《古易考原》

Confucius said: “The forms of the hexagrams are upright and wise in their function; they enable us to understand and preserve the principles of the past. The Changes accords with Heaven and Earth and can therefore encompass the patterns that govern them. Looking up to observe the signs in the heavens and down to examine the features of the earth, we can understand the changes between the hidden and the manifest. Tracing things back to their beginnings and examining them through to their ends, we can understand the principles of life and death. Jing and Qi gather to form tangible things; when the hun and po souls disperse, change takes place. Thus we can understand the conditions of spirits and ghosts.”

Confucius also said: “Thunder shakes all things, and wind and rain nourish them. The sun and moon move through the heavens, bringing the alternation of cold and heat. The Way of Qian, which represents Heaven and the force of Yang, gives rise to men; the Way of Kun, which represents Earth and the yielding force of Yin, gives rise to women. Qian governs the beginnings of all things, while Kun brings them to completion. Qian grasps things through ease; Kun accomplishes them through simplicity.” All these words explain the Changes of the hexagram forms drawn by Fuxi.

The author argues that Fuxi first devised the hexagram figures, enabling people to understand their forms and preserving within them the principles of Heaven, Earth, and all things as they had been in the past. On this foundation, the Changes later performed by means of yarrow stalks could be put into practice. The Changes of the Xia, Shang, and Zhou dynasties all elaborated on Fuxi’s yarrow-stalk divination and served the purposes of divination, but none explored the meaning of the hexagram figures themselves in depth. Confucius alone truly explained the Changes of the hexagram figures. That is why the author begins Kao Yuan by discussing Fuxi’s Changes of the hexagram figures, believing that this better conveys Confucius’s original intent. Later Confucian scholars failed to understand this point and even claimed that the Zhouyi was added at a later time. The author laments: How could they be so unaware of the Changes’ fundamental origins and exalted intent?

The Creation of the Eight Trigrams, Part One

The Commentary on the Appended Statements, Part Two says: “In ancient times, when Fuxi ruled the world, he looked up to observe the signs in the heavens and down to examine the patterns of the earth. He also observed the markings on birds and beasts, and the ways in which different terrains could be used. He took models from himself at close range and from all things at a distance. Thus he created the Eight Trigrams, to make the virtue of the spirits understood and to classify the conditions of all things.”

Zhuo says: Fuxi looked up and observed the patterns in the heavens, using them to create the trigrams. For example, Qian represents Heaven, Li the sun, Zhen thunder, Xun wind, and Kan the moon, as well as clouds, stars, and other celestial phenomena. He looked down and observed the forms of the earth, also using them to create the trigrams. For example, Kun represents Earth, Dui marshes, Gen mountains, and Kan water.

The markings and habits of birds and beasts, too, could be used as images in the trigrams. Qian represents the dragon, the fine horse, and the old horse; Kun represents the young ox and the cow; Zhen represents the dragon and the horse known for its loud neigh; Xun represents the hawk; Kan represents the pig and the horse with a full back; Li represents the ox, pheasant, crab, tiger, and leopard; Gen represents the dog and mouse; and Dui represents the sheep. The plants suited to particular soils could also be used as images in the trigrams. Qian represents tree fruits; Zhen represents blue-green grains, bamboo, and reed-like plants, as well as things that grow downward, flourish, or shine brightly; Xun represents trees and poplars; Kan represents hard, many-hearted timber, ridgepoles, clumps of thorny plants, and vines; Li represents trees with hollow trunks and branches, or with withered tops; and Gen represents hard timber with many knots.

Images could be drawn from the human body close at hand, and were not limited to eight bodily parts: they included every category associated with the eight trigrams. For example, Qian represents the ruler and the father. Images could also be drawn from the many things in the world at a distance; these were not limited to clothing, food, and utensils. Even if the myriad things in the world were said to number in the tens of millions, all could serve as images—for example, gardens and orchards, jade, metal, cold, ice, largeness, and the color red.

Fuxi created eight basic trigrams, from which the sixty-four hexagrams were formed. The phrase “creating the eight trigrams” names the basic trigrams and, by extension, encompasses all the hexagrams derived from them. Why can naming the basic trigrams encompass the derived hexagrams? Qian is one of the basic trigrams. Take it as an example: when Qian is placed below, each of the eight trigrams—Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun—can be placed above it, forming eight hexagrams. The same is true of each of the other seven basic trigrams.

Thus Qian, Guai, Da You, Da Zhuang, Xiao Chu, Xu, Da Chu, and Tai are all said to begin with the Qian trigram; Lü, Dui, Kui, Gui Mei, Zhong Fu, Jie, Sun, and Lin begin with Dui; Tong Ren, Ge, Li, Feng, Jia Ren, Ji Ji, Bi, and Ming Yi begin with Li; Wu Wang, Sui, Shi He, Zhen, Yi, Tun, Yi, and Fu begin with Zhen; Gou, Da Guo, Ding, Heng, Xun, Jing, Gu, and Sheng begin with Xun; Song, Kun, Wei Ji, Jie, Huan, Kan, Meng, and Shi begin with Kan; Dun, Xian, Lü, Xiao Guo, Jian, Jian, Gen, and Qian begin with Gen; and Pi, Cui, Jin, Yu, Guan, Bi, Bo, and Kun begin with Kun.

The mind of the sage Fuxi encompassed the patterns of Heaven, the forms of Earth, plants and animals, and all things both near at hand and far away. He then created the eight trigrams and transmitted them to the world for later generations. The subtle meanings of the trigram images can therefore encompass the forms of Heaven and Earth, plants and animals, the human body, and all kinds of things, containing every principle. The eight trigrams can help people understand the subtle principles of the spirits; from them, the method of divination with milfoil stalks was devised to communicate with the spirits’ De. One can also take the trigrams as models for making objects, using corresponding images and analogies to represent the conditions of the myriad things, so that whatever one draws upon has a basis.

Han dynasty Confucians believed that Fuxi drew the trigrams based on the Yellow River Chart; Song dynasty Confucians believed that even seeing a rabbit could inspire someone to draw a trigram. The author considers both claims baseless speculation: they fail to grasp the deeper purpose behind Fuxi’s creation of the trigrams and misunderstand Confucius’s intent. More than that, some claim that Fuxi created only the eight three-line trigrams, and that King Wen later doubled them to make the sixty-four hexagrams. The author firmly holds that these claims are all incorrect, for the reason explained here. The relevant diagrams and tables are presented below.

With Qian below and Qian above, it is still called “Qian.” Zhuo says: This is the Qian trigram among the primary trigrams.

With Qian below and Dui above, it is called “Guai”; with Qian below and Li above, “Great Possession”; with Qian below and Zhen above, “Great Strength”; with Qian below and Xun above, “Small Accumulation”; with Qian below and Kan above, “Waiting”; with Qian below and Gen above, “Great Accumulation”; and with Qian below and Kun above, “Peace.” Zhuo says: From Qian through Peace, these are the various transformed hexagrams formed with Qian as the lower trigram.

Zhuo says: These eight hexagrams above describe how Fuxi first established the Qian hexagram. It is appropriate to call Qian, as a primary trigram, “the first creation of Qian.” But why are the transformed hexagrams that have Qian as their lower trigram also all said to be “creations of Qian”? Because Qian is below, serving as the inner foundation; then each of the eight trigrams is placed above it in turn to display the different transformations of Qian. Thus they are collectively called “creations of Qian.” When Qian is above another trigram, however, it is no longer the governing trigram, but merely a component of another hexagram.

With Dui below and Qian above, it is called “Treading”; with Dui below and Dui above, it is still called “Dui.” Zhuo says: This is the Dui trigram among the primary trigrams.

With Dui below and Li above, it is called “Opposition”; with Dui below and Zhen above, “The Marrying Maiden”; with Dui below and Xun above, “Inner Truth”; with Dui below and Kan above, “Limitation”; with Dui below and Gen above, “Decrease”; and with Dui below and Kun above, “Approach.” Zhuo says: From Treading through Approach, these are the various transformed hexagrams formed with Dui as the lower trigram.

Zhuo says: These eight hexagrams above describe how Fuxi first established the Dui hexagram. It is appropriate to call Dui, as a primary trigram, “the first creation of Dui.” But why are the transformed hexagrams that have Dui as their lower trigram also all said to be “creations of Dui”? Because Dui is below, serving as the inner foundation; then each of the eight trigrams is placed above it in turn to display the different transformations of Dui. Thus they are collectively called “creations of Dui.” When Dui is above another trigram, however, it is no longer the governing trigram, but merely a component of another hexagram.

With Li below and Qian above, it is called “Fellowship with Others”; with Li below and Dui above, “Revolution.”

When both the lower and upper trigrams are Li (one of the Eight Trigrams in the Classic of Changes, symbolizing fire and brightness), the hexagram is still called “Li.” Zhuo says, “This is the Li trigram among the primary trigrams.”

With Li below and Zhen above, the hexagram is called “Feng.”

With Li below and Xun above, it is called “Family.”

With Li below and Kan above, it is called “Already Fulfilled.”

With Li below and Gen above, it is called “Adornment.”

With Li below and Kun above, it is called “Darkening of the Light.” Zhuo says, “From ‘Fellowship with Others’ through ‘Darkening of the Light,’ these are all derived hexagrams formed with Li as the lower trigram.”

Zhuo says, “The eight trigrams listed above explain how Fuxi began creating the Li hexagram. It is naturally appropriate to say that the Li among the primary trigrams is the ‘beginning of the creation of the Li hexagram.’ But why, then, are the derived hexagrams formed by combining Li with other trigrams also described as ‘creating the Li hexagram’? Because Li is below and serves as the governing trigram of the inner hexagram. The other trigrams among the Eight Trigrams are then placed above it simply to show the different forms Li takes when combined with them. For this reason, they are all collectively called ‘creating the Li hexagram.’ When Li is above another trigram, it is no longer the governing trigram, but only one part of the combination.”

With Xun (one of the Eight Trigrams, symbolizing wind and penetration) below and Qian above, the hexagram is called “Encounter.”

With Xun below and Dui above, it is called “Great Exceeding.”

With Xun below and Li above, it is called “The Cauldron.”

With Xun below and Zhen above, it is called “Heng.”

When both the lower and upper trigrams are Xun, the hexagram is still called “Xun.” Zhuo says, “This is the Xun trigram among the primary trigrams.”

With Xun below and Kan above, the hexagram is called “The Well.”

With Xun below and Gen above, it is called “The Decay.”

With Xun below and Kun above, it is called “Ascending.” Zhuo says, “From ‘Encounter’ through ‘Ascending,’ these are all derived hexagrams formed with Xun as the lower trigram.”

Zhuo says, “The eight trigrams listed above explain how Fuxi began creating the Xun hexagram. It is naturally appropriate to say that the Xun among the primary trigrams is the ‘beginning of the creation of the Xun hexagram.’ But why, then, are the derived hexagrams formed by combining Xun with other trigrams also described as ‘creating the Xun hexagram’? Because Xun is below and serves as the governing trigram of the inner hexagram. The other trigrams among the Eight Trigrams are then placed above it simply to show the different forms Xun takes when combined with them. For this reason, they are all collectively called ‘creating the Xun hexagram.’ When Xun is above another trigram, it is no longer the governing trigram, but only one part of the combination.”

With Kan (one of the Eight Trigrams, symbolizing water and peril) below and Qian above, the hexagram is called “Conflict.”

With Kan below and Dui above, it is called “Oppression.”

With Kan below and Li above, it is called “Not Yet Fulfilled.”

With Kan below and Zhen above, it is called “Deliverance.”

With Kan below and Xun above, it is called “Dispersion.”

When both the lower and upper trigrams are Kan, the hexagram is still called “Kan.” Zhuo says, “This is the Kan trigram among the primary trigrams.”

With Kan below and Gen above, the hexagram is called “Youthful Folly.”

The hexagram with Kan below and Kun above is called “Shi” (The Army). Zhuo says, “From ‘Song’ onward through ‘Shi,’ these are all different hexagram forms that take Kan as their inner foundation.”

Zhuo says, “The eight hexagram forms above explain the process by which Fuxi first created the Kan hexagram. It is appropriate to call the basic hexagram of three lines ‘the initial creation of Kan.’ Why, then, are the hexagrams made by combining two basic trigrams, one above the other, also all called ‘creating Kan’? This is because Kan is below, serving as the hexagram’s inner foundation. Each of the eight basic trigrams is then placed above it to show the different transformations of the Kan hexagram, so they are collectively called ‘creating Kan.’ When Kan is above another hexagram, it is no longer the governing inner trigram, but a variation of that hexagram.”

The hexagram with Gen below and Qian above is called “Dun” (Retreat); with Gen below and Dui above, “Xian” (Influence); with Gen below and Li above, “Lü” (The Wanderer); with Gen below and Zhen above, “Xiao Guo” (Small Exceeding); with Gen below and Xun above, “Jian” (Gradual Progress); with Gen below and Kan above, “Jian” (Obstruction); and with Gen both below and above, it is still called “Gen” (Keeping Still). Zhuo says, “This is the basic Gen hexagram of three lines.”

The hexagram with Gen below and Kun above is called “Qian” (Modesty). Zhuo says, “From ‘Yun’ onward through ‘Qian,’ these are all different hexagram forms that take Gen as their inner foundation.”

Zhuo says, “The eight hexagram forms above explain the process by which Fuxi first created the Gen hexagram. It is appropriate to call the basic Gen hexagram ‘the initial creation of Gen.’ Why, then, are the hexagrams made by combining two basic trigrams, one above the other, also all called ‘creating Gen’? This is because Gen is below, serving as the hexagram’s inner foundation. Each of the eight basic trigrams is then placed above it to show the different transformations of the Gen hexagram, so they are collectively called ‘creating Gen.’ When Gen is above another hexagram, it is no longer the governing inner trigram, but a variation of that hexagram.”

