《易象图说外篇(张理)》

An Explanatory Treatise on the Images of the Changes: Outer Chapters is a three-volume work on the study of the Changes, written by Zhang Li of the Yuan dynasty. The extant text is based on the edition in the Ming-dynasty Zhengtong Daoist Canon, with reference to the Wenyuange edition of the Complete Library of the Four Treasuries.

An Explanatory Treatise on the Images of the Changes: Outer Chapters, Upper Volume

Zhang Li, a later scholar from Qingjiang, courtesy name Zhongchun.

The Yijing is the Dao (the Way); it speaks of the principles governing Heaven, Earth, and humanity. The sages of antiquity received the Dao of Heaven, established standards, and laid the foundations of human relations and social order. Fearing that later generations might fail to perceive and understand these principles, they made the Dao visible to people.

The Dao has no traceable beginning and no end that can be measured, for it moves without ceasing. It is so small that nothing is more subtle, yet it reaches through the most minute things; it is so vast that it has no boundaries and encompasses Heaven and Earth. When Heaven follows it, the sun and moon can travel on enduring courses. When Earth follows it, rivers and mountains can bear their weight in stability.

The sages looked up and observed the deep, unfathomable patterns of Heaven, symbolizing them with two kinds of line. They looked down and observed how Earth receives and supports, symbolizing it with lines as well. In the diagrams of the Yijing, the odd line above and the even line below express the Supreme Ultimate (Taiji) giving rise to the Two Modes. Zhou Dunyi said that when the Supreme Ultimate moves, it generates Yang; when it becomes still, it generates Yin. Heaven has Yin and Yang, while Earth has the yielding and the firm. Thus the two kinds of line, odd and even, each produce an odd and an even line in turn, forming the Four Images. The patterns of Heaven appear above, while the Qi (vital energy) of Earth rises from below. The Yin-Yang and firm-yielding lines in the Yijing diagrams express the Two Modes giving rise to the Four Images. Zhou Dunyi held that the transformations of Yang Qi and the union of Yin Qi generate the Five Phases (Wood, Fire, Earth, Metal, and Water).

Heaven has the four seasons of spring, summer, autumn, and winter; Earth has the four directions of east, west, south, and north. As each of the Four Images divides again into Yin and Yang, the Eight Trigrams (Bagua) emerge. Qian, Dui, Li, and Zhen are arranged above, derived from looking up at the patterns of Heaven; Kun, Gen, Kan, and Xun are arranged below, derived from looking down at Earth’s terrain. This is the Four Images giving rise to the Eight Trigrams. Zhou Dunyi said that the original reality of the Non-Being and the Qi of Yin-Yang and the Five Phases mingle and gather in a wondrous union: the Way of Qian gives rise to the male, and the Way of Kun gives rise to the female.

Each of the Eight Trigrams has its own symbol. Pure Yang represents Qian’s strength and vigor; yielding Yin represents Kun’s creative beginning. Bright Yang shines outward, and Li represents fire; Yin holds light within, and Kan represents water. What rises high and flourishes is like the mountain represented by Gen; what lies low and gathers water is like the marsh represented by Dui. What surges and shakes is like the thunder represented by Zhen; what breathes and blows is like the wind represented by Xun. As these eight images interweave, the principles of the Yijing become clear.

Human beings stand between Heaven and Earth and, in themselves, can embody the principles of all things. The Book of Rites says that human beings gather the De (Virtue/Power) of Heaven and Earth, and are formed through the union of Yin and Yang, the mingling of spirits, and the essence of the Five Phases. The human body, too, can be explained through the Eight Trigrams: the rounded part at the top is the head, corresponding to Qian; the part that covers and hangs down is the abdomen, corresponding to Kun. Zhen represents the arms, Xun the legs and feet; Gen the nose, Dui the mouth; Kan the ears, and Li the eyes. People drink when thirsty and eat when hungry, work in the morning and rest at night, and go about their busy lives. In appearance, they are no different from other living beings. Only those who are not governed by external things can be called sages. Ordinary people live by the Dao every day without knowing it; sages rise above the ordinary and become outstanding among them.

