9-fold Magic Square Pattern of Tao Te Ching Insights

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As discussed in the related papers (Commentary on Tao Te Ching Interpretation: and the possibility of higher order patterning 2003; Hyperspace Clues to the Psychology of the Pattern that Connects, 2003; Musical Articulation of Pattern of Tao Te Ching Insights: experimental sonification based on magic square organization, 2003) the prime concern in this experiment is with the possibility of configuring fundamental insights in ways which facilitate their comprehension. A particular concern is with their interrelationship as a pattern, or system of checks and balances, rather than on the significance of any particular insight.

Potentially the sets of insights developed in ancient Chinese culture, and fundamental to the philosophy of life and governance, is therefore especially relevant at this time. Great importance was then attached to both the coherence of the pattern as a whole and its capacity to model the changes experienced and to be anticipated. The use of three of them for purposes of divination [review], now considered inappropriate by some [discussion], should not distract from their insights into the operations of complex psychosocial systems.

This is especially the case in the light of the increasing emphasis now placed on "values" and "wisdom" in relation to global governance, whether "faith-based" or not, and on elaboration of more appropriate strategies. If the sets of insights effectively functioned, or were used, as what would now be termed "global models" or "world models", then the adequacy of their predictive capacity should be distinguished from the adequacy of their descriptive/explanatory capacity -- especially given the requirements of them by their culture. The most comprehensive of these present day models of the world system face a particular challenge in that the "predictions" they offer fail to engage the individual as coherent and credible -- and therefore fail to engender political support for appropriate concerted action (cf Donnella Meadows, et al. Limits to Growth: the 30-Year Update, 2004).

These concerns also follow from an earlier exploration of the possibility of higher orders of cognitive engagement in strategic issues (Governance through Patterning Language: creative cognitive engagement contrasted with abdication of responsibility, 2006; Creative Cognitive Engagement: beyond the limitations of descriptive patterning, 2006).

This is an exercise in building on the tables in the separate paper 9-fold Higher Order Patterning of Tao Te Ching Insights: possibilities in the mathematics of magic squares, cubes and hypercubes (2003). There the 81 insights of the Tao Te Ching (Book of the Way and its Virtue) were presented experimentally in cells in a 9 x 9 square to explore the possible existence of higher order patterns of significance. Titles have here been added to the insights in the cells -- but these titles are derived from the 81 insights of the T'ai Hsüan Ching (Tai Xuan Jing / Canon of Supreme Mystery /The Great Dark Mystery) of Yang Hsiung (Yang Xiong), thus establishing a relationship between the two sets of insights. This paper is therefore a development of the previous one only through the addition of points relating to the T'ai Hsüan Ching in order to faciliate comprehension of any possible relationship with the Tao Te Ching.

Although the T'ai Hsüan Ching is a different publication, it is of the same era in Chinese culture. It has been described as one of the world's great philosophic poems comparable in scale and grandeur to the De Rerum Natura of Lucretius. As noted in the valuable clarificatory commentary by Michael Nylan and Nathan Sivin (The First Neo-Confucianism: an introduction to Yang Hsiung's "Canon Of Supreme Mystery", 1995) in distinguishing the T'ai Hsüan Ching ("the Mystery") from the I Ching ("the Changes") :

The Mystery was the most influential among the many meant to remedy inconsistencies in the Changes and to add to the old discourse current ideas about the cosmic order, the sagely life, and the beauty and precision that can be drawn from words. Until the thirteenth century Yang Hsiung's writings were considered central to the orthodox search for universal pattern, and thereafter were forgotten...The Mystery made considerable demands on its readers. The clarity of its structure was intentionally balanced by the complexity of language that strives above all for allusiveness....The Mystery, like the Changes, was said to be hopelessly abstruse and of no practical benefit....Yang's aim in writing the Mystery [was] 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....It does not offer magical power over nature. It simply aids reflection on the eternal patterns that underlie every aspect of experience and action. Assimilating those patterns, Yang was convinced, could guide the renewal of human creativity and the eventual recovery of order....His book applies rigorously and reflects, in its texts and guides to interpretation, the basic seasonal rhythms, the fundamental social relationships, and the functions of yin-yang and the Five Phases that pervade the natural and human worlds.

Although Nylan and Sirvin make no explicit mention of any relation between the Mystery and the Tao Te Ching, as purportedly articulated by Lao-Tzu, they do, like others, refer to the Tao Te Ching as "the Lao-Tzu" and note Yang Hsiung's recognition of such a connection in the following terms:

It is from Lao-tzu's Mystery that that of Yang derives, although his moral stance differs: "As for Lao-tzu's discussion of the Way and its power, I have drawn upon it; but from his rejection of Good (jen) and Right (i), his elimination of ritual and study, I have taken nothing."

As with the I Ching, the T'ai Hsüan Ching was orginally one of several works that formed the Ta Pu or Grand Oracle. It is considered to be a companion volume to the I Ching -- which is far better known. Like the Tao Te Ching, the T'ai Hsüan Ching has 81 insights known in this case as Shou. Like the I Ching these are associated with a diagram of broken and unbroken lines. In the case of the 64 insights of the I Ching, each is represented by six such lines (a hexagram), each of which may be unbroken (yang), or broken once only (yin). In the case of the T'ai Hsüan Ching, these are represented by four such lines (a tetragram or quadgram), each of which may be unbroken, or broken once or twice. The sequence of numbers in the Tai Hsuan Ching is conventionally arranged into three groups of three called T'ien (1-27), Jen (28-54) and Ti (55-81) as discussed below.

Each of the 64 hexagrams of the I Ching is traditionally associated with a descriptive name for the explanatory details associated with it. There is no such descriptive name associated with the 81 insights of the Tao Te Ching , which are each presented through a set of poetic verses. These were reduced, experimentally, to a single phrase in an earlier phase of this experiment (Tao Te Ching Interpreted Succinctly: a 9-fold pattern of 81 insights presented as phrases, 2003). In the case of the T'ai Hsüan Ching, each of the 81 insights ("Heads"), has a title and is explicated through 9 very short philosophical verses (or "Appraisals", known as Tsan), typically presented in allegorical form -- and totalling 729 (as analyzed by Walters) or 731 (as analyzed by Nyland and Sivin). Although not immediately relevant to the following experiment, it is appropriate to note that each of the 81 insights is linked to one of the 64 hexagrams of the I Ching (with some duplication, of course) to evoke the old meanings and associations.

For Nylan and Sivin:

The philosophic interest of Yang's Head texts lies in their intricate, nuanced picture of a grand cycle of change, his recognition of complexity within regular order. Conversely, his Appraisals are remarkable because, through highly figurative language and the interplay of cycles within cycles, Yang suggests regula

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