The hexagram with Kun below and Qian above is called “Pi” (Standstill); with Kun below and Dui above, “Cui” (Gathering Together); with Kun below and Li above, “Jin” (Progress); with Kun below and Zhen above, “Yu” (Enthusiasm); with Kun below and Xun above, “Guan” (Contemplation); with Kun below and Kan above, “Bi” (Holding Together); and with Kun below and Gen above, “Bo” (Splitting Apart).

In the lower and upper trigrams of the Kun hexagram, both are Kun, so it is still called “Kun.” Zhuo says, “This is the Kun hexagram among the eight primary trigrams.” He also says, “From the Pi hexagram down to the Kun hexagram, these are the derived hexagrams composed of Kun.”

Zhuo explains: “The earlier section on the Eight Trigrams discusses Fuxi’s original creation of the Kun trigram. It is certainly appropriate to call Kun among the primary trigrams the original Kun. But why, then, are the various derived hexagrams composed of Kun also said to be ‘creating Kun’? Because Kun occupies the lower trigram, the inner governing position of the hexagram. Other Eight Trigrams are added above it to show the different hexagram forms that Kun composes, so they are collectively called ‘creating Kun.’ But when Kun is above another trigram, it no longer occupies the governing position; instead, it serves as one component of that other hexagram.”

Circular Movement of the Eight Trigrams, Part Two

The Shuogua says: “Heaven and Earth establish the positions above and below; mountains and marshes exchange their influences; thunder and wind stir one another; water and fire do not reject one another.” It also says: “To calculate the changes of the past, one proceeds in the forward direction.”

Zhuo says: This passage discusses the circular arrangement of the sixty-four hexagrams attributed to Fuxi. The scripture speaks only of the images of the Eight Trigrams, using the trigrams it lists to sum up the different kinds of hexagram images within the arrangement.

Heaven is in the south, so all the hexagrams associated with Heaven are in the south. Earth is in the north, so all the hexagrams associated with Earth are in the north. Mountains connect with Qi in the northwest, so all the hexagrams associated with mountains connect with the northwest. Marshes connect with Qi in the southeast, so all the hexagrams associated with marshes connect with the southeast. Thunder stirs against thunder in the northeast, so all the hexagrams associated with thunder stir against one another in the northeast. Wind stirs against wind in the southwest, so all the hexagrams associated with wind stir against one another in the southwest. Water does not clash with water in the west, so all the hexagrams associated with water do not clash with one another in the west. Fire does not clash with fire in the east, so all the hexagrams associated with fire do not clash with one another in the east.

The scripture does not give the names of the hexagrams because Confucius speaks only of their images. Earlier Confucian scholars thought this passage referred only to the Eight Trigrams, each made up of three lines. That is not the case. What does “counting what has gone by proceeds in order” mean? Heaven is in the south. Moving left from the south, the sequence is Heaven, Marsh, Fire, Thunder; moving right from the south, it is Wind, Water, Mountain, Earth. These positions all run from south to north, from top to bottom. Thus, counting the positions already fixed proceeds in order, not in reverse; this has been so from antiquity to the present.

The Third Arrangement of the Eight Trigrams by Direction

The Treatise on the Trigrams says: “The Eight Trigrams are arranged in alternating sequence. To understand what is to come, count in reverse; hence the Yi counts in reverse.” It also says: “Thunder sets things in motion, wind disperses them, rainwater moistens them, sunlight illuminates them, Gen brings things to rest, Dui brings them joy, Qian governs them, and Kun receives and stores them.”

Zhuo says: This passage discusses the directional arrangement of the sixty-four hexagrams of Fuxi. The text says only “the Eight Trigrams,” using them as a general description of the arrangement that follows. “The Eight Trigrams interweave” refers to the sequence in which Heaven and Earth, Mountain and Lake, Thunder and Wind, and Water and Fire move through the circular diagram described earlier. They cross and interweave with one another to form the square diagram.

Shao Yaofu believed that “the Eight Trigrams interweave” means that the Eight Trigrams (three-line trigrams) from the earlier passage are each combined with another set of Eight Trigrams to form the sixty-four hexagrams. In other words, he interpreted “interweave” as “stack together.” But this reading is mistaken. “Interweave” means that things cross and move among one another, whereas “stack” means adding one set of lines on top of another. The two should not be conflated. Otherwise, the statements that follow, such as “Thunder sets them in motion,” cannot be explained: the arrangement of the Eight Trigrams in the square diagram describes how they interweave; it does not merely list the three-line trigrams, nor does it add six-line hexagrams to the circular diagram.

“Thunder sets them in motion” means that thunder stirs all things into activity. In the square diagram, Thunder is just left of center. “Wind disperses them” means that wind spreads and scatters all things. Wind is just right of center. Taken individually, all eight Zhen hexagrams, which symbolize thunder, lie just left of center, while all eight Xun hexagrams, which symbolize wind, lie just right of center. “Rain moistens them” comes immediately after Wind, and “the Sun warms them” immediately after Thunder. Taken individually, all eight Kan hexagrams, which symbolize rain, come after Wind, while all eight Li hexagrams, which symbolize the sun, come after Thunder. “Mountain brings them to rest” comes after Rain, and “Lake delights them” after the Sun. Taken individually, all eight Gen hexagrams come after Rain, while all eight Dui hexagrams come after the Sun. “Heaven rules them” means that Heaven governs all things; Qian is in the north. “Earth stores them” means that Earth gathers and holds all things; Kun is in the south. Taken individually, all eight Qian hexagrams lie in the north, and all eight Kun hexagrams lie in the south.

Although the hexagram positions in the square diagram still have corresponding opposites, their order differs greatly from that of the earlier passage. There, Heaven and Earth come first; here, Li and Kan occupy the middle, while Qian and Kun come last. Qian and Kun therefore take on the roles of governing and storing all things. In the earlier passage, Mountain and Lake form the second pair; here, Gen and Dui form the third pair, so Mountain and Lake interweave with Thunder and Wind. Thunder and Wind form the second pair in the earlier passage; here they occupy the middle, so they interweave with Heaven and Earth. Water and Fire form the fourth pair in the earlier passage; here, Rain and the Sun form the second pair, so they interweave with Mountain and Lake.

Consider the directions more closely. In the earlier passage, Heaven is in the south and Earth in the north; here, Qian is in the north and Kun in the south, so their positions are interchanged. Earlier, Lake is in the southeast and Mountain in the northwest; here, Dui is on the northern side and Gen on the southern side, so their positions are interchanged. Earlier, Fire is in the east and Water in the west; here, the Sun is on the northern side and Rain on the southern side, so Li and Kan are interchanged. Earlier, Thunder is in the northeast and Wind in the southwest; here, Thunder is just north of center and Wind just south of center, so Zhen and Xun are interchanged.

The hexagram images follow the sequence Qian, Dui, Li, Zhen, Xun, Kan, Gen, Kun, arranged from north to south and from bottom to top. Hence the text says, “To know what is coming is to move in reverse.” Since the earlier statement “the Eight Trigrams interweave” is brief and unclear, the author sets out these eight points in detail to explain what “interweave” means in the square diagram. Earlier scholars therefore misconstrued the circular diagram when they called Qian, Dui, Li, and Zhen “counting what has passed in the forward direction,” and Kun, Gen, Kan, and Xun “knowing what is coming in reverse.” This interpretation does not hold up. The sequence of Fuxi’s hexagrams, from Qian to Kun, is not in itself a matter of forward or reverse movement. Confucius’s point was to use the circular diagram’s forward movement and the square diagram’s reverse movement to explain the principle in the “Appended Judgments”: “Wisdom stores what has passed; spirit knows what is coming.” The final sentence, “Now I set out the diagram on the left,” means that the diagram will be presented below on the left.

Fuxi’s Square Diagram of the Sixty-Four Hexagrams

Zhuo says: Some Confucian scholars believe that the secret teachings of the Classic of Changes were kept among practitioners of occult arts, and that they were first elucidated only when Chen Xiyi (Chen Tuan) passed them on to Shao Yaofu (Shao Yong). This view was probably formed without much reflection. Confucius’s words are as clear as the sun, moon, and stars: Fuxi originally expressed his ideas through the hexagrams, while Confucius developed them by drawing on the images of the hexagrams. Without reflection, one cannot grasp their subtle meaning.

I have therefore set out this diagram in detail, so that later generations may know that what practitioners of occult arts call secret teachings originally comes from Confucius’s words, and is nothing to doubt. As for the practice of arranging the three-line trigrams into a square diagram of directions, this was not the original form of Fuxi’s hexagram diagram, nor did Confucius ever describe it that way. I have now removed such diagrams to keep them from misleading later generations.

These two diagrams illustrate the principle of Yin-Yang opposition and mutual dependence: the circle belongs to Yang, and the square to Yin. The moving circle symbolizes Heaven; the still square symbolizes Earth.

Zhuo says: From “Heaven-Heaven” to “Earth-Heaven,” the Eight Trigrams show that Heaven is positioned in the south; from “Heaven-Earth” to “Earth-Earth,” they show that Earth is positioned in the north. From “Heaven-Mountain” to “Earth-Mountain,” the Eight Trigrams show that the breath between mountains is connected, and that their direction is northwest; from “Heaven-Lake” to “Earth-Lake,” they show that the breath between lakes is connected, and that their direction is southeast; from “Heaven-Thunder” to “Earth-Thunder,” they show that thunderclaps stir one another, and that their direction is northeast; from “Heaven-Wind” to “Earth-Wind,” they show that winds stir one another, and that their direction is southwest; from “Heaven-Fire” to “Earth-Fire,” they show that fires do not clash with one another, and that their direction is east; from “Heaven-Water” to “Earth-Water,” they show that waters do not clash with one another, and that their direction is west.

The circular arrangement of these sixty-four hexagrams runs from south to north and from top to bottom, and is therefore called “following the sequence.” The Thunder hexagram sets the myriad things in motion, while the Wind hexagram scatters them: this is the scene of all things sprouting in spring. The Rain hexagram moistens the myriad things, while the Sun hexagram warms them and enables them to grow: this is the scene of all things reaching maturity in summer. The Gen hexagram brings the myriad things to rest, while the Dui hexagram fills them with joy: this is the scene of all things drawing inward in autumn. The Qian hexagram governs the myriad things, while the Kun hexagram stores them away: this is the scene of all things lying dormant in winter.

The square arrangement of these sixty-four hexagrams runs from north to south and from bottom to top, and is therefore called “reversing the sequence.” The source of the Xiantian Diagram handed down by Shaozi, the Northern Song scholar of the Changes, can also be discerned here. The discussion above begins with the horizontal diagram, then turns to the circular diagram, and finally to the square diagram. The principles of the Changes expressed in Fuxi’s hexagram figures can be examined on this basis.

In the phrase “the Gen hexagram stops things with the character quan,” the original character quan is retained.

End of Volume One of Gu Yi Kao Yuan.

1. In Zhouyi Benyi, these two sentences read: “Looking up, he observed the patterns in the heavens; looking down, he observed the forms on the earth.”

2. The character originally written as “xu” was “ri”; it has been corrected to “xu” according to Zhouyi Benyi.

3. The character originally written as “mei” was “mei” with the meaning “obscure”; it has been corrected to “mei” with the meaning “younger sister” according to Zhouyi Benyi.

4. The character originally written as “zheng” in the sense of “government” has been corrected to “zheng” in the sense of “upright” according to the surrounding text.

5. The character “ye” was missing from the original and has been supplied according to the surrounding text.

6. The character “di” was missing from the original and has been supplied according to the surrounding text.

Gu Yi Kao Yuan, Volume Two

The Yi of Fuxi’s Drawings and Numbers

Confucius said: “The function of milfoil stalks, used by the ancients in divination, is subtle and wondrous; through their subtle wonder, one can foresee what is to come.” He also said: “They resemble Heaven and Earth, and so do not violate their principles. Their knowledge encompasses all things, and the Dao can be used to aid the world; therefore, they make no mistakes. They move freely and widely without straying from the right path. Gladly following the course of Heaven and understanding destiny, they have no worries. At ease where they are, and earnestly putting benevolence into practice, they can love others; thus their workings are unfathomable.”

Confucius also said: “Heaven is exalted and Earth is low; from this, Qian and Kun—the two fundamental hexagrams of the Yi representing Heaven and Earth—were established. High and low are set in order, and the places of noble and humble are thereby determined. Movement and stillness each have their regular patterns, and firmness and yielding are thereby distinguished. Things gather according to their kinds, and the myriad beings are sorted into groups; from this arise good fortune and ill fortune. In Heaven, the celestial patterns take shape; on Earth, the forms of things take shape; and change thereby becomes visible. Thus firmness and yielding act upon one another, and the Eight Trigrams (Bagua) stir and transform one another.”

These passages all discuss the Yi formed by Fuxi through drawing the hexagrams and arranging their numerical patterns. It is precisely because these hexagram numbers are subtle and wondrous that one can seek the principles of Heaven, Earth, and the myriad things in the hexagram drawings that record the past, and thereby infer future good fortune, ill fortune, regret, and distress.

For this reason, the book Gu Yi Kao Yuan next discusses “The Yi of Fuxi’s Drawings and Numbers.”

The Yellow River Chart, Chapter One

The “Appended Statements” says: “The Yellow River produced the River Chart, and the Luo River produced the Luo Writing; the sages modeled themselves on them.” It also says: “The numbers of Heaven are one, three, five, seven, and nine; the numbers of Earth are two, four, six, eight, and ten. Heaven has five numbers, and Earth has five as well. Each has its place; they correspond to one another and each has its own pairing. The numbers of Heaven add up to twenty-five, and the numbers of Earth to thirty, making fifty-five in all. These numbers bring about change and set the spirits in motion.”

