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Omei I Ching: Mechanics of the I ChingMonica Salyer and Gilbert LealOmei Institute of Applied Oriental Studies, 2341 Vance Jackson, San Antonio, TX 78213.This review originally appeared in Volume 2, Number 10 of The Oracle: the Journal of Yijing Studies, January 2000. OverviewThe first thing to say is that, basically, I like potential of the work presented in this small volume. The authors have provided what I believe is a genuinely new analysis of the square Fu Xi arrangement and given an interesting mathematical characterisation of its axes of symmetry at the level of constituent trigrams and the complement operation on those trigrams.They then go on and present a novel diamond shaped arrangement for the hexagrams that is clearly derived from their original analysis of the Fu Xi square in that it is characterised in terms of axes and operations around those axes. Taking the name of martial arts tradition that they study, they describe this new arrangement as the "Omei" Layout. DetailsOK - on to the more detailed analysis. I shall begin by discussing their introductory material, and then proceed to a critique of their technical presentation.What is the Yi?At the outset the authors describe the Yi both as a process of analysis the result of that process. I think this is a reasonable statement to make, it certainly captures, from an abstract perspective, the use of the Yijing. However, they go on from this and press the point of generality: they suggest that data analysis techniques and pie charts also fall under the category of Yi "play".I think one has to be very careful here. It shouldn't be forgotten that there are certain philosophical and cosmological assumptions built into the construction of the Yi. Specifically, I'm thinking of ideas like the separation of wuji through taiji into yin and yang and the analysis of all phenomena in terms of the interaction of those two fundamental principles; the idea that one of those principles is yielding and the other is firm; that these principles do not oppose each other but act as complementary interacting forces in the dynamic of the Universe. The idea that there are three domains of reality: Heaven, Humanity and Earth. Neither modern data analysis nor pie charts embody these kinds of cosmological primitives as an integral part of their formalism, and as such I'd suggest that they are not candidates for manifestations of the Yi. Which is not to say that one could not characterise the Yi using pie charts, in fact I'm sure you could, but pie charts as pie charts, do not make a Yijing. I was reminded of the images for Hexagram 60 which speaks of the need for defining things, giving measure and limitations to distinguishing things. If definitions are too broad they lose their meaning. Although I agree that the Yi is not bound to any one form, I do feel that, whatever form it does take, it is bound to embody certain principles. NotationIn the Omei I Ching the following notation is used. The letters I and J are used to symbolise the two trigrams that compose a hexagram. Then I/J means that the given hexagram is composed of the trigrams I and J.The authors use (I) to represent the complement operator. Thus, if I was Shock , then (I) would be , Penetrating. Although there seems to be no accepted standard notation for this operation in the Yi literature, my preference is to go with one of the notations current in mathematics. In that case a better choice would have been ~I. The Fu Xi AnalysisThe authors divide the Fu Xi square arrangement into four quadrants with a horizontal axis and a vertical axis. If we characterise each quadrant by the hexagram at its outer corner then we have a quadrant containing Hexagram 2, the Receptive, one containing Hexagram 1, the Creative, one containing Peace, 11, and finally one containing Standstill, Hexagram 12. The reader should note that these are my attributions to aid my descriptions in this review, the authors themselves do not characterise the quadrants in this manner.The Omei mechanism then assigns symbols to each quadrant. These symbols are derived by considering a hexagram as composed of its two trigrams. Starting with the Receptive quadrant they assign the symbol I/J indicating the two trigrams. For the Peace quadrant they assign the symbol I/(J) indicating that, compared to I/J, the lower trigram is complemented. Similarly, the Stagnation quadrant is assigned the symbol (I)/J, indicated that its upper trigram is complemented relative to I/J. Finally, the Creative quadrant is given the symbol (I)/(J) to indicate that both trigrams are complemented. The basic insight is that mapping from any hexagram in the Receptive I/J quadrant to its corresponding hexagram in another quadrant involves the transformation described by the given symbol. Thus, if Splitting Apart was in the Receptive quadrant, then its corresponding hexagram in the Standstill quadrant would be Gathering Together , its