economist. Iberica, 2010; Antonella Luporini, Metaphor in Times of Crisis: metaphorical representations of the global crisis in The Financial Times and Il Sole 24 Ore 2008, 2013; Daniele Besomi, Tempests of the Business World: weather metaphors for crises in the Nineteenth Century, 2014).

It is appropriate to emphasize again that in practice -- as indicated in The Economist, The Financial Times, and the business press in general -- use is made of weather metaphors rather than climate metaphors, irrespective of any other discussion of the politics and economics of "climate change" and reference to the "business climate" -- but not to "business weather" (cf. Ifo Business Climate Index). It could be emphasized that it is through weather that people experience globality -- not through climate.

In the case of the continuing crises of politics, use of a range of metaphors has been noted by Andrew J. Gallagher (A Perfect Storm! Metaphors of Weather, Metaphor in American Politics, 28 July 2014):

weather, climate, rain money, rain check, rain on the parade, get wind of, windfall, swirling rumors, cloudy skies, black cloud hanging over, clouded judgment, stormy weather, brainstorming, perfect storm, storm back, storm out, lightning round, distant thunder

As a means of referring indirectly (if not surreptitiously) to crisis conditions, the role of weather metaphors has been noted by Ping-hui Liao (Weather as Metaphor in Modern Chinese Literature, 2007):

However, modern Chinese writers and artists do deploy from time to time bitter weather conditions as metaphors to give expression to people's struggles against hardships and interregna, against alienation or pollution. Cao Yu's theatrical treatment of thunder and storm immediately comes to mind, while many other literary references to drought and flood abound to suggest that Chinese modernity is filled with tensions and difficult transitions. But most surprising of all is that quite a few modern Chinese literary texts, together with some by prominent Japanese poets and novelists who visited such colonies as Taiwan, highlight heat and humidity as a modern albeit colonial (or even postcolonial) theme of cultural predicament... In Cao Yu, the storm serves as an allegorical background to raise question of the condition of possibility for liberation that does not take place. The sentiment of entrapment and despair functions to keep critical enterprises of modernity in check. Weather is used here metaphorically, as a critical trope, to address risks and anxieties embedded in social change....

Literal or figurative, the allusions to weather conditions in modern Chinese literature appear to be operant on exposing the limits of pre-modern cosmology and moral-political orders. Detailed descriptive accounts of drought, incessant rain, and heat, among others, function to lay bare the traditional belief that heaven provides holistic support to the people. But the miserable weather conditions also serve to criticize Chinese (or, in the case of Taiwan) and Japanese regime for their misdirected modernity projects. Bad weather sums up as a metaphor of entrapment and despair. Pollution and poverty, along side with new energy generated by hot money and speed, are often issues surrounding the weather conditions and human miseries. Of course, these literary expression s call attention to problems embedded in Chinese modernity. And Chinese intellectuals are now urging us to do something about the strange weather we are having

Intelligent analysis through weather metaphors: Given the above-mentioned comments by Krugman (2012), it is remarkable to note the case made for the use of weather as a framework for systemic analysis, as presented by Phillip J. Ayoub, et al (Weather Systems: a new metaphor for intelligence analysis. Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 2007):

With the recent catastrophic outcomes in U.S. intelligence capabilities we suggest that current design metaphors are inadequate to address the changing reality of U.S. intelligence needs. In-depth interviews and concept mapping efforts with intelligence analysts suggest that the intelligence domain be characterized as a distributed cognitive work system. Current mechanical or information processing metaphors that encourage techno-centric system design solutions neglect the emergent, pluralistic and distributed nature of information that supports situational awareness and decision making in the intelligence domain. Instead, we suggest that weather systems are a more appropriate metaphor for understanding the cognitive activity of intelligence analysts and to guide the design of cognitive aides, information sharing and knowledge management systems, and data processing tools used to support intelligence work.

Especially intriguing, in the light of Krugman's reference to the "dishpan" simulation by Fultz, is the initiative at the MIT Media Lab to construct a "weathertank" (Stefan Marti, Deva Seetharam and Hiroshi Ishii, WeatherTank: a tangible interface using weather metaphors, 2001), framed in the following terms:

Metaphors -- concrete images that illuminate abstract ideas -- are common in user interface design. We propose to use the rich and well-understood natural phenomena of weather as metaphors to represent abstract information from other domains. Many people, irrespective of educational level, literacy, and profession, understand weather metaphors intuitively. In this paper, we present WeatherTank, a tangible visualization system that uses weather metaphors to give an overview over information, employing our visual, tactile, and -- indirectly -- aural and olfactory senses. WeatherTank conveys a weather metaphor in a different way than a verbal description does, because it predominantly uses cognitive resources of our spatial/visual thinking (right hemisphere), conflicting less with our busy verbal/vocal brain processes (left hemisphere). Furthermore, unlike pictures and movies of weather, WeatherTank also employs our tactile and olfactory senses, taking advantage of the richness of multimodal human senses and skills developed through our lifetimes of interaction with the physical world

Applications for the approach have been explored by the authors (Stefan Marti and Deva Seetharam, WeatherTank: interface for non-literate communities and ambient visualization tool). Within the context of this argument, the challenge lies in the literacy required to read "the writing on the wall", given the script in which it may be written, and the contrast between non-literate and experiential.

The recognized relevance of metaphor to national security is made apparent by the launch of a major new programme -- The Metaphor Program of the US Intelligence Advanced Research Projects Activity (Alexis Madrigal, Why Are Spy Researchers Building a 'Metaphor Program'?, The Atlantic, 25 May 2011). A significant participant is the US Army Research Laboratory -- slogan: Technology Driven - Warfighter Focused.

Ironically the focus on metaphor in the Media Lab "weathertank" experiment serves to reinforce the point made above with respect to the dishpan experiment. To an unexplored degree, people are now both "dishpans" and "weathertanks". The Media Lab effectively offers a metaphor of its operations as a renowned "think tank" which merits separate attention in this context ("Tank-thoughts" from "Think-tanks": metaphors constraining development of global governance, 2003; Meta-challenges of the Future for Networking through Think-tanks, 2005). Given this preoccupation with forecasting and decision-making, think tanks illustrate the ambiguity between "weather tank" and "whether tank".

Weather, emotions and psychosocial unease: The relationship between weather and emotion has long been a theme of research (Alan E. Stewart, Assessing Human Dimensions of Weather and Climate Salience, 2005). It is usefully noted by Tina B. Tessina (Emotions as Weather).

In a period of intense global modelling of climate change, it is to be expected that the use of simulation should be extended to tendencies to "social unrest", now of increasing concern to security services. These tendencies are now gleaned from use of characteristic phrases in social media and other electronic communications mined for such purposes -- as an extension of surveillance for security purposes.

One useful summary of modelling and simulation in relation to social unrest is provided within the context of the OECD /IFP Project on "Future Global Shocks" (Ortwin Renn, Aleksandar Jovanovic and Regina Schröter, "Social Unrest", 2011). It might be asked whether their reference to "weather" is usefully distinguished from "climate" in the following:

Agent-based models run computer simulations to explore emerging dynamical patterns, free from any top-down assumptions. In contrast to conventional models, ABMs make no assumptions about the existence of efficient policies or general equilibrium, these may or may not emerge due to the dynamical rules. The policies and social behaviors that they generate are more like the weather system, subject to constant storms and seizures of all sizes. Big fluctuations and even crashes are often inherent features. That is because ABMs allow feedback mechanisms that can amplify small effects, such as the herding and panic that generate bubbles and crashes. In mathematical terms the models are -- non-linear, meaning that effects need not be proportional to their causes...

Nevertheless, a real-time simulation, fed by masses of data that would operate rather like the current traffic or weather forecasting models (projecting various possible futures!) is the only way to go in the future and if a suite of such models is to be used, such a suite will probably have to be built step-by-step, probably around a core system which will serve as a reference.

How "emotional weather" patterns are to be simulated globally as a means of detecting "unease" may then prove to be a preoccupation of ambitious initiatives such as:

Weather metaphors in poetry and prose: As indicated with respect to use of weather metaphors to articulate understanding of crisis conditions in Chinese society, it is in literature and poetry that subtler distinctions may be meaningfully made between the experience of many different kinds of weather. One remarkable study is that of Judit Nagy (Metaphors of Weather in Canadian Short Prose, Brno Studies in English, 2011) summarized as follows:

The first part of the paper presents some theoretical grounding, proceeding from the overt-covert and direct-indirect relationship of tenor and vehicle to Lakoff's cognitive concept of metaphor (1980, 1993). Based on this concept, the linguistic Great Chain of Weather Metaphors is created. The second part of the paper makes an attempt at examining the most typical source and target domains of weather, and, based on a pilot sample, it also looks into conceptual weather metaphors built by mapping at each level of the Great Chain of Weather Metaphors

This offers two orderings, as indicated below. In that on the left Great Chain characters are projected onto weather, whereas in the second type, weather is projected onto Great Chain characters.

