Challenges to Comprehension Implied by the Logo
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27 May 2012

Swastika as Dynamic Pattern Underlying Psychosocial Power Processes

Implicate order of Knight's move game-playing sustaining creativity, exploitation and impunity

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Quest for more powerful metaphors
Swastika as a cultural universal?
Intuitive sense of subtle processes expressed through metaphor
Knight's move thinking: appreciated or deprecated
Insights from Knight's move thinking
Alternative representations: Knight's move, Swastika and BaGua ?
Naturomimicry: sourcing nature for strategic metaphors
Stratagems and ploys characteristic of Knight's move thinking
Complementary patterns of higher dimensional "avoidance"
Competition as war -- between the "faculties"
Eight clusters of players in the global financial board game?


This speculative exploration is not about the problematic (neo) Nazi use of the Swastika, nor is it about the use of the Swastika as a traditional symbol much valued in many cultures of the world. However it does suggest further insights into why the Swastika has been recognized in such contexts and why those contrasting uses merit further reflection.

The concern here is the nature of the game-playing in society amongst those empowered to engage in it. More specifically it is concerned with the cognitive and strategic skills associated with such game-playing -- whether for imaginative purposes enhancing social well-being, or in the devious and irresponsible exploitation of that well-being. In this sense, rather than preoccupation with the Swastika as a symbol, the concern is with the nature of a well-hidden game of which it is indeed an appropriate symbol, enabling a powerful pattern of thinking.

Of particular concern is why that confidence game is so difficult to identify -- to "put one's finger on" -- namely why it appears to operate beneath the level of collective consciousness. Being "under the radar", it is perhaps consistent with the arguments of John Ralston Saul (The Unconscious Civilization, 1995). Of further concern, is why those who engage in it so blatantly are able to escape any effective indictment -- as so well illustrated by the denial of any responsibility on the part of those with key roles in enabling the current financial crisis.

The argument here presents the form of the Swastika as emerging from a pattern of Knight's moves, both as recognized in chess and as valued in imaginative strategic processes. This is typically named as "Knight's move thinking" -- also recognized in a pathological form, appropriate to the ambiguity calling for recognition. This move has been a key to consideration of the nature of surprise in strategic competition, whether from the perspective of the winner or of the loser. As a potentially key systemic pattern in a period of crisis, the consequence of banning the display of the Swastika then merits further consideration as an inhibition of collective learning. This obscures potential recognition of how crimes against humanity are engendered and perpetrated as well as the nature of a possible key to a sustainable pattern of development dynamics.

The concern here is to go beyond simple acknowledgement of that strategic modality -- for good or ill -- in order to distinguish a pattern emerging from the variety of such "moves". This is considerably facilitated by relating that pattern to the Chinese traditional configuration of the BaGua. Of particular relevance at this time is the interface this may offer for cognitive engagement with natural processes. Beyond recognition of biomimicry, this suggests the possibility of "naturomicry" as a means of ensuring a missing psychological engagement with sustainability, as previously explored (Psychology of Sustainability: embodying cyclic environmental processes, 2002).

Quest for more powerful metaphors

At the time of writing, in the midst of unprecedented global financial crisis, the International Herald Tribune (19-20 May 2012) carries an article by Robert J. Shiller titled A metaphor for finances that deceives (p.12), continuing on a later page under the title The improper metaphor can pose a threat to national economies (p.14). It is however carried in the online edition of its associated publication as  How National Belt-Tightening Goes Awry (The New York Times, 19 May 2012). Citing the cognitive linguistic work of George Lakoff and Mark Johnson (Metaphors We Live By, 1980), Shiller asks:

Why is there such strong political support for fiscal austerity, for government cuts and layoffs, at a time of widespread unemployment? Maybe it's because we have the wrong metaphor stuck in our minds, and it's framing policy choices in a misleading way... Our metaphors are like the icons on our computer screen, little pictures by which we condense complexities into manageable packets to refer to in our decision-making. Our brains may be hard-wired for them. Consider our current thinking about taxes and government spending. We seem caught up in a "family belt-tightening" metaphor, in which the nation is a family that has outspent its income and is trying to get back in control.

He concludes:

And the family belt-tightening image continues to dominate public discussion worldwide, making the public-stimulus debate largely off-center and irrelevant. Clearly, if we want to garner public support for some much-needed balanced-budget stimulus, we have to work on our metaphors.

He offers as an alternative metaphor "a winter on the family farm" -- to which bloggers have responded critically (Metaphorically Speaking, Econospeak, 20 May 2012), but without being able to offer a better alternative. Inspired by the use by John Maynard Keynes of "animal spirits" as descriptors of emotional drives, Shiller is co-author with George A. Akerlof of a study of the role played by the emotions in influencing economic decision-making (Animal Spirits: how human psychology drives the economy, and why it matters for global capitalism, 2009).

In a period when the retreat of NATO forces from Afghanistan is to be framed by the slogan Afghanistan, Good Enough, Shiller's argument could be framed as Belt-tightening, Not Good Enough. The more general argument developed here is that global civilization is faced with a metaphorical crisis which calls for more powerful metaphors -- of the kind of which the Swastika is indicative.

The need for a new metaphor has been variously articulated by Subhash Sharma (Towards A New "Earth Sastra": rethinking economics through integration of Indian thought and economics, Indian Economic Association, 2011; Holistic Globalisation: implications for women in management and development. In: Globalization at the Crossroads, 2008):

 In fact, for achieving holistic globalisation i.e. a balancing in the society, we need a new metaphor i,e, wisdom metaphor because wisdom implies a balancing and it also represents 'grounded praxis' wherein philosophy, reality and action are integrated.... To understand the concept of holistic globalisation, we need to understand the dynamics of forces that influence the globe. Four fundamental forces that influence us are as follows: (1) Force of Market; (2) Force of State/Government; (3) Force of People/Force of Social Movements/People's Institutions; (4) Force of Self/Spirituality. These four forces constitute the 'world-swastika' and when they are in harmony, there is synergy in the society. (pp. 307-308)

Sharma has also presented a "swastika analysis" of Indian society in terms of social discourse analysis (Indian Society 2004: Matrix and the Circle. Southern Economist, 43, 8, August 15, 2004, pp. 5-8).

Swastika as a cultural universal?

For Rhawn Joseph (Multi-Regional Symbolism From: Neuropsychiatry, Neuropsychology, Clinical Neuroscience, 2000):

Across time and over the centuries humans have also "invented" the same symbols, and/or respond to the same symbols with similar feelings of emotion or spiritual awe (Campbell, 1988; D'Alviella, 1894; Frazier, 1950; Joseph, 1996; Jung, 1964). This includes, for example, the "cross" and the "swastika" as well as the triangle and circle. The sign of the cross is a religious symbol employed by the Sumerians, Babylonians, Egyptians, Africans, and the ancient Europeans and Americans including the Mayas, Aztecs, and plains Indians. The swastika also appears world wide, and has been employed for thousands of years.

The question meriting continuing reflection is why the Swastika has been so widely appreciated across cultures and down the ages. This usage is well-indicated by the following poem.

The Original Swastika
(reproduced with permission from Michael Meyerhofer, Damnatio Memoriae, 2011)
Look for it on Thor's hammer,
shards of Greek pottery, silk tapestries
from old China. Whittled by Ukrainians
in spans of mammoth bone, sewn
into the feathered gowns of Quetzalcóatl.
Raised rune over the Buddha's heart.
Crest of the early Christians
who borrowed from the very Romans
they were hiding from, long after
its axles and rays symbolized rebirth
in the belly of a Trojan goddess.
In Hinduism, marking thresholds and doors.
A Navajo prayer for good fortune,
a metaphor balancing mountains and rain.
Sometimes backwards, sometimes not.
Sometimes, the arms are replaced
with a woman's blowing hair.
Sometimes the tips end in playful swirls
to symbolize migration. Luck
tattooed in lime, scattered
on the pewter coins of Gaul.
Ages before the cross or the ankh,
before black snow piled on the hoods
of German sedans, this one symbol
spread across oceans. A genetic dream.
Our birthright, our redemption-fueling
the pyres of all we've already lost.

Many have noted the manner in which Hitler exploited the Swastika. Less evident is why this exploitation of the symbol "worked" so evidently and tragically. The argument here is that the symbol is indicative of subtle processes which cannot be readily "grasped", however effectively they may be enacted in practice. The question is what are those processes and how to approach an understanding of them -- given that conventional efforts at "grasping" them may be completely incompatible with their nature.

Some sense of this is offered in the following elegant description of these processes by a personage, variously considered problematic in his own right, notably as a consequence of his strategic skills, namely Bhagwan Shree Rajneesh. In discussing the Swastika and the Cross embedded in it, he argues that science and religion are different in that science is a kind of "rape" of reality, seeking to conquer, disrupting its natural equilibrium and harmony. He contrasts that with religion, which he understands as a process of wooing reality -- a courtship (The Dhammapada: The Way of the Buddha, Vol. 4 Chapter 10: Aes Dhammo Sanantano). This can be argued otherwise, contrasting "discover" with "enchant" (Beyond Harassment of Reality and Grasping Future Possibilities: learnings from sexual harassment as a metaphor, 1996). He emphasizes the subtlety required for certain forms of understanding, as recognizes in the extensive literature on apophasis, the indirection of "not saying" -- in contrast to the assertive discourse of cataphasis. The distinction has implications for the understanding of identity (Being What You Want problematic kataphatic identity vs. potential of apophatic identity? 2008).

