Conclusion

9-fold Magic Square Pattern of Tao Te Ching Insights (Part #11)

Natural appropriateness: Yang Hsiung is understood to have shared the vision of the I Ching of an order that united the cosmos, the sphere of action, and the individual. The concern of all such works, notably the Tao Te Ching, might be said to be with appropriateness in terms of the patterns and dynamics of nature -- the Way of Nature, exemplified by the insights of the Tao Te Ching. Any explorations of such matters merit careful consideration in the light of contemporary challenges of global governance of an endangered planet -- exemplified by the paradox of "sustainable development".

With respect to the title of the work, T'ai Hsüan Ching, as noted by Michael Nylan and Nathan Sivin (The First Neo-Confucianism: an introduction to Yang Hsiung's "Canon Of Supreme Mystery", 1995):

In the Way, which was also Yang Hsiung's Mystery, science and ethics were one. This Han vision was not a reduction of science to subjectivity. Nature and human nature constitute a single order.... "Hsuan" carries a range of meaning from "black" to "darkness" to "hidden" to "mystery." Its overtones are stillness, solitude, isolation, nondifferentiation, and inaccessibility by purely rational processes. In Chinese thought the ideas at the philosophical end of this range bear no unpleasant connotations. They express that aspect of experience that can be known only by quiet and deep contemplation, or by illumination. Yang Hsiung uses hsuan in his book's title and throughout to mean the profound darkness, silence, ambiguity, and indefiniteness out of which creation comes. In cosmogony it is the undifferentiated state out of which yin-yang and eventually the myriad phenomena separate. In Nature as humans experience it, it is the latency out of which individual things are spontaneously born, and out of which events shape themselves. In the sage--that is, the human being as he should be, as the student of the Mystery is striving to be--it is the spiritual inwardness that precedes conscious decision and action and spontaneously accords them with natural process.

Complementarity: For its author, Yang Hsiung, the intent was to evoke a sense of the inseparability and complementarity between mystery and rational pattern. Again for Nylan and Sevin:

Despite the superficiality of this essay, we have adduced more than enough evidence to illustrate Yang's aim in writing the Mystery: to instigate and guide the personal striving for integrity that is the only possible basis for a sound polity. This virtue is more than a matter of moral and psychic integration; it involves union with the Way of Nature and its Mystery. As the inquirer aligns his own decisions and actions with the cosmic course, he is able to promote harmony in every external sphere, renovating society on the pattern of the Tao.

Degree of relationship: With respect to the significance of the pattern of relationships between the T'ai Hsüan Ching and the Tao Te Ching -- both pointing to a subtle understanding -- the tables above could be usefully seen as raising questions as to the nature or degree of that relationship, or of any ability to recognize it. It is of course highly unsatisfactory to assess such a relationship through a matching of single-word insight titles from the T'ai Hsüan Ching to succinct representations of insights from the Tao Te Ching. Each such "insight" is a memetic complex at the nexus of the pattern of associations it evokes. It is severely distorted by reducing its dimensionality in this way through the use of a somewhat arbitrary choice of term in English.

A simpler variant of this challenge was central to the methodology of isolating "human values" from the maze of relevant words and connotations in English -- which identified 2,200 "values" and 14,500 associative links between them in the Human Values Project of the Encyclopedia of World Problems and Human Potential. The 9 "Appraisals" associated with each insight in the T'ai Hsüan Ching might be understood as a systemization of the pattern of possible connotations. In addition to the possibility of a fruitful koan-like relationship (suggested above), there is of course the interesting implication of the so-called small world hypothesis that everyone in the world could be reached through a short chain of social acquaintances. This gave rise to the concept of six degrees of separation with generic implications (cf Duncan J Watts, Six Degrees: the science of a connected age, 2004), notably for knowledge diffusion (cf Sara Grant, Caves, Clusters, and Weak Ties: the six degrees world of inventors, Working Knowledge for Business Leaders, November 2004) and web-related products (Dan Farber, Less than six degrees of social networking and Web 2.0 goodness, June 2006).

Might there therefore be an analogous phenomenon in the knowledge universe whereby even the most seemingly disparate concepts could be linked through a short chain of semantically relevant associations?

Mnemonic interlocking: The focus here on the potential of magic squares can be usefully understood as a mnemonic device for comprehending a complex pattern of associations. It might possibly be compared with the everyday challenge of comprehending a subway network map as a whole -- or any systems diagram, and perhaps most notably those associated with global modelling exercises (cf Limits to Growth, as first commissioned by the Club of Rome in 1972). These were initally based on the world dynamics models of Jay Wright Forrester (see also an early effort at relating these to the individual World Dynamics and Psychodynamics: a step towards making abstract "world system" dynamic limitations meaningful to the individual, 1971).

As with a song or poem, it is the recurring elements and associations that ensure the integrity and memorability of the whole -- arguments developed in an associated proposal (A Singable Earth Charter, EU Constitution or Global Ethic?, 2006). A sense of the challenge, and willingness to address it, may be seen in current widespread enthusiam for sudoku -- which have their origin in magic squares. The objective is to achieve interlocking of symbols (of any kind) in an array -- an intellectually "satisfying" design "fit". The 81 memetic complexes of the T'ai Hsüan Ching and the Tao Te Ching pose the challenge of how to identify, understand, remember and communicate an appropriately interlocked pattern -- of relevance to an appropriate lifestyle and style of governance. As with sudoku, they point to the possibility of more challenging complex patterns of interconnectedness (including bimagic squares, cubes and hypercubes).

Individual engagement: The additional dimension introduced by the preoccupations of the two works linked here, notably through the 9x9 pan-magic square presentation (centered on #1: Centering), is the sense of a central focus for order with which the individual may fruitfully identify. This can be contrasted with conventional systems diagrams that have no such centre, singificantly failing to design in the individual observer, as a focus for action within the system. The closest to this is ironically the arrow on a subway may indicating the user's current location. However the "centering" in the pan-magic square is an extremely subtle notion that, paradoxically and provocatively, calls into question the naming and condition of the centre itself -- as often quoted from the Tao Te Ching in many variations :

The way that can be told is not the common way
The name that can be named is not the common name
What has no name is the beginning of heaven and earth
What has a name is the mother of the myriad creatures
Those without desires contemplate its secrets
Those who have desires contemplate its periphery
These two emerge together, but differ in name
Being together, they are called Mystery
Mystery upon mystery
Gateway to the myriad secrets.
[Nylan amd Sirvin]

Readers of any systems diagram, like the magic squares above, are therefore challenged as much to ask "who they think they are" and "where they think they are going", rather than simply to expect a simple answer that in no way challenges their sense of identity or the validity of their quest. They offer a puzzle that merits being taken seriously.

Focus of cognitive engagement: It is from such a perspective that it is worth recalling that magic squares were traditionally placed at the centre of mandalas as a focus for meditation. These mandalas might then be viewed as a form of cognitive "gearbox" through which "power is transmitted to an output device, normally rotary in form, and generally at a reduced rate of angular speed but at a higher motive torque". The "gears" presented in such mandalas typically involve concentric sets of (3, 4, 5, 6, 7, 8, 9, 10 or 12) archetypal symbols as conduits for particular modes of understanding. From such a perspective, the challenge of appropriateness for an individual lifestyle, and for collective governance, is to identify such "gears" and to ensure that they intermesh fruitfully.

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Conclusion