The Great Chain of Weather Metaphors
x<w correspondences w<x correspondences
  • G<w (God-to-weather correspondences)
  • p <w (person-to-weather correspondences)
  • a<w (animal-to-weather correspondences)
  • pl<w (plant-to-weather correspondences)
  • o<w (object-to-weather correspondences)
  • abstr<w (abstract-notion-to-weather correspondences)
  • w<G (weather-to-God correspondences)
  • w<p (weather-to-person correspondences)
  • w<a (weather-to-animal correspondences)
  • w<pl (weather-to-plant correspondences)
  • w<o (weather-to-object correspondences)
  • w<abstr (weather-to-abstract-notion correspondences):

A related study has been made by Izabela Zolnowska (Weather as the source domain for metaphorical expressions. Avant: the Journal of the Philosophical-Interdisciplinary Vanguard, 2011)

The aim of the study is to demonstrate the pervasiveness of concepts related to "weather" that indicate the presence or absence of problems in human mind. The linguistic material that is the subject of the analysis is the language used in everyday communication. An additional claim is that the directionality of metaphorical transfer is uniform and proceeds from concrete to abstract concepts. Furthermore, I will try to show that talking about the presence or absence of problems in terms related to "weather" is systematic and forms a coherent network of metaphorical expressions whose structuring is partial. The final claim I would like to make is that the expressions that reflect the concept have a common experiential basis, and it is only because of its presence that the metaphor can be comprehended

The paper categorized the examples collected into certain conceptual metaphors. The source domain for all these concepts constitutes the lexicon describing "weather conditions", whereas the target domain constitutes the presence or absence of problems. The following conceptual metaphors were identified by Zolnowska:

  • rain is misfortune
  • fog is confusion
  • storm is aggressive behaviour / reaction
  • storm is hard times
  • heavy weather is problems
  • grey skies is difficult period
  • clear skies is lack of problems
  • sunny is optimistic
  • anything that shines is happiness
  • haze is problematic
  • thunder is negative emotions
  • thunder is sudden action
  • hurricane is negative state of mind
  • cloud is a symbol of present or forthcoming problem

A valuable checklist of common weather metaphors is provided by John D. Casnig (A Language of Metaphors., 1997-2013), who also has more extensive examples in each case:

  • Shower: He showered her with gifts. Giving is dropping from above.
  • Cloud: The event was clouded over by protests. Protests are an intrusion of light.
  • Fog: My memory is a little foggy. Memory is a visible object.
  • Rain: Into each life some rain must fall. Hardship is a precipitate (from above).
  • Hail: A hail of bullets. (Cold, hard and driven).
  • Wind: The winds of change. Change is the product of (lateral) forces.
  • Sunshine: You are the sunshine of my life. Happiness is light (see "cloud").
  • Sunset: He'd entered his sunset years. One's life is a single day.
  • Clear skies: It's gonna' be clear skies from now on. Clear skies are not a threat.
  • Lightening rod: He became a lightening rod for party criticism. Criticism is (negative) energy from above.
  • Blow:You'll be blown away! Our position is susceptible to sudden change.
  • Gust: Criticism began to gust in from all sides. Critics are blow-hards!
  • Thaw: Relations between the two countries began to thaw. Relationships can be frozen solid, making change or growth impossible.
  • Thunder: The boss thundered into the room. Anger is hostile weather.
  • Breeze: This homework is a breeze. Challenge is an opposing force.
  • Dawn: The dawn of civilization. Civilization has its day.
  • Grey skies: Grey skies are gonna' clear up! Rain is bad (see "cloud").
  • Cold:A cold reception. A gathering has a climate.
  • Dry spell: Business suffered a long dry spell. Revenue is the welcome rain of business.
  • Chilly: It's been a little chilly around the office since Mr. Ironbritches became boss! An office has an emotional climate, which may be invaded by a cold front.
  • Blizzard: There was a blizzard of activity at the emergency room. (Seemingly erratic movement).
  • Whirlwind: It was a whirlwind romance that spun out of control. Romance may be phenomenal and brief.
  • Drift: He was a drifter, of origin unknown. A lack of will is a lack of destination.
  • Misty: Misty, water-coloured memories... Memories are neither solid nor distinct.
  • Season: It is the season of change. Change is natural, occurring in phases, spaced by a lack of change.
  • Winter:She entered a spiritual winter. Our spirit has seasons, and may cause us to hibernate.
  • Autumn: They had entered their autumn years. One's life is a single year (see "sunset")
  • Twilight:He entered his twilight years a broken man. (see "sunset")
  • Darken: The skies of his future began to darken. Darkness is a threat.
  • Weather: His face was weathered by a long, troubled life. Bad events wear the youth from our face.
  • Storm: She was unsure if her proposal could weather the storm of scrutiny. Scrutiny is harsh weather to one's ideas.

Cognitive implication in a Chinese system articulated through weather-related metaphors

The relative lack of clarity with regard to climate classification, as noted above, and the extensive use of weather metaphors to frame existential "ease" and "dis-ease", suggest a revaluation of the classic Chinese pattern of BaGua as a device for holding and interrelating weather as existentially experienced.

Weather and Whether: As the "Book of Changes", the I Ching (an articulation of the BaGua pattern) is known to have been influential in Chinese politics over several thousand years (Tze-ki Hon, The Yijing and Chinese Politics, 2012). It offers an explicit interplay between weather and decision-making through the metaphors on which it based. Ironically, whether it is to be recognized as the earliest Global Weather Model, it could also be recognized as the earliest Global Whether Model -- to be compared with modern exploratory simulations of relevance to forecasting, decision-making and governance.

Drawing inspiration from a Chinese framework could be seen as consistence with the argument of Susantha Goonatilake (Toward a Global Science: mining civilizational knowledge, 1999). This draws attention to the creativity from which non-western cultures may benefit in drawing upon the connectivity enabled by metaphors engendered by their culture.

Why 8? Whilst Chinese literature has long accepted the following articulation into an 8x8 pattern of 64 conditions denoted by hexagrams, much attention has focused on the various ways in which these might be most fruitfully arranged. This is not the concern in what follows, but is discussed separately (Strategic patterns in terms of knowing, feeling and action: using a Chinese perspective, 2008). It is ironic to note that debate continues with regard to alternatives ways of organizing the periodic table of chemical elements, especially now that this 8-fold pattern is informed by new insight into the associated mathematics (Dennis H. Rouvray and R. Bruce King, The Mathematics of the Periodic Table, 2006)

Of particular interest is "why 8"? Seemingly this follows from the insight in the much-cited paper of George Miller (The Magical Number Seven, Plus or Minus Two: some limits on our capacity for processing information Psychological Review, 1956). It is extraordinary that this constraint is so widely evident in categorization, but with relatively little comment on its implications, as discussed separately (Representation, Comprehension and Communication of Sets: the role of number, 1978; Patterns of Conceptual Integration, 1984). It would seem to be "natural" that both "climate" and "weather" distinctions should reflect this constraint in some way. The pattern is of course evident both in the organization of the periodic table of chemical elements and in the octave structure of a particular tuning system of music (and the instruments by which it is played).

Memorability: Since a concern in what follows is that any "weather categories" should be memorable, some preliminary attention can be given to the terminology by which the 8 conditions are distinguished in order to derive unique single letter abbreviations -- following the coding approach favoured with respect to climate regimes. Possibilities include:

With respect to memorability, the question might be asked as to how memorable is any conventional classification of climates, irrespective of how recognizable are the categories of weather. A similar question can be asked of the clusters of the periodic table of chemical elements, recognized as a challenge to memory (Kyle Buchanan, Memorize the Periodic Table: the fast and easy way to memorize chemical elements, 2013).

A better recognized challenge is that of the multiplication table, given the importance it now has in a quantitative society (How to Easily Memorize the Multiplication Table; Teach the Times Tables with Pictures and Stories). Learning the complex set of interrelated metabolic pathways is enabled by a set of songs (Harold Baum, The Biochemists' Songbook, 1995). What might be the corresponding challenges for a qualitative array of relevance to "cognitive weather"? Are there (cognitive) weather pattern songs?