It is in this context that the nature of that subtlety may be better comprehended through metaphoric allusion, through parables and stories -- avoiding a mode of seeking to "grasp" it. This has been well expressed by the 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, pp. 288-9)

The question in the following exploration is the nature of the subtlety, underlying representation by the form of the Swastika, whether it is expressed creatively or exploitatively. As implied by apophasis, the subtlety is characterized by a form of emptiness as expressed in Thomas Merton's interpretation of The Pivot of Chuang Tzu:

Tao is obscured when men understand only one of a pair of opposites, or concentrate only on a partial aspect of being. Then clear expression also becomes muddled by mere word-play, affirming this one aspect and denying all the rest.... The possible becomes impossible; the impossible becomes possible. Right turns into wrong and wrong into right -- the flow of life alters circumstances and thus things themselves are altered in their turn. But disputants continue to affirm and to deny the same things they have always affirmed and denied, ignoring the new aspects of reality presented by the change in conditions. The wise man therefore... sees that on both sides of every argument there is both right and wrong. He also sees that in the end they are reducible to the same thing, once they are related to the pivot of Tao. When the wise man grasps this pivot, he is the center of the circle, and there he stands while "Yes" and "No" pursue each other around the circumference.(The Way of Chuang Tzu, 1970)

To what extent does the form of the Swastika allude to such subtlety in practice?

Intuitive sense of subtle processes expressed through metaphor

Use of metaphor: The argument here is that there is a degree of recognition, through common (metaphorical) expressions, of processes that cannot be fully "grasped" through rational categories. In relation to the following argument regarding the L-shaped Knight's move in chess, the longer portion of the "L" can be understood as a form of  normalcy and linearity -- the phase of longer duration which purportedly characterizes it. Whereas the shorter phase in the process is the unexpected necessarily more sudden). In chess either may precede the other: predictability followed by surprise, or surprise followed by predictability.

Some examples, used metaphorically, might include:

These have reverse possibilities in which the sudden surprise precedes a form of predictability, which follows over a more extended period of time. This gives two variants: "do the dirty", then "go clean" (under a cloak of respectability), or else "go clean" (building credibility), then "do the dirty". Perhaps:

The change in orientation may be expressed through "geometrical" metaphors, as with went "round the bend" (implying a degree of craziness), but especially as being "bent" or "crooked" (implying a degree of evil). The "geometry" may take the form of recognition of "closedness" in contrast to "openness". Ball-game and marching metaphors may be used as in "switching foot", namely taking a new stance facing the opposite direction, possibly "wrong-footing" others (who experience this as being "off-footed)

Attention may focus on the lack of transparency, namely a perception of stealth rather than openness, as with being "under-the-table" rather than "on-the-table". There may be a sense that "dirty tricks" are used on occasion, cloaked by the highest respectability -- perhaps recognition of a "wolf in sheep's clothing".  The exception to normalcy in marital relationships may be expressed as a "bit on the side". More generally this may be recognized as betrayal of a bond or agreement, or more simply "cheating". Following the switch, the perpetrator may be considered to be "unrecognizable" -- having "shifted shape".

As questioned by observers, relationships may involve one partner "getting their hooks into" the other, who may not recognize the process until it is too late.

For those experiencing the process there may be considerable difficulty in "putting their finger on" how they have been "screwed" or "shafted" -- despite sensing that this has occurred. This may be the essence of the most artful confidence tricks. It may be a case of "now you see it, now you don't", which in the case of corrupt practices may be the equivalent of the "Find the Lady" fair game.

Collective instances: As with individual instances, in the collective case what might be claimed to be inappropriate is readily a focus of denial, accompanied by vigorous claims of innocence and assertions of offended honourablity. Any blame may simply be deflected. On a larger scale much use may be made of the media "spin", as recognized in questionable marketing and politics.

A previous effort to articulate the nature of the intimate cognitive involvement in recognizing the pattern of assumed innocence and vigorous denial of implication, used the "who me?" experience of snoring (Snoring of The Other a politically relevant psycho-spiritual metaphor? 2006). The experience also characterizes the difficulty of discussing it "objectively". The surprising nature of the "unforeseen" phase has been most usefully explored on a larger scale as black swan theory by Nassim Nicholas Taleb (The Black Swan: the impact of the highly improbable, 2007). This can be understood as clarifying the challenge to the expectation of the predictability of the longer phase. An appropriately shocking example was provided by the scandal of the "creative accounting" of the Enron corporation in 2001.

The current period of financial crisis has focused heightened attention of those various complicit in its emergence. One particular concern, when remedies are sought through austerity strategies, is the extent to which major multinational corporations engage in tax avoidance -- the legal utilization of the tax regime to reduce the amount of tax that is payable by means that are within the law. This compounds issues relating to tax evasion  -- the evasion of taxes by illegal means -- especially when this cannot be satisfactorily proven in a court of law.

People are increasingly aware of "injustice" when confronted with facts relating to these matters. In the USA for example, a recent study found that of 280 companies, all of them on the Fortune 500 list, while the federal corporate tax code ostensibly requires big corporations to pay a 35 percent corporate income tax rate, on average, the 280 corporations in our study paid only about half that amount. And those who paid even half the statutory corporate tax rate paid far more than many of their competitors.  78 corporations had at least one year (in the past three) where they paid no federal income tax at all, while 30 corporations paid nothing, even though they made $160 billion in profits over that period (Robert S. McIntyre, et al., Corporate Taxpayers and Corporate Tax Dodgers 2008-10, Citizens for Tax Justice and Institute on Taxation and Economic Policy, November 2011). Equivalent situations exist within the European Union where questionable advantage can readily be taken of the different tax regimes.

Clearly the phenomenon is even more extensive elsewhere, as implied by the rankings of the Corruption Perceptions Index (CPI) published by Transparency International. Beyond the question of strict legality of such avoidance, where this is claimed, are the moral and ethical issues at a time when individual tax payers are called upon to endanger their livelihoods, and those of their descendants, in order to bailout corporate entities and the financial system in which they are implicated.

In a world much characterized by crime, corruption, racketeering and blackmail of every kind, the issue is increasingly how major institutions acclaiming their respectability, and even their social responsibility, manage to place themselves in this advantageous situation -- with the complicity of governments competitively engaged in offering tax avoidance regimes. The sense for many is that such corporations increasingly merit recognition as being "bent" in some manner, if only in the manner in which they successfully "bend" the law to justify actions which are challenged as morally unjust.

In the following exploration the legality can be understood as the longer portion of the "L", whereas the "creative accounting" is the shorter "deviant" portion which is morally suspect, even if it can be upheld as legal. Ironically, at a time when the quest for "alternatives" is officially deprecated, the "deviant" portion effectively operates under an "alternative" logic, irrespective of whether this justifies "dirty tricks".

The advantage for the perpetrators -- but a difficulty in demonstrating their innocence -- is that in many instances they have the right to shield their activities under confidentiality laws. Suspicions are compounded by the facility with which corporations can seek injunctions on release of relevant details -- further compounded by the existence of "superinjunctions" to prevent any discussion of the existence of such injunctions or the matters to which they apply. Their employees are necessarily obliged to sign non-disclosure agreements. Commentators may well challenge any criticism as totally unjustified -- especially when employed by media owned by the corporations in question.

Whilst much may be legal, "stink" is a metaphor many find relevant. Just how do they do that? The following image is the first of others (below) -- offering a visual metaphor of the cognitive challenge.

Schematic representation of Knights of Industry
at a negotiation table ?

(necessarily concealing what is "under-the-table")
Schematic representation of Knights of Industry at a negotiation table ?

Knight's move thinking: appreciated or deprecated

Chess and Go: In chess the movement of the knight is unusual compared to other chess pieces. It can either move two squares horizontally and one square vertically, or two squares vertically and one square horizontally. In both cases the move resembles the form of the letter "L". Unlike other pieces, the knight can "jump over" others to reach its destination -- capturing a piece of the opposite colour if it occupies that destination square. In the game of go, a Keima is recognized as a "Small Knight's move" and an Ogeima as a "Large Knight's move" -- because of their resemblance to the move in chess.

Considerable attention has been given in graph theory, to the pattern of such moves over an 8x8 chess board (or those of larger size). 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). One, discovered byEdward Falkber yields a pattern at its center resembling a stylized swastika.

Many potentially valuable insights are to be associated with explorations of the Knight's tour and its representation, most notably following the work of Dan Thomasson (Knight Tours. Internet Chess Club, 2001; Knight Tour Tessellations). Mathematical interest is especially focused on the Knight's Tours associated with the so-called magic squares on boards of various sizes, as previously discussed (Sustainability through Magically Dancing Patterns: 8x8, 9x9, 19x19 -- I Ching, Tao Te Ching / T'ai Hsüan Ching, Wéiqí (Go), 2008; 9-fold Magic Square Pattern of Tao Te Ching Insights -- experimentally associated with the 81 insights of the T'ai Hsüan Ching, 2006).