corresponding hexagram in the Peace quadrant would be Taming Power of the Great , and its corresponding hexagram in the Creative quadrant would be Break Through . The Omei ArrangementThe authors then present a new arrangement of the hexagrams, which takes the form of a diamond. As before it is divided into quadrants, but now the quadrants are given the symbols I/J, J/I, (J)/(I) and (I)/(J). Again, these symbols indicate the nature of the transformations when moving from a hexagram in one quadrant to a hexagram in another. However, now, in addition to the complement operators, the authors are using the technique of switching the upper and lower trigrams.A key difference between the Fu Xi square and the Omei diamond is that, whilst in the Fu Xi square, the axes that divide the hexagrams fall between the hexagrams themselves, in the Omei diamond the axes are actually composed of hexagrams. This is interesting and it leads to the identification of certain hexagrams as critical to the layout. In the Omei notation, the vertical axis is composed of the hexagrams that satisfy I=J (i.e. the two trigrams are identical) whilst the horizontal axis is composed of those hexagrams that satisfy I=(J) (i.e. the trigrams of each hexagram are complementary). It is interesting that these critical hexagrams turn out to be the same hexagrams that appear in the heart of Z. D. Sung's cubical arrangement (the horizontal Omei axis) and at the corners of his cube (the vertical Omei axis). See [Sun69] for details of the cube arrangement, or refer to my review of Sung here. When correlations between otherwise unconnected works turn up like this I'm inclined to suggest that both works gain some extra measure of credence. When different structures show similar features I'm happy that something quite fundamental is being represented. The authors go on to note that the completion of the Omei diamond involves a subjective placement of the gua. This is an important observation, and marks another key difference with the Fu Xi square. However, I would have liked to have seen more discussion of this. For example, what constraints, if any, exist on the placement of the gua within the Omei framework? Do some arrangements yield more subjectively satisfying results that others? Is there any mathematical principle that these more satisfying arrangements exhibit? None of these questions are addressed, leaving the reader without a clear idea of the authors' intent in this regard. Static and Dynamic ArrangementsThe authors make a clear distinction between static and dynamic arrangements of the gua. They see the Fu Xi arrangement as static because the movement from one quadrant to another is achieved by reflection through the axes, but those axes are separate from the Fu Xi square itself; as noted above, the axes fall between the hexagrams. However, in the Omei diamond the axes actually contain hexagrams; the authors say that those hexagrams are seen as transition functions and provide the means of getting from one quadrant to another. Again, this is not really explained in detail and no concrete examples are given.On p41 the authors say of their system that it creates a dynamic view that makes it possible to analyse events as they occur. They say that this is impossible for someone whose Yijing skills are based on traditional casting methods. I think this is unfair. Someone who has spent a long time with the Yi, whatever their approach, will have internalised a great deal of its imagery and will be quite capable of applying this to events as they happen without resorting to coins or yarrow stalks. There is more to reading the Yi, even for a "traditionalist", than coins or stalks. The Use of ExamplesIn general more examples are needed throughout the book to shop the application of the techniques that the authors are proposing.On pp42-44 the authors do give a couple of examples of the application of their system. I have to say that I didn't really feel that this was about the Yi, rather it is about the abstraction of the Omei diamond. I guess that's fair enough, but the examples would have been much more convincing if, instead of simply using their own I/J notation, they had actually shown some specific hexagrams applied to the situations and then shown how they relate to each other using the Omei notation. Later examples on pp56-58 go some way towards rectifying this - at least here we're shown the trigrams and how they relate to some martial arts applications, but what's missing in that is enough description - this needs to be spelt out in more detail. At Odds with Tradition?In this section I shall discuss two key departures from the classical literature in the Omei analysis of the Yijing. Whilst such departures are not necessarily a bad thing, they do need to be carefully explained and justified.Fu Xi or Not Fu Xi?As already stated, the authors begin by analysing the Fu Xi square. Except that the square arrangement that they use is not actually the Fu Xi square.The