As with multiplication tables and the periodic table, how is the following pattern to be remembered? The form of the trigram coding is traditionally held to offer some indication, but the combination of two trigrams in the body of the table is a far greater challenge -- as in the case of the chemical elements. Given its importance in training for the civil service in various stages of Chinese governance, it would be useful to explore how the pattern was learned and taught (Geoffrey Redmond and Tze-Ki Hon, Teaching the I Ching (Book of Changes, Oxford University Press, 2014). This could be usefully compared with how conditions of governance were ordered and arranged in the prestigious degree course at the University of Oxford -- Psychology, Philosophy and Physiology ("PPP") -- valued as preparatory to engagement in the British civil service.

Weather-patterned conditions: The table below is a presentation of the traditional combination of the 8-fold pattern of weather-related conditions. In terms of "weather", it is interesting to explore whether it is capable of holding the extended variety of extreme weather and severe weather conditions discussed above -- especially in terms of extremes of "unseasonal weather", as experienced rather than as conventionally categorized. Wikipedia, for example, distinguishes: heat waves, cold waves, heat bursts, tornados, downburst and derecho, squall lines, cyclones, waterspout, dust storms, wildfires, hail, heavy rain (monsoons), heavy snowfall, ice storms, drought. Inclusion of "mountain" (M) in the pattern of the table is of interest given the major role played by mountains in engendering weather, as with the microclimates engendered by rivers (A).

However, of equal interest is the exclusion of some so-called natural disasters (landslides, earthquakes, volcanoes, flooding, lightning, tsunamis) from the conventional categories of severe or extreme weather. These could however be considered as usefully encompassed by the following table. This exemplifies the distinction between climate framed from an external, global observational perspective and weather as experienced locally as including such phenomena. Ironically, with respect to the discussion of "dis-ease" (above), "dis-aster" derives etymologically from "ill-starred", offering a traditional association of "ease" to auspiciously starred.

This challenging correspondence is the first of 5 correspondences tentatively correlated in this discussion. It is interesting that those with most skills in populating the table below with distinct forms of weather might include poets and the locally weather-wise. From a Chinese perspective, the literature on this correspondence is notably associated with the traditional geomantic discipline of feng shui. Indicative in this respect is the government fact sheet provided by the Hong Kong Observatory (Weather Feng Shui?). As with those of a poet, the methodological concern would be how to disassociate most fruitfully any such insights from the magical beliefs with which they may be more popularly associated (Jerry Alan Johnson, Daoist Weather Magic and Feng Shui, 2012)

Combinations of 8 trigrams forming the pattern of 64 hexagrams of the I Ching
  Sky (S) Thunder (T) Abyss (A) Mountain (M) Earth (E) Wind (W) Fire (F) Lake (L)
Sky (S)
Sky (S)
Thunder (T)
Sky (S)
Abyss (A)
Sky (S)
Mountain (M)
Sky (S)
Earth (E)
Sky (S)
Wind (W)
Sky (S)
Fire (F)
Sky (S)
Lake (L)
Sky (S)
Sky (S)
Thunder (T)
Thunder (T)
Thunder (T)
Abyss (A)
Thunder (T)
Mountain (M)
Thunder (T)
Earth (E)
Thunder (T)
Wind (W)
Thunder (T)
Fire (F)
Thunder (T)
Lake (L)
Thunder (T)
Sky (S)
Abyss (A)
Thunder (T)
Abyss (A)
Abyss (A)
Abyss (A)
Mountain (M)
Abyss (A)
Earth (E)
Abyss (A)
Wind (W)
Abyss (A)
Fire (F)
Abyss (A)
Lake (L)
Abyss (A)
Sky (S)
Mountain (M)
Thunder (T)
Mountain (M)
Abyss (A)
Mountain (M)
Mountain (M)
Mountain (M)
Earth (E)
Mountain (M)
Wind (W)
Mountain (M)
Fire (F)
Mountain (M)
Lake (L)
Mountain (M)
Sky (S)
Earth (E)

Thunder (T)
Earth (E)

Abyss (A)
Earth (E)
Mountain (M)
Earth (E)
Earth (E)
Earth (E)
Wind (W)
Earth (E)
Fire (F)
Earth (E)
Lake (L)
Earth (E)
Sky (S)
Wind (W)
Thunder (T)
Wind (W)
Abyss (A)
Wind (W)
Mountain (M)
Wind (W)
Earth (E)
Wind (W)
Wind (W)
Wind (W)
Fire (F)
Wind (W)
Lake (L)
Wind (W)
Sky (S)
Fire (F)
Thunder (T)
Fire (F)
Abyss (A)
Fire (F)
Mountain (M)
Fire (F)
Earth (E)
Fire (F)
Wind (W)
Fire (F)
Fire (F)
Fire (F)
Lake (L)
Fire (F)
Sky (S)
Lake (L)
Thunder (T)
Lake (L)
Abyss (A)
Lake (L)
Mountain (M)
Lake (L)
Earth (E)
Lake (L)
Wind (W)
Lake (L)
Fire (F)
Lake (L)
Lake (L)
Lake (L)

The weather-related distinctions associated with the pattern above are presented below with their traditional metaphorical connotations basic to the use of the I Ching as a "whether model" in articulating psychosocial tendencies to change. This challenging correspondence is the second of the 5 correspondences tentatively correlated in this discussion.

Upper Sky (S) Thunder (T) Abyss (A) Mountain (M) Earth (E) Wind (W) Fire (F) Lake (L)
Lower creative,
heaven, sky

arousing, thunder,
shake, initiative,
inciting, movement
abysmal, water, gorge, dangerous, in-motion mountain,
keeping still, bound, resting, stand-still, completion
earth, receptive, devoted, yielding, field gentle, wind,
clinging, fire
light giving,
clarity, flame
open, tranquil,
S: creative,
heaven, sky
(S/S) [1
Power of the great
(T/S)  [34
(A/S) [5
Taming power of the great
(M/S)  [26
(E/S) [11
Taming power of the small
(W/S) [9
Possession in great measure 
(F/S) [14]
(L/S) [43
T: arousing, thunder,
shake, initiative,
inciting, movement
(S/T) [25
(T/T) [51
Difficulty at the beginning
(A/T) [3
Corners of the mouth  (M/T) [27 Return  
(E/T) [24
(W/T) [42
Biting through  
(F/T) [21
(L/T) [17
A: abysmal, water, gorge, dangerous, in-motion Conflict  
(S/A) [6
(T/A) [40
(A/A) [29
Youthful folly  
(M/A) [4
(E/A) [7
(W/A) [59
Before completion (F/A) [64 Oppression  
(L/A) [47
M: mountain,
keeping still, bound, resting, stand-still, completion

(S/M) [33

of the small 
(T/M) [62
(A/M) [39
Keeping still  
(M/M) [52
(E/M) [15
(W/M) [53
(F/M) [56
(L/M) [31
E: earth, receptive, devoted, yielding, field Standstill  
(S/E) [12
(T/E) [16
Holding together
(A/E) [8]
Splitting apart  
(M/E) [23
(E/E) [2
(W/E) [20
(F/E) [35
Gathering together  
(L/E) [45
W: gentle, wind,
Coming to meet  
(S/W) [44
(T/W) [32
(A/W) [48
Work on what has
been spoiled
(M/W) [18
Pushing upward  
(E/W) [46
(W/W) [57
(F/W) [50
Preponderance of the great
F: clinging, fire
light giving,
with men
(S/F) [13
(T/F) [55
After completion 
(A/F) [63
(M/F) [22
of the light 
(E/F) [36
(W/F) [37
(F/F) [30
L: joyous,
open, tranquil,
(S/L) [10
(T/L) [54]
(A/L) [60
(M/L) [41
(E/L) [19
Inner truth  
(W/L) [61
(F/L) [38
(L/L) [58]

Varieties of emotional experience: Clarifying the distinctions in the table would again be aided through associations offered by poets (and song lyrics). Whilst there have been many efforts to clarify the varieties of religious experience, it is curious that in a world in which many suffer from their experience in relationships, that so little effort is made to clarify the variety of emotional experiences systematically. This is despite the suggestions of William James in that respect (Phil Oliver, Varieties of Emotional Experience: James's Radical Turn, American Philosophy, 2002). The challenge of doing so has been noted by William Cunningham and Jay Van Bavel (Varieties of Emotional Experience: differences in object or computation?, Emotion Review, 2009) following a century of research, as noted by P. J. Lang (The Varieties of Emotional Experience: a meditation on James-Lange theory, Psychological Review, 1994).

Similarly with regard to the experiential challenge of relationships, there is little effort to clarify the spectrum of relational experience in any ordered manner, as previously noted (An Approach to Systematic Classification of Interpersonal Relationships conceived as essential to alternative life styles, social and personal transformation, 1978).The above table suggests the possibility of a more complex patterning. The evolution of transactional analysis to relational transactional analysis offers pointers in this respect. Useful also are the indications of Carmen Lynch and Victor Daniels (Patterns of Relationships: the relational gestalt: which movie are we in? 2000).