Strategically creative: The Knight's move has long been associated with creativity and strategic surprise. 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. It featured as the name of a German military operation (Operation Rösselsprung) to kill or capture Josip Broz Tito at Drvar during World War II. With respect to business strategy, Richard Pech and Greg Stamboulidis make the point that:

Utilizing a chess metaphor, they each deployed a knight's-move strategy, leaping forward and sideways in a manner that has caught, and continues to catch their linear-thinking competitors by surprise. (How strategies of deception facilitate business growth, Journal of Business Strategy,  31, 2010, 6, pp. 37-45)

In a discussion of the current disruptive dynamics of global governance, termed "monkeying" for the purpose, as case was made for Reframing "monkeying" in terms of Knight's move patterns (2011). As discussed in another context (Navigating the psychological forces of "communication space", 2003), the knight's move in chess is especially interesting given their potential significance as the moves of a knight -- as a "noble" rather than as a "commoner". The strangeness of the knight's move, and its numerical symbolism, has traditionally been the focus of hypotheses connecting the origins and structure of chess with secret magical and religious rituals of ancient India.

Further insights into the contrast between Predictability and pattern-breaking with respect to the Knight's move, featured in a subsequent exploration (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics,  2011). This notably featured the following animation.

Animation of 8 of the Knight's moves
(potentially suggestive of dynamics within the blame game
and amongst the Knights of the Round Table)
Animation of 8 of the Knight's moves (in chess)

Defamiliarization: As indicated above, the longer portion of the "L" in the Knight's move can be usefully associated with predictability -- especially that of linear thinking. The shorter portion is then usefully indicative of non-linear thinking. In literature, Victor Shklovsky, in relation to his technique of "Making Strange" has associated the Knight's move with the concept of ostranenie or defamiliarization, also translated as "estrangement" (The Knight's Move, 1923, p. 39). He argued for the need to turn something that has become over-familiar, like a cliché in the literary canon, into something revitalized. Michael Dorland (The Knight's Move: Reflections on the Translation of Culture/s.  In: Jean-Paul Baillargeon (Ed.) The Handing Down of Culture, Smaller Societies, and Globalization):

The Russian formalist critic Viktor Schlovsky once remarked that the movement of ideas corresponds to "the knight's move" in chess. In other words, it is not direct; it seems direct at first, then veers unexpectedly. An example is provided by the Russian Revolution itself. Undertaken on the gamble that the European proletariat would also rise up following the Bolshevik lead, and so provide the developmental basis for worldwide socialism, what occurred instead was "socialism in one country," a very different scenario from that of the Marxist theory of stages of historical development. Similarly in China, what began as an urban working-class movement became the basis for the encirclement of cities by peasant guerrillas; an idea further modified by the Cuban and Latin American experience in which "self conscious" revolutionary intellectuals willed revolution into being through acts of armed struggle.

The Knight's move has been related to a "leap of faith" by James E. Loder and W. Jim Neidhardt (The Knight's Move: the relational logic of the spirit in theology and science, 1992). In his extensive review, Richard H. Bube (The "Strange Loop" of Complementarity, Perspectives on Science and Christian Faith 45, December 1973, 270):

The book is concerned basically with an expression of complementary thinking that facilitates positive interaction between science and Christian theology. The symbol of "the Knight's move" refers to the unique move of the chess piece that is the only one not moving in a straight line, as an indicator of a leap of insight or a leap of faith. The book also draws heavily on the symbolism of the Moebius strip, the two-dimensional "strange loop" twisted in the middle, which has a two-dimensional surface that can be totally traversed with continuous motion along the strip.

The purpose of the book is described as an effort to "engage the contemporary cultural fragmentation between theology and science in such a way as to counteract any assumption that each is a universe of discourse closed off from or radically incommensurate with the other." "The creative work of this book has attempted to disclose a bipolar-relational unity in which science and theology, while preserving their respective disciplinary identities, participate in dialogue according to the strange loop model" (p. 307). Or again, "The central concern behind this study is not a critique of culture. It is rather an interdisciplinary search for ways, models, and patterns by which we can approach the inherent order of creation and facilitate some reintegration of the fragmented fields of study in our culture" (p. 7).

In an Appendix, the authors summarize "some of the significant strange loop relationality structures in theology and science." In theology, examples given are: deity/humanity in the nature of Jesus Christ; Holy Spirit/human spirit in the concept of spirit; the presence of Christ/community of believers in the church; and prayer/reflective study in theological productivity. In science, examples given are: contingent intelligibility/physical structures of the universe in the ontology of natural science; mathematical pattern/empirical structures in the epistemology of natural science; wave-like/particle-like behavior in quantum science, and mind/body in human consciousness.

Pathological and schizophrenic: Curiously, but most appropriate to this argument, "Knight's move thinking" is defined by the medical profession as a thought disorder denoting a lack of connection between ideas, namely a loosening of associations. Considered to be similar to derailment of thought, it is characterized by odd, tangential associations between ideas that lead to disruptions in the smooth continuity of speech. The association between ideas is interpreted to be illogical, notably wandering between various trains of thought. The Knight's move is then a metaphor for the unexpected, and illogical, connections between ideas. The illogicality of the loosening of associations, which is found in schizophrenia, is contrasted with the flight of ideas which characterises hypomania. "Knight's move thinking" therefore features in the early diagnosis of schizophrenia.

Gerard Drennan and Leslie Swartz (The paradoxical use of interpreting in psychiatry, Social Science and Medicine, 2002) argue that features such as loose associations, Knight's move thinking and derailment are well-defined and can therefore be quite clearly taught and illustrated, whereas others are more amorphous and rely a great deal on an overall impression of the patient's speech. For G. J. Turnbull (The Psychiatric Evaluation of Air Crew, 2006), "Knight's move" thinking is equated with "thought loss".

A literary perspective is offered by Elizabeth Anderson is offered in a critique ("The Knight's Move": fluidity of identity and meaning in Mary Butts's Armed with Madness, Women: A Cultural Review, 18, 3, 2007, pp. 245-256).

There seems to have been no effort to reconcile the cognitive implications in the two contrasting usages of Knight's move thinking. Worse, it would seem that there is an effort by the psychotherapeutic professions to treat non-linearity (valued in creativity, especially strategic creativity) as pathological. The so-called "loosening of associations" has proven to be variously essential to non-linear recognition of "correspondences" in both the sciences and the arts. The cognitive challenge has been highlighted in the question raised by Kenneth Lyen (Beautiful Minds: is there a link between genius and madness? SMA News, March 2002, 34, 3)

Certain mental disorders like schizophrenia and bipolar disorder are characterized by sudden jumps in one's thinking. These leaps from one idea to another can be quite unexpected and illogical, and are referred to as Knight's Move thinking. This way of thinking is important in the creative process because it enables a person to make innovative leaps without being anchored to preconceived ideas or imprisoned by one's sense of logic.

The issue is how to distinguish the pathological correspondences from the healthy, especially when the distinguishing process may overly rely on a form of rationality which inhibits such recognition. When is an aesthetic correspondence, perhaps enshrined in poetry, to be considered pathological -- and by whom? Understandings of correspondences have been explored separately, notably in the light of monstrous moonshine mathematics (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007; Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).

It would appear that the psychotherapeutic professions have trapped themselves into equating linearity with desirable normalcy and non-linearity with the pathological -- as they choose to define it. This might be understood as an explanation for the conclusions of the study by James Hillman and Michael Ventura (We've Had a Hundred Years of Psychotherapy - And the World's Getting Worse, 1993).

In this respect it is amusing to note that the proposed new edition of the "bible" of psychiatric diagnosis -- the Diagnostic and Statistical Manual of Mental Disorders -- is currently faced with controversy regarding the reliability of diagnoses. The reliability in some cases has been claimed to be little better than chance (Peter Aldhous, DSM-5 in New Scientist: psychiatry's new diagnostic bible is creating headaches for doctors and patients alike, New Scientist, 19 May 2012). The final wording determines those who receive psychoactive drugs, insurance health coverage, or indefinite incarceration in secure mental hospitals. (cf H. A. Archera, et al., Knight's move thinking? Mild cognitive impairment in a chess player, Neurocase: the neural basis of cognition, 2005; Ashley Rule, Ordered Thoughts on Thought Disorder, The Psychiatrist, 2005 29, pp. 462-464). It might be asked whether any one school of psychotheraphy would fail to diagnose another as suffering from some form of Knight's move thinking.

The contrast between the appreciation of Knight's move thinking and its deprecation as pathological is usefully summarized in uses of "crazy" in relation to creativity. In the scientific arena this is neatly articulated by the following much-cited exchange.

"Craziness" and Knight's move thinking

Physicists proudly refer to the much-quoted statement by Niels Bohr in response to Wolfgang Pauli -- both Nobel Laureates:

"We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough."