Zhuo says: “The sages modeled themselves on the River Chart, and thus the ‘fivefold presence’ came into being … The numbers of Earth are thirty, and the numbers of Heaven and Earth total fifty-five. These numbers bring about change and set the spirits in motion.”

Zhuo says: The sages took the River Chart as their model and thus devised the method of divination with yarrow stalks; they took the Luo Writing as their model and thus devised the method of divination with tortoise shells. Since the passage above says, “Nothing is more important than divination with yarrow stalks and tortoise shells,” the Luo Writing is mentioned here as well.

When the Book of Han: Treatise on Pitch Pipes and the Calendar quotes this chapter, the sixty-four characters from “Heaven One” through “moving ghosts and spirits” appear together as a single passage. Sometime after Ban Gu, though it is unclear when, someone moved the twenty characters from “Heaven One” through “Earth Ten” into the following chapter. Here I follow the emendations of Cheng Yi and Zhu Xi and correct this misplaced passage.

This is the numerical pattern of the so-called River Chart. A dragon-horse emerged from the Yellow River, and the whorls on its back were arranged in circles, like stars. Hence it was called a “chart”; since it appeared in the Yellow River, the account says, “The River brought forth the Chart.”

The numbers under Heaven begin with one and end with ten: there are only ten numbers. By repeatedly adding numbers within ten, one can calculate hundreds, thousands, tens of thousands, and hundreds of millions, so it may seem that these numbers all extend beyond ten. The numerical pattern of the River Chart, however, does not work this way.

The numbers of Heaven begin with one. Three of Heaven combines with one of Heaven to make four: one contributes its one, three contributes its three, and the two numbers are joined. Five of Heaven then combines with one and three to make nine; seven of Heaven combines with one, three, and five to make sixteen; and nine of Heaven combines with one, three, five, and seven to make twenty-five. Here, five is the fundamental number of Heaven; twenty-five is the number derived from it. Though twenty-five is derived, it in fact remains within the scope of Heaven’s five.

The numbers of Earth begin with two. Four of Earth combines with two of Earth to make six: two contributes its two, four contributes its four, and the two numbers are joined. Six of Earth then combines with two and four to make twelve; eight of Earth combines with two, four, and six to make twenty; and ten of Earth combines with two, four, six, and eight to make thirty. Here, five is the fundamental number of Earth; thirty is the number derived from it. Though thirty is derived, it in fact remains within the scope of Earth’s five.

The numbers of Heaven and Earth together total fifty-five. Ten is their fundamental number, and forty-five is the number derived from Heaven and Earth. The derived number, in fact, still does not exceed the fundamental scope of ten. The numbers of Heaven and Earth together make fifty-five: the numbers of Heaven are originally odd, yet through the transformations of Yang they can become Yin; the numbers of Earth are originally even, yet through the transformations of Yin they can become Yang. By means of these fifty-five numbers, the myriad things come into being and change, contracting and extending, coming and going, with inexhaustible subtle workings. Since the numbers of Heaven and Earth circulate in this way, how could a sage such as Fuxi fail to take them as his model, use them as the “Great Expansion number,” and employ yarrow stalks to divine and derive the hexagrams? The specific method of modeling them is explained below.

The number of the Great Expansion is fifty, but only forty-nine stalks are used in divination. Divide the forty-nine yarrow stalks into two piles to symbolize Heaven and Earth, the Two Forms. Take one stalk from either pile and place it between the fingers to symbolize the Three Powers of Heaven, Earth, and Humanity. Then count the stalks in each pile in groups of four to symbolize the four seasons. Set aside the remainder from each count beside the stalk taken out at the beginning to symbolize an intercalary month. Since there are two intercalary months in five years, perform this procedure twice before proceeding to “set aside one.” This describes the method of divination using yarrow stalks.

Zhuo says: This passage follows from what came before and explains how Fuxi, drawing on the numerical principles of the Yellow River Diagram, used yarrow stalks to derive the hexagrams. In the Yellow River Diagram, there are five Heaven numbers, which, when extended, become twenty-five; there are also five Earth numbers, which become thirty. Together they make fifty-five, but this has not yet reached the full extent of the Great Expansion’s derivation, so the intercalary months must be added to complete it. Since there are two intercalary months in five years, the procedure is performed twice before proceeding to “set aside one.”

Zhuo explains: This continues the discussion above. Fuxi used the numbers of the Yellow River Chart to derive hexagram images through divination with milfoil stalks.

In the Yellow River Chart there are five Heavenly numbers, which expand to twenty-five, and five Earthly numbers, which expand to thirty. But this does not yet bring the expansion of the numbers to its utmost. Fuxi therefore continued to derive numbers from the Chart and arrived at ninety-nine. The term “Great Expansion” refers to adding adjacent numbers: one and two make three, two and three make five, three and four make seven, and four and five make nine. Together, three, five, seven, and nine make twenty-four. Next, five and six make eleven, six and seven make thirteen, seven and eight make fifteen, eight and nine make seventeen, and nine and ten make nineteen. Adding the units digits of these numbers also gives twenty-four, while there are five tens digits. These are the structural numbers within the Great Expansion, which is why it is said, “The number of the Great Expansion is fifty.” Add the first twenty-four, the later twenty-four, and the one in the middle, and the total is forty-nine. This is the number used in the Great Expansion, which is why it is said, “Of these, forty-nine are used.” Although the derivation arrives at ninety-nine, it still remains within the range from Heavenly One to Earthly Ten. This is what it means to derive from the numbers of the Yellow River Chart and carry that derivation to its utmost.

Confucius used the word “expansion” to reveal the meaning of the Yellow River Chart, then added the word “great” to explain that Fuxi derived his method from the Chart. The writing of the sages is like the transforming and nurturing of the myriad things: its subtlety is boundless, yet it is also clear and easy to understand. Truly, it is so.

Divining with milfoil stalks uses changes in numbers to obtain an oracle. This involves drawing on the words of the hexagram, on the function of the hexagram, and on its structure. Though fifty is the number of the Great Expansion derived from the Yellow River Chart, it belongs to stillness within change and to structure within function, so it is set aside and not used. Forty-nine belongs to change within change and function within function, and so it is used specifically for obtaining hexagrams with milfoil stalks.

From the start, counting toward either side gives one, three, five, seven, and nine. These five numbers belong to the Heavenly numbers and symbolize the pure, unified essence of the Qian hexagram, without any admixture of Yin, the even numbers. The twenty-four at the front and the twenty-four at the back symbolize dividing the numbers into two parts; the one in the middle symbolizes “suspending one”; the four numbers three, five, seven, and nine symbolize dividing and counting; and a second set of three, five, seven, and nine symbolizes dividing and counting again. All of this follows a pattern that arises naturally; it is not something devised deliberately according to human preference. From this we can see how wondrous Fuxi’s creation of the method for forming hexagrams was, beyond ordinary understanding. The Lianshan and Guicang traditions, and the dynasties of Xia, Shang, and Zhou, all followed and used it. Even when the order of the hexagrams differed, their principles did not go beyond these rules.

In the Jin dynasty, some people explained the Zhouyi through the thought of Laozi and Zhuangzi. They said that the forty-nine milfoil stalks meant setting aside one of the fifty, unused, to symbolize the Supreme Ultimate (Taiji). The Supreme Ultimate is the pivot of Heaven and Earth’s transformations and the root from which the myriad things arise; it is also the source where things, principle, and Qi come together. By its nature, it cannot be separate from the myriad things. Yet now one stalk is taken out and placed in a box of unused things, withdrawn into stillness. Does this not imply that Heaven, Earth, and the myriad things can at times be separated from their pivot and root, and that principle and Qi can at times be divided? The operations of dividing into two, suspending one, dividing by four, and gathering the odd stalks are plainly performed with the forty-nine stalks. The one that symbolizes the Supreme Ultimate is put in a box and has no part in governing these operations. Does this interpretation not go against reason?

The stalk that is set aside and the forty-nine that are actually used are no different in length or size. Yet by casually setting one aside, people claim that it has changed from a material object into Dao, from physical form into principle, and exalt it as the Supreme Ultimate, granting it a status of incomparable dignity and mystery. Meanwhile, the forty-nine stalks in use are deprived of their pivot and root and can only busy themselves with change on the outside, unable to be compared with the stalk that was set aside. One side receives such favor while the other is treated so unjustly. This is plainly unreasonable and shows how mistaken the Jin scholars’ interpretation was. Moreover, the number derived from the Yellow River Chart is fifty-five. After the Great Expansion, five are now missing. How, then, can it still be called the “Great Expansion”?

Zhuo’s examination of the sources states: The Treatise on the Five Phases in the Book of Han records that Liu Xin believed Fuxi received the Yellow River Chart and drew the Eight Trigrams (Bagua) in accordance with it; when Yu the Great controlled the floods, he obtained the Luo Writing and formulated the Great Plan (Hongfan) in accordance with it. Shao Yong said that the circle symbolizes Heaven, and that the principles underlying the calendar’s numbers probably came from it; the square symbolizes Earth, and the methods of dividing regions into provinces and laying out fields in the well-field system probably came from it. The circle is the numbers of the Yellow River Chart, while the square is the pattern of the Luo Writing. Thus Fuxi and King Wen created the Changes (Yi) based on these, while Yu and Jizi composed the Great Plan based on them.

Master Wu said that the Yellow River Chart appeared when a dragon horse emerged from the Yellow River, its swirling hair patterns displaying ten numbers. The Luo Writing appeared when a spirit tortoise emerged from the Luo River, its shell cracks displaying nine numbers. Swirling hair resembles stars arranged in circles, so it is called a “chart”; the tortoise-shell cracks resemble strokes of writing crossing vertically and horizontally, so it is called a “writing.” The horse in the Yellow River Chart was no different from an ordinary horse, and the tortoise in the Luo Writing was no different from an ordinary tortoise. Even today, the swirls on a horse’s back still resemble stars, though they are usually not arranged as ten numbers; and the cracks on a tortoise’s back still resemble written strokes, though they are usually not arranged as nine numbers. Zheng Xuan said that the Yellow River Chart appeared from the Yellow River as a natural pattern, and the Luo Writing appeared from the Luo River as natural writing.

Zhuo says: Fuxi, the legendary ruler of high antiquity, devised the method of divination with yarrow stalks on the basis of the Yellow River Diagram, a propitious pattern said to have appeared in the Yellow River. He also devised tortoise-shell divination on the basis of the Luo River Writing, a propitious pattern said to have appeared in the Luo River. The principle embodied in the Yellow River Diagram is the Great Expansion, the rule for calculating the yarrow stalks in divination from the Changes. The diagram is now placed on the left. The principle embodied in the Luo River Writing is still unclear. Later, in the time of Yu the Great, a divine writing also appeared in the Luo River, and Yu used it to establish the Nine Great Categories of the Great Plan, the nine fundamental principles for governing the realm. In the time of King Cheng of Zhou, Chen Bao displayed the Yellow River Diagram at Shu Xu. Confucius also said that the Yellow River no longer produced the Diagram, and mentioned it alongside the phoenix, indicating that both were auspicious signs of the age of sagely rulers. This account has a long history.

The numbers of Heaven are one, three, five, seven, and nine. Each of these five numbers combines with another and corresponds to it; their total is twenty-five.

□ The “five positions” are the five places occupied by the numbers of Heaven. They combine with one another, each has its corresponding number, and through calculation their sum becomes twenty-five.

The numbers of Earth are two, four, six, eight, and ten. Each of these five numbers combines with another and corresponds to it; their total is thirty.

□ The “five positions” are the five places occupied by the numbers of Earth. They combine with one another, each has its corresponding number, and through calculation their sum becomes thirty.

The numbers of Heaven and Earth together total fifty-five.

□ Heaven has only five numbers. Through calculation and combination they become twenty-five, yet they never exceed the bounds of those five numbers. Earth likewise has only five numbers. Through calculation and combination they become thirty, and they too never exceed the bounds of those five numbers.

The celestial numbers originally consist of five numbers; through derivation they become twenty-five, for a total of twenty-five. Yet their root does not go beyond the number five. The terrestrial numbers also originally consist of five numbers; through derivation they become thirty. They too do not go beyond the number five. The celestial and terrestrial numbers together make fifty-five, still within the scope of the numbers of Heaven and Earth. In the Yellow River Chart, the numbers from the celestial one to the terrestrial ten belong to five positions and total ten numbers. Beyond these, fifty-five more are derived, as though interpolated text had been added to the original writing. I therefore call these numbers “the derived numbers of the Yellow River Chart.”

Zhuo says: Han dynasty Confucian scholars explained “the five positions correspond to one another, each having its counterpart” to mean that one and six, two and seven, three and eight, four and nine, and five and ten pair off. If that were really the meaning, the text should say “ten positions,” not “five positions.” It should also go on to state the total of fifty-five celestial and terrestrial numbers, rather than discussing the celestial total of twenty-five and the terrestrial total of thirty separately. Since the text presents them separately, it is clear that “the five celestial positions” continues the preceding passage on the five celestial numbers, and “the five terrestrial positions” continues the passage on the five terrestrial numbers. So this cannot mean that ten numerical positions pair off with one another. These are errors made by Han dynasty Confucian interpreters of the classics, and they must be examined.

Subtract ten from each of eleven, thirteen, fifteen, seventeen, and nineteen, and the results are the five odd numbers one, three, five, seven, and nine. Together, these five numbers form the substance—the root numbers—of the “Great Expansion.” There are twenty-four on either side of them, making forty-eight; add the single number at the center, and the total is forty-nine. This is the function—the numbers put into use—of the “Great Expansion.” The substance is set aside, and only the function is used, because the divination method employs such steps as “suspending one, dividing in two, counting by fours, and gathering the remainder again”: first one yarrow stalk is set aside; the remaining stalks are divided into two piles, counted in groups of four, and finally the remainders are gathered together. The images drawn from this process express the principle that the celestial numbers are purely one and the Yang numbers are odd, while the Yin numbers are interspersed with even numbers. Fuxi adopted this method to teach the people how to practice divination.