The association of the distinctions to the experience of weather accords with the common framing of relational conditions (thundery, stormy, cold, hot) and with idiomatic expressions such as "raining on my parade". Given the "severe weather" characteristic of many relational experiences, there is a case for an analogue to any study of severe weather processes (cf. Amy McGovern, et al, Understanding Severe Weather Processes through Spatiotemporal Relational Random Forests, 2010 Conference on Intelligent Data Understanding).

Interpretations of patterns of empowering and disempowering conditions

Cognitive adaptation of the I Ching conditions for the existentially challenged: The following exercise is an adaptation of portions of texts offering a sense of the "conditions of change" (above) in various domains, as previously presented (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching) -- for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). The intent of this adaptation is however to highlight the "cognitive weather conditions" of the increasing numbers of people faced with conditions of despair, depression, nothingness, and the like (as indicated in a section below). With this concern, the wording in the earlier exercises appeared to lack this sense of angst -- although the Chinese original claims specifically to frame the relationship between fundamental conditions of uncertainty and the associated decision-making dilemmas.

As typically expressed the conditions recall too readily a form of moralistic, deterministic, "motherhood statement", namely directives ("shoulds" and "musts"). Although these appear unquestionably appropriate, they are readily experienced as objectionable by many in existential agony -- namely as too bland for those who are living "on the edge", under conditions framed by such terms as depression, disillusion, despair, disgust, denigration and denial.

The point is well made by the protest of Jack Nicholson (in the movie As Good As It Gets): I am drowning here and you are describing the water. Such concerns, with similar references, are reflected to a higher degree in the compilation by Jon Jenkins and Maureen Jenkins (The Other World, in the Midst of Our World, 2001) describing 64 states of being experienced in ordinary life -- as excerpted below.

The approach taken was therefore to use portions of the previous exercise for the 64 traditionally recognized condition,s but to amend the text using two "devices":

The result is far from satisfactory since it leaves the reader with the (useful) challenge of associating meaning with "??¿??" -- otherwise typically over-defined. Ideally this might imply dimensions such as:

Of particular interest, given the contrast with "climate" as a more enduring characteristic, is the sense in which there are likely to be cultural preferences and biases with respect to interpretations and emphases. These can be explored in the light of the articulations proposed by various authors, as summarized separately (Systems of Categories Distinguishing Cultural Biases, 1993). Most notable are the mindscapes of Magoroh Maruyama (Mindscapes, social patterns and future development of scientific theory types. Cybernetica, 1980). Of further relevance, given the preoccupation here with ease and disease, is the commentary on Maruyama's work, and its development (Maurice Yolles and Gerhard Fink, Personality, Pathology and Sagiv-Schwartz Mindscapes, Social Science Research Network, 2012).

The wording in the interpretations remains unsatisfactory, and perhaps necessarily so, if the qualities of the "cognitive weather conditions" listed thereafter are somehow to be associated with the pattern.

Indicative list of first 4 adapted interpretations of conditions of I Ching sequence
(for complete table see Annex 2)
S/S 1

Creative (Ch'ien) [primal power]: As a result of ??¿??, can creative energy and inspiration engender new patterns?

  • [In order to bear fruit, creativity eventually requires the existence of a receptive environment. (Resulting in: Receptivity).]
E/E 2

Earth (K'un) [receptivity / primal structuring]: Can ??¿?? respond to the actions and opportunities of its environment and thereby bring about change?

  • [Initiatives emerging in a receptive environment first experience difficulties. (Resulting in: Initial difficulty). ]
A/T 3

Initial difficulty (Chun) [beginning growth / sprouting]: Can a cooperative response bring order out of chaos as a result of the profusion of changes being brought about by ??¿?? -- constituting confusing obstacles to its further development?

  • [When first launched, initiatives tend to be handicapped by inexperience. (Resulting in: Inexperience). ]
M/A 4

Inexperience (Meng) [enveloping / clouded awareness / young shoot]: Aided by enthusiasm, can ??¿?? succeed despite inexperience, provided appropriate guidance is sought with the right attitude?

  • [After overcoming problems of inexperience, initiatives await further support. (Resulting in: Waiting). ]

Psychosocial dis-eases and the eases they imply: The concern here is to recognize in more appropriate language the nature of eases and diseases -- of which the latter are framed conventionally by the above-mentioned Diagnostic and Statistical Manual of Mental Disorders (DSM). This of course uses the conventions of a purportedly healthy, detached observer -- a "normal" person unchallenged by any such uneases. In that sense it is especially unhelpful to those who have to live in a world challenged by the pattern of dis-eases and eases -- as usefully highlighted by the game of snakes and ladders.

The previous section interpreted the language of the I Ching in the metaphorical terms of its traditional weather-related pattern. However, as noted, that language remains inadequate to the existential experience of someone somewhere "in the game". The concern here is whether other vocabulary can be used to approximate more closely to that experience. It is in this sense that the above-mentioned work of Jon Jenkins and Maureen Jenkins (The Other World, in the Midst of Our World, 2001) is especially relevant in describing 64 states of being experienced in ordinary life. This is effectively the result of a collaborative effort of hundreds of people associated with the Institute of Cultural Affairs (ICA) in the 1970s. It took an earlier form as The Other World: a spirit journal (1987).

Use of the phrase "other world" helpfully distinguishes the internal existential focus on personal "cognitive weather" from the detachment of the external perspective -- echoing the distinction made above between "climate regimes" as categorized globally and "weather" as experienced locally and personally. Stressing that the sense of an "other world" is not particularly religious, it is considered there as a poetic image pointing to the finally incomprehensible dimension of reality.

The authors indicate their sense of a "state of being" as an experience which is simultaneously an awareness, a feeling and a resolve. They offer a description of such a state in the words of Joseph Wesley Mathews (The Recovery of the Other World, from a speech given on 3 July 1972):

One day a man [sic] is driven by whatsoever vicissitudes of life into the consciousness that he himself must die. It is like being in a state of shock. A strange force intrudes. Suddenly he is submerged in awe; he feels it hovering all about him; he feels its penetration into the deepest corners of his innermost being. In quiet terror, and with an inexplicable fascination, he knows the fragility of his total existence; he feels his contingency, and beholds the passingness of all things. It is like a mortal wound from which he knows he will never recover. As the absurdity, the irrationality of it all seeps deep within, a burning objectless anger rises and rages until futility itself turns into a heavy numbness and everything becomes disoriented; all is nothingness; and there is no place any more to stand, just terrifying mystery. And hanging helplessly, swirling in emptiness, engulfed in awe, it dawns at long last, like the rising of a black sun, that exactly here is the final real before which he is fated and invited to live and die his life. This is the great encounter with the aweful mystery.

The question raised in what follows is the nature of any correspondence between the 64-fold pattern of the I Ching and the 64-fold pattern articulated in the particpative ICA context. This challenging correspondence is the third of the 5 correspondences tentatively correlated in this discussion. As with the I Ching, each of the numbered conditions is accompanied by extensive commentary. The states of being are clustered into groups of four, termed "treks". Four such treks form an area, of which there are four, making a total of 64 conditions. As with the I Ching, the pattern constitutes a map. There is no particular starting or ending point -- resembling snakes and ladders to a degree -- rather it frames a perpetual journey.

The move from awareness of surface appearance to profound consciousness of the self and of reality is never finally achieved. People always face new crises which challenge their assumptions, violate their expectations and demand their creativity, regardless of the perceptual level they have achieved.

A major contrast with the I Ching is that no effort is made to indicate pathways between conditions -- along which a journey could be recognized. This might be implicit to a degree in the clustering by "treks" -- possibly to be considered as circuits, with some suggestion of being patterned cognitive feedback loops or metabolic pathways.