To that Freeman Dyson added:

"When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope!" (Innovation in Physics, Scientific American, 199, No. 3, September 1958)

The question with regard to the much-sought "new thinking" with respect to "global governance", and the "governance of globalization, is whether any theory is "crazy enough" -- as may well be essential.

Reproduced from: Quest for a "universal constant" of globalization? Questionable insights for the future from physics (2010)

Insights from Knight's move thinking

Irrespective of any admiration associated with Knight's move thinking, the challenge is to locate articulations of how it works -- other than as a symbol. This may be clear in board games such as chess and go, but it is not clear how strategic competitive advantage in those arenas translates into other domains -- where it may indeed be valued as a symbol.

It is therefore a pleasure to discover the keynote speech to the 3rd Redesigning Pedagogy International Conference (Singapore, 2009) by Erica McWilliam (The Knight's Move: its relevance for educational research and development, 2009):

This paper utilises the "knight's move" in chess as an analogy for broadening our repertoire of research epistemologies, methodologies and relationships. It explores the imperatives for moving on from a simple reliance on 'straight line' thinking in educational inquiry and pedagogical practice in order to utilize and enhance our epistemological agility and thereby mobilize a more nuanced "second generation" of educational research. It is argued that the strategic deployment of "knight's move" methodologies is more in keeping with contemporary forms of cultural production but will better serve inquiry into the very complex problems that need successful resolution in this century, and the sorts of relationships we will need to develop with other non-traditional players.

McWilliam reinforces the case for recognizing the future as requiring Knight's move thinking as articulated by William Gosling (Helmsmen and Heroes: control theory as a key to past and future, 1994):

As has been demonstrated in recent times, the future is not what is used to be. According to control theorist William Gosling (1994), the future will be neither more of the same nor a gradual process of improvement or decline....Change in the twenty-first century will be, according to Gosling, of an order that he terms "the knight's move". In other words, change will not have a gradual trajectory in the future, yet neither is it likely to be chaotic. In anticipating irregular patterns of 21st century change, we are challenged to re-think 'straight road' programs of educational research and development, and the assumptions they make about the linear-cumulative nature of learning....

Usefully McWilliam associates the Knight's moves with epistemological agility:

Epistemological agility, then, is an important ingredient in building the "second generation" research teams needed to tackle the very complex problems we have yet to grapple with successfully in this century. It is a creative capacity for holding disparate things together long enough to generate a new or third space or idea, or, as Norman Jackson puts it "to move an idea from one state to another"... Albert Einstein once explained this intellectual activity as a form of combinatorial play that connects concepts rarely combined. It demands an ability (on the part of individuals and groups of individuals) to hold large numbers of associations together and then select the particular associations that offer interesting possibilities.

However it is the detailed articulation of how patterns of Knight's move thinking may be combined that McWilliam offers the most valuable insights of relevance to the case made here. Helpfully she contrasts her use of that approach:

The knight's move is The knight's move is not
1. It is an analogy.
2. It is a tool for thinking with.
3. It is unpackable as an impetus to strategy.
4. It keeps us focused on the main game - explanatory power.
1. It is not a methodology.
2. It is not an attempt to re-enter or restore old qualitative vs. quantitative debates.
3. It is not a rejection of the value of rational science.
4. Like all other metaphors, it is not endlessly milk-able.

Especially valuable is McWilliam's ability to adapt the formal insights of Dan Thomasson mentioned above, as a means of showing the complementarity of four disparate cognitive modes, notably with respect to representatives of different sets of stakeholders or disciplines who are called upon to work together.

Patterns of Knight's moves on a 8 x 8 matrix
(images reproduced from Dan Thomasson, Knight Tour Tessellations, 2002)
Mapping of 4 different sets of Knight's moves Integrative interlocking of the 4 different sets of moves
Distinct patterns of Knight's moves on a 8 x 8 matrix Distinct patterns of Knight's moves (Integrative interlocking)

McWilliam look at the tessellated patterning produced by multiple Knight's moves as a metaphor for designing respectful and productive research partnerships. This is seen as a break from the taken-for-granted field of partnerships and the strategies for achieving and sustaining them. In the case of education, it would mean that more time  could be devoted to engaging with innovative thinkers and designers in the commercial and not-for-profit sectors, rather than staying inside the smaller world of professional educators alone.

Alternative representations: Knight's move, Swastika and BaGua ?

Pattern of distinct Knight's moves: The variety of Knight's moves is usefully represented within a 3x3 matrix as shown below. Two sets of patterns may be distinguished: those passing around the central cell and those passing through the central cell (without starting or finishing there). Both bear a resemblance to the traditional yantra.

Pattern of Knight's moves in a 3x3 Matrix
Note that a move cannot start or finish in the central cell in a 3x3 matrix
8 Moves passing through the central cell 8 Moves passing around the central cell
Pattern of Knight's moves in a 3x3 Matrix (through centre) Pattern of Knight's moves in a 3x3 Matrix (around centre)

Formation of Swastika from Knight's moves: Complementary (or mirror image) paths, taken by two Knight's moves through the centre (left-hand image above), may be combined -- thereby to form opposite branches of a Swastika. This can be represented through the following animations.

Swastika emergent (by optical illusion) from the dynamics of Knight's moves across a 3x3 Matrix of cells
(note that any Knight's move goes from white to black or from black to white, through the centre)
Left-facing Swastika Right-facing Swastika
Emergent Swastika  from the dynamics of Knight's moves across a 3x3 Matrix of cells (through centre) Emergent Swastika  from the dynamics of Knight's moves across a 3x3 Matrix of cells (around centre)

A similar approach can be taken with the "Contextual" set of Knight's moves -- those avoiding the centre.

"Avoidance container" emergent (by optical illusion) from the dynamics of Knight's moves across a 3x3 Matrix of cells
(note that any Knight's move goes from white to black or from black to white, around the centre)
Left-facing "container" Right-facing "container"
 Avoidance container (left facing)  emergent from the dynamics of Knight's moves across a 3x3 Matrix of cells Avoidance container (right facing) emergent  from the dynamics of Knight's moves across a 3x3 Matrix of cells

The "Avoidance Container" and Swastika can be readily combined together in further experimental animations -- of which the following is one example.

Animation cycle showing emergence of "avoidance container"
from merged Swastikas (left- and right-facing)
Animation cycle showing emergence of  avoidance container as a Swastika

Swastika and BaGua: The Knight's moves, and the Swastika in both its forms, can be understood in relation to the Chinese BaGua and the 8 trigrams of which it is composed configured around an empty centre. Each trigram is denoted and distinguished by a characteristic configuration of broken and unbroken lines. The relation is represented in the following animation.

Animation of superposition of Swastika on BaGua "Earlier Heaven" Arrangement
(transformation of trigram coding consistent with Knight's move,
namely reflection across the centre or change of line pattern for the "sting")
Left-facing Swastika
Right-facing Swastika
Animation of superposition of Swastika (left facing) on BaGua - Earlier Heaven Arrangement Animation of superposition of Swastika (right facing) on BaGua Later Heaven Arrangement

Qualitative distinctions: The BaGua pattern is of special interest in that it has been traditionally used to hold and distinguish the eight fundamental meanings associated with them as indicated below. As conditions of nature, these offer cognitive significance through their metaphorical implication.

Chinese interpretation of the eight trigrams -- ?? Baguà
(reproduced from Wikipedia)
? Qián
? Duì
? Lí
? Zhèn
? Xùn
? Kan
? Gèn
? Kun
Heaven/Sky Lake/Marsh Fire Lightning Wind Water Mountain Earth
? Tian ?(?) Zé ? Huo ? Léi ?(?) Feng ? Shui ? Shan ? Dì
As suggested here, this makes a qualitative distinction between the different Knight's moves -- each effectively defined by a pair of BaGua conditions (at the start and end of the move) -- in contrast to the purely formal distinction conventionally made between them as in chess. Note that if direction is taken into account there are then 32 Knight's moves. In a Swastika pattern this means that the left- and right-facing Swastika each then holds 16 moves.

Animation of succession of Knight's moves across the BaGua
engendering both forms of Swastika: left-facing (green) and right-facing (red)
Note the switch in colour and direction -- to the "other" Swastika -- following each "move"
Animation of succession of Knight's moves across the BaGua

Naturomimicry: sourcing nature for strategic metaphors

Biomimicry: There is much current interest in biomimicry as a source of inspiration for technical innovation. That argument with respect to the features of the environment can be extended to include the artefacts of technology, as separately discussed (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011). The argument can be extended further to the processes of nature -- perhaps as "naturomimicry".

A degree of recognition to learning from natural processes is offered by Adi Wolfson, Dorith Tavor and Shlomo Mark (Sustainable Services: the natural mimicry approach, Journal of Service Science and Management, 2011). They argue, with respect to their sector, that a natural mimetic approach follows the ground rules of nature to characterize the sustainability of a service and to choose the most sustainable service alternative.

