IN order to adjust quickly to the changing weather conditions for farming, our ancestor along the Yellow River observed the change of the sun and the moon and then developed a set of symbols to record it.

We have reason to believe that the 64 6-yao gua in I Ching are a system of symbols relating to the tropical year. Our wisdom ancestor, also known as Fu Xi, invented the I Ching system as a calendar-making tool following the movement of sun between the Tropic of Cancer and the Tropic of Capricorn.

The macro circulation in I Ching is mainly based on rules regarding the intensity of yang, or Yangdu Rules. Yangdu is measured by the intensity of sunshine. In detail, the more yang yao an I Ching gua has, the stronger its Yangdu is. With the same number of yang yao, the higher positions of the yao in a gua, the stronger the gua’s Yangdu is. (See Picture 1)

Alternatively, Yangdu can be determined by yin yao in a similar way. The Yindu (opposite to Yangdu) is growing stronger as a gua has more yin yao or the position of yin yao is higher. As “opposites yet complementary,” Yindu grows while Yangdu weakens, and vice versa. Please note that the sum of Yindu and Yangdu of any I Ching gua is the same value, 32.

For example, in the yang sphere, Qian Gua is arranged behind Shi Gua as the former Yangdu is stronger than the latter. The only yang yao in Qian Gua is positioned higher than that in Shi Gua. However, Qian Gua’s Yangdu is weaker than Lin Gua as the latter has two yang yao. Similarly, the Yangdu of Mingyi Gua is stronger than Lin Gua as the former’s yang yao is positioned higher. In the yin sphere, gua are arranged in order by the decline of Yangdu (or the increase of Yindu). For example, Tongren Gua is after Gou Gua for the former gua has a weaker Yangdu due to the only yin yao in Tongren Gua is positioned higher than that of Gou Gua.

Spring and autumn equinox and summer and winter solstice are the most important astronomical events of the year. Actually, there are four matching I Ching gua to the four events:

In the above order, the four events occur when the sun reaches the 90o, 180o, 270o and 0o of the ecliptic, respectively. China is located in the northern hemisphere with the Tropic of Cancer running through. As the sun orbits, it passes the equator twice a year, when the daytime is as long as the nighttime, called the spring and autumn equinox. The hexagrams of Tai Gua and Pi Gua show the concept clearly — the intensity of sunshine with equal number of yang yao and yin yao. The summer solstice, when the sun reaches the Tropic of Cancer, is matched with Qian Gua (six yang yao and no yin yao) while the winter solstice is matched with Kun Gua (six yin yao and no yang yao) ) as the sun reaches the Tropic of Capricorn, when the intensity of sunshine is the weakest during the year. So the Yangdu and Yindu of the spring and autumn equinox are equivalent 16 in Yangdu and 16 in Yindu. The Yangdu of summer solstice is the strongest, which is 32 while its Yindu is 0. The Yangdu of winter solstice is 0 while it Yindu is 32.

In the last issue, we introduced that Xiaoxi (Informative) Gua is a set of milestones, marking the change of intensity of sunshine. The Yangdu of six yang gua is increasing from Fu Gua to Qian Gua. The latter has six yang yao with the Yangdu as 32. On the contrary, the Yindu of six yin gua is increasing from Gou Gua to Kun Gua. The latter has six yin yao with the Yindu as 32.

In detail, positioned between Kun Gua and Tai Gua, Fu Gua’s and Lin Gua’s Yangdu are both below 16, which is on the rise while the opposite yindu is declining.

Similarly, Dazhuang Gua and Guai Gua are in between Tai Gua and Qian Gua. The Yangdu of both are above 16 and continue to increase till Qian Gua. However, Gou Gua and Dun Gua are situated between Qian Gua and Pi Gua. The Yangdu of both are above 16 but on the decline (or the Yindu is below 16 but on the rise). Guan Gua and Bo Gua are positioned between Pi Gua and Kun Gua. Their respective Yangdu is below 16 and continues to decline until Kun Gua, with a Yangdu of 0.

The sequence of the 64 I Ching Gua in Picture 1 shows the change between yin and yang.

The number before each gua in Picture 1 is the sequential number in Zhouyi. The first number behind a gua is its own ID number while the last number indicates the gua’s sequential number in the macro circulation in I Ching.

If the last number is in red, it is a yang gua. If that is in blue, it is a yin gua. The number indicates the intensity of yang, or “Yangdu,” and its relative location.

The 64 gua are highlighted in different colors based on their number of yang yao in the picture: (For example: One Yang Gua and Five Yin Gua has the same number of yang yao and yin yao though they belong to different spheres.)

In conclusion, there are:

1 Zero Yang Gua and 1 Pure Yang Gua

6 One Yang Gua: 3 of them are Five Yin Gua

15 Two Yang Gua: 9 of them are Four Yin Gua

20 Three Yang Gua: 10 of them are Three Yin Gua

15 Four Yang Gua: 6 of them are Two Yin Gua

6 Five Yang Gua: 3 of them are One Yin Gua

However, you may notice that the gua are not arranged in a strict order based on the Yangdu Rules in the picture. That’s a compromise due to the difference between the solar and lunar calendar.

In fact, a solar year has about 365.244 days, rather than a whole number of 365 days. A lunar month has about 29.5306 days. It takes 19 years to have exactly the same days on both calendars, which are 235 lunar months as 12 years plus 7 leap years.

If you dig a little deeper, you’ll find that the lunar year is actually a mix of both solar and lunar calendars, which is a compromise made between the solar calendar and the Islamic calendar.

Now it will be easy to turn the square diagram of Picture 1 into a circular one. The 64 gua can be arranged in a clock-wise order based on the Yangdu, from Fu Gua (1), Shi Gua (2) … Guai Gua (31), Qian Gua (32) … Gou Gua (33), Tongren Gua (34) to Bo Gua (63) and Kun Gua (0). Thus, we have the Picture 2 , the underlying meaning of which will be elaborated in next issue.