Zhuo says: Confucius praised the subtle workings of the Yellow River Chart’s number system, saying that it could bring about change and set the spirits in motion. The celestial numbers are purely one, and the primordial Qi belongs to Yang; the Yin numbers, by contrast, appear mixed and irregular because they are interspersed with even numbers. Fuxi therefore drew on this system of numbers to teach the people.

Zhuo said: Confucius praised the subtle mathematics of the River Chart, saying that it could bring about transformations and set the spirits in motion. He also said that those who understand the way of change can perhaps know how the divine powers act. Confucius further said that the mysterious has no fixed form, and that the transformations of Yin and Yang are impossible to fathom; this is called “the spirit.” The sage subtly assists the way of the divine powers, giving rise to divination with yarrow stalks. The numbers of the hexagrams are established according to the principle of three for Heaven and two for Earth, enabling one to comprehend the Virtue of the divine powers.

None of these statements mentions arranging the numbers of the River Chart into a diagram to depict the Eight Trigrams. The claim that links the two was Liu Xin’s fabrication, which later Confucian scholars mistakenly accepted and passed down. I have therefore drawn this diagram to clarify Confucius’s original intent. Readers should consider it carefully.

Third: Establishing Hexagrams and Producing Lines with Yarrow Stalks

The Virtue of the yarrow stalks used for divination is rounded and mysterious, because seven multiplied by seven gives forty-nine, symbolizing the number of roundness. The Virtue of the hexagrams is square and lucid, because eight multiplied by eight gives sixty-four, symbolizing the number of squareness. The meaning of the six lines—the six lines arranged from bottom to top in a hexagram—emerges through change. The two line numbers, nine and six, represent the Yang line and the Yin line; they transform into one another to disclose good and ill fortune in human affairs. The sage uses them to cleanse the mind, allowing the spirit to withdraw and rest in a quiet, secluded depth, and then to work with the yarrow stalks and hexagram lines…

The virtue of yarrow, used for divination, is complete and wondrous. Its numbers are grouped in sevens, and seven multiplied by seven symbolizes completeness. The virtue of the hexagrams is upright and discerning. Their numbers are grouped in eights, and eight multiplied by eight symbolizes uprightness. The function of the six lines is to reveal the principles of things through change. Nine and six represent yang and yin lines; the firm and the yielding transform one another, thereby conveying information to people.

The sages used the yarrow and the hexagram lines to cleanse their minds, withdrawing to a secluded and quiet place. They used the hexagrams and six lines to wash away their concern for worldly affairs, gathering their minds in a still and deep realm, yet they continued to share the people’s hardships. Through their wondrous power, the sages foresaw the future; through their discerning wisdom, they understood the past. Since the sages did not forget the people’s hardships, how could they withdraw to a secluded place? It was because the yarrow’s wondrous power could foretell good and ill fortune, while the hexagrams’ wisdom could reveal the definite principles behind them. The text does not separately explain how the lines display change because their function is already included in the wisdom of the hexagrams. People could obtain hexagram images through divination, move toward good fortune, and avoid danger. The sages could then cease to bear the people’s concerns alone and withdraw to a quiet place. Who could accomplish this? It was Fuxi, the ancient sage of penetrating insight and exceptional wisdom, who possessed wondrous power yet did not rely on killing or warfare.

Fuxi understood the Way of Heaven and the practical needs of the people, so he created a wondrous instrument for divination for them to use. The “spiritual object” here refers to yarrow. Through it, the sages purified themselves so that their virtue could reach the spiritual realm. Purification means focusing and gathering the spirit; abstention means carefully observing the prohibitions during the period of dispersed purification. The sages entrusted the wondrous power to the virtue of the yarrow and discernment to the virtue of the hexagrams. Without purification and abstention, they could not make their own spirit clear, nor could they bring forth the virtues of the yarrow and the hexagrams.

Closing the gates is called Kun; the yarrow is held in the hand. Opening the gates is called Qian; the yarrow is separated and counted in groups. One closing and one opening are called change; each counting operation with the yarrow embodies this change. The yarrow’s changes come and go without end; this is called continuity. The number obtained each time may be greater or smaller and cannot be fixed in advance; what becomes manifest is called an image. After three changes, the yarrow reveals a number: an odd remainder represents young yang, seven; an even remainder represents young yin, eight; old yang is nine, and old yin is six. The unending coming and going of change is continuity.

Once the Four Images have taken shape, they become concrete implements. By drawing on hexagram images to infer the forms of things, one can make various implements. Establishing methods and putting them to use is called a method; when implements make life easier for people and everyone can use them, this is called the wondrous. The opening and closing of the gates, change, and continuity are the principles, images, implements, and methods presented by the yarrow. The fact that everyone can use them expresses the yarrow’s wondrous power.

Thus the Changes has the Taiji, the Supreme Ultimate. Here, “Changes” refers to the process of counting the yarrow and deriving hexagram images. The separating and joining of the yarrow already symbolizes the opening and closing of the gates. When the yarrow is still in its tube and has not yet been taken out, are the Four Images already present? This can be compared to the main beam of a roof: the timbers of the four sides of the roof frame converge upon it, and for this reason the beam is called the “ultimate.” When the forty-nine stalks of yarrow are mixed together in the tube, all the possible processes are already contained within them: the first change, the third change, the ninth change, and all the way through the eighteenth. Like the high roof beam, this is called the Great Ultimate.

The Great Ultimate gives rise to the Two Modes. “Gives rise” means taking the yarrow out of its tube and beginning the divination. The gates closed are Kun; the gates opened are Qian. These two together are why it is said that the Great Ultimate gives rise to the Two Modes. In some places today, the two leaves of a gate are called an “Yi Gate,” a name that also draws on the meaning of the Two Modes. The Two Modes give rise to the Four Images, and the Four Images give rise to the Eight Trigrams: all are results produced by counting the yarrow. The Four Images are seven, eight, nine, and six, representing young yang, young yin, old yang, and old yin. Distinguishing the old from the young, and the firm from the yielding, makes the hexagram images visible to people. Once each of the Four Images has taken shape, the Eight Trigrams are arranged. Mentioning only the eight trigrams of the inner trigram makes those of the outer trigram understood as well, so they are left unstated.

The Eight Trigrams determine good and ill fortune. After eighteen changes, both the inner and outer trigrams have taken shape. The diviner presents the hexagram image and can then observe it and examine the oracle text to judge good and ill fortune. Once these are determined, people can move toward good fortune and avoid ill fortune without doubt, thereby accomplishing great undertakings.

Accordingly, nothing surpasses Heaven and Earth as models for taking forms and depicting things; nothing surpasses the four seasons in making change and circulation apparent. The first statement follows from the account of the Two Modes giving rise to hexagram images: Qian takes Heaven as its model, and Kun takes Earth as its model. The second follows from the account of the gates opening and closing and change continuing without end: it refers to counting the yarrow, with the Four Images representing the four seasons. Among the heavenly images that hang above and appear clearly, nothing surpasses the sun and moon. This follows from the statement that what becomes manifest is called an image: old yang represents the sun, and old yin represents the moon. Among the things that confer high standing and abundant wealth, nothing surpasses honor and riches. This follows from the account of good and ill fortune and great undertakings. Having the resources to accomplish things, together with the status and ability to do so, and then pacifying the people, punishing tyrants, bringing stability to Heaven and Earth, and nurturing the myriad beings—all these belong to great undertakings.

No one can match the sages in preparing all that divination requires for people’s use, making it into implements, and benefiting all under Heaven. The sages prepared yarrow for the people, established hexagram images and made implements, enabling everyone under Heaven to divine, observe the principles embodied in the images, and accomplish great undertakings. Only sages of exceptional intelligence and wondrous power, who do not misuse force, could do this.

To investigate the hidden depths of things, seek subtle principles, reach into the obscure, and infer distant changes, so as to judge good and ill fortune under Heaven and accomplish its undertakings—nothing is more important than yarrow and tortoiseshell. This emphatic praise of the wondrous power of yarrow and tortoiseshell explains how the sages used them to benefit all under Heaven, and how great their significance was. The passage that follows then brings the discussion to a further conclusion.

Heaven gives birth to spiritual objects, and the sages take them as their models. The spiritual objects include the yarrow and tortoiseshell mentioned earlier: yarrow is used to derive hexagram images, and tortoiseshell for divination. When Heaven and Earth change, the sages take their changes as models; when Heaven displays signs and reveals good and ill fortune, the sages imitate those signs. “Displaying signs” means hanging forth the images of Heaven; “revealing good and ill fortune” means making hexagram images visible so that people can use them to divine good and ill fortune. When the Yellow River produced the River Chart and the Luo River produced the Luo Writing, the sages took them as models: they drew on the River Chart to use yarrow in divination, and on the Luo Writing to make tortoiseshell implements for divination. This sums up the two statements, “Heaven gives birth to spiritual objects, and the sages take them as their models.”

Zhuo says: This chapter is devoted to the wondrous power of yarrow. Yarrow is wondrous because it can draw forth the upright and discerning principles contained in the hexagram images and display them through the changes of the six lines. People can use this to judge good and ill fortune and accomplish great undertakings. That is where its wondrous power lies. Earlier Confucian scholars explained the Great Ultimate as the Dao, the Two Modes as the first two lines, and the Four Images as the next four lines. The errors in these explanations all stem from Shaozi. The relevant diagrams and explanations are appended below.

Zhuo says: Confucius said that the Changes arose from the Supreme Ultimate (Taiji): the Supreme Ultimate gave rise to the Two Modes, the Two Modes to the Four Images, and the Four Images to the Eight Trigrams. But he did not say that the Eight Trigrams then gave rise to sixteen, sixteen to thirty-two, and thirty-two to sixty-four. Shaozi (Shao Yong, a Northern Song scholar of the Changes) said that once the Supreme Ultimate differentiated, the Two Modes were established. The Yang line joined with the Yin line above it, and the Yin line joined with the Yang line below it, producing the Four Images. Yang joined with Yin, and Yin with Yang, forming the Four Images of Heaven; firmness joined with yielding, and yielding with firmness, forming the Four Images of Earth. In this way the Eight Trigrams came into being. The Eight Trigrams crossed and combined with one another, and from them all things arose.

Shaozi’s account is therefore: one divides into two, two into four, four into eight, eight into sixteen, sixteen into thirty-two, and thirty-two into sixty-four. This is like a tree: roots grow into a trunk, the trunk into branches, and the branches into leaves. The larger the whole, the fewer its branches; the finer the divisions, the greater their number. Gathered together, they are one; unfolded, they are the myriad things.

Master Zhu (Zhu Xi, a Southern Song Neo-Confucian scholar) said: the changes between odd and even Yin and Yang during the day, and the fact that a trigram consists of three lines, arise naturally; they are not arranged by human hands. This is the guiding principle of the study of the Changes, and the first thing one must understand when reading the Changes. Yet throughout history, it seems no one truly understood it. Only when Master Kangjie (Shao Yong’s style name) transmitted the learning of the Earlier Heaven did this account become clear; he held that it was the Changes of Fuxi.

Yet when I read these words as a child, I could not help feeling doubts. By the time I reached adulthood, my doubts had only deepened, so I have carefully set them down below.

The Yi means “change.” Earlier Confucian scholars believed that between Heaven and Earth there are only the two Qi of Yin and Yang. Fuxi drew a solid Yang line to represent Yang and a broken Yin line to represent Yin. The Yin and Yang lines combine to form the Four Images and the Eight Trigrams, which develop in turn into the sixty-four hexagrams. These are all changes in the diagrams. Later, divination also came to rely on changes in the number of yarrow stalks, and for this reason the text was called the Yi.

Zhuo (the author’s self-designation) considers this explanation imprecise. Confucius says earlier that “when the four operations are completed, the Yi takes form.” Here, “Yi” refers back to the method of divination with yarrow stalks. The following passage goes on to discuss “extending the process to produce the Four Images and Eight Trigrams, determining good and ill fortune, and accomplishing great undertakings”; this too is specifically about the changes involved in yarrow-stalk divination. If “Yi” here is also taken to mean changes in the hexagram diagrams, that would conflict with the account of Fuxi creating the forms of the Eight Trigrams. For a detailed explanation, see the discussion of the Two Modes and the Four Images below.

The same applies elsewhere. In the “Appended Statements, Part Two,” the passages “Qian and Kun are the gateways of the Yi” and “Once Qian and Kun are arranged, the Yi is established within them” use “Yi” in the same sense as it has here.

Some say that the name “Yi” did not yet exist in Fuxi’s time. This is incorrect. The Rites of Zhou records that the Grand Diviner was responsible for three methods of divination using the Yi: the first was Lianshan, the Yi of the Xia dynasty; the second was Guicang, the Yi of the Shang dynasty; and the third was the Zhou Yi. The Xia, Shang, and Zhou dynasties all called these divination texts “Yi,” a name inherited from Fuxi. Although the Xia and Shang texts each had their own specific titles, the name “Yi” did not first appear in the Zhou dynasty. The Rites of Zhou also records that the Diviner used the Eight Trigrams to divine and judge good and ill fortune, while the Yarrow Diviner was responsible for the three Yi texts and used them to distinguish nine methods of divination. These records all show that the name “Yi” was not established only in the Zhou dynasty.

If one maintains that writing and the name “Yi” did not exist in Fuxi’s time, then the Two Modes; the Four Images; Qian, Kun, Gen, Xun, Zhen, Li, Kan, and Dui; the numbers seven, eight, nine, and six; the division and grouping of yarrow stalks; and divination procedures such as “suspending two and adding one” must all have been additions by later generations. In that case, Fuxi—also honored by the title Taihao—would be left with nothing but names bestowed retrospectively, without any concrete historical trace. Even if he created a sacred and wondrous book of hexagrams, its name “Yi” would still have to be granted by later generations. This is surely to show too little regard for Fuxi.