A form of biomimicry is of course to be recognized in management texts such as that of Dudley Lynch and Paul Kordis (Strategy of the Dolphin; scoring a win in a chaotic world, 1988). Here management is urged to think like a "dolphin", rather than a "shark", in order to keep on top of the "carps". A reviewer in a management journal greeted it as "a welcome respite from other management books that urge us to think like samurais, Attila the Hun, or members of the Prussian General Staff.".The point to be made, as discussed separately, is whether a more systematic approach is required to discover what metaphors are beneficial to management thinking under what circumstances (Governance through Metaphor, 1987; Metaphoric Revolution: in quest of a manifesto for governance through metaphor, 1988). It may indeed be useful to think like a shark, or like a carp, under certain circumstances. A more surprising metaphor has been explored by Greg Hearn (If Your Company Were a Cockroach: how to survive in the new business ecology, 2007)

Metaphors from nature: Much valuable inspiration from nature in general, rather than any particular species, has however been intimately related by the Chinese to the philosophy of BaGua -- whose formalism is presented above. The strategic applications, and their cognitive implications, have notably been recognized in one of the three schools of martial arts: Baguazhang. This adapts the BaGua principles in the light of understanding of the eight trigrams (identified above) -- each intimately associated with a natural condition or process.

A classic Japanese text on swordsmanship, and the martial arts in general, by Miyamoto Musashi (The Book of Five Rings / Go Rin No Sho) continues to be valued for its strategic insights. The "rings" correspond to five chapters: The Book of Earth, The Book of Water, The Book of Fire, The Book of Wind and the The Book of Void. These could be readily associated with the BaGua/Swastika pattern above.

It is such possibilities which are justified in some detail by Susantha Goonatilake (Toward a Global Science: mining civilizational knowledge, 1999) as discussed separately (Enhancing the Quality of Knowing through Integration of East-West metaphors, 2000). It should be noted that many strategic management texts currently emerging from Asia  already derive insights from such cultural resources. Valuable insights are offered by A. C. Graham (Yin-Yang and the Nature of Correlative Thinking, The Institute of East Asian Philosophies, 1986).

Transformation pathways characteristic of nature: Given the arguments above regarding "naturomimicry" in relation to the distinctions of the BaGua, there is a case for exploring the logical connectivity favoured by the psychiatric professions in terms of the degree of looseness of associations evident in the different states of matter, most typically water -- a symbol of human consciousness in its own right. In the case of water, the "connectivity" is framed there in terms of degree of molecular bonding. Clearly the mode favoured by those professions requires a high degree of bonding as an exemplification of normalcy -- corresponding to "solid" in the phase diagram below. Other modes are effectively deprecated without question. Water can however transform from its solid form into a liquid form, or into a gaseous form -- as the degree of bonding decreases. All forms are valued. One might ask what form might be associated with "wisdom".

Data -- Information -- Knowledge
Tentative adaptation of general phase diagram (for water)
to suggest their non-linear relationship
(Reproduced from a discussion of Reification of the present, 2003)
Phase diagram showing relationship: Data -- Information -- Knowledge
Curves: Indicate the conditions of "temperature" and "pressure" under which equilibrium between different phases of insight can exist
Critical point: The "temperature" above which the gas cannot be liquefied no matter how much pressure is applied (the kinetic energy simply is too great for attractive forces to overcome, regardless of the applied "pressure")
Triple point: The particular condition of "temperature" and "pressure" where all three states are in equilibrium
NB: Phases may be subdivided into a complex pattern of sub-phases (exemplified by the variety of forms of ice as solid water) [more]

The obsession with linear associations, and the deprecation of more fluid associations, has been explored from a strategic perspective by Edward de Bono (I Am Right and You are Wrong; From Rock Logic to Water Logic, 1991). It has been explored otherwise by Douglas Hofstadter (Fluid Concepts and Creative Analogies: computer models of the fundamental mechanisms of thought, 1995).

Ecopsychological embodiment: In excluding consideration of the Swastika purely as a symbol, the above argument has presented the insights associated with appreciation of Knight's move thinking. This too, although the subject of extensive formal analysis -- both strategic (chess and go) and mathematical (Knight's tours) -- fails to identify qualitative distinctions between the different moves, possibly as intuitively sensed. These become evident to a degree in relation to the BaGua pattern. Consideration of "naturomimicry" -- as a degree of inspiration of inspiration to Asian strategic thinking -- highlights the possibility of a far higher degree of intimate cognitive engagement with the processes characteristic of nature.

This has been discussed separately in relation to water, in the light of the work of Viktor Schauberger, as discussed separately (Enabling Governance through the Dynamics of Nature: exemplified by cognitive implication of vortices and helicoidal flow, 2010).

Contextual Knight's moves and BaGua "Later Heaven" arrangement: The animations above have focused on the "Earlier Heaven" arrangement of the BaGua in relation to the Swastika. Of potential interest is the possibility that the "contextual" Knight's moves may be related to the "Later Heaven" arrangement", as tentatively explored in the following image. Given the experimental manner in which the contextual moves have been arranged, the correspondence would appear to be less successful. Other arrangements of those moves may prove more fruitful.

Knight's move "avoidance container" framing BaGua "Later Heaven" Arrangement
(experiment to determine if any systemic relationship is apparent, whether in
in the light of the trigram line coding or the traditional environmental connotations of them -- and current equivalents.
Note arrows are presented as bidirectional, with each cell as origin or endpoint to two of them)

Knight's move "avoidance container" framing BaGua "Later Heaven" Arrangement

Climate change pathways: The argument above suggests the possibility of providing a form of tentative dynamic integration, through creative play, of the elements of climate as they figure in the external and inner environments, as explored separately (Playfully Changing the Prevailing Climate of Opinion: climate change as focal metaphor of effective global governance, 2005).

The suggestion there is that computer-mediated play can provide templates through which to explore variants and possibilities, whether these are meaningful and acceptable or not. There is also the possibility that this process would highlight isomorphism -- and a form of resonance -- between pathways of changing climate and those characteristic of the shifting moods of individuals and groups that characterize the dynamics of public opinion.

Transactional games: Elsewhere (Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2005) an eightfold pattern of relationships was described in terms of a generalized understanding of transactional games understood as constituting a cycle. The "relationship games", in the light of the work of Edward Haskell (Generalization of the structure of Mendeleev's periodic table, 1972) and its development by Timothy Wilken (The Relationship Continuum, 2002), are there defined in terms of a "control component" and a "work component" as follows:

Possible 8-fold Positive-Negative Hybrid Conditions
. . X = "Work component"
. . Negative Neutral Positive
Y =
Positive predation
(positive negativity)
(positive neutrality)
(positive positivity)
Neutral amensalism
(neutral negativity)
(neutral neutrality)
(neutral positivity)
Negative synnecrosis
(negative negativity)
(negative neutrality)
(negative positivity)

Lauburu: The possibility, and the challenge, can be highlighted through traditional static symbols of the "four elements" of both climate and of psychic integration (whether individual or collective) -- such as the four-fold lauburu (the Basque cross) or its many cross-like equivalents in other cultures -- most notably including the Swastika. In the case of the lauburu, each head (or arm) is drawn with three sweeps of a compass (upon a scribed cross, employing in each head a common centre but two settings, one the half of the other). Superimposing the two variants gives rise to another form of cross.

In the Basque culture, the heads on the vertical axis represent female expression (emotional and perceptual) or the elements of fire and water. Those on the horizontal axis represent male energy (mental and physical) or the elements air and earth. Imanol Mujica (The Lauburu and Its Symbolism) considers that the lauburu symbolizes mankind, made up of four elements: Form, Life, Sensibility and Conscience. The first head symbolizes form or density, the second head symbolizes life or vitality, the third head symbolizes sensibility and the fourth head is the conscience state. Together they are held to represent nature in action and can be associated with the movement of the Earth around the Sun.

Lauburu (Basque cross)
(readily suggestive of a relationship to the pattern of the Swastika)
Left-facing (symbolizing death) Right-facing (symbolizing life)
Superposition of left and right-facing variants (demonstrating construction)
Superposition of left and right-facing variants (demonstrating construction of Laubauru)

The lauburu could be related to conventional four-quadrant representations by rotating the symbol 45 degrees. It then lends itself to mapping both the 4-fold "elements" and their corresponding 4-fold personality types of thinking, feeling, sensation and intuition (as extensively explored by depth psychology following C G Jung). Such explorations relate to the four-quadrant synthesis of Ken Wilber [more | more]. A valuable commentary, informed by mathematical insights comparing the perspective of Jung and Wilber, is provided by Peter Collins (Clarifying Perspectives 2: Perspectives, Personality Types and Strings). Collins relates the 4-fold mapping to 8-fold mappings, to the 16-fold mapping of the Myers-Briggs Type Indicator, and to a 24-fold mapping necessary to handle a further ("missing") 8 personality types.

Construction of the lauburu in its two forms can be understood in several ways. The symbol itself, in its positive (right-facing) and negative (left-facing) variants, is derived from selectively colouring the result. On one count, this may be understood as giving rise to 24 parts. This is an interesting 2D variant on the notion of closest packing in 3D. Thought can also be given to the way in which the result is a 2D projection of a 3D variant -- with its extra axis having the same constructions on it.

