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correlations with the I Ching
The sixty-four numbered 'hexagrams' in the Chinese classic I Ching Book of Changes are stacks of six horizontal yin/yang (broken/unbroken) lines. Commentaries describing the significance of each hexagram, I find, correspond remarkably with the sixty-four isomorphic corners of my Model (shown in the eight Figures of Part 4). Here I show how this is possible and why the depiction of the hexagrams on a hypercube gives advantages not found in their traditional arrays around a circle or in the spaces of a chessboard.
Such an arrangement was possible because the hexagrams have lower and upper sets of three lines, called trigrams. As has often been observed, the properties of each trigram can be seen as the eight corners of a cube. I have found it necessary to arrange the trigrams' oppositions according to the clock-like contrasts attributed to the Emperor Fu Hsi, circa 1,000 B.C..
You will see from the diagram that Fu-Hsi's opposing trigrams are symmetrical opposites, with broken and unbroken lines reversed. This is the arrangement I will follow throughout this presentation. The more common asymmetrical one in the bulk of I Ching literature reverses the trigrams shown here at 1:30 and 4:30 I reject. It does not permit the reproduction of my paradigm's distribution of problem-contexts and response-modes. (It has been suggested that the more popular arrangement of the trigrams results from an ancient flawed reconstruction of destroyed Texts.)
Fu-Hsi's oppositions are shown below. Each trigram is given its usual Chinese name and its usual English label. To each is assigned a color, and its opposite has the opposite color. These same sets of opposites will hold for both the Lower and Upper trigrams. This is shown tri-dimensionally in Figure 28. Colors of the Lower problem-context trigrams will be capitalized, and those of the Upper response-mode trigrams will be without a capitalized first letter.
Following the digital contrasts described in Part 1, the lower trigrams may be seen to depict 'problem-contexts' and the upper ones 'response-modes', I produced a hypercube with the Commentaries on its sixty-four corners (see Figure 31). It is strikingly similar to my Model's isomorphic combinations of hypercubes for individuals and collectivities as depicted in the cubic depictions of Part 4.
The correspondence becomes understandable when one sees the lower trigram's problem-context defined by the presence or absence of the three types of learning:
This resulted in the lower trigram offering eight distinct three-dimensionally opposite, problem contexts, at its cubic corners:
For the upper trigram of response styles,
This resulted in the 'upper' trigram offering eight distinct three-dimensionally opposite, styles of response, at its cubic corners:
[I stumbled upon this formulation while vacationing from France in California after completing my first paper on the paradigm: Stylistic Statics: The Isomorphic Mapping of Semantic Space (1991). The correspondence was so remarkable and seemingly significant that I immediately took out a copyright under the title Systems Design for the I Ching : A Proposed Distribution of Hexagrams within Human Systems.]
This unanticipated complication of my retirement publication project began when I noticed several I Ching volumes in a Dana Point, California book store. Having once read Cary F. Baynes' Bollington Series translation from German (Princeton Univ. Press, 1973) of Hellmut Wilhelm's (1960) Eight Lectures on the I Ching , and recalling that he mentioned sixty-four hexagrams, I bought what seemed to be a user-friendly book to see how they were described. It was when I saw cubic potentials in the trigrams that I began hours of trials on opened grocery bags that finally yielded, to my amazement, a striking correspondence with the isomorphic versions of my paradigm's prototypes as illustrated in the figures in part 3.
On rereading Wilhelm after returning to Paris, I found his view that the trigrams' three dimensions formed "a remarkably compact cube". I disagreed, however, with his conclusion that a graphic representation of the hexagrams "cannot but be inadequate, because three dimensions do not suffice." My arrangement of 'cubes within a cube' would seem to overcome that difficulty in a way infinitely preferable to the usual presentations of the sixty-four hexagrams around the rim of a circle or in the chessboard-like spaces of an eight-by-eight square.
[No "oracular" significance is claimed or implied.]
Figure 31 below shows, with their conventional numbering, the sixty-four hexagrams in the hypercubic context of my Model. The four pages that follow present the "evidence" for my contention that the correspondence exists. The reader will judge its validity and significance.
An advantage from picturing this hypercubic context for the hexagrams is the way it helps to underline oppositions - especially the four major ones at the extremes of:
Erich Fromm might have termed them, respectively, the four existential oppositions existing between:
These contrasts will appear below, at the beginning of each archetype's set of three-dimensional oppositions.
What should we make of this correspondence between my model of semantic space and the ancient oracle of the I Ching? Let it not be too quickly dismissed because of the oracular aspect seen by Carl Jung  (1968) as evidence of "synchronicity", an acausal connecting principle. Fritjof Capra says in The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism (1985), "The use of the I Ching as a book of wisdom is, in fact, of far greater importance than its use as an oracle. It has inspired the leading minds of China throughout the ages.." (p.110) and in his Preface to this second edition, "I have found that a natural extention of the concepts of modern physics to other fields is provided by the framework of systems theory...the systems approach strongly enforces the parallels between modern physics and Eastern mysticism". Recently, Johnson F. Yan, in DNA and the I Ching: The Tao of Life (1991). arguing for a correspondence between hexagrams and both amino acids and the genetic code, notes that "..von Leibnitz, the inventor of binary arithmetic and an early investigator of probablility, was aware of the I Ching... Neils Bohr was so impressed with the connection between the I Ching and the various dualities in quantum theory that, when he was knighted, he made the Tai Chi symbol a part of his coat of arms."(p.x)
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