The way of the sage is for De to accord with Heaven and Earth, and wisdom to shine as brightly as the sun and moon. The sage can grasp the principles of Heaven, Earth, and all things, and harmonize Yin and Yang. Benevolence and wisdom extend throughout the world, and their grace reaches later generations. The sage brings about balance and harmony, so that Heaven and Earth each settle into their proper place and all things can grow. With utmost sincerity, the sage reaches the spirits and makes birds and beasts tame. Only with such De can one be said truly to fulfill the endowment contained in human nature and bodily form.

Mencius said that although all people are human, those who follow what is great in themselves and cultivate their De are great people, while those who chase the small desires of the body are small people. The principles of all things are complete within me: that is, I should seek within myself and make my heart sincere. Benevolence, righteousness, propriety, and wisdom are inherent in human beings. Benevolence and wisdom follow the changes of Yin and Yang in Heaven; righteousness and propriety follow the order of firmness and yielding on Earth. More specifically, benevolence belongs to Yin and wisdom to Yang; propriety is yielding and righteousness is firm.

The Dao of Heaven is strong and vigorous, and people should model themselves on it by striving ceaselessly. The Dao of Earth is yielding and receptive, and people should model themselves on it by bearing all things through generous De. Like Li, carry forward the light and discern what is right. Like Kan, maintain steadfast De. Like Gen, know where to stop and hold to one’s proper bounds. Like Zhen, act with alertness and caution, examining oneself. Like doubled Xun, repeatedly make commands clear and carry out affairs. Like Dui, study and discuss with friends. The six trigrams from Qian through Zhen urge people to examine themselves; Xun and Dui explain how to deal with others and conduct affairs.

When in the flourishing conditions represented by the Tai hexagram, one should bring the ways of Heaven and Earth to completion, assist them in what is fitting, and help the people. The Image Commentary on the Tai hexagram says, “Heaven and Earth unite: this is Tai.” The noble person therefore brings the ways of Heaven and Earth to completion and assists them in their fitting arrangements, in order to govern the people. When in the blocked conditions represented by the Pi hexagram, one should restrain one’s De and not covet honor or position. The Image Commentary on the Pi hexagram says, “Heaven and Earth do not unite: this is Pi.” The noble person should gather in their De and avoid calamity, seeking no prominence for the sake of salary or rank. When faced with the Yi hexagram, learn from what is good and correct one’s mistakes; when faced with the Sun hexagram, restrain desires and curb anger.

On a grand scale, the principles of yielding the throne and overthrowing tyrants are contained in the Yijing; on a small scale, so are the principles behind one’s movements and conduct, and one’s words and silences. What appears in the world takes the form of ritual and music; what is hidden and hard to see is expressed through the workings of spirits. Ethical orders such as the Three Bonds and Five Constant Virtues have likewise been passed down through the generations. The Commentary on the Yijing says, “Heaven and Earth establish their positions, and transformations unfold between them.” Preserving and continually nourishing one’s innate nature is the gateway to the Way of righteousness. The Yijing is the classic through which sages elevate De and expand their work. Fearing that later generations would not understand its principles, the sages composed the Yijing to enlighten people. Though I call myself a later student of modest standing, I too dare to aspire to the sages, the wise, and even the Dao of Heaven. I have therefore observed the hexagram images, drawn and described their diagrams, and arranged them in sequence, giving the work the title The Origins of the Diagrams of the Great Changes.

Image and Number I

The Commentary on the Book of Changes says, “The Book of Changes contains the Supreme Ultimate (Taiji).” Zhu Xi explained, “The Book of Changes speaks of the changes of Yin and Yang; the Supreme Ultimate refers to the principle within them.” “Supreme Ultimate” means the highest and most ultimate, and also carries the sense of a guiding standard. It is the key to the generation and transformation of all things under Heaven and Earth, and the root of every kind of thing.

The Supreme Ultimate originally had no form, sound, or smell that could be identified. In the Song dynasty, Master Zhou Dunyi began depicting it as a circle, a convention followed by later Taiji diagrams. The Shuowen Jiezi says, “In the beginning was the Supreme Ultimate. The Dao was established from the One, which differentiated to form Heaven and Earth and transformed to generate the myriad things.” “One” is the beginning of number.

