Sung: Part II - Their Exibits

Chapter I - Mathematial Exhibits - Eight Trigrams

Although Sung does not discuss this, it is interesting to begin by recapping the origin of the terms "yin" and "yang". The characters for these two terms are shown on the left, and my (poor) dictionary of Manderin gives the definition of "yin" as shady and "yang" the sun.

Both Wilhelm [Wil82, p30] and Javary [Jar97, pp5-6] expand on the precise meanings of these characters. The reader will note that there is a component common to both characters. This common component means "mound" or "hill"; thus, literally, "yin" can be taken as the shady side of the hill and "yang" as the sunny side of the hill.

The beauty of these terms, then, is that they show directly how yin and yang cannot exist as separate entities. Rather, they are to be seen as two complementary and interdependant aspects of the same underlying reality.

We are now in a position to appreciate Sung's material from pp12-14; his "cubical faces" construction. This shows in detail how the corners of a cube generate the 8 trigrams. It is easy to see that light and shadow can generate a single dimension of yin and yang, a single line in a gua. What Sung shows, is that by taking a slightly more complex shape, it is possible to get light and shadow to generate the trigrams. The relevant figure is shown below:

From Z.D. Sung, p12

When the cube is lit from a corner, 3 faces are light and 3 are shadow; the corner with 3 light faces is Heaven, the corner with 3 dark faces is the Receptive. Further, there are three corners each with 2 light and one dark face, and similarly 3 corners with 1 light and two dark faces. In the figure shown the cube is lit from the front face, top left corner. This really is yin and yang.

This is identical in structure with the trigram lattice I develop in my Boolean Algebra paper, although I don't think that Sung is aware of that mathematical construction and the resulting gua ordering.

Sung then presents two further ways of generating the same structure. The first of these is "the geometry of the cubical edge lines" (pp15-18). I must admit that I find this particular constrution hard to follow and less convincing than the "cubical faces" construction discussed above. However, it does lead Sung to the following expression (p17):

Equation 1: The Trigram Space
(A+B)3 = A3+3A2B+3AB2+B3
Which is Charlie Higgin's trigram space polynomial equation, with the superficial difference that where Sung uses the terms "A" and "B" for yang and yin respectivly, Higgins uses the terms "a" for "active" (or yang) and "i" for inactive (or yin).

This equation, in turn, leads to what Sung refers to as an "algebraic exhibit". This figure is shown below:

From Z.D. Sung, p18

The reader will again notice the structural similarity with the basic lattice figure. However, now we have the addition of the terms from the polynomial given as Equation 1. Notice that each term is associated with a particular level of structure and each such term encodes the relative amounts of yin and yang in the gua at that level of structure.

Similarly, on pp24-25 the author divides 3-dimensional space into eight octants according to the Cartesian co-ordinates axies. This is the same as Higgin's (di)mensional analysis of the trigram space (specifically, his 3D spacial analysis of the trigrams). The following figure, showing this division into octants, with the algebraic formulae superimposed, is from page 26 of the book.

From Z.D. Sung, p26

This particular construction is of great importance in Sung's work as it forms the basis of his cubical structure arrangement of the hexagrams themselves. We shall review this in the following section.