IF we combine the circular and square diagrams we introduced in the last issue, it will help us to understand the circulations and structure of I Ching gua as well as the connections between them. As we explained before, the Yangdu goes up from Fu Gua (1) to Tai Gua (16). The Yangdu continues to increase from Jie Gua (17) until the peak Qian Gua (32). Each gua has their own level of Yangdu and Yindu, which sum to 32. Then, the Yangdu declines from Gou Gua (33) to the bottom Kun Gua (0). In the aspect of yin, the Yindu in fact increases from Gou Gua (33) to Kun Gua (0), which is a process wherein the Yangdu declining from 31 to 0, while the Yindu increasing from 1 to 32.

The essence that Yangdu grows as Yindu weakens is clearly shown when we transform the square diagram into a circular one, which was mentioned in the last issue. In Picture 1, a scale of Yangdu and Yindu is added to the left for your reference. It’s clear to us that the sum of Yangdu and Yindu of any gua is 32 while the Yangdu of a paired gua totals 32. So does the sum of Yindu of a paired gua. Therefore, the Yangdu of a prior gua is the same to the Yindu of a rear gua, and vice versa. The Yangdu and the Yindu of Qian Gua are expressed as (32, 0) while Kun Gua as (0, 32); thus, Tai Gua is (16, 16) and Pi Gua is (16, 16); Jiji Gua is (18, 14) and Weiji Gua is (14, 18); Ding Gua is (28, 4) and Tun Gua is (4, 28) and so on.

Here we introduce a simple way to remember each gua’s Yangdu and Yindu as well as its connection. There are 32 gua in the yang sphere from Fu Gua (1) to Qian Gua (32). The Yangdu of a gua equals its sequential number. So the Yindu equals 32 minus its Yangdu. Similarly, in the yin sphere, the Yindu of a gua equals its sequential number minus 32 while its Yangdu is 32 minus its Yindu, or 64 minus its sequential number. For example, Zhen Gua (7) is a yang gua. As its Yangdu is 7, its Yindu is 25. So the Yindu of its paired gua Xun Gua (39) is 7 (39-32=7) while its Yangdu is 25 (64-39=25). A line that connects Xun Gua and Zhen Gua in the circular diagram (shown in last issue) must pass the circle center. Xun Gua’s Yangdu and Yindu are the same to Zhen Gua’s Yindu and Yangdu, respectively. Yin and yang the two spheres are, you see, “contrary yet complementary.”

In I Ching, there are 64 gua with 32 levels of Yangdu. It’s obvious that two gua share the same level of Yangdu (or Yindu). We can discover the trait easily in the Picture 1 as there are two gua positioned on the same row as they have the same level of Yangdu (or Yindu). For instance, Zhen Gua (7) and Cui Gua (57) are in the same row as the Yangdu and Yindu of both gua are the same. So, their paired gua Xun Gua (39) and Dachu Gua (25) are in the same row too, with the same Yangdu and Yindu. Cui Gua and Xun Gua are lined in the same column. The Yangdu of Xun Gua is the same as the Yindu of Cui Gua as Xun Gua is (25, 7) and Cui Gua is (7, 25). The four gua, Zhen, Dachu, Xun and Cui, have a certain connection regarding the intensity change between yin and yang. The same connection can be discovered in other four gua, such as Kan, Gu, Li and Sui: Kan Gua 10 (10, 22), Gu Gua 22 (22, 10), Li Gua 42 (22, 10) and Sui Gua 54 (10, 22).

In fact, four gua on the four corners of any one rectangle in the diamond diagram are two pairs of gua, which contain the connection mentioned above. To locate a gua in the diagram, define it as A. If its sequential number is smaller than 32, it’s easy to get the sequential number of another gua, which is “32-A.” (If the sequential number is larger than 32, define it as B to get the sequential number “B-32.”) Then , we can easily find these two pairs of gua.

For example, if A is Gen Gua (12), the other gua with the same Yangdu is Sun Gua (20) for “32-A=20.” So the paired gua of Gen Gua and Sun Gua are Xian Gua (52) and Dui Gua (44). If we define Meng Gua (58) as B, its paired gua is Ge Gua (26) for “B-32=26.” Then it’s easy to find the matching pair of gua, which is Sheng Gua (6) and Wuwang Gua (38). However, please note that Qian Gua-Kun Gua don’t have a matching pair of gua. It’s the same with Tai Gua-Pi Gua. That’s because the “rectangle” is “collapsed” into a “line” in the diagram: the line connecting Qian Gua and Kun Gua being the vertical-axis while the line connecting Tai Gua and Pi Gua being the horizontal axis.

It’s crucial to bear in mind that the macro circulation of I Ching gua is transmuted over time. However, the “periodically varying” movement is not merely repeating itself but an extension toward the future. As Kun Gua can be viewed as Kun Gua (0) or Kun Gua (64), such expressions show an idea that the circulation of I Ching gua doesn’t return to Kun Gua (0) but get into another circulation starting from Kun Gua (64), then the next period starting from Kun Gua (128) ... A similar concept can be found in Percy Bysshe Shelley’s famous poem “Ode to the West Wind: ‘If winter comes, can spring be far behind’?”

We thus get the Picture 2 if we add a coordinate system showing the solar year to the Picture 1. The macro circulation of I Ching gua can be viewed as a system developed by the Chinese ancestor to record the Sun path.

As shown in the Picture 2, Kun Gua (0) corresponds to the date with the least sunshine of the year (or the winter solstice) when the Sun reaches the Tropic of Capricorn. From Fu Gua (1) to Qian Gua (32), the Sun moves to the north as the intensity of sunshine increases on to the Chinese mainland. Tai Gua (16) corresponds to the spring equinox as the daytime equals the nighttime when the Sun passes the equator. The intensity of sunshine increases as the Sun continues to move to the north until reaching the Tropic of Cancer, which is corresponded by Qian Gua (32), when the Yangdu. The Yangdu reaches its peak.

Then the intensity of sunshine starts reducing as the Sun “returns” to the south. In the I Ching system, the gua after Qian Gua (32) are in the yin sphere. Pi Gua (48) corresponds to the autumn solstice, when the Sun passes the equator again. Its Yangdu and Yindu are both 16 as the daytime equals the nighttime. The Sun continues to move to the south until reaching the Tropic of Capricorn. In the Northern Hemisphere, the intensity of sunshine is at the weakest in a year. The Yangdu becomes 0, which is corresponded by Kun Gua (64).

In the Picture 2, the horizontal-axis shows the time coordinate while the vertical-axis shows the intensity of Yangdu. The gua between two Kun Gua (winter solstice) forms an upside-down “V” shape with the vertex sitting on the Tropic of Cancer. The gua between two Qian Gua (summer solstice) forms a “V” shape with the vertex sitting on the Tropic of Capricorn. From Tai Gua to Tai Gua (spring equinox), the gua traces a sine wave while it forms a cosine wave from Pi Gua to Pi Gua (autumn equinox).

Is it beautiful? We’re only to know that the marvelously shaped curves are not marvel!