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Knight's move thinking: appreciated or deprecated
AWOL: American Way Of Life: Assumptions -- justifying worldwide imposition of democratic imperialism (Part #5)
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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) |
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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:
To that Freeman Dyson added:
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) |
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