This claim arises because, when Confucius speaks of “making the Yi,” people take “making” to mean creating the entire Yi. In fact, Confucius’s phrase “making the Yi” refers to composing the Zhou Yi. It does not mean creating the three Yi texts, nor does it mean that he created the whole body of Yi learning from Fuxi onward. The following phrase, “perhaps he had worries,” clearly refers to the circumstances between King Wen and King Zhou. A detailed explanation has already been given in the preface.

In “Taiji,” “ji” originally means the main ridge beam of a house, while “tai” means greatest or utmost.

Han Kangbo’s commentary explains that all things arise from the primal beginning, and thus Taiji gives rise to the Two Forms. Taiji is the name for the state of primordial beginning. Since it is inherently difficult to name, “Taiji” can only describe the ultimate foundation reached by all things.

Kong Yingda’s subcommentary explains that Taiji refers to the state before Heaven and Earth separated, when primordial Qi was blended into one. This is also called “Great Beginning” or “Great Unity.” Laozi says, “The Dao gives birth to One”; Taiji here is that “One.” Once the blended Qi divided, Heaven and Earth took shape. Hence the saying, “Taiji gives birth to the Two Forms,” corresponding to Laozi’s statement, “One gives birth to Two.” The classic says “Two Forms” rather than “Heaven and Earth” because it focuses on their respective shapes and appearances; the “Two Forms” are two kinds of form.

In his Original Meaning, Zhu Xi says that the One dividing into Two is a natural principle. The Changes discusses the transformations of Yin and Yang, and Taiji is the principle that underlies those transformations.

Zhuo believes that Han Kangbo and Kong Yingda interpret the Changes through the thought of Laozi and Zhuangzi, and their arguments need no extensive refutation on their own terms. But if their claims are followed through, the result would be that the Dao gives birth to Heaven and Earth; Heaven and Earth then give birth to Metal, Wood, Water, and Fire; and these in turn give birth to the Eight Trigrams drawn on bamboo slips. Would that not be strange?

If we follow Zhu Xi’s account, the transformations of Yin and Yang and their underlying principle would at the outset give rise to the first and second lines drawn on bamboo slips. These two lines would then give rise to four lines, and the four lines to the Eight Trigrams. In that case, Yin and Yang would initially have no distinction of size, and only later would their differences emerge. Then three lines would form the symbols of the “Three Powers”: Heaven, Earth, and Humanity. Does this mean that the Yin or Yang of the first line was not yet clear, while the top line of the Eight Trigrams could already embody the symbols of the Way of Heaven, the Way of Earth, and the Way of Humanity? It is indeed difficult not to find this puzzling.

Some earlier Confucian scholars say that when Fuxi, the legendary creator of the Eight Trigrams, drew the trigrams, he first drew a solid line to symbolize Yang, then a broken line to symbolize Yin. Later generations called these two lines the Two Modes. Zhuo says, “I have read the Ten Wings, the ten commentaries on the text of the Zhouyi, over and over. Confucius’s words say only that Fuxi began creating the Eight Trigrams; they do not say that Fuxi first created the Two Modes. Which scripture, or which of the Wings, says that Fuxi first drew a solid line to symbolize Yang and then a broken line to symbolize Yin?”

The horizontal chart is formed by arranging the Eight Trigrams and can be distinguished into the sixty-four hexagrams; the circular and square charts work the same way. The chart merely labels, beneath each hexagram, which trigram is above and which is below. It does not say that Yang and Yin lines are each first divided into two kinds, then successively into four, eight, sixteen, thirty-two, and finally sixty-four hexagrams.

The six lines of the sixty-four hexagrams are equal in length, width, and status. If the original single Yang line or single Yin line is taken as the source from which everything is derived in successive stages, then when examining the Four Images, the sixty-four hexagrams would have to be cut into two groups; when examining the Eight Trigrams, into four groups; when examining the sixteen hexagrams, into eight groups; and when examining the thirty-two hexagrams, into sixteen groups. If they are not divided this way, one Yang line would have to support the thirty-two lines above it, and one Yin line likewise the thirty-two lines above it. Such an arrangement plainly makes no sense.

If the Two Modes are said to possess wondrous transformative power, with a single line giving rise to all things and corresponding to the number thirty-two above, there should be clear evidence of this in the writings of the sages. If this diagram is held to be correct, then the first line of each of the sixty-four hexagrams in the horizontal, square, and circular charts transmitted by the sages should be cut apart. If instead we follow the original charts of the sixty-four hexagrams passed down by the sages, then this diagram is not the method of drawing hexagrams that the sages used.

Earlier Confucian scholars held that adding one yin line and one yang line to the yin-yang symbol of a single line produced four combinations. These “Four Symbols” are what we call old yin, old yang, young yin, and young yang. Zhuo argues that it is mistaken to say the Four Symbols lie between the first and third lines of the Eight Trigrams.

The word “symbol” in “Two Modes” follows from the word “door” in the preceding phrase “closing the door and opening the door,” and refers to two corresponding kinds of door. The “symbols” in “Four Symbols,” by contrast, follows from the word “symbol” in the preceding phrase “what appears is called a symbol.” It means that only at this stage do the images of the trigrams begin to appear in the drawn lines: seven represents young yang, eight young yin, nine old yang, and six old yin. Hence the term “Four Symbols.”

Confucius said, “The Changes has four symbols, which serve to show.” This means that the Changes has four symbols for displaying the state of things. Only then do the drawn hexagrams appear, indicating gain and loss, movement and stillness, and providing a basis for divining good fortune, misfortune, regret, and anxiety. If this were not so, why say that what appears is called a symbol? And why say that the Four Symbols serve to show the principles of things?

If we insist on assigning them positions in the sequence of the six lines, then Qian and Dui correspond exactly to old yang, while Zhen and Li correspond to young yin; Kun and Gen correspond exactly to old yin, while Xun and Kan correspond to young yang. In Fuxi’s system of the Changes, old lines change and young lines do not. So consider the examples of hexagrams used in divination during the Three Dynasties, as recorded in the Zuo Tradition: Qian changes into the resulting hexagram Li, and Dui changes into Zhen. Xun and Li appear only as the original hexagrams, since young yin does not change. In other words, Qian and Dui transform because their yin lines change; Zhen and Li appear as both original and resulting hexagrams, but in effect they are simply Zhen and Li doubled, with no Qian or Dui.

Likewise, Kun changes into the resulting hexagram Kan, and Gen changes into Xun. Xun and Kan appear only as the original hexagrams, since young yang does not change. Kun and Gen transform because their yang lines change; Xun and Kan appear as both original and resulting hexagrams, but in effect they are simply Xun and Kan doubled, with no Kun or Gen. Thus Qian, Dui, Kun, and Gen disappear, while Zhen, Li, Xun, and Kan appear twice. This shows that the Four Symbols generate four trigrams. How, then, can one claim that they generate the Eight Trigrams?

Earlier Confucian scholars held that when a yang line is placed above a yang line, the yang Qi is pure and unified, so this represents old yang; when a yang line is placed above a yin line, yang is mixed within yin, so this represents young yang; when a yin line is placed above a yang line, yin is mixed within yang, so this represents young yin; and when a yin line is placed above a yin line, the yin Qi is pure and unified, so this represents old yin. Zhuo argues that this account was devised to avoid the difficulty posed by the principle that old lines change and young lines do not, but it was not thought through. If placing yang above yang and yin above yin makes them “old” because yin and yang are pure and unified, what should we call a hexagram whose six lines are all pure? Should it be called “Supreme Elder Old Yin” or “Supreme Elder Old Yang”? This argument does not examine the underlying principles carefully; it merely seeks a satisfying explanation in the moment. Zhuo does not accept it.

Confucius said that Fuxi began creating the Eight Trigrams. The Trigrams of Fuxi also provides separate explanations beneath each trigram, yet nowhere does it say that the first line of Qian was a shared yang line (an odd line), the same as those of Dui, Li, and Zhen. Nor does it say that Qian’s second line was a shared yang line, the same as Dui’s alone.

Likewise, the text nowhere says that the first line of Kun was a shared yin line (an even line), the same as those of Gen, Kan, and Xun, or that Kun’s second line was a shared yin line, the same as Gen’s alone. Nor does it say that Qian became a complete yang line only at the third line, making it different from the first two; or that Kun became a complete yin line only at the third line, making it different from the first two. The same applies to all six trigrams following Dui.

It follows that the first, second, and third lines of the Eight Trigrams should all be consistent in length and width. Only then can they be called the Eight Trigrams. If the lines differ among groups of four or two trigrams, and their lengths and widths are inconsistent, they cannot be called the Eight Trigrams. This plainly was not how the sages drew the trigrams.

Sixteen lines.

Early Confucian scholars held that each of the Yin and Yang lines gives rise to one Yin line and one Yang line, as a natural principle. Thus, adding one Yin line and one Yang line to each hexagram produces sixteen lines. But Confucius did not say this at the outset. After discussing the Eight Trigrams, he went straight on to explain how they are used to determine good and ill fortune.

Reasoning backward from the phrase “the Eight Trigrams determine good and ill fortune,” we can see that when the Four Images (Young Yang, Old Yang, Young Yin, and Old Yin) give rise to the Eight Trigrams, they generate both the inner and the outer trigrams. Only after both inner and outer trigrams have formed can a hexagram be said to have been produced through “eighteen changes.” This differs from the incomplete process in which only the inner trigram has formed. It is only at this stage that good and ill fortune can be determined.

It follows that the upper three lines of a doubled hexagram—the fourth, fifth, and sixth lines—are already included in the process described by the phrase “the Four Images give rise to the Eight Trigrams.” Confucius therefore did not originally say that doubling the Eight Trigrams produces sixteen lines. To claim that Shao Yong’s statement, “the Eight divide into sixteen,” expressed Confucius’s original meaning is to add words that Confucius never spoke, and lacks a sound basis.

Thirty-Two Lines

The fourth, fifth, and sixth lines of a doubled hexagram are already included in the process by which “the Four Images give rise to the Eight Trigrams.” Confucius therefore did not originally speak of thirty-two lines either. Is it not superfluous to insist that words Confucius never spoke were what he meant? Shao Yong’s statement that “the sixteen divide into thirty-two” is likewise without a sound basis.

Thirty-Two Lines

The fourth, fifth, and sixth lines in a doubled hexagram—a six-line figure formed by stacking two three-line trigrams—are already included in the process by which the Four Images generate the Eight Trigrams. Thus, when Confucius says in the Xici that “the three powers are each doubled, hence there are six,” he is not proposing a separate sequence of “initial and primary thirty-two lines.” To put words into Confucius’s mouth that he never said—is that not needless argument? It follows that Shao Yong’s claim that “sixteen divide into thirty-two” is clearly not credible.

Alas, if this claim merely ran counter to Fuxi’s method of drawing the trigrams, or contradicted Confucius’s original intent, it might still be open to discussion. But consider it by its own account: the number of the fourth line in the outer trigram is four times that of the third line in the inner trigram; the number of the fifth line in the outer trigram is twenty-four greater than that of the third line in the inner trigram. The increases and decreases between the inner trigram’s third line and the outer trigram’s fourth and fifth lines are all calculated in the same way. Yet in the six-line figures represented by Fuxi’s horizontal, square, and circular diagrams, the lines do not differ in length or width. When, then, are they supposedly doubled? When are they reduced? And how are lines added to make up the three so-called circular diagrams? Does this account not depart from Fuxi’s method of drawing the trigrams?

Confucius’s original intent was that the Eight Trigrams in both the inner and outer trigrams are generated by the Four Images; hence he says, “The Eight Trigrams determine good and ill fortune.” But this account forces the generation of sixteen and thirty-two hexagrams between “the Eight Trigrams” and “determine good and ill fortune.” This is neither stated explicitly by Confucius nor anything more than elaborate speculation without a basis. Does it not contradict Confucius’s original intent? Since it is neither Fuxi’s method of drawing the trigrams nor Confucius’s original intent, it is certainly not worth following.

Sixty-four Lines

What is being discussed here is the topmost line of the six-line hexagram, which Song dynasty Confucian scholars called the “diagram of hexagram generation.” Every one of the sixty-four hexagrams has this line. It is no more excessive to place it here than it would be deficient to place it elsewhere. To regard the sixty-four hexagrams as the outcome of thirty-two hexagrams dividing into further forms is not Fuxi’s method of drawing the hexagrams, and it also runs counter to Confucius’s original intent.

In the sixty-four hexagrams drawn by Fuxi, all six lines—from the first line to the top line—are equally important. It is correct to say that adding either a yang line or a yin line above each five-line hexagram produces the six-line hexagrams, yielding sixty-four in all. But if one works backward from six lines, one would then say there are thirty-two five-line hexagrams, forty-eight four-line hexagrams, fifty-six three-line hexagrams, sixty two-line hexagrams, and sixty-two one-line hexagrams. Once earlier Confucian scholars proposed the theory of “hexagram generation,” the lines below the six-line level were all deprived of their proper place and inevitably broken apart into fragments. How could such an account be considered the sages’ model or the central, balanced teaching of the Yi?

Now the ancient method has been restored, and interpretations that differ from those of earlier Confucian scholars have been set right, in the hope that the sages’ method will no longer be implicated. The hexagram diagram and its explanation are therefore recorded below, to clarify Fuxi’s original method of drawing the hexagrams and Confucius’s original intent.

Fuxi’s Die Cao Diagram of Hexagram Generation

End of Volume Two of Investigations into the Origins of the Ancient Yi

The Yi is a book handed down by six sages. Its source lies with Fuxi: Fuxi first drew the Eight Trigrams, then added the Eight Trigrams to each of them…

The Changes is a book handed down by six sages. It began with the Eight Trigrams, first drawn by Fuxi. Later, another trigram was placed over each one, producing the sixty-four hexagrams.