  Indicative presentation of first 16 of 64 states of being in terms of four of 13 defining categories
(excerpted from The Other World: a spirit journal, 1987; for complete table see Annex 3)
Areas /
(a sense of...)
(like being...)
(it's like...)
1/1 1 radical contingency terrifying numbness mortally stunned hearing the worms cough
2 absurd existence benign madness critically disoriented riding a tilt-a-whirl
3 ultimate reality intense shock irrevocably outcast wandering in a thick fog
4 primordial wonder total paralysis helplessly suspended hanging over molten lead
1/2 5 incarnate living double identity fatally split experiencing bi-location
6 ubiquitous otherness constant pursuit under surveillance having nowhere else to run
7 final limits chronic weakness perpetually conquered racing in a field of tar
8 total exposure deep guilt perpetually embarrassed standing nude in Times Square
1/3 9 vibrant powers eerie strength intensely enlivened opening the floodgates
10 transformed existence joyful anxiety radically relocated waking up on another planet
11 second birth trustful expectation unconditionally recast recovering from amnesia
12 dynamic selfhood forever surprised ceaselessly evolving watching a pinwheel explode
1/4 13 essential dubiety irrational self-doubt shatteringly ridiculed feeling you've really been had
14 cryptic disclosure secret resentment totally injured being finally excommunicated
15 transcendent immanence insatiable yearning chronically homesick knowing you'll never go home
16 singular adoration burning desire hopelessly enamored being reluctantly love-sick

The contrast between the two is intriguingly evident in the first being framed as conditions, implying the potential for change (hence The Book of Changes), with the second emphasizing "states of being" -- but as stages on a journey (possibly to nowhere). The I Ching could even be considered as a map of a complex network of cognitive snakes and ladders. The particular transitions between conditions in the numbered sequence forms a continuous circuit in that case (as indicated by the animation below).

Insights from comparable ordering initiatives: In the process of any effort to map either of the above patterns onto the other, of particular interest is what could be considered (by some) to be emphases (or dimensions) missing from both. In this respect a useful test would be provided by comparison with the insights formulated in the Brahmajala Sutta. This is considered to be one of the Buddha's most important and profound discourses, weaving a net of 62 cases capturing all the philosophical, speculative views on the self and the world (Bhikku Bodhi (Tr). The Discourse on the All-Embracing Net of Views; the Brahmajala Sutta and its commentarial exegesis, 1978). A summary is presented separately (Comprehensive set of ways of knowing: the All-Embracing Net of Buddhist culture, 2009).

Relevant insights might also be derived from use of the periodic table as a metaphor to order modes of human knowing, as discussed separately (Periodic Pattern of Human Knowing: implication of the Periodic Table as metaphor of elementary order, 2009; Periodic Pattern of Human Life: the Periodic Table as a metaphor of lifelong learning, 2009; Tuning a Periodic Table of Religions, Epistemologies and Spirituality -- including the sciences and other belief systems, 2007).

Given the poetic form through which the Chinese metaphorical description is traditionally expressed (notably for mnemonic purposes), could some form like haiku -- with its "cutting edge" emphasis -- be adapted to carry (in English) the poignancy of each condition (Ensuring Strategic Resilience through Haiku Patterns: reframing the scope of the "martial arts" in response to strategic threats, 2006). This would go further in framing the existential nuances of the respective conditions.

As a cognitive challenge, as mentioned with respect to learning the multiplication table, it is appropriate to note the skills required and widely developed in response to Rubik's Cube. This 3x3x3 cube can be explored as a metaphor for engaging with the relationships between the cognitive weather conditions variously represented in the above tables -- but presented in three dimensions (with surfaces to be appropriately marked or colour-coded, possibly according to the BaGua mirror pattern). There are different variants of Rubik's Cubes with up to seventeen layers: the 222 (Pocket/Mini Cube), the standard 333 cube, the 444 (Rubik's Revenge/Master Cube), and the 555 (Professor's Cube), the 666 (V-Cube 6), and 777 (V-Cube 7). Virtual variants also exist in 4D and 5D. Arguably these suggest possible designs of forms of "wellness/illness" cubes through which patterns of coherence can be explored.

Path-ology: eliciting dynamic patterns of empowering and disempowering conditions

Board games: References were made above to the sense in which engagement in board games such as snakes and ladders can be understood as serving a representative and instructive function, notably including chess and go, as discussed separately (Sustainability through Magically Dancing Patterns: 8x8, 9x9, 19x19 -- I Ching, Tao Te Ching / T'ai Hsüan Ching, Wéiq? (Go), 2008). The association with relational insights through other systematically organized Chinese classics has long elicited commentary (Hyperspace Clues to the Psychology of the Pattern that Connects -- in the light of the 81 Tao Te Ching insights, 2003). The Western-framed challenge of recognizing the "pattern that connects" is necessarily relevant (Walking Elven Pathways: enactivating the pattern that connects, 2006).

There is therefore a case for recognizing the exploration of such "cognitive metabolic pathways" as constituting a discipline which might be appropriately named "path-ology" -- as reflection on experiential engagement in the pathways of snakes and ladders, and the like. As noted above, in a period characterized by widespread depression, disillusion, despair, disgust, denigration and denial, understanding the pathways in which these are embedded merits particular attention. These conditions complement the unquestioned focus on their opposites in an era named by John Michael Greer (The Era of Pretense, Resilience, 14 May 2015). The increasing recognition accorded to bipolar disorder is one reflection of this.

As discussed separately (Playing the Great Game with Intelligence, 2013), such associations offer curious echoes to the elaboration of a "game of spheres" by Nicholas de Cusa (De Ludo Globi, 1463), written as a contribution to both a literature and a practice of moral game-playing. This formed part of the tradition of the forgotten chess-like game Rithmomachia ("The Battle of Numbers" or Rythmomachy), which combined the pleasures of gaming with mathematical study and moral education. Intellectuals of the medieval and Renaissance periods who played this game were not only seeking to master the principles of Boethian mathematics but were striving to improve their own understanding of the secrets of the cosmos (Ann E. Moyer, In The Philosophers' Game, 2001). This was undoubtedly an inspiration for the magnum opus of Nobel Laureate Hermann Hesse, as noted by Todd R. Harris (The Interplay of Opposites, the Language of Experience, and the Geometry of Ascent: a comparison of Hermann Hesse's "Das Glasperlenspiel" and Nicholas of Cusa's "De Ludo Globi", 2001).

Animations: Underlying the pattern of the I Ching, the traditional circular pattern of the BaGua (termed the BaGua Mirror) necessarily lends itself to animations consistent with the dynamics between its various conditions, as presented and discussed separately (Animation of Classical BaGua Arrangements: a dynamic representation of Neti Neti, 2008). The latter illustrated the dynamics of a related mapping of the hexagrams (Mapping of I Ching hexagram coding onto Star of David, 2008). The argument can be developed as an explicitly cross-cultural exercise, using a circular configuration of the hexagrams (Dynamic Exploration of Value Configurations: interrelating traditional cultural symbols through animation, 2008).

Another approach is to explore the dynamics between the conditions indicated by the hexagrams in forming a hypercycle (Adaptive Hypercycle of Sustainable Psychosocial Self-organization: designing a mapping of a Chinese metaphorical pattern language, 2010). This offers a reminder of the subtle complexity of the pattern with which individual experience is required to engage -- irrespective of the more constrained frameworks promoted conventionally as adequate models to explain that process.

Spiral configuration of hexagrams
(8 arms to the spiral, one for each of the 8 hexagram "house" clusters, namely 8 hexagrams per spiral arm)
[provisional image in anticipation of resolution of technical issues -- Disabled]
Spiral arrangement of 64 hexagrams of I Ching

Transcending polarity: Of particular interest in such exercises is the manner in which polarity is handled and the possibilities of its transcendence are indicated. This concern is of special relevance in a period preoccupied by full-spectrum dominance and global hegemony of a particular nature -- to which no challenge is admissible. This framework plays out in the bloody conflicts engendered by an us-or-them logic (Us and Them: Relating to Challenging Others: patterns in the shadow dance between "good" and "evil", 2009).

As a foreign policy articulated as You're either with us, or against us it favours retrogression to Stone Age mindsets (Nick Cullather, Bomb them Back to the Stone Age: an etymology, History News Network, 10 June 2006). However, switching metaphors, there is always value in using "first-gear" during start-up operations and in engaging with problematic terrain -- even though this may be completely inadequate for "take-off", as argued separately (Counteracting Extremes Enabling Normal Flying: insights for global governance from birds on the wing, 2015).

It is within this context that the argument can be taken further through an exercise in rendering dynamic the circular arrangement of the 64 I Ching hexagrams as shown below (based on the original static depiction). The two levels of the hexagrams are separated to allow an inner ring of trigrams to rotate with respect to an outer ring. This brings trigrams successively into association with one another in order -- indicative of the distinctive condition engendered. It can be understood as framing and sustaining an elusive transcendent condition indicated by the central circle.

64 Hexagrams of I Ching formed by animation of inner circle of trigrams relative to outer circle
(also mp4 version)

Aside from technical defects, this animation lends itself to a variety of indicative improvements to highlight those relationships which might be considered "activated" under certain conditions (as suggested in the experiments below). It is interesting to note the degree to which such a cognitive device is reminiscent of the form of the traditional geomantic feng shui compass, which may have many separate rings (Stephen Skinner, Guide to the Feng Shui Compass, 2008). It also strangely resembles the circular logarithm table. In an information context, this would then raise the question of any understanding of the cognitive psychogeography of cyberspace -- or of any information context.

