WE have introduced in the last issue that the 64 I Ching gua are divided into two spheres: Exactly half of them belong to the yang sphere, while the other half belongs to the yin sphere. Please note that a pair of gua consists of a yang gua and a yin gua. Thus, there’s a total of 32 pairs of gua. That’s what we call the 32 micro circulations in “I Ching.” Let’s name the yang gua of a paired gua as “prior gua” and the yin gua as “rear gua.” It is clear that the locations of a prior gua and a rear gua in the square diagram (Picture 2) are symmetrical to the center point. For example, the coordinates of Qian Gua and Kun Gua are (7, 7) and (0, 0) respectively while those of Tai Gua and Pi Gua are (0, 7) and (7, 0). Any one pair of the 32 micro circulations shows the same characteristic ­— symmetry to the center point in the diagram.

In conclusion, if one of a paired gua is located in the Column a and Row b, then the coordinate of the other gua must be (7-a, 7-b). For example, as Tun Gua is Water above Thunder (2, 1), its paired gua’s coordinate is (5, 6), which is Ding Gua ­— Fire above Wind. That’s because Water is paired with Fire while Thunder is paired with Wind in the Bagua. It is also clearly shown in the circular diagram, known as the Fuxi Xiantian Diagram by Shao Yong.

From a three-dimensional perspective, Song Gua ­— Sky above Water — is located in the Water (☵) in the small Rubik’s cube within the Sky (☰) of the big Rubik’s cube. Meanwhile, its paired Mingyi Gua ­— Earth above Fire ­­— is positioned at the Fire (☲) in the small Rubik’s cube within the Earth (☷) of the big Rubik’s cube. It means that the two paired gua must be symmetric to the center in a three-dimensional space, or in a six-dimensional space.

The 32 micro circulations in paired gua are formed based on “Opposites yet Complementary,” the core concept of “I Ching.” Let’s use two micro circulations, Ding Gua ­— Tun Gua, and Jiji Gua­ — Weiji Gua­, for illustration. The yao on the same position of a prior gua and a rear gua are opposite to each other. As the top yao of Ding Gua is yang, then the top yao of its paired Tun Gua must be yin. This basic relationship surely holds for the second yao of Jiji Gua and Weiji Gua.

Does this relate to the original 32 paired gua in “Zhou Yi?” In “Zhou Yi,” Tun Gua is paired with Meng Gua while Ding Gua is paired with Ge Gua instead of Tun Gua (2,1) ­— Ding Gua (5,6), Ge Gua (4,5) ­— Meng Gua (3,2) in pair. As a matter of fact, in “Zhou Yi,” the gua are paired indirectly. This understanding is critical for us to interpret the name and meaning of each gua and then the content of each yao.

Now let’s move to the macro circulation in “I Ching.” In short, the macro circulation is about the sequence of the 32 paired gua and the reason underlying such a sequence.

There is a special group of 12 gua listed in Picture 1. These gua are named the “Twelve Xiaoxi (informative) Gua.” Six of them belong to the yang sphere while the other six belong to the yin sphere, hence six pairs of Xiaoxi Gua.

The Xiaoxi Gua are positioned along the edges in the square diagram. A Xiaoxi Gua consists of at least one Sky or Earth. The four Xiaoxi Gua at the four corners of the diagram are Qian Gua (two Skys), Kun Gua (two Earths), Tai Gua (Earth above Sky), and Pi Gua (Sky above Earth). The Xiaoxi Gua are believed to carry special meaning. They are regarded as a set of “milestones,” showing the change of intensity between yin and yang.

As shown in the Picture 1, the number of yang yao (whole line) of a yang Xiaoxi Gua is increased by one at a time from left to right as Fu Gua has only one yang yao while Qian Gua features all six. A similar pattern can be seen in the yin gua group. The alterations of the number of yin /yang yao indicate the change of the degree of intensity between yin and yang.

For example, the group of yang gua shows yang is growing while yin is weakening from Fu Gua to Qian Gua. In detail, Fu Gua has one yang yao and five yin yao. It is transformed from Kun Gua, which has no yang yao at all.

Thus, Fu Gua is the weakest yang milestone. On the contrary, Gou Gua has one yin yao and five yang yao. It is transformed from Qian Gua, which has none yin yao. Therefore, Gou Gua is the milestone indicates the weakest yin degree. The same rule can be applied to the remaining eight Xiaoxi Gua.

The message that the Twelve Xiaoxi Gua deliver is that the sequence of I Ching gua should be arranged based on the intensity of yang of each gua in the macro circulation. The intensity of yang is also called “Yangdu (yang degree)” while the intensity of yin is called “Yindu (yin degree).”

The yang Xiaoxi Gua are organized in the following sequence based on the “Yangdu” of each gua from weakest to the strongest:

Fu — Lin —Tai — Dazhuang — Guai — Qian

The six yin gua are, to the contrary, based on their respective “Yindu” from the weakest to the strongest as follows:

Gou —Dun — Pi — Guan — Bo — Kun

In Picture 2, we can see that there are two big triangles, one of them is kept in a darker shade. The 32 yang gua from Fu Gua to Qian Gua are positioned in the triangle at the bottom left with Zhen Gua, Kan Gua and Gen Gua sitting on the diagonal line from northwest to southeast. The 32 yin gua from Gou Gua to Kun Gua are in the shaded triangle on the top right with Xun Gua, Li Gua and Dui Gua sitting on the diagonal line. The numbers in the picture represent the sequential numbers of I Ching gua in the macro circulation. The gua are arranged in an order based on their “Yangdu,” the intensity of yang. The number of yang yao and their positions in the hexagram all matter. The more yang yao with higher positions indicate the stronger “Yangdu” of the gua. For example, both Qian Gua (3) and Shi Gua (2) have only one yang yao. However, the position of the yang yao of Qian Gua (3) is in the third yao, higher than that of Shi Gua (2), the second yao. Meanwhile, the “Yangdu” of Qian Gua (3) is weaker than that of Lin Gua (4) as the latter has two yang yao. That’s how the gua are ranked in the diagram.

The sequence of yin gua is comparatively easy to arrange as it is inferred on the basis of “opposites yet complementary” and the symmetry in the square diagram.

Since the sequential number of Fu Gua is 1, its paired Gou Gua’s sequential number is 33. That is, the “Yindu” of Gou Gua is 1 (or its “Yangdu” is 31), just like the “Yindu” of Fu Gua is 31. Similarly, the “Yindu” of Dazhuang Gua is 9 because its sequential number is 23. The sequential number of its paired Guan Gua is 55, as its “Yindu” is 23 and “Yangdu” is 9.

But how come in the macro circulation of I Ching gua, the difference between the sequential numbers of any pair of gua is 32, the same number as the sum of “Yindu” and “Yangdu” of any gua? What is the implication and significance of the number 32? Let’s explore more next time!