Three lines make up a trigram. Fuxi drew the Qian trigram. When three more lines are added above it, the result is labeled “Qian below, Qian above” and is still called “Qian.” The other seven trigrams are formed in the same way. These are called the foundational trigrams, the basic figures from which the sixty-four hexagrams are made. When the Dui trigram is placed above Qian, the resulting figure can no longer be called Qian or Dui, so it is named “Guai.” This is the first hexagram formed by changing Qian. Qian can also change into eight other hexagrams, and each of the other seven foundational trigrams can do the same, giving sixty-four hexagrams in all.

The names of the sixty-four hexagrams are characters first devised by Fuxi; their names in speech are pronunciations first established by him. Across generations and through the work of many sages, no one dared alter the shapes of the hexagram figures or the pronunciations assigned to them in Fuxi’s time. The characters Fuxi devised are like the founding ancestor of a family: from them, later generations multiplied and the lineage continued without end.

The sages of the Xia, Shang, and Zhou dynasties—such as Yu, Tang, King Wen, the Duke of Zhou, and Confucius—each expounded the principles of the Changes, helping Fuxi’s Changes endure through the ages. Their contribution was great. Yet each wrote according to the direction of his own understanding, so some works begin with Gen, others with Kun, and still others with Qian. The Duke of Zhou and Confucius, by contrast, took the Zhou Changes as their sole foundation and further expounded its meaning and principles.

Fuxi’s Changes uses spare, plain language, yet its meaning is subtle and inexhaustible, encompassing the writings of the Xia, Shang, and Zhou dynasties. The classics of those three dynasties are vast and profound, with inexhaustible meaning, and in turn they illuminate the principles of Fuxi’s Changes. Fuxi’s Changes is like the primordial Qi of Great Harmony, circulating through the four seasons; the classics of the three dynasties are like spring, summer, autumn, and winter, each presiding over its own season.

Confucius said that in ancient times there was the Lianshan clan, and that the Xia dynasty’s Book of Changes later took the name Lianshan, presumably carrying on the clan’s Book of Changes. Ancient commentators explained “Lianshan” as referring to clouds rising among mountains and stretching on without end. I find this explanation unsound: the original text contains no word for “clouds,” so how can “stretching without end” refer to clouds? The Commentary on the Image for the Gen hexagram says “mountains joined together.” Does the Gen hexagram really place a mountain alongside clouds?

Gen symbolizes a mountain; this image has existed since the time of Fuxi. The Xia dynasty’s Book of Changes began with the Gen hexagram, so two Gen trigrams were stacked, one above the other, and the result was still called “Gen.” Hence the name “Lianshan”: there is one mountain within the hexagram and another outside it, the two mountains joined together. To add the idea of clouds rising would lead away from the original meaning. The “mountains joined together” in the Commentary on the Image means essentially the same thing as “Lianshan.”

Today, what can be established about the Xia dynasty’s Book of Changes is limited to its name, Lianshan, the related records, and the fact that it began with the Gen hexagram. The order of its sixty-four hexagrams can no longer be determined.

Zhuo says: The Book of Changes speaks of probing the subtle and seeking out the hidden, delving deeply and tracing what lies far off, in order to determine the good and ill fortune of all under Heaven and bring their affairs to completion. Nothing is more important than this.

Zhuo explains: “When the Classic of Changes speaks of probing subtle and hidden mysteries and pursuing profound principles in order to determine good and ill fortune throughout the world and accomplish its affairs, nothing is more important than turtle divination. The text then concludes with the words, ‘The Yellow River brought forth the Diagram, the Luo River brought forth the Writing, and the sages modeled themselves on them.’ This shows that Fuxi, the legendary founder of the Changes tradition, modeled stalk divination on the Yellow River Diagram and devised turtle divination on the Luo River Writing.

“By the time Yu was controlling the floods, the Luo River had again brought forth a Writing. On its basis, Yu established the Nine Categories, the nine principles for governing the world. He applied the seven methods Fuxi had established by modeling himself on the Yellow River Diagram to stalk divination under ‘Examining Doubts’ in the Nine Categories. He applied the seven methods Fuxi had devised by modeling himself on the Luo River Writing to turtle divination under ‘Examining Doubts.’

“The court appointed diviners to perform divination and judge among signs such as rain, clear skies, and obscurity, then make a choice accordingly. It also appointed stalk diviners to conduct the primary and secondary judgments. To prevent errors that might arise if one person presided over both turtle and stalk divination, and to allow their judgments to be checked and corrected, the number of diviners was increased so they could review one another’s results. Thus, three officials were assigned to turtle divination and three to stalk divination. Each person judged according to one method: if all the results were auspicious or all were inauspicious, they acted accordingly; if two judged the result auspicious and one inauspicious, they treated it as auspicious; if one judged it auspicious and two inauspicious, they treated it as inauspicious. That is why the majority opinion should be followed when making a divinatory judgment.

“The Zuo Tradition (referred to here as the Inner Tradition) records: ‘The primary hexagram is Wind; the changed hexagram is Mountain,’ and neither is auspicious. Here, the inner trigram is called ‘primary’ (zhen), and the outer trigram ‘secondary’ (hui). In statements such as ‘the primary hexagram is Difficulty at the Beginning, and the secondary hexagram is Joy,’ however, the original hexagram is called ‘primary,’ and the transformed hexagram ‘secondary.’ The Classic of Changes uses the terms in the same way in phrases such as ‘favorable to constancy,’ ‘unfavorable to constancy,’ ‘may be held to constancy,’ and ‘constancy in illness,’ as well as ‘regret disappears.’ In broad terms, these methods were transmitted from Fuxi and gradually expanded and developed through the Xia, Shang, and Zhou dynasties.

“The Changes of the Shang.”

Kong says: In ancient times there was a clan called the Guicang. The Book of Changes of the Shang dynasty was called the Guicang, and it probably adopted the Changes of the Guicang clan. “Guicang,” or “Returning to the Hidden,” means that all things return to their root and return to their nature, all being contained within the earth. Kun represents the earth, and “Returning to the Hidden” embodies the Way of the earth. That is why this book begins with the Kun hexagram. The “Discussion of the Trigrams” says, “Kun stores things within it”; this is what it means.

Today, all that can be known about the Shang dynasty’s Changes is its name, the existence of the book, and the fact that it began with the Kun hexagram. The sequence of its sixty-four hexagrams can no longer be established. In the Book of Rites, in the chapter “The Conveyance of Rites,” Confucius tells Ziyou the names of hexagrams including Kun and Qian. From this, one might infer that Kun came before Qian. King Wen of Zhou considered it inappropriate for Kun to precede Qian, and therefore placed Qian first and Kun second. The sequence of the remaining hexagrams may also be inferred to some extent. Still, even if only the order of Qian and Kun was switched, while the pairings among the other hexagrams remained unchanged, the Shang Changes may have had the same hexagram pairs as the Zhou Changes, though their precise order and spacing may not have been identical. This cannot be determined with certainty.

Several statements in the Zhou Changes refer to people and events from the Shang dynasty. The six in the fifth place of the Tai hexagram says, “The Emperor Yi gives his younger sister in marriage; this brings blessing and supreme good fortune.” The six in the fifth place of the Mingyi hexagram mentions that Jizi suffered in the calamity of Mingyi and says that upholding what is right brings benefit. The six in the fifth place of the Guimei hexagram also mentions Emperor Yi giving his younger sister in marriage, and describes a difference between the ruler’s sleeve and that of the woman accompanying the bride. The nine in the third place of the Gen and Jiji hexagrams mentions Gaozong’s campaign against the Guifang, which ended in victory after three years. The nine in the fourth place of the Weiji hexagram likewise speaks of a campaign against the Guifang, followed three years later by a reward from a great state. Earlier Confucian scholars believed that people of the time had received these statements through divination and later cited them when discussing the events in question.

I have examined the records in the Rites of Zhou. The Grand Diviner was in charge of three methods of turtle divination, called jade patterns, tile patterns, and plain patterns. Each type of divination crack had a prescribed form. Altogether there were 420 forms of cracks and 1,200 written interpretations. The Grand Diviner was also in charge of three methods of the Changes: Lianshan, Guicang, and Zhouyi. The basic images in all three were the eight trigrams, from which sixty-four hexagrams were derived. This also shows that the Zhou Changes’ statement that “nothing is more important than turtle divination” had a basis in the institutions of the time.

Fuxi’s sequence of the trigrams begins with Qian, followed by Dui, Li, Zhen, Xun, Kan, Gen, and Kun. The sixty-four hexagrams are also arranged according to the sequence of these eight basic trigrams. The Changes of the Xia dynasty began with Gen, but its precise sequence cannot be established. The Changes of the Shang dynasty began with Kun, and its sequence is likewise unknown. There are no reliable records to show whether the sixty-four derived hexagrams were arranged according to the sequence of the basic trigrams.

The text then quotes the Rites of Zhou on the methods of divination with stalks. Officials were in charge of the three methods of the Changes and used them to distinguish nine kinds of divinatory designations—geng, xian, shi, mu, yi, hua, ci, can, and huan—in order to determine good or ill fortune. For major state affairs, divination with milfoil stalks was performed first, followed by divination with a turtle shell. In spring, officials also examined the condition of the milfoil plants, and the divinatory implements required for state affairs were prepared by the officials responsible.

At root, all methods of divination with turtle shells and stalks follow the principles established by Fuxi. The round stalks are used to derive the square, orderly images of the hexagrams. Taking the stalks from their container and holding them in the hand is called “closing the door”; dividing them by hand, hanging off stalks, and gathering the remainder is called “opening the door.” One closing and one opening constitute a single change. Three changes form one line, and nine changes initially form the inner trigram. Continuing the procedure for eighteen changes completes all six lines and produces a full hexagram; one then determines the outer trigram. A line formed through three changes may be one of four types—seven, eight, nine, or six—called the “Four Images.” When the result is seven or eight, the original hexagram is taken as the primary figure and the resulting hexagram, or changed figure, as the secondary figure. When the result is nine or six, the original hexagram is the primary figure and the hexagram produced by the change is the secondary figure.

Judgment combines the results of turtle divination and stalk divination. At times the two agree, and the outcome is judged auspicious. At other times the turtle divination approves while the stalk divination does not, or the inner trigram is auspicious while the outer trigram is inauspicious. There are also cases in which neither method gives its approval. For matters that call for holding steady and preserving what is established, the result may be auspicious; acting rashly, however, may bring misfortune. From this we can infer that divination in the Xia dynasty followed the same method as Fuxi’s divination, adhering to the principles he handed down.

The Upper Canon of the Zhouyi consists of thirty hexagrams. Apart from six hexagrams, including Qian and Li, the remaining twenty-four form twelve pairs. This arrangement follows the Xia dynasty tradition and the hexagram sequence of Fuxi.

The Lower Canon of the Zhouyi consists of thirty-four hexagrams. Apart from Zhongfu, Xiaoguo, Jiji, and Weiji, the remaining thirty are paired with their opposites, forming fifteen pairs.

Zhuo says: In the Image Commentary, Confucius discusses the coming and going, rising and falling, and advancing and retreating of hexagram images. He develops these ideas from King Wen’s explanations of the hexagrams Tai and Pi: “the small goes out, the great comes in” and “the great goes out, the small comes in.” King Wen adopted Fuxi’s hexagram sequence and arranged the hexagrams in paired correspondences. Confucius then explained their relations of coming and going by considering how the images in each pair stand opposite one another.

Take Tai and Pi as an example. In Tai, the three Yang lines are inside and the three Yin lines are outside; in Pi, the three Yin lines are inside and the three Yang lines are outside. A line that is outside and enters the inner trigram is said to “come”; a line that is inside and moves toward the outside is said to “go.” Confucius followed this same approach when explaining other hexagrams.

The phrase in the text “the firm rises above and the yielding descends below” means that the Yang lines are indeed above and the Yin lines below. “The yielding rises above and the firm descends below” means the same in reverse. These phrases describe the forms of the hexagram images when two hexagrams are viewed side by side. They do not mean that one hexagram changes into another, or that the lines of one hexagram are exchanged for those of another. To understand them as changes of lines would mistake the seven and eight lines of young Yin and young Yang for the six and nine lines of old Yin and old Yang—a serious error. King Wen and Confucius do not speak of “coming and going” or “above and below” when discussing the eight pure hexagrams or hexagrams that do not form opposite pairs. This, too, shows what they originally meant.

The hexagram Tai says: “The small goes out; the great comes in.”

The hexagram Pi says: “The great goes out; the small comes in.”

This is where the discussion of “going” and “coming” in the statements of the hexagrams begins. Confucius goes on to speak of above and below, advance and retreat, ascent and descent, and coming and going, all on this basis.

But King Wen and Confucius did not mean that the three yin lines moving outward in the Tai hexagram were the same three yin lines returning in the Pi hexagram. Nor did they mean that the three yang lines returning in Tai were the same three yang lines moving outward in Pi. Given the opposing relationship between the Tai and Pi hexagrams, a line that leaves the inside and moves outward is called “going”; one that enters from outside and moves inward is called “coming.”

If we say that this year’s three yang lines are the same three yang lines as in the first month of last year, and that this year’s three yin lines are the same three yin lines as in the seventh month of last year, we are effectively claiming that only one Qi exists between Heaven and Earth, hidden somewhere and waiting for the right moment to move in or out, with no new Qi continually succeeding it. How could such a notion have made sense at any time, past or present?

Some people today say that the Tai hexagram derives from the Gui Mei hexagram: the six line moves up to the fourth position, while the nine line comes to the third position. They say that the Pi hexagram derives from the Jian hexagram: the nine line moves up to the fourth position, while the six line comes to the third. This not only explains the originally static form of the hexagram figures through changes in the lines; it also uses the changes between yin and yang in the third and fourth lines to alter, implicitly, King Wen’s account of “three yin lines” and “three yang lines.” How could this possibly accord with the consistent teachings of the sages’ classics?