Prayer beads: Whether static or dynamic, this circular presentation usefully recalls the experiential significance associated by some religions with the practice of progression through circlets of beads (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000). As noted there, it is intriguing that the number of beads in such experiential circlets is of a similar order to the number of hexagrams:

As mnemonic aids, these raise the question of what devices reflecting equivalent diversity are developed or envisaged with respect to personal management of ease and dis-ease.

Rotation of magnetic field: The relatively simple animation above suggests a relationship to the thinking of Nikola Tesla which gave rise to his insight into the rotating magnetic field, as discussed separately (Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014). This notably included sections on:

As described there, the breakthrough in Tesla's thinking with respect to alternation/rotation is eloquently described by John J. O'Neill (Prodigal Genius: the life of Nikola Tesla, 1968):

As separately discussed, the question is whether there is an analogous form of "rotation" which would prove significant to the transcendence of the Stone Age world view now actively seeking to dominate global strategic governance (Massive Elicitation of Psychosocial Energy Requisite: technology for collective enlightenment, 2011). Can the indicated transformations between conditions in the animation above be understood as equivalent in some way to the wiring pattern on the electromagnetic coil of motors and dynamo?

As indicated by the screen shots below, experimental modifications of the animation above are suggestive in this respect, potentially as catalysts for further reflection (In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007).

Screen shots of experimental animations of 64 hexagrams of I Ching (presented separately in Annex 4:
Experimental Revolutionary Animations of a Chinese Pattern of Metaphors)
With rotation of outer ring
[slower] [faster]
With counter-rotation of 2 outer rings
With counter-rotation of 4 outer rings
Screen shots of experimental animation of circular arrangement of 64 hexagrams fromI Ching Screen shots of experimental animation of circular arrangement of 64 hexagrams fromI Ching Screen shots of experimental animation of circular arrangement of 64 hexagrams fromI Ching

Paradoxical indication of polarity: The challenge of positive vs negative in electromagnetism is indicative of an equivalent challenge with respect to controversial psychosocial insights into duality, whether positive-negative, objective-subjective, internal-external, upper-lower, inner-outer, right-wrong, etc -- with the valued and deprecated associations they elicit. In the case of electromagnetism, it is a matter of convention -- a technical fiat -- as to what is "positive" and what is "negative" (as it is with respect to electrons and protons). It is curious that that the disorder of "bipolarity" (noted above) is also recognized as a feature of both electromagnetism and of international relations.

The reading of a hexagram, and its indications, can be challenged in such terms -- whether presented in isolation or configured with others in a circle.

Alternative conventions for indication of conditions
reading (in table)
reading (in table)
= positive
= negative
reading (in circle)
reading (in circle)
begin end     outer inner
end begin     inner outer

Whilst seemingly trivial, the direction of reading and the manner in which significance is then attributed to it, may go to the heart of the slippery, paradoxical nature of polarity and duality. This is evident in the associations with "top", and the striving to be "top-most" -- with the deprecation of the "bottom-most". It is evident with respect to those in any "inner" circle -- and those consequently deprecated as "not-in", who may be striving to be "in". This becomes more problematic when "inner" is associated with "subjective" (or internal) and "outer" with "objective" (or external) -- as with many of the natural sciences.

There is also the strange convention of associating an "unbroken" line with "positive", in contrast with the alternative of associating it with "negative" -- with all the consequent implications for "male" and "female". More intriguing still is the inversion in which the lines are marked in white, rather than black -- on a black background rather than a white one. This has implications for the "good" being associated with "white" and the "evil" with "black".

It is appropriate to note that another Chinese classic also makes use of a diagram of broken and unbroken lines. In the case of the 64 insights of the I Ching, each is represented by six such lines, each of which may be unbroken (yang), or broken once only (yin). By contrast, in the case of the T'ai Hsüan Ching (or Canon of Supreme Mystery), these are represented by four such lines, each of which may be unbroken, or broken once or twice, as discussed separately (9-fold Magic Square Pattern of Tao Te Ching Insights: experimentally associated with the 81 insights of the T'ai Hsüan Ching, 2006).

Curiously these issues, notably commentary on the origins of the I Ching notation, recall the famed arguments of George Spencer-Brown (Laws of Form, 1969). This is highly relevant to the vexatious issue of how boundaries are established and defined -- with all the controversy that can result. LoF is introduced by use of a symbolic element termed a mark or a cross. As explained in Wikipedia,

In Spencer-Brown's inimitable and enigmatic fashion, the Mark symbolizes the root of cognition, i.e., the dualistic Mark indicates the capability of differentiating a "this" from "everything else but this." In LoF, a Cross denotes the drawing of a "distinction", and can be thought of as signifying the following, all at once:

All three ways imply an action on the part of the cognitive entity (e.g., person) making the distinction. As LoF puts it: The first command: Draw a distinction can well be expressed in such ways as:

  • Let there be a distinction,
  • Find a distinction,
  • See a distinction,
  • Describe a distinction,
  • Define a distinction,

Or: Let a distinction be drawn....

The counterpoint to the Marked state is the Unmarked state, which is simply nothing, the void, represented by a blank space. It is simply the absence of a Cross. No distinction has been made and nothing has been crossed. The Marked state and the void are the two primitive values of the Laws of Form. The Cross can be seen as denoting the distinction between two states, one "considered as a symbol" and another not so considered. From this fact arises a curious resonance with some theories of consciousness and language. Paradoxically, the Form is at once Observer and Observed, and is also the creative act of making an observation. LoF... closes with the words:

...the first distinction, the Mark and the observer are not only interchangeable, but, in the form, identical.

Reflexivity and higher orders of cybernetics: So framed it is interesting to speculate on the relevance of such insights -- and the potentially "slippery" reading of the marks constituted by any hexagram -- with respect to currently emerging distinctions between different orders of cybernetics. Insights into more appropriate means of managing connectivity and disagreement are now suggested by exploration of higher orders of cybernetics (Maurice Yolles and Gerhard Fink, A General Theory of Generic Modelling and Paradigm Shift: cybernetic orders, Kybernetes, 44, 2015).

These notably take account of self-reflexivity -- itself to be distinguished in varying degrees meriting exploration and recognition. As phrased by the authors:

Especially relevant is the earlier collaboration of the principal author with a Chinese scholar (Ye Zude and Maurice Yolles, Cybernetics of Tao, Kybernetes, 39, 2010). As noted there:

Here, autopoiesis is a term that can now be simply seen as a network of processes that enables noumenal activity to become manifested phenomenally, and in autonomous systems this is conditioned by autogenesis -- a network of principles that create a second order form of autopoiesis that guides autopoietic processes. Autopoiesis may be thought as a process in which virtual images are manifested phenomenally. Autogenesis provides a network of principles that ultimately drives autopoiesis.

Beyond dispute in 5-dimensional space: Pentagramma Mirificum?

The cybenetician Stafford Beer is known for his application of such insights to new patterns of dialogue (Beyond Dispute: the invention of team syntegrity, 1994). These processes were organized in terms of the 3-dimensional structure of the icosahedron, notably characterized, by 15 great circles. Given the questions raised by "dis-" in relation to "ease", a degree of closure to the pattern of correspondences of this argument can be explored through recalling the etymology of "dispute" -- from the Latin dis-"separately" with putare"to count or consider".

Wu Xing: A speculative closure to the pattern of 5 correspondences tentatively correlated in this discussion could be consistent with the arguments of A. C. Graham (Yin-Yang and the Nature of Correlative Thinking, 1986). Given the above-mentioned conventional recognition that a region's climate is generated by a climate system of five components (atmosphere, hydrosphere, cryosphere, lithosphere, and biosphere), these can be associated through a circular pattern fundamental to Chinese thinking, namely the dynamics of 5-phase Wu Xing.

The trigrams of BaGua are related to the five elements of Wu Xing, used by feng shui practitioners and in traditional Chinese medicine. The elements correspond with the trigrams: water and fire directly; earth corresponds with two (earth, mountain), wood with two (wind, thunder), and metal with two (heaven, lake). Hence the implied relationship to the pattern of I Ching hexagrams -- suggesting the possibility of a "collapsed" variant of the latter.

Curiously this pattern is very similar to a diagram fundamental to the Pythagoreans. The former continues to be valued with respect to understanding of health, the latter is at the origin of the understanding of hygiene, as may be variously discussed (Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012; Memorable dynamics of living and dying: Hygeia and Wu Xing, 2014).