Stratagems and ploys characteristic of Knight's move thinking

Potentially to be considered as a further elaboration of the BaGua/Swastika pattern are the 36 classic stratagems of China (Gao Yuan, Lure the Tiger out of the Mountains: the thirty-six stratagems of ancient China, 1991). These are themselves reproduced from a document arguing for recognition of the Emergence of a Global Misleadership Council: misleading as vital to governance of the future? (2007).

Table of Stratagems
Adapted from Gao Yuan: Lure the Tiger Out of the Mountains:
the thirty-six stratagems of Ancient China
(Piatkus, 1991)
(Encyclopedia of World Problems and Human Potential)

. Assertion Denial Assertion with denial Neither assertion
nor denial
. When holding superiority For confused situations
Invention Cross the sea by fooling the sky [1]

Besiege kingdom A to save kingdom B [2]

Kill with a borrowed knife [3]

Relax while the enemy exhausts himself [4]

Loot a burning house [5]

Make a feint to East while attacking to West [6]

Steal the firewood from under the cauldron [19]

Fish in troubled waters [20]

Slough off the cicada's shell [21]

Shut the door to catch the thief [22]

Befriend distant state while attacking neighbour [23]

Obtain safe passage to conquer the kingdom of A [24]

  For confrontation For gaining ground
Rigidity Create something out of nothing [7]

Pretend to take path A while taking path B [8]

Watch the fires burning across the river [9]

Conceal a dagger in a smile [10]

Sacrifice the plum tree for the peach tree [11]

Take the opportunity to pilfer a goat [12]

Replace the beams and pillars with rotten timber [25]

Point at the mulberry and curse the locust [26]

Play dumb while remaining smart [27]

Pull down the ladder after the ascent [28]

Deck the tree with bogus blossoms [29]

Make the host and guest exchange places [30]

  For attack For desperate straits
Ambiguity Beat the grass to startle the snake [13]

Raise a corpse from the dead [14]

Lure the tiger out of the mountains [15]

Snag the enemy by letting him off the hook [16]

Cast a brick to attract jade [17]

Catch the ringleader to nab the bandits [18]

Use a woman to ensnare a man [31]

Fling open the gates to the empty city [32]

Let enemy's own spy sow discord in enemy camp [33]

Inflict injury on self to win enemy's trust [34]

Chain together the enemy's warships [35]

Run away [36]

The strategic "deviousness" of the Knight's move may be usefully considered in terms of confidence ploys -- tricks

Table of Confidence Ploys
Pattern of confidence ploys essential in the processes of governance responding to challenges.
(Encyclopedia of World Problems and Human Potential)

formal response
Postponed response
Strong short-term response followed by no further action 

Token response with phased out follow-up
Strong continuing response but ineffectual implementation Inappropriately
implemented response
. When holding superiority For confused situations
Repress [1]
Denial of issue (possibly with non-recognition of its promoter) Denial of issue, delaying any covert determination of its significance Denial of issue with covert token monitoring of its significance Denial of issue with covert long-term monitoring of little significance
Discredit Distract
Harass [2]
Discrediting and harassment of issue and promoter to ensure lack of action Discrediting and harassment of issue and promoter to delay covert action significantly Discrediting and harassment of issue and promoter to legitimate any token action Discrediting and harassment of issue and promoter to legitimate other inappropriate programmes
Acknowledge [3] Publicised recognition of issue without further implications for action Publicised recognition of issue delaying covert action implications Publicised recognition of issue oriented around token action response Publicised recognition of issue around enduring action of unchecked relevance
. For confrontation For gaining ground
Displacement Bluster/Protest Scapegoat [4] Bluster and scapegoating to displace concern and effectively justify inaction Bluster and scapegoating to shift priorities and justify covert action delay Bluster and scapegoating to give credibility to token action Bluster and scapegoating to disguise inappropriateness of other action taken
Disinform [5]
Provocation in order to disguise inaction Provocation in order to delay need for covert action Provocation by short-term action of little consequence Continuing provocation disguising inappropriateness of other action taken
Commitment [6]
Expressed commitment to action without any intention of taking any Expressed commitment to overt action which is systematically postponed Expressed commitment to action conceived as token and short-term Expressed commitment to enduring action of unverified appropriateness
. For attack For desperate straits
Honour [7]
Publicized invitation to participate -- in action which never takes place Publicized invitation to participate -- in action which is postponed Publicized invitation to participate -- in token short-term initiatives Publicized invitation to participate -- in other long-term inappropriate projects
Overload [8]
Enthusiastic encouragement to take action -- without any valid support Enthusiastic encouragement to take action -- delaying any necessary support Enthusiastic encouragement to take action - with rapid termination of support Enduring encouragement and support -- without adequate check on its appropriateness
Action on issue [9] Action specifically designed to have no effect Action delayed so that it is ineffective Strong action of brief duration (rendering it ineffective) Strong enduring action -- without adequate check on implementation effectiveness

These tables help to highlight the issue of the strategic ingenuity required to engage effectively with turbulent global conditions. The recognition of metaphorical inadequacy is then usefully seen as defective ingenuity, as argued by Thomas Homer-Dixon (The Ingenuity Gap, 2000). The book argues that the nature of problems faced by our society are becoming more complex and that our ability to implement solutions is not keeping pace. Homer-Dixon focuses upon complexities, unexpected non-linear results, and emergent properties. He takes an inter-disciplinary approach connecting political science with sociology, economics, history, and ecology. ***

Complementary patterns of higher dimensional "avoidance"

Ungraspable subtlety: In introducing this argument, attention was drawn to the challenge of subtlety and the associated difficulty and inappropriateness of seeking to "grasp" it and "define" it. As with the "dark energy" and "dark matter" hypothesized by physicists, there are no categories and modalities by which to describe it. Asserting that it is "below the radar" of consciousness is therefore in itself inadequate. That astrophysicists should currently hypothesize this "unknown" to represent 84% of what "matters" in providing a coherent understanding of the universe offers a humbling thought with respect to the adequacy of "logical" explanation if a global knowledge society (Global Strategic Implications of the "Unsaid", 2003).

Indications of cognitive inaccessibility of implicate order
Portrayed as "dark unknown"
of the unconscious
in contrast to "light of logic"
  Portrayed as "enlightened"
absence of constraint
in contrast to constraining logical rigidity
Cognitive inaccessibility of implicate order   Cognitive inaccessibility of implicate order

The contrast between implicate and explicate orders has been extensively discussed by physicist David Bohm (Wholeness and the Implicate Order, 1980). He relates the conditions through "holomovement" which might be frutifully associated with the dynamics of the Knight's move in the Swastika pattern between the conditions of the BaGua. The implicate central order might also be associated with the subtle dynamic of life itself -- whether biological or psychosocial. It is necessarily much "finer" than any "de-finition" thereof. This may also be the case with the elusive nature of the confidence and "truth" capable of engendering belief -- especially in the forms and proposals of governance.

Logically inaccessible: The manner in which the implicate domain is not "logical" could be related to the law of excluded middle (or the principle of excluded middle) whereby, for any proposition, either that proposition is true, or its negation is. Given the polarization across the diagrams above -- from the condition implied at one circumferential point to its opposite -- these can both be understood as features of an explicate order in cognitive terms. As the various Swastika diagrams illustrate, as with their "avoidance containers", it is the central cell of the 3x3 matrix which is cognitively inaccessible through conventional logic -- a "no go zone".

As mentioned above with respect to use of poetic metaphor, there is a possibility of relating cognitively to that space through what might better be understood in terms of "complicity" -- or perhaps as a form of cognitive entanglement. In terms of a sense of identity, the argument could be considered consistent with that of Douglas Hofstadter (I Am a Strange Loop, 2007), as discussed separately (Sustaining a Community of Strange Loops: comprehension and engagement through aesthetic ring transformation, 2010).

Topological insights into paradox: The following images, using the Möbius strip, were used in a previous exploration of the challenge how (not) to engage with this cognitive paradox (¡¿ Defining the objective ∞ Refining the subjective ?! Explaining reality ∞ Embodying realization, 2011). Both suggest understandings which relate to the discussion above.

Interweaving Möbius strips as "paradox containers"
within 2 interwoven Möbius strips
BaGua Earlier Heaven arrangement
embodied within four interwoven Möbius strips
Interweaving Möbius strips as "paradox containers" Interweaving Möbius strips as "paradox containers"

Traversing subtlety on the Swastika pathways: With respect to the dynamics, of which the Swastika is a useful representation, the point was emphasized above that any Knight's move passes "through" the central cell -- though the implicate order and the "cognitive complicity" potentially associated with it. This may be understood as one form of "avoidance" -- of that cognitive void. Considering each cell as a potential "station", the Knight's move "train" cannot "stop" at the central "station". It might be understood as travelling "underground" there. The location is inaccessible through conventional logic, recalling the insight of Albert Einstein: The significant problems we face can not be solved at the same level of thinking we were at when we created them.