The Xu hexagram says, “occupying the heavenly position, correctly centered.” This means that the line is in the position of Heaven, the fifth position. In light of the opposing relationship between the Xu and Song hexagrams, it is both in the correct position and in the central position.

The Song hexagram says, “the firm comes and finds the center.” This means that a yang line comes to the central position. In light of the opposing relationship between the Song and Xu hexagrams, the line in Xu is both correctly placed and centered, while the line in Song is centered but not correctly placed.

Zhu Xi says, “The Dispute hexagram changes from the ‘Pursuit’ hexagram, which has four yang lines and two yin lines. Fourteen hexagrams arise through changes from the Pursuit hexagram. The Dispute hexagram is one of those formed by a change in the first line: the firm yang line moves to the second place, while the yielding yin line rises to the third.”

Qiu says, “This is where the Explanation of the Judgments begins to describe changes in the hexagram images.” Some hold that the central yang line of the Water hexagram moves to the fifth place, thereby becoming ‘centered and correct,’ or moves to the second place, thereby ‘attaining the center.’ Is this not a direct, clear, and easy-to-understand explanation?

The Following hexagram says, “The firm line comes beneath the yielding line; there is movement and joy, and so the Following hexagram is formed.” The Original Meaning, Zhu Xi’s commentary on the Changes, says that the ninth line of the Distress hexagram comes to the first place, and the ninth line of the Biting Through hexagram comes to the fifth place; the Already Across hexagram combines both changes. All these explanations describe the Following hexagram as formed when a firm line comes among yielding lines. Is this not a direct, clear, and easy-to-understand explanation?

The Following hexagram says, “The firm line comes beneath the yielding line; there is movement and joy, and so the Following hexagram is formed.” The Original Meaning says that the ninth line of the Distress hexagram comes to the first place, while the ninth line of the Biting Through hexagram comes to the fifth; the Already Across hexagram combines both changes. In each case, a firm line comes beneath a yielding line.

The Decay hexagram says, “The firm line is above and the yielding line below; they are modest and compliant, yet come to a stop, and so the Decay hexagram is formed.” Xun says that the Decay hexagram changes from the Adornment, Well, and Already Across hexagrams, all of which show firm lines rising and yielding lines descending. This describes changes in the hexagram images, but that is not what is happening here.

Zhuo says, “Compare the two hexagrams: the firm line above in the Decay hexagram comes from the outer trigram into the inner trigram, then moves down to the second, third, and top places. The yielding line follows the firm line in the first place, moving upward from below. The yielding line above also moves downward. Earlier scholars further forced explanations using the six basic images of Heaven, Earth, Thunder, Wind, Water, and Fire. They said that the first line of the Standstill hexagram and the top line of the Following hexagram exchange places, and that the first line of the Peace hexagram and the top line of the Decay hexagram exchange places. This account is especially mistaken.”

The Biting Through hexagram says, “The yielding line is centered and moves upward.” Earlier scholars held that the Biting Through hexagram changes from the Standstill hexagram, with the yielding line rising from the first place all the way to the fifth. This is incorrect.

The Adornment hexagram says, “The yielding line comes to the lower trigram and adorns the firm lines; a firm line is sent upward to adorn the yielding line.” Some explain this as a change from the Peace hexagram, saying that its firm line moves upward. Earlier scholars also held that it changes from the Standstill hexagram, with the yielding line rising from the first place to the fifth. All these explanations are incorrect.

The Adornment hexagram says, “The yielding line comes to the lower trigram and adorns the firm lines; a firm line is sent upward to adorn the yielding line.” Some hold that this describes a change from the Peace hexagram, in which its firm line moves upward. This explanation is incorrect.

Zhuo says, “In the phrase ‘firm and yielding are divided,’ the word ‘divided’ means that a firm line is sent upward and takes the place of a yielding line. The preceding hexagram says that the yielding line moves to the fifth place; the following hexagram says that yielding lines move to the second and fifth places. The fifth place is centered but not correct, while the second place is both centered and correct, and is therefore especially valued.”

In the Yuanwang hexagram, a firm Yang line comes from the outer trigram into the inner trigram and becomes its ruling line. Some say this results from three successive changes from another hexagram. That interpretation is incorrect.

In the Daxu hexagram, a firm Yang line occupies the upper position, honoring the worthy. Some say this results from four changes to the Dazhuang hexagram, with the upper and lower trigrams exchanging places. That interpretation is incorrect.

Zhuo says: The firm Yang line in Yuanwang is the Yang line in the upper trigram of Daxu, which comes from the outer trigram into the inner one and becomes its first line. The firm Yang line in Daxu, in turn, is the first line of Yuanwang rising to the upper position, thereby honoring the worthy. Here, the hexagram images are understood by observing the two hexagrams as opposites.

Lower Images (hexagram images in the lower section).

In the Xian hexagram, a yielding Yin line is above and a firm Yang line below. Some say it changes from the Pi hexagram. That interpretation is incorrect.

In the Heng hexagram, a firm Yang line is above and a yielding Yin line below. Some say it changes from the Tai hexagram. That interpretation is incorrect.

Zhuo says: Here, the meaning of the hexagrams is understood through their opposite images, and it is entirely clear.

The image of the Jin hexagram is one of compliance and attachment to brightness, with a yielding Yin line advancing upward. Some say the Yin line rises from the fourth position of the Guan hexagram to the fifth. That interpretation is incorrect.

The Mingyi hexagram.

The Jiaren hexagram.

The image of the Gui hexagram is one of joy and attachment to brightness, with a yielding Yin line advancing upward. Some say the Yin line rises from the fourth position of the Xun hexagram to the fifth. That interpretation is incorrect.

Zhuo says: All four of these hexagrams have the image of the Li trigram, which represents brightness. The sages preferred to speak of a yielding Yin line advancing upward rather than retreating and moving downward because they valued the succession and flourishing of brightness. The meaning of the hexagrams is best understood by comparing these four with one another, and this calls for careful reflection.

The Jian hexagram says: “It is beneficial to go southwest, for going forward brings one to a balanced position. It is not beneficial to go northeast, for the road comes to an end. It is beneficial to meet a great person; going forward will bring results.” Some say this comes about by exchanging the first line of the Zhen trigram with the fifth, and the fourth line with the third. That interpretation is incorrect.

The Xie hexagram says: “It is beneficial to go southwest; going forward, one can gain the people. Returning brings good fortune, for this brings one to a balanced position. If there is somewhere to go, setting out early is auspicious; going forward will bring results.” Some say this comes about by exchanging the top line of the Gen trigram with the second line, and the second line with the top. This claim has no basis.

Zhuo says: This too is entirely clear.

The Sun hexagram diminishes what is below and enriches what is above; its force moves from below upward. Some say this comes about when the third line of the Tai hexagram changes into the top line. That interpretation is incorrect.

The Yi hexagram diminishes what is above and enriches what is below; in other words, benefit is bestowed from above downward. Some say this comes about when the fourth line of the Pi hexagram changes into the first. That interpretation is incorrect.

Zhuo says: The Diminishing hexagram reduces what is below and increases what is above, so it is called “Diminishing.” The Increasing hexagram reduces what is above and increases what is below, so it is called “Increasing.” Turn these two hexagrams upside down and examine their images: the statements about them are quite clear, and their meanings are far-reaching. If one says they developed from the Great Peace and Obstruction hexagrams, what does that have to do with the principles of these two hexagrams?

The Gathering hexagram means coming together. The yielding Yin follows and delights, while the firm Yang occupies the center and receives a response; thus gathering is possible.

In the Rising hexagram, yielding strength rises in accord with the times. Advancement is humble and compliant, while firm Yang occupies the center and receives a response, so there is great success.

Zhang says, “‘Yielding’ refers to the six in the fourth place.” Xu says that the six in the second place of the Release hexagram rises to become the six in the fourth place of the Rising hexagram. According to this view, when Confucius speaks of “yielding rising,” he says only that the six in the fourth place rises, without saying that the six in the fifth place and the top six rise as well. To distort the classics and go against the sages’ intent in this way is truly excessive. Moreover, explaining an entire hexagram through the change of a single line shows a failure to grasp even the basic distinctions. Why, then, do the classics not say, “yielding strength descends at the proper time”? It is because rising can be singled out for explanation, whereas descent needs no special emphasis. The sages wrote this way to bring out what is good in things. The explanations of the Brightness-Hiding and Household hexagrams follow the same pattern.

Complete Diagram of Hexagram Changes

This is what the Duke of Zhou meant by “using the nines” and “using the sixes.” Through this kind of change, one hexagram can become any of the sixty-four hexagrams.

Six Lines Without Change

An unchanged line in a hexagram can only be called a “line,” so the Book of Changes says that a hexagram is made up of six lines. Unchanged lines come in only two kinds: a Yang line is called “nine,” and a Yin line is called “six.” Thus, there are only two kinds of unchanged lines: seven and eight. King Wen established the hexagram images, examined them, and attached statements beneath the hexagrams. These are the kinds of images he meant, and this is the subject matter of the study of the Changes. Earlier Confucian scholars also held that a hexagram is made up of six lines.

Some mistakenly believe that one hexagram can directly become all sixty-four hexagrams. In fact, only when divination yields a line marked as a nine or a six is it called a “changing line”; only then does a change take place.

From the six hexagrams produced by changing a single line onward, the explanations use the Creative and Receptive hexagrams as their basis. The remaining sixty-two hexagrams can be understood by applying the same method.

Calculating nine means that a yang line is about to become a yin line; calculating six means that a yin line is about to become a yang line. So we begin with the first line. A “change” means that the first nine or the first six undergoes transformation.

Here, the two hexagrams Qian and Kun serve as examples. When the first line of Qian changes, it becomes Gou; when the first line of Kun changes, it becomes Fu. When the second nine of Qian changes, it becomes Tongren; when the second six of Kun changes, it becomes Shi. When the third nine of Qian changes, it becomes Lü; when the third six of Kun changes, it becomes Qian. When the fourth nine of Qian changes, it becomes Xiaochu; when the fourth six of Kun changes, it becomes Yu. When the fifth nine of Qian changes, it becomes Dayou; when the fifth six of Kun changes, it becomes Bi. When the top nine of Qian changes, it becomes Guai; when the top six of Kun changes, it becomes Bo. The same method can be used to derive all sixty-two hexagrams. The changes described by the Duke of Zhou in the Xici belong to this same category.

When two lines change, there are fifteen pairs of hexagrams:

The first and top lines change: Daguo and Yi; the first and fifth lines change: Ding and Tun; the first and fourth lines change: Xun and Zhen; the first and third lines change: Song and Mingyi; the first and second lines change: Dun and Lin; the second and top lines change: Ge and Meng; the second and fifth lines change: Li and Kan; the second and fourth lines change: Jiaren and Xie; the second and third lines change: Wuwang and Sheng; the third and top lines change: Dui and Gen; the third and fifth lines change: Huan and Jian; the third and fourth lines change: Zhongfu and Xiaoguo; the fourth and top lines change: Xu and Jin; the fourth and fifth lines change: Dachu and Cui; the fifth and top lines change: Dazhuang and Guan.

When three lines change, there are twenty pairs of hexagrams:

The first, second, and top lines change: Xian and Sun; the first, second, and fifth lines change: Lü and Jie; the first, second, and fourth lines change: Jian and Guimei; the first, second, and third lines change: Pi and Tai; the first, third, and top lines change: Kun; the first, third, and fifth lines change: Weiji and Jiji; the first, third, and fourth lines change: Huan and Feng; the first, fifth, and top lines change: Heng and Yi; the first, fourth, and top lines change: Jing and Shihe; the first, fourth, and fifth lines change: Gu and Sui; the second, third, and top lines change: Sui and Gu; the second, third, and fifth lines change: Shihe and Jing; the second, third, and fourth lines change: Yi and Heng; the second, fifth, and top lines change: Feng and Huan; the second, fourth, and top lines change: Jiji and Weiji; the second, fourth, and fifth lines change: Kun; the third, fifth, and top lines change: Guimei and Jian; the third, fourth, and top lines change: Jie and Lü; the third, fourth, and fifth lines change: Sun and Xian; the fourth, fifth, and top lines change: Tai and Pi.

There are fifteen combinations in which four lines change. The text lists the corresponding hexagram names according to the positions of the changing lines. For example, “the first, third, fifth, and top lines change” means that those four lines change; the related hexagram names are then listed.

There are six combinations in which five lines change. The text likewise lists the corresponding hexagram names according to the positions of the changing lines. This section of the original is repeated, and the combinations in the later passage include “the first, third, fourth, fifth, and top lines change: Shi and Tongren” and “the first, second, fourth, fifth, and top lines change: Lü,” among others.

There is one combination in which all six lines change: “using nine” refers to the Qian hexagram changing into Kun, while “using six” refers to Kun changing into Qian.

The foregoing is said to come from the Duke of Zhou’s “Appended Statements” (Xici) and discusses only “using nine” and “using six” in the Qian and Kun hexagrams. Zhu Xi says that there are six combinations in which one line changes, fifteen in which two lines change, twenty in which three lines change, fifteen in which four lines change, six in which five lines change, and one in which all six lines change. These total sixty-three; adding the original hexagram, in which none of the six lines changes, gives sixty-four. A single hexagram can thus change into sixty-four hexagram configurations. When each of the sixty-four hexagrams undergoes its own changes, the total is 4,096. Jiao Gan’s Yilin uses precisely this method.

When one line changes, the divination should consider the original hexagram and the line that changes.

Wang says: the lines of the original hexagram are called “zhen” (the subject of the divination), while the corresponding lines of the changed hexagram are called “hui” (what results from the change). If two lines change, both should be considered.