Fu Xi square is built from a binary sequence which can be most simply characterised by saying that yang lines enter from above. Thus, starting with the Receptive, we get Splitting Apart followed by Holding Together and Contemplation (see, for example, [Bir89, p239] or [Wil82, p84] for presentations of the Fu Xi square). Now, the Omei rendition of this square has yang lines entering from below. That is, after the Receptive comes Return , then the Army , then Approach , and so on. Clearly, given this fundamental difference in construction, the hexagrams will now be in different places. For example, the hexagram Peace is in the top right rather than the bottom left corner and Stagnation is in the bottom left rather than the top right. That is, the I/(J) and the (I)/J quadrants are swapped around. Also, even though the I/J and (I)/(J) quadrants remain unaltered, the hexagrams they contain are changed: in the genuine Fu Xi square Splitting Apart is in the Receptive I/J quadrant, but in the Omei rendition it is in the Standstill quadrant (I)/J. Again, in the genuine Fu Xi square Return is in the Peace quadrant I/(J), but in the Omei rendition it is in the Receptive quadrant. What effect does this have on the Omei analysis? Fortunately for the authors, not much. Their basic idea of mapping from hexagrams in one quadrant to hexagrams in another via a set of characteristic equations still works. CosmologyOn p62 there is a curious paragraph that implies that the authors see the two trigrams in a hexagram as corresponding to Heaven and Man. This is counter to the usual interpretation that I am familiar with which takes the two trigrams to be Heaven and Earth, whilst the bigrams represent Heaven, Man and Earth. There is no attribution given for this interpretation, so I'm curious as to how the authors have arrived at this different view point.Given the importance of such a fundamental shift in cosmology to the interpretation of the hexagrams, it is vital that the reasoning for this change is given. How else can one judge the merits of such an alteration? Also, the authors seem to suggest that some key element of representation is missing from hexagrams because they only have two trigrams. Specifically, given their interpretations of the trigrams, they feel that Earth is omitted from the system. I'd cite the Ta Chuan, Chapter 2 Verse 4, where it say says clearly "The movement of the six lines contains the ways of the three primal powers." [Wil83, p289]. I can see no basis for these two differences and I feel that any author stepping so far outside of the traditional structure of the Yijing owes some detailed explanation to their readers on the matter. No explanation seems available. ConclusionsSo, my overall impression?Putting aside the fact that I feel that the interpretation of the manifestation Yi is too broad to be meaningful, I think that the work is basically sound - they provide an interesting new structural principle for arranging the gua. However, I don't think that the authors really do it justice. Most of the text is insufficiently detailed with a lack of examples. Those examples that they do give are not really related back to the Yi itself. Getting the basic layout of the Fu Xi square wrong in a book that claims to present an analysis of that structure is really unforgivable. It shows one of two things: either a lack of familiarity with some of the basic literature about the Yi, or a sloppy approach to research. I can make no judgment on that issue. That the basic principles of their analysis still hold good is down to the fundamentally structured nature of mathematical truth. There is also some material towards the end of the book (specifically the description of the roles of the trigrams and the suggestion that a third trigram might be needed to generate nonograms) that, if I'm understanding it correctly, I find to be mistaken and misleading. From an academic perspective, I have to say that the list of references the authors give is sorely lacking in detail: they list a range of material without saying how it's directly relevant to what they have written and they don't provide detailed references for people who might like to explore further. For example, if I'm new to literature on the Yijing, there's no indication as to where I could read up on the Fu Xi arrangements of the gua. This is a small volume, only 82 pages with large type and a lot a white space that make it a quick read. For people not familiar with some basic mathematics it might not be easy to follow all of the material, but the mathematics required is not difficult and a basic introduction to the necessary concepts is given. To reiterate: even though the volume has some quite fundamental problems, the basic research seems a valuable starting point. It is my hope that the authors will correct the basic errors, provide sensible explanations for their radical choices and continue to develop their work. |
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