Insights from Knight's move thinking

AWOL: American Way Of Life: Assumptions -- justifying worldwide imposition of democratic imperialism (Part #6)

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

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.

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Insights from Knight's move thinking