When two lines change, the divination should consider the two changing lines in the original hexagram, giving priority to the upper line.

Wang says: the line that changes first should be taken as “zhen,” and the one that changes later as “hui.” Examine the changed situation in two stages, then compare it with the relevant rules to reach a judgment.

When three lines change, the divination should consider the original hexagram…

Wang says: The line that changes first should be taken as “zhen” (the primary basis for divination), and the line that changes afterward as “hui” (the supplementary part of the divination). The judgment should be made in two stages, following the order of the changes.

When three lines change, consult both the original hexagram and the changed hexagram. The Tuan Commentary (the text explaining the meaning of a hexagram) treats the original hexagram as zhen and the changed hexagram as hui. The accompanying note argues that the Tuan Commentary cannot be used to divine changes in individual lines. Instead, the line that changes first should be taken as zhen, and the two lines that change afterward as hui; the judgment should be made in three stages, following their order.

When four lines change, consult the changed hexagram. Of the two lines that do not change, the lower one remains the primary line.

When five lines change, consult the sole line in the changed hexagram that does not change.

Wang says: In all these cases, the line that changes first should be taken as zhen, and the old lines that change afterward (that is, lines transformed from old Yin or old Yang) as hui; the judgment should proceed in order through four or five stages. Xia says: If a line does not change, how can one use the line statement for a changing line? The line statements written by the Duke of Zhou were originally intended for changing lines such as nine and six, not for unchanging lines such as seven and eight. If the Zhou Changes did not use seven and eight, how could line statements for nine and six be applied to seven and eight? When all six lines change, divination for the Qian and Kun hexagrams uses the “two special lines” (special line statements used in divination for the Qian and Kun hexagrams); for the other hexagrams, consult the changed hexagram.

The accompanying note argues that the Tuan Commentary and the hexagram statements were established for unchanging lines such as seven and eight. How, then, can they be used to divine changes in lines? It is acceptable to use the “two special lines” for divination with the Qian and Kun hexagrams. Lu’s note: Zhu Xi reached this judgment on the basis of references in the Zuo Commentary to “Gen changing to eight” and to “zhen, Tun, hui, Yu.” All these references involve “eight.” Some divination records in the Zuo Commentary are thought to use the Changes of the Xia and Shang periods, while records using the Zhou Changes explicitly say “Zhou Changes.” The relevant evidence, however, has not all been examined.

Hexagram Authority

The text used for divination must have a primary source that serves as its basis.

Among the Twelve Monthly Hexagrams, which represent the waxing and waning of Yin and Yang through the twelve months of the year, Fu and Gou take the first line as the governing line; Lin and Dun the second; Tai and Pi the third; Da Zhuang and Guan the fourth; Guai and Bo the fifth; and Qian and Kun the top line.

Among the doubled hexagrams of the Six Children, Zhen and Xun take the fourth line as governing, Kan and Li the fifth, and Gen and Dui the top line. Among the combined hexagrams of the Six Children, Heng and Yi take the first line as governing; Ji Ji and Wei Ji the second; and Xian and Sun the third. Of the Yuan reversal hexagrams formed by combining Zhen, Xun, Gen, and Dui, Yi and Da Guo take the top line as governing, while Zhong Fu and Xiao Guo take the fourth.

Among hexagrams formed by combining opposite images, Sui and Gu take the first line as governing, while Jian and Gui Mei take the third. In hexagrams containing Kan or Li, the middle line of Kan or Li is the governing line. Song, Kun, Jie, Huan, Meng, Shi, Tong Ren, Ge, Feng, Jia Ren, Bi, and Ming Yi all take the second line as governing. Xu, Jie, Tun, Jing, Jian, Bi, Da You, Guai, Shi He, Ding, Lü, and Jin all take the fifth line as governing.

When Zhen or Xun is the principal trigram, the fourth line of the hexagram is taken as governing. For example, Yu and Xiao Chu take the fourth line, while Sheng and Wu Wang take the first. When Gen or Dui is principal, the third line of the hexagram is taken as governing; for example, Qian and Lü take the third line. Shi and Da Chu take the top line as governing. In the Judgment of the Kun hexagram, the phrase “later, one finds a lord” refers to the top line as Kun’s governing line.

The first nine in Mingyi says, “The host has something to say.” Here, “host” means the line that takes the leading role in the Mingyi hexagram. The second line is the host of Mingyi.

The second nine in Mingyi says, “Meet the host.” Here, “host” refers to the hexagram’s ruling line; the second line is the host of Mingyi. The third nine in Mingyi also mentions the “host.”

The first nine in Feng says, “Meet the host who is paired with oneself.” The fourth nine in Feng says, “Meet the host.” The second line is the host of Feng.

The Wuwang hexagram says that a firm and strong line comes from the outer trigram and becomes the leading line of the inner trigram. The first line is the host of Wuwang.

Zhuo says: In its historical records, the Spring and Autumn Annals calls the state of Lu “inside” and the other feudal states “outside,” and therefore often uses “we” to refer to Lu. This is because the Annals takes Lu as the center of its narrative. For example, in phrases such as “The people of Qi, Song, and Chen attacked us” and “The burial of our ruler’s consort,” “us” and “our” both refer to Lu.

The Book of Changes works in the same way. Whenever “I” appears in a hexagram statement or a line statement, it refers to that hexagram’s ruling line. The following examples illustrate this.

The Meng hexagram says, “The young and inexperienced seek me; it is not I who seek the young and inexperienced.” The second line is the ruling line, so it is called “I.” The fifth line belongs to the Gen trigram, which symbolizes a young man; hence the phrase “the young and inexperienced.”

The Xiaoxu hexagram says, “Dense clouds gather, but no rain falls; they rise from the western outskirts where I am.” The fourth line is the ruling line, so “I” refers to the fourth line.

The third six in Guan says, “Observe me, and decide whether to advance or retreat.” The fourth line is the ruling line, so “me” here refers to the fourth line. One observes the fourth line’s actions to judge whether to advance or retreat; the Xun trigram symbolizes advancing and retreating.

The first nine in Yi says, “Put down your spiritual tortoise and watch me chew.” The nine is the ruling line, so it is called “me.” The first nine occupies a low position and would not ordinarily be responsible for nourishing others. Like a spiritual tortoise, it lies low, seeming able to sustain itself. Yet although it lies below, it still looks upward. The top nine envies those in a higher position who can nourish those below, but has no intention of setting itself aside and turning to nourish others.

The fifth nine in Yi says, “With sincerity in your heart, extend benefits to others. Without divining, it will be greatly auspicious; others will also sincerely repay my kindness.”

The second and fifth lines correspond directly. The fifth line occupies the position of the heart. This means that the second line, with sincerity, wishes to benefit the fifth line; its auspiciousness is clear without needing to ask. Yet the second line treats the fifth with sincerity and aids it through kindness, while also sincerely treating the first line with kindness and bestowing virtue upon it. The first line is the governing line of the whole hexagram, so it is called “I.” The second and fifth lines are far apart, hence “a kind heart”; the first line is strong and substantial, and lies close to the second, receiving its support, hence “kindness in virtue.” The second line of the Well hexagram also says that it receives aid from the fifth line while also benefiting from the first line’s not opposing it. The meaning of the two line statements is exactly the same: here, the statement refers to the fifth line’s correspondent and also mentions the line close to it; in the Well hexagram, it refers to the second line’s correspondent and also mentions the line close to the sixth.

The third line of the Well hexagram says: “The well’s water is deep, but no one drinks from it; this saddens my heart.”

The fifth line is the governing line of the whole hexagram, so it is called “I.” The third line lies beneath the Dui trigram (which symbolizes the mouth). Thus, although the well water has been cleaned and made pure, no one drinks from it. The fifth line therefore feels sad and pities the third line for being unable to serve the people. The fifth and third lines of the Increase hexagram belong to the same category, but the fifth line lies above the Dui mouth of the upper trigram, symbolizing that people can drink; the third line lies below the Dui mouth of the lower trigram, symbolizing that no one drinks. This is why the fifth line feels sad for the third.

The second line of the Cauldron hexagram says: “There is food in the cauldron. My mate is ill and cannot come near me. Good fortune.”

The fifth line is the governing line of the whole hexagram, so it is called “I.” Here the hexagram’s governing line speaks: the second line possesses substantial virtue within and is a worthy mate who corresponds directly to me. Unfortunately, his Qi and blood are out of balance and he is ill, so he cannot come near me. How could I not go and see him myself? A scholar does not abandon the Dao in order to seek an audience, hence the phrase “I”; a ruler can humble himself and personally honor a worthy person, hence the good fortune.

The fourth line of the Travel hexagram says: “My heart is troubled.”

In a hexagram, “Nine in the Fifth” usually means that the fifth line occupies a position associated with yang, while “Six in the Fifth” means that the fifth line occupies a position associated with yin. The “hexagram ruler” is the line regarded as governing the meaning of the hexagram.

The statement of the Nine in the Second line of Zhongfu says, “I have a fine cup; I share it with you.” Here the Nine in the Fourth is called “I” because it is the hexagram ruler. The commentator takes the line as the Nine in the Fourth speaking to the Nine in the Second: the Nine in the Fifth is strong, centered, and properly placed, and possesses a noble rank as if bestowed by Heaven. Its position is higher than that of the Nine in the Fourth, so the Nine in the Second should admire and be attached to it. The Nine in the Fourth is adjacent to the Nine in the Fifth, while the Nine in the Second occupies the same line position as the Nine in the Fifth; for these reasons, the Nine in the Fourth gives this counsel to the Nine in the Second.

The statement of the Six in the Fifth line of Xiaoguo says, “Dense clouds gather, but no rain falls; the clouds rise from the western outskirts where I am.” Here, too, “I” refers to the Nine in the Fourth, since it is the hexagram ruler. The Nine in the Third obscures the lower trigram Kan, where the Nine in the Fifth is located, symbolizing dense, obstructing clouds and thus the lack of rain. The Nine in the Fourth represents the west and lies beyond the inner trigram, so it is called the “outskirts.” The Nine in the Fourth does not rise to unite with the Six in the Fifth, making it difficult for Yin and Yang Qi to meet. How, then, could rain be expected?

In the Earlier Heaven diagram, the sixty-four hexagrams are paired with their counterparts to form a single hexagram. Thus, the thirty-two hexagrams in the middle layer are identical on the left and right, leaving only sixteen distinct forms. In the thirty-two hexagrams of the middle layer, each pair is again matched with its counterpart to form a single hexagram. This leaves sixteen hexagrams in the inner layer, whose four sections are identical, yielding only four distinct forms.

Mr. Hao says: In the past, explanations of “Huti” (nuclear trigrams, formed by taking the middle line patterns of a six-line hexagram and arranging them into new trigrams) usually only noted that four of the six lines are taken to form two hexagrams, without examining the subtle patterns of images and numbers involved. Viewed now through the Xiantian diagram (a diagram that arranges the trigrams in their predetermined sequence), the sixteen hexagrams formed by Huti are each eight positions apart. Taking one hexagram every four positions gradually reveals their arrangement.

Starting from the left side of the diagram, after Qian and Guai, every eighth hexagram comes in sequence: Kui and Guimei, then Jiaren and Jiji, and finally Yi and Fu. Starting from the right side, after Gou and Daguo, every eighth hexagram comes in sequence: Weiji and Jie, then Jian and Jian, and finally Bo and Kun. There are two hexagrams on each side; the three sets combine to form all sixty-four hexagrams. Huti can form only sixteen hexagrams; applying Huti to these sixteen produces only four more: Qian, Kun, Jiji, and Weiji. The Zhouyi begins with Qian and Kun and ends with Jiji and Weiji. Perhaps this is why.

Mr. Zhu says: In the middle layer, there are sixteen hexagrams on each side. Their lower trigrams are adjacent in pairs and follow the sequence “Qian one, Kun eight.” The sixteen hexagrams in the upper trigrams cycle through this sequence twice, and their arrangement can be examined closely. Looking further into the inner layer, the lower trigrams are Qian, Li, Kan, and Kun, in that order; the upper trigrams are Qian, Kan, Li, and Kun. Each of these two sequences cycles four times, making them especially worthy of close observation.

Zhuo says: The final chapter of the “Miscellaneous Hexagrams” in the Zhouyi selects Daguo, Zhen, and Cui from among the Eight Trigrams because their inner hexagrams belong to Qian. It selects Yi because its inner hexagram belongs to Kun. It selects Jian and Jiji because their inner hexagrams belong to Weiji. It selects Guimei and Weiji because their inner hexagrams belong to Jiji.

Qian and Kun are omitted because they have already appeared at the beginning of the text. Bo and Fu are omitted because they contain many yin lines and are therefore passed over. Kui and Xie are omitted because, once Weiji is selected, Guimei is passed over. Jiaren and Guai are omitted because, once Jiji and Jian are selected, they are passed over. Qian corresponds to three hexagrams, while Kun corresponds only to Yi; Jiji corresponds only to Guimei, and Weiji only to Jian. This is because Qian holds the more exalted position.

Jiji and Weiji appear in the latter part of the text, reflecting the Zhouyi’s practice of concluding with the meanings of Jiji and Weiji. Guai and Fu come before Jiji and Weiji; this, too, is the order Confucius used in arranging the “Miscellaneous Hexagrams.” Although the names given to things in the Xia, Shang, and Zhou dynasties are varied, they each follow their own order. The names Confucius used are likewise varied, yet remain orderly.

The second volume of A Study of the Origins of the Ancient Changes is complete.

A propitious day during the Shangyuan Festival, in the thirty-fifth year of the Wanli era of the Great Ming (Dingwei year, 1607).

By imperial command, Zhang Guoxiang, Grand Perfected One of the Zhengyi lineage, charged with transmitting the teaching, devoted to sincerity and the Dao, spreading the mysteries and promoting the teaching, and overseeing Daoist affairs throughout the realm, supervised the carving of this edition.