The pattern is now being explored from a mathematical perspective in China (Ziqing Zhang and Yingshan Zhang, Mathematical Reasoning of Economic Intervening Principle Based on "Yin Yang Wu Xing" Theory in Traditional Chinese Economics. Modern Economy, 2013; Yingshan Zhang and W. Shao. Image Mathematics: mathematical intervening principle based on "Yin Yang Wu Xing" theory in traditional Chinese mathematics, Applied Mathematics, 2012; Guang-hong Ding and Tao WanG, Mathematical analysis of Yin-Yang Wu-Xing Model in TCM, Journal of Acupuncture and Tuina Science, 2008; Zhaoxue Chen, Researches on Mathematical Relationship of Five Elements of Containing Notes and Fibonacci Sequence Modulo 5. The Scientific World Journal, 2014).

Correspondence between 5-fold patterns from contrasting cultures
Chinese 5-phase Wu Xing cycle
(Image adapted from Wikipedia)
Hugieia Pentagram of Pythagoreans
(Image adapted from Wikipedia)
Chinese 5-phase Wu Xing cycle Hugieia Pentagram of Pythagoreans

The pattern can be speculatively used to order current understanding of a climate system. It is closely associated with the requisite attitudes identified in the organization of the famed Japanese strategic study The Book of Five Rings.

Speculative ordering of current understanding of a climate system
Speculative use of Wu Xing cycle to order climate Book of Five Rings arrayed according to Wu Xing
Wu Xing / Book of 5 Rings

The original use of rings in this depiction, and with respect to strategic attitudes, invites reflection on its relevance to the adequacy of comprehension of any system of climate. The question acquires greater focus through the symbolic value associated worldwide with the Olympic Games

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

"Sparsity" of the "pattern that connects": The juxtaposition of the above patterns, with the suggestion that they are indicative of an underlying pattern, raises the question as to how disparate and "disconnected" can the elements of the "pattern that connects" appear to be in correlative thinking, as suggested by research on structured sparsity (Junzhou Huang, Tong Zhang, et al, Learning with Structured Sparsity, Journal of Machine Learning Research, 2011).

This returns to the indications of small world theory of six degrees of separation, cited in the introduction. Whereas connection to any "other" may indeed be possible through six intermediaries -- as with the problems of society -- is this also the case amongst seemingly disparate categories characteristic of requisite variety in cybernetic terms? How unrelated may distant intermediaries be credibly asserted to be? A corollary to that theory might then call for recognition that there are 5 (or 6) degrees of "cognitive separation" from an experiential sense of globality, namely its comprehension -- despite the expressed belief that "everything is connected to everything".

The challenge to comprehension of the coherence of global patterns -- aided by "path-ology" -- may lie in the confusing "subliminal" intuitions regarding the elusive nature of that complexity, so dimly apprehended. This challenge is clarified to a degree by the mathematics of Ron Atkin (Multidimensional Man: can man live in 3-dimensional space? 1981) and by the arguments of Magoroh Maruyama (Peripheral Vision: polyocular vision or subunderstanding? Organization Studies, 2004).

Is weather a valuable key to engaging with patterns of a higher order (Engaging with Insight of a Higher Order: reconciling complexity and simplexity through memorable metaphor, 2014)?

Embedding in higher dimensional space: In commemoration of the tragic death of Nobel Laureate John Nash at the time of writing, further speculation is justified in the light of his work on the mathematics of isometric imbedding, This resulted in the discovery that any surface can be embedded into 5-dimensional space (, Every world in a grain of sand: John Nash's astonishing geometry, The Conversation, 27 May 2015; Ben Andrews, Notes on the Isometric Embedding Problem and the Nash-Moser Implicit Function). For John Conway: Nash's result is one of the most important pieces of mathematical analysis in the 20th century.

Might this have implications for the "superficial" cognitive possibilities by which the above 5-fold speculations are indicated? Of relevance to this argument is the considerable psychological unease from which Nash suffered for many decades -- possibly not unrelated to his remarkable innovations in game theory and his later quest for more collaborative games.

Of particular relevance is the comment of the physicist Gerard 't Hooft with regard to a holographic principle, which explains that the information about an extra dimension is visible as a curvature in a spacetime with one fewer dimension. Such "curvature" is clarified in a discussion of Is the universe 5 dimensional space-time or 4? (Carlos Romero, et al, The Embedding of General Relativity in Five Dimensions. General Relativity and Gravitation, 1996). How might this be recognized in efforts to comprehend the coherence of globality?

Pentagramma Mirificum: Potentially relevant to such considerations is the unusual 5-fold structure known as the Pentagramma Mirificum, so named by the mathematician Carl Friedrich Gauss -- after its discovery by John Napier in exploring the hypergeometric origin of spherical action (deriving what are termed Napier's rules for right spherical triangles). Gauss later showed how the spherical pentagramma, and its projection, are both artifacts of an elliptical function, which itself is an artifact of a superseding hypergeometry. The argument relating to this pattern is developed separately in further detail with animations (Annex 5: Global Psychosocial Implication in the Pentagramma Mirificum, 2015)

Related details and epistemological implications of non-Euclidean geometry are articulated by various authors (Joel Silverberg, Napier's Rules of Circular Parts, 2008; Fragmentary Notes from Carl F. Gauss' Work on the Pentagramma; Bruce Director, From Plato's Theaetetus to Gauss's Pentagramma Mirificum: a fight for truth, EIR, 7 October 2005; Pentagramma Mirificum: investigations in geometry, The latter includes many helpful schematics and animations. As noted by Bruce Director ( Riemann for Anti-Dummies: Part 65 : On the 375th Anniversary of Kepler, LYM Canada, 16 November 2005)

Gauss was intrigued by the relationship of Napier's spherical pentagram to his elliptical transcendentals. He realized that Napier's pentagramma mirificum established that a spherical surface had an intrinsic five-fold periodicity.

Recognizing metaphorical self-closure: The point to be stressed is that this unusual form is generated by 5 great circles. It derives from the most fundamental characteristic of spherical geometry, the "great circle-pole" relation, making of it a reflection of spherical geometry itself. It thereby makes evident a 5-fold periodicity as being intrinsic to the sphere and to globality.

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

Napier's diagram indicates the unusual self-closure of a chain of 5 spherical right triangles to form a non-regular spherical pentagon. The spherical pentagon is self-polar, which means that each vertex is the pole of the opposite side. The form offers an insight into globality in non-Euclidean terms, which otherwise remain even more elusive.

There is a degree of irony to the sense in which a sequence of perspectives, each upheld as "upright" in contrast to that preceding it, suggests that the progression brings one back to the point of departure -- but seen from a "humbler" angle. This recalls the insight of T. S. Eliot:

We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know it for the first time.

(Little Gidding, 1942)

Comprehension of globality through 5-fold patterns of metaphor? Exploration of the possible relationship between the pattern of Wu Xing, Hygeia and the Pentagramma Mirificum can be usefully related to that of the non-sequiturs of so-called Knight's Move thinking. As a move in chess, with its correspondence in go, it offers a pattern for metaphor as being orthogonal to conventional linearity. The Wikipedia entry on orthogonality offers a valuable summary of the challenges this constitutes to communication in various domains. For example: In communications, multiple-access schemes are orthogonal when an ideal receiver can completely reject arbitrarily strong unwanted signals from the desired signal using different basis functions. Metaphor enables this conventional constraint on connectivity to be transcended -- notably that between information silos. Ironically it might be said, following the argument of the introduction with respect to birds, metaphors enable arguments to "fly". The point is carefully argued by Douglas Hofstadter and Emmanuel Sander (Surfaces and Essences: analogy as the fuel and fire of thinking, 2013).

Appropriately Knight's move thinking is both valued as such for strategic creativity and deprecated as a thought disorder -- a pathology of disconnected thinking, notably categorized in DSM (Knight's move thinking: appreciated or deprecated, 2012). Consequently the Knight's move can be considered as a valuable indication of use of metaphor in reframing linearity in complex systems. As a feature of spherical geometry, the self-closing sequence of right angles is the defining characteristic of Napier's pentagon -- the Pentagramma Mirificum. Aspects of the argument can be explore in terms of the relation between "planarity" and "globality" (Adhering to God's Plan in a Global Society: serious problems framed by the Pope from a transfinite perspective, 2014).

The experience of the abnormal is necessarily a matter of surprise -- as extensively explored by Nassim Nicholas Taleb (The Black Swan: the impact of the highly improbable, 2007). The surprising nature of the abnormal -- in contrast with linear "business as usual" -- can be creatively envisaged through metaphor as an exercise in cognitive preparedness. Alternatively, any disaster (consequent on failure to do so) may also be framed through metaphor -- typically weather metaphors (as indicated above), for lack of any more meaningful framework. Strategically, the orthogonal transformation of direction is indicative of the need to see the process "in another way" -- an indication of the creative challenge of "new thinking".