A Knight's move can indeed be considered as a pathway, as in the mathematics of Knight's tours,  however it may be more fruitful to consider it as a cognitive "tube" or conduit along which understanding may pass -- constrained by the tube as a container, as on an underground train. This allows reflection on the topological organization of such tubes in a cognitive space of higher dimensionality, suggesting the merits of exploring a Swastika network in three dimensions -- or more? The Klein bottle offers another way of reflecting on the "location" of the "no go area".

Avoidance of subtlety: The complementary form above is the "avoidance container" -- in which the Knight's moves variously travel the circumferential cells "avoiding" the central cell. The understanding of such avoidance, and the associated style of communication, has been remarkably articulated in mathematical terms by Ron Atkin (Combinatorial Connectivities in Social Systems; an application of simplicial complex structures to the study of large organizations, 1977; Multidimensional Man: can man live in three dimensions? 1981) as separately summarized (Comprehension: Social organization determined by incommunicability of insights, 1995).

Complementarity of cognitive modes: The two complementary patterns might then be contrasted as:

Avoidance in practice: The Knight's move processes of the "avoidance container" -- indicated to some degree by arrangements made with "a nod and a wink" -- have been succinctly expressed in the light of his cybernetic perspective by Stafford Beer in his adaptation of Le Chatelier's Principle:

Reformers, critics of institutions, consultants in innovation, people in short who 'want to get something done', often fail to see this point. They cannot understand why their strictures, advice or demands do not result in effective change. They expect either to achieve a measure of success in their own terms or to be flung off the premises. But an ultrastable system (like a social institution)... has no need to react in either of these ways. It specializes in equilibrial readjustment, which is to the observer a secret form of change requiring no actual alteration in the macro-systemic characteristics that he is trying to do something about. (The cybernetic cytoblast: management itself. Chairman's Address to the International Cybernetics Congress, September 1969.)

Aspects have been separately explored in discussion of The Hidden Art : category manipulation (The Art of Non-Decision-Making -- and the manipulation of categories, 1997). This may be understood as a cognitive form of gerrymandering, as more recently discussed (Scientific Gerrymandering of Boundaries of Overpopulation Debate, 2012). An "Avoidance Container" can also be fruitfully explored in terms of the projection of a pattern of Knight's moves onto a torus (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011).

On a larger scale, this is the dynamic of the multiplicity of worthy fora in which urgent issues are discussed. Strategically such contextuality may be reviewed as a device for problem avoidance, as separately discussed (Lipoproblems: Developing a Strategy Omitting a Key Problem -- the systemic challenge of climate change and resource issues, 2009). The situation might be caricatured by the following "map", discussed separately (Mapping the Global Underground Articulating Insightful Population Constraint Consideration (IPCC), 2010).

Global Underground Map

Confidelity: confidence in confidentiality? Strategic engagement involving Knight's move thinking requires a degree of secrecy to benefit from surprise. When  undertaken by a group, the emphasis is on confidentiality. The irony in relation to governance is the need to elicit confidence -- as has been only too evident in the current financial crisis. This suggests a curious problematic relationship between confidentiality and confidence  -- highlighting the illusive nature of "confidelity", as separately explored (Primary Global Reserve Currency: the Con? Cognitive implications of a prefix for sustainable confidelity, 2011)

Configuration of axes of biases
containing the consensual processes
potentially fundamental to global confidelity (based on W.T. Jones, 1961)
Configuration of axes of biases

Competition as war -- between the "faculties"

As noted above, business "growth" can be understood as facilitated by the forms of deception characteristic of Knight's move thinking (Richard Pech and Greg Stamboulidis, How strategies of deception facilitate business growth, Journal of Business Strategy, 31, 2010, 6, pp. 37- 45)

Recognizing corporate competition as warfare: The extent to which competition by business is to be characterized as war, is remarkably explored by Burkard Sievers (Competition as War: Towards a socio-analysis of war in and among corporations, Socio-Analysis, 2000). He argues:

Despite the daily reality of war in the media - and indeed in many people's political and social lives - it would seem, that it is not considered part of the business world, organisations or the world built around them. We are consistently led to believe that the economy of war and warfare refers to the gains derived from the production of war equipment, the maintenance of military forces (both in times of war and peace), and the repair work and reconstruction necessary after battle is done.

The absence of bloodshed or casualties in business organisations invites us to assume that the frequent reference made to war is merely metaphorical. In organisation or management theory it is seldom acknowledged that extreme violence, sadism, pain and loss - experiences and dynamics characteristic of every war - are typical of the contemporary business world. It has become almost impossible to unveil the reality of business enterprises hidden behind the rhetoric of free markets and unrestricted competition typical of contemporary neo-liberalism....

Sievers endeavours to show how capitalist competition is effectively a form of ongoing warfare in and among corporations. With a focus on Volkswagen, his hypothesis is that "similar dynamics are found throughout the automobile industry and have a major impact on the business strategies of many, if not most, corporations in their desperate longing to gain or maintain a predominant role as global players". In the case of Volkswagen:

All that seemed to be required was to exchange the swastika (former national Volkswagen emblem) for a dove of peace, thus leaving the former spirit of mobilization and the determination to achieve victory totally unaffected....

Unthought thought: Sievers highlights the role of the "unthought thought", citing various authors (C. Bollas, The Shadow of the Object: psychoanalysis of the unthought known, 1987, F. Fornari, The Psychoanalysis of War, 1966; V. D. Volkan, The Need to Have Enemies and Allies: from clinical practice to international relationships, 1988):

In a paradoxical sense, it would seem that the increasing use of war metaphors in the car and other industries is primarily intended to keep unthought the known truth. That is, that both in many corporations and in war major sectors of the global economy the world is in a state of ongoing and ever intensifying war. The lie is embedded in the belief that despite appearances, competition is not actually war at all. That this lie hides the known as well as the unthought underlying reality is exemplified by the paradox that, as a member of a corporation or as a consultant, one is often confronted by the fact that whereas many if not most of the organisation's role holders will openly confirm their emotional experience in the organisation as being at war, this truth will not and cannot be acknowledged or even expressed publicly. Reference to organisational warfare is banned from all ongoing business processes and meetings, and does not play a part in business administration, which one might expect to be most equipped to reveal and deal with this unthought known part of organisational and societal reality. Most of the major international corporations and their "internal establishments" have induced social and global thinkers into nurturing the lie that the world is a global village where everyone lives in peace.

Psychotic organization and the shadow: Very usefully, in relation to the arguments regarding Knight's move thinking, Sievers draws upon his own insights into "psychotic organization" (Psychotic Organisation as a Metaphoric Frame for the Socio-Analysis of Organisational and Interorganisational Dynamics, Administration and Society, 1999) as well as work by W. G. Lawrence (Thinking Refracted in Organisations: the finite and the infinite / the conscious and the unconscious, 1999) as presented to a symposium of the International Society for the Psychoanalytic Study of Organizations. Such "refraction" could well be considered a characteristic of framing through the Knight's move pattern -- and the associated tendency to denial and "passing the buck". Whereas organizational practice and contemporary literature on mergers focuses predominantly on rational economic and managerial perspectives, the shadow side of these ventures has been explored by Jinette de Gooijer (The Murder in Merger: a systems psychodynamic exploration of a corporate merger, 2009).

The "shadow side", characterized by the "unthought thought", can be associated with unasked questions (Portia Bell Humea and Joan V. Bonduranta. The significance of unasked questions in the study of conflict. Inquiry: an interdisciplinary journal of philosophy, 7, 1964, 1-4, 1964, pp. 318-327)

... it is time to take a further step, a step or perhaps (to borrow a chess term) a knight's move away from ... more significantly to a new manner of man, one whose vision keeps up with his power of locomotion, and his action with his boundless thinking. ...

Conflict between academic faculties: Controversially, the nature of this conflict was recognized amongst academic faculties in 1798 by Immanuel Kant (The Conflict of the Faculties, including  The Conflict of the Philosophy Faculty with the Theology Faculty, 1794) -- usefully framed as follows:

The class of the higher faculties (in a manner of speaking the right wing of the parliament of knowledge) defends the statutes of the government; however, in it free constitution, as any which I respects the truth must be, there must also exist an opposition audience (the left), for, without the severe scrutiny and objections of the latter, the government would not he sufficiently informed of what can he helpful or harmful to it.

Conflict between cognitive faculties: The theme of conflict of the faculties has been variously explored. Of interest here is the manner in which it extends to the contrasting cognitive faculties and metaphors of strategic significance. For example, it is useful to explore the manner in which "vision" is used as the primary metaphor of strategic thinking and presentation, whereas other "competing" metaphors may play a vital role even if neglected in some many fora, as discussed separately (Developing a Metaphorical Language for the Future, 1994). Politicians, talking "vision", avoid at their peril any  apparent neglect of the ability to "hear" and even to "touch". Their proposals may be framed by opponents in terms of their "smell".

Eight clusters of players in the global financial board game?

