Experimental context

9-fold Magic Square Pattern of Tao Te Ching Insights (Part #2)

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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 regular patterns emerging from the inexhaustible variety and ambiguity of moral circumstances.

The sequence of 81 insights of the Tao Te Ching are however typically not clustered in any way. In the previous experiment, the conventional order was used to cluster the 81 insights into a 9 x 9 table to derive groups of 9 insights by row and, separately, by column. The question was whether a magic square clustering, much favoured in that period in China, would enable new insights to be elicited from the resultant pattern. It is important to note that the mathematical properties of magic squares continue to be of great interest to mathematicians -- but very little attention is paid to their potential role in ordering systems of concepts. In that period however the 3 x 3 Lo Shu magic square was essential to the ordering of the most fundamental Chinese insights.

The 81 insights of the T'ai Hsüan Ching were much more closely associated with magic square orderings than the Tao Te Ching. The following experiment is based on the work of Derek Walters (The T'ai Hsüan Ching: the hidden classic -- a lost companion of the I Ching, 1983, subsequently titled The Alternative I Ching, 1987) who reconstructed and translated it. Walters notes the relationship of the order of the T'ai Hsüan Ching to the arrangement of the classic Magic Square of Master Tsan -- using the first modern numbering system of the Han dynasty (a base ten system like that of the Romans) [more]. Walters explores the use of magic squares as a means of ordering the sets of philosophical verses (tsan) clarifying each of the 81 insights.

Prior to Nylan, Walters is emphatic at the contrast between the T'ai Hsüan Ching and the earlier I Ching it was designed to improve upon. He notes that in the I Ching:

• the texts of the hexagrams are an assembly of heterogeneous phrases which range from magic formulas to complete poems, often repeated in other hexagrams (although he later notes that the texts of the T'ai Hsüan Ching are "a curious mixture of the deeply philosophical and the domestically banal; the romantically poetic and the tritely mundane; the clear and the abstruse")
• the unexplained random order contrasts with the logical sequence of the T'ai Hsüan Ching based on a unifying philosophy

The principal difference for Walters is that:

the T'ai Hsüan Ching holds that there are three forces at work in nature; two of these Yin and Yang, represent the positive and negative fluxes of electro-magnetism; but there is also a third force which accounts for the creation of the truly novel. With Yin and Yang [alone] there is nothing new under the Sun. While everything can be classified as belonging to Yin and Yang, the dual philosophy can only account for what exists already; no matter what resultant products or ideas are spawned by the action of Yin and Yang, there is no entirely new element created...But new ideas, and new species, only arise from the third creative force... The third force, according to the T'ai Hsüan Ching, is the Jen (Mankind) force... the philosophy of the triad is totally at variance with the duality of the I Ching, and yet, paradoxically as though it might seem the T'ai Hsüan Ching is a work of tremendous originality (pp 8-9).

Part of the study by Walters is on the relevance of the tri-partite focus of the T'ai Hsüan Ching to current scientific thought. Understanding of such a third force could be usefully compared with the concept of morphogenesis as developed by Magoroh Maruyama (The Second Cybernetics: deviation-amplifying mutual causal processes, 1963; Morphogenesis and Morphostasis, Methodos, 12, 1960, pp. 251-296).

However as a reviewer of Nylan's translation, Richard Hunn strongly argues:

Like Walters, Nylan claims special advantages for the 'tri-partite' division of the Tai Hsuan Ching. Walters had argued that the Tai Hsuan Ching accorded a more complete, active role to 'man' -- as against the Yi-Chings allegedly 'fixed' dualistic system. All of this shows a poor grasp of what the Yi Ching (and Tai Hsuan Ching) actually teach. The Tso chuan section of the Yi-Ching stresses that 'Heaven, Earth and Man' are what comprise the Tao. Every trigram (and hexagram) in the Yi Ching reflects this threefold unity ('the 'three powers' or san-tsai) - and the Yi-Ching makes this clear on every count. Human 'agency' is therefore vital to the Yi-Ching. It was not a 'new' idea with the Tai Hsuan Ching. The antiquity of this intuition is evident in the formation of the Chinese script, the old Ku-wen forms, giving the character for 'king' or 'kingship' as a representation of the san-tsai or 'three powers' -- linked by a vertical stroke, anciently, the kingly-priest in whom the san-tsai were united or focused. It is a basically a 'trigram' -- crossed by a vertical line. Like Walters, Nylan makes some rather bold claims for the Tai Hsuan Ching. But trying to place it in 'competition' against the Yi-Ching -- is naive. [more]

Part of the challenge of this experiment is to render comprehensible a dynamic framework through which such differences of perspective, so typical of academic dialogue, are understood as intrinsic to psychosocial dynamics rather than in some way external to them. The widespread emphasis on correct and incorrect views too readily reinforces the style of binary discourse that justifies bloody conflicts -- as common today as at the time at which such works originated -- and a reason for their elaboration.

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