Related arguments were developed in separate sections (Insights from Knight's move thinking; Alternative representations: Naturomimicry: sourcing nature for strategic metaphors; Stratagems and ploys characteristic of Knight's move thinking). The Knight is part of the emblem for the US Psyops as a traditional symbol of "special operations" -- signifying the ability to influence all types of warfare. A challenging comparison may be made between the Knight's move, BaGua and the Swastika, illustrated by separate animations (Knight's move, Swastika and BaGua? 2012).

There is a case for recognizing that the 10 Napier's Rules for navigation in spherical geometry are indicative of the distinctive forms of metaphor required for the navigation of globality (Napier's Nifty Rules, ThatsMaths, 12 August 2012). Ironically these are associated with what are termed Napier's Analogies (What is the analogy in Napier's Analogy? Quora).

Cycle of self-closure: A knight's graph is a representation of all legal moves of the Knight over the board. A Knight's tour is the mathematical problem of determining the path the Knight may follow in order to visit each square on the board only (see animation in Wikipedia article). Further insights into the contrast between Predictability and pattern-breaking with respect to the Knight's move are presented separately (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011). Of potential relevance in this respect, in the light of development of the work of Nash, is progress in the visualization of Flat tori in three-dimensional space and convex integration -- the focus of the Hevea Project.

The animation on the left below derives from the argument regarding the Knight's moves. It was notably used to address the challenges of the "blame game" in public discourse -- and the use of weasel words (namely the "slithers", "flips" and "twists" between possible interpretations). In the animation on the right, both forms of the Swastika: left-facing (green) and right-facing (red) are engendered (note the switch in colour and direction -- to the "other" Swastika -- following each "move"). The animations do not necessarily take account of additional patterns of directionality or arrangement. In the case of the BaGua mirror, these are clarified by the screen shots which follow the animations.

Experimental animations indicative of a cyclic pattern of metaphors
(each use of metaphor within an animation is associated with an orthogonal direction)
8 of the Knight's moves across
neighbouring cells of a chess board
Wu Xing cycle (one direction) superimposed
on one BaGua mirror arrangement
Knight's moves superimposed on
one BaGua mirror arrangement
Animation of 8 of the Knight's moves in chess Bagua Wu Xing cycle Animation of succession of Knight's moves across the BaGua

These animations together highlight the role of orthogonality, as indicative of the metaphorical connectivity required to achieve self-closure -- in a global context. Orthogonality is thus indicative of a creative leap of association to a new framework -- engendered at each of the 5 right-angled points of the Wu Xing cycle. There are 4 possible metaphorical transformations at each such right angle, as indicated by the following screen shots -- each of the 5 points constituting a 4-fold nexus. This makes a total of 20 such transformations, suggesting a further correspondence meriting exploration (Memetic Analogue to the 20 Amino Acids as vital to Psychosocial Life? 2015).

The 5 circles on the traditional depiction could be considered a reminder that the Wu Xing pattern is a spherical pentagram -- not planar. Of related significance is the fact that on a sphere the points of the Pentagramma Mirificum are not visible from each other, being effectively "over the horizon" in terms of any "flat earth" perspective from each -- suggesting a fundamental challenge for the comprehension of globality and the implementation of any "global plan"..

Indication of 4 distinct Wu Xing patterns in terms of the Knight's Move transition at each of the 5 points
(colours of no significance; left-most corresponds to the central animation above)
Distinct Wu Xing pattern in terms of the Knight's Move transition at each of the 5 points Distinct Wu Xing pattern in terms of the Knight's Move transition at each of the 5 points Distinct Wu Xing pattern in terms of the Knight's Move transition at each of the 5 points Distinct Wu Xing pattern in terms of the Knight's Move transition at each of the 5 points

The formal contrasts and commonalities between the animations recall arguments regarding the value of exploring the relationship between the 5- and 6-pointed stars that are held to be so profoundly symbolic in the conflicts in the Middle East (Middle East Peace Potential through Dynamics in Spherical Geometry: engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks, 2012). The possibility that belief systems of any significance are necessarily embedded in a 5-dimensional cognitive space then reinforces the arguments for investment in mathematical theology (Mathematical Theology: Future Science of Confidence in Belief: self-reflexive global reframing to enable faith-based governance, 2011).

Integrative inversion: Missing from such 2-dimensional animations is the sense implied by the Pentagramma Mirificum framed by the spherical geometry of globality. There is therefore the implication that only through recognizing the operation of such connectivity on a 3-dimensional surface that the alternative directionalities (indicated by the screen shots above) can be integrated into a single global pattern.

Of relevance in this sense is the fact that the Pentagramma Mirificum has an inverted variant on the reverse side of the sphere -- both being connected by the 5 great circles around the sphere (namely the extension of the 5 curves in the middle animation above). This geometry is remarkably illustrated by the interactive animations of the LaRouche group (Full Circle; The Pentagramma Solid). Less evident are the cognitive, epistemological and experiential significance. Rather than being understood as circles in terms of spherical geometry, the 5 great circles are more appropriately understood as 5 cyclic processes through which the two variants of the Pentagramma Mirificum / Wu Xing are globally integrated.

The nature of the sphere onto which the complementary forms of the Pentagramma Mirificum may be mapped is usefully indicated by exploration of the possibility of mapping the 64 I Ching hexagram conditions onto a sphere (József Drasny, The Reconstruction of the Yi-globe: the spherical arrangement, 2011) as discussed separately (Correspondence between blastosphere and spheroidal I Ching? 2010).

Requisite global connectivity requiring 5-dimensionality? It is through such devices that it may be appropriate to explore the nature of the connectivity characteristic of 5-dimensional space -- and the challenge to its comprehension. Self-closure is presumably a characteristic of the coherence of a "pattern that connects". Indeed if Napier's insights proved vital to navigation around a sphere, why should such insights not be of some relevance to cognitive navigation in a (virtual) global context -- if not a necessity?

It could be argued that this characteristic is helpful with respect to the ordering of cybernetics through the greater degrees of self-reflexivity, implying increasing degrees of cognitive closure. The following schema exploits the Pentagramma Mirificum to offer a tentative holding pattern for seemingly disparate cognitive modalities. It derives in part from the 15 elements of that pattern (separately coloured) which compose the Knight's Move style transformations (3 segments per move), with 4 types of move passing through each pentagram point. Not to be forgotten is that on the other side of the globe there is a second such pattern indicative of a totality of 30 elements of the pattern as a whole, variously associated with the 5 great circles.

Holding pattern for disparate cognitive modes of global integration?
Holding pattern for disparate cognitive modes of global integration?

Of particular interest is the manner in which 5, 10, 15, 20 and 30 can be transformed between each other, most comprehensibly through mappings onto polyhedra and their duals, as separately illustrated (Global strategic significance of 20-fold configurations, 2015; Geometrical configuration of Alexander's 15 transformations, 2010). The work of Beer inspired an effort to map the 1992 Earth Summit issues in that way (Spherical Representation of Icosidodecahedral Net of Strategies: configuring strategic dilemmas in intersectoral dialogue, 1992)

Given the references to chess, go and the Olympic games, to what extent is the complexity of global governance intuitively understood through play (at least to some degree), as separately argued with respect to "Playing" with interrelated metaphors (in Playfully Changing the Prevailing Climate of Opinion; climate change as focal metaphor of effective global governance, 2005; Enacting Transformative Integral Thinking through Playful Elegance, 2010)? It is in this sense that there is a delightful irony to the strategy of the "Pentagon" in seeking to achieve global hegemony through monopolar comprehension.

Poetics of cognitive weather patterns: This argument has emphasized the value of weather in facilitating comprehension of complexity through its multiple manifestations -- beyond those promoted by conventional models. The self-reflexive cognitive mirroring offered by "weather" (and its relation to "whether") is succinctly framed in terms of poetry by biologist/anthropologist Gregory Bateson in explaining why "we are our own metaphor" to a conference on the effects of conscious purpose on human adaptation:

One reason why poetry is important for finding out about the world is because in poetry a set of relationships get mapped onto a level of diversity in us that we don't ordinarily have access to. We bring it out in poetry. We can give to each other in poetry the access to a set of relationships in the other person and in the world that we are not usually conscious of in ourselves. So we need poetry as knowledge about the world and about ourselves, because of this mapping from complexity to complexity. (Cited by Mary Catherine Bateson, Our Own Metaphor, 1991, pp. 288-9)

Curiously it could be said there is a long tradition of representing humans as "5-dimensional", as exemplified by the Virtruvian (hu)man of Leonardo da Vinci. -- although little is made of the cognitive dimensionality corresponding to that visual metaphor. As remarked by Kenneth Boulding:

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

Vitruvian animation?
Vitruvian animation


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