Game-playing: The above argument has been designed to give sharper focus to both game-playing and blame-gaming characteristic of the response to the financial crisis -- in which all are variously accused (most notably by each other), whilst denying effective responsibility, and arranging their collective avoidance of indictment. The argument follows previous efforts to explore these dynamics (Monkeying with Global Governance Emergent dynamics of three wise monkeys in a knowledge-based society, 2011; Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011). A further degree of denial of responsibility is evident in the conversion of a financial crisis engendered by humanity into what amounts to a natural disaster beyond human control -- and therefore the perfect excuse for past mismanagement (Responsibility for Global Governance: Who? Where? When? How? Why? Which? What?, 2008)

Identification of clusters: Has there been any formal attempt at a cluster analysis to determine the clusters of players on the board -- as a prelude to any systemic analysis of their interaction? If not, why not?

To the extent that the "players" complicit in the game engendering the financial crisis can be usefully understood as constituting a "team" within the collective unconscious, the question is what role they respectively play in the psychodrama. In that respect it is appropriate to note the interest of Shklovsky as a political activist in both the Knight's move and in dramatic plots. The roles may be understood as echoing in part an "eightfold way" as yet to be discovered, or the team roles  clustered by Meredith Belbin in the Belbin Team Inventory.

Those playing strategically on the financial scene -- "in confidence" but "with confidence" -- could be clustered as follows, for example

The players  are likely to engage in both risk-taking and risk-avoidance strategies. Those who are risk averse then engage in dynamics characterized by the "avoidance container" around the centre -- maintaining the status quo. The Swastika -- across the centre -- then characterizes risk taking. More generally it may characterize deicsion-making and commitment. The Swastika pattern of moves is then usefully associated with perpetration and inducing shock. The contrast recalls the distinction made in a report to the Club of Rome between "maintenance learning" and "shock learning" (James W. Botkin, Mahdi Elmandjra and Mircea Maltiza, No Limits to Learning: Bridging the Human Gap, 1980).

Forms of cognitive order: As indicated by such as Magoroh Maruyama, each cognitive framework ("mindscape") potentially offers a distinct sense of "law and order" (Systems of Categories Distinguishing Cultural Biases, 1993). It might well be asked why only one single sense of "law and order" is currently considered appropriate to the governance of a complex system. A contrast is offered by translation systems which typically assess validity through a variety of "modules". A further sense is offered by social contexts in which attention is accorded to both conventional law and to that of the tradition of an indigenous people, or to that associated with a a religion (canonic law, sharia law). What varieties of alternative "law and order" merit consideration?

Quest for a strategic eightfold way through metaphor? The classical constraints on human information processing capacity focus the quest for configuration of complementarity strategies in terms of "seven plus or minus two" -- namely a possible "eightfold way" (George A. Miller, The Magical Number Seven, Plus or Minus Two: some limits on our capacity for processing information, Psychological Review, 63, 1956, 2, pp. 81-97). Consistent with that constraint, Eugene Bardach has developed an Eightfold Path of policy analysis.

A distinct approach of relevance to the above argument is the identification of clusters of cognitive modes which might dispose to preference for particular strategic styles, as discussed separately (Systems of Categories Distinguishing Cultural Biases, 1993). As with the symbolism associated with the BaGua, a further approach is through sets of symbols and associated categories, conveniently summarized by the Duversity group (References for the Octad).

There is the curious possibility of exploring financial derivatives through the array of fundamental particles in the light of the proposed eightfold way of physics -- in that, as vehicles for confidence, a key issue with respect to derivatives is their viability in terms of credibility over time, imaginatively analogous to the period of existence prior to the decay of subatomic particles ordered by that proposal. As with the financial derivatives, such particles are also distinguished by a degree of "spin" and are variously to be understood as derivatives of other particles. Such a speculative approach suggests a "language" through which tentatively to explore the array of derivatives in  the light of the more fundamental forms of confidence and credibility from which they derive. Given the degree of dependence on such confidence, the possibility merits attention. A degree of feasibility is evident from the paper by William F. Sharpe (Nuclear Financial Economics, Stanford Research Paper 1275, 1993; subsequently published in: Risk Management: Problems and Solutions, 1995, pp. 17-35).

Human psychology and sustainable development: The following animations, whilst clearly caricatures, suggest an alternative to the conventional linear representation of the dynamics of the global economy. Whilst consistent with recognition of economic cycles and business cycles, they suggest a further relation to the psychological dimensions so usefully documented by Shiller and Akerlof (2009) -- and beyond their argument to the many 8-fold articulations of personality types and modes of thought.

Indication of the Swastika as an emergent pattern within those dynamics suggests how surprising transformation relationships may become apparent as creative strategic opportunities -- for good or for ill. Their nature is of course more likely to be seriously explored within Asian mindsets -- and only tardily acknowledged by the currently dominant economic mindsets of the West. Now that China is expected to emerge as the dominant superpower, it is fruitful to recall the early analysis of Scott A. Boorman (A Protracted Game: a wei-ch'i interpretation of maoist revolutionary strategy, 1971), as discussed separately (System Dynamics, Hypercycles and Psychosocial Self-organization: exploration of Chinese correlative understanding, 2010).

Engaging with "Animal Spirits" in the global economy?
Conventional linear image
(adapted from the cover of Animal Spirits:
how human psychology drives the economy,
and why it matters for global capitalism
, 2009
by Robert J. Shiller and George A. Akerlof, )
Cyclic image
based on Swastika dynamic
ordering the "animal spirits" otherwise?
(suggestive of the possible dynamics
of a sustainable global economy)
Animation of engaging with "Animal Spirits" in the global economy?  (Linear variant) Animation of engaging with "Animal Spirits" in the global economy? (Cyclic variant)


The argument has drawn attention to a subtle strategic (sixth) sense -- implicit rather than explicit -- typically associated with intuition for many in every walk of society. It is evident in the detection of an opportunity for a deal, or for a confidence trick. It is a sense familiar to players of chess and go, and clearly in other games where "instinct" is valued, whether or not it proves to be illusory in a given instance. It is much valued in various Eastern martial arts. It could be associated with "being in the zone" of flow psychology.

The concern here is indeed the manner in which this sense is exploited in giving rise to questionable patterns of action (as with the exacerbation of the financial crisis). However there is also the possibility that more fruitful recognition of the strategic role of that sense could be a vital key to the challenges of governance in turbulent conditions. It is not for nothing that chess and go have long been valued in the cultivation of strategic insight.

It is sadly ironic that as the noble characteristic of a "Knight" it is also characteristic of the historical exploitation by the nobility, and their current equivalents, in abusing public confidence (Abuse of Faith in Governance, 2009). Given the curious strategic relationship in chess between rook (castle) and Knight, and in the absence of a relevant verb "to Knight", it is somewhat extraordinary that the verb form of "rook" is used to name various forms of cheating, as in "they rooked me of my inheritance".

It is perhaps appropriately strange that  strategic engagement involving Knight's move thinking implies a degree of secrecy. When  undertaken by a group, the emphasis is on confidentiality. The irony in relation to governance is the need to elicit confidence -- as has been only too evident in the current financial crisis. This suggests a curiously problematic relationship between confidentiality and confidence which merits exploration.

Exploring the possibility of a degree of relationship with related insights from Chinese culture would seem to be appropriate in this period of an emerging role of China on the global scene. Whilst such relationships may seem questionable from a Western strategic perspective, it is improbable that the evolution of Asian strategic thinking will be handicapped by deprecation of insights they have long valued. As with appreciation of strategic insights from chess in the West, Asian cultures may continue to seek competitive advantage from the subtler insights of go -- as previously demonstrated by Scott A. Boorman (A Protracted Game: a wei-ch'i interpretation of maoist revolutionary strategy, 1971). The question is whether marrying Eastern and Western metaphors in some way can elicit a pattern more relevant to sustainable development, as implied by the articulation of James P. Carse (Finite and Infinite Games: a vision of life as play and possibility, 1986). Do the animations above offer a sense of the nature of infinite games?

As a technical footnote, the various animations are suggestive of many further refinements using other transition effects and more extensive consideration of design -- in particular in relation to the speed of the animations and the possibility of their control by the user. These could improve their educational and mnemonic potential (cf. In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007). The transformation of the Swastika into the "Avoidance Container", and back, is very suggestive of the well-known variants of the Tetris game.

One experiment in clarifying such visualization possibilities is through the use of SVG rather than GIF animation (as above). The following SVG, although not interactive, has the advantage that the code takes the form of ordinary text which can be modified with relative ease -- notably changing colours and speed according to aesthetic preferences (right-click to see source). Currently the cycle terminates after a minute.

 For a related animation of greater subtlety, see Dynamic Exploration of Value Configurations: interrelating traditional cultural symbols through animation (2008), especially the following SVG example .

Screen shot from a more complex animation
Shown halfway to completion of cycle of 64 hexagrams; - this version features explicit labelling of completed hexagrams; the correspondence between the line-coding of the central hexagram and the star may be seen; - a smaller version of the current central hexagram is visible in movement towards its final position on the circle (on the right); an emerging central symbol (a Medicine Wheel) is faintly visible

Yantra, Yi Jing and Star of David animation


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