The diagram on the right shows that Heaven, Earth, and Humanity—the Three Powers—each have a Taiji (Supreme Ultimate). Shao Kangjie said that Heaven began in the hour of Zi, Earth was formed in the hour of Chou, and humanity came into being in the hour of Yin.

The Xia dynasty used the month beginning with Yin as the first month of the year, a system known as the “Human Order.” Among the Yi texts, the Lianshan takes the Gen trigram as its first trigram; Gen symbolizes humanity. The Zhouyi also draws on the human body when explaining the six lines of the Gen trigram. The Shang dynasty used the month beginning with Chou as the first month, a system known as the “Earth Order.” Among the Yi texts, the Guicang takes the Kun trigram as its first trigram; Kun symbolizes Earth. The Zhou dynasty used the month beginning with Zi as the first month, a system known as the “Heavenly Order.” The Zhouyi takes the Qian trigram as its first trigram; Qian symbolizes Heaven.

Commentators hold that mountains breathe out and take in cloud Qi, Earth stores and nurtures all things, and Heaven extends throughout the six directions—above, below, and the four quarters. These explain the meanings of Qian and Kun, but the interpretation of Gen remains incomplete. Gen symbolizes the transition of all things from ending to beginning anew. Since humans are the most spiritually attuned of all beings, humanity is made the focus here in explaining Gen. From this we can see that the Xia dynasty valued the humane way of loyal sincerity, the Shang embodied the principle of Earth’s plainness and capacity to sustain, and the Zhou embodied Heaven’s pattern and order.

The Xia, Shang, and Zhou dynasties rose in succession, each upholding a different legitimate tradition. When Confucius answered Yan Hui’s question about governing a state, he said to adopt the Xia calendar, ride in a carriage of the Shang style, and wear a ceremonial cap of the Zhou style. This expresses the principles of following the timing of Heaven, making use of the advantages of the land, and putting human relations and social order into practice. It was regarded as a great law that rulers of every age should not change. Thus it is said that Confucius carried on the traditions of Yao and Shun while taking the institutions of Kings Wen and Wu as his model; to follow the timing of Heaven above and rely on the land and its conditions below is precisely what this means.

Han Feizi says: What appears above is called Heaven; what appears below is called Earth; what receives Heaven’s mandate and dwells between Heaven and Earth is called the human. The sun, moon, stars, and constellations belong to Heaven; plants, mountains, and rivers belong to Earth. The Yi and Di peoples—ancient names for groups in distant regions—as well as birds and beasts, all belong to the human category in its broader sense.

Master Cheng says: Heaven and Earth join, and all things come into being between them. Only then are the Three Powers—Heaven, Earth, and the human—complete. Humans are the most spiritually perceptive, and therefore stand at the head of all things. Everything that grows between Heaven and Earth belongs to the human way: the order and principles governing life between Heaven and Earth.

Images and Numbers, Part Three

The principles governing the numbers of Heaven and Earth center on “five.” The diagrams of the River Chart and the Luo Writing also reveal the number five, and the “Supreme Pole”—the highest principle for governing the state—likewise rests upon it. “Five” means occupying the center; the center is where the four directions converge.

The Five Phases correspond to the cardinal directions: the East belongs to Wood, the West to Metal, the South to Fire, and the North to Water. In their sequence of operation, they are Wood, Fire, Earth, Metal, and Water. Wood and Fire are Yang; Metal and Water are Yin. Earth occupies the center and has qualities of both Yin and Yang. The generating sequence of the Five Phases is Water, Wood, Fire, Metal, and Earth. In this sequence, Water and Wood are Yang, while Fire and Metal are Yin.

The River Chart pairs numbers with the directions and the Five Phases. Heaven, through the number one, gives rise to Water, and Earth, through the number six, brings it to completion; thus one and six are in the North and belong to Water. Earth, through the number two, gives rise to Fire, and Heaven, through the number seven, brings it to completion; thus two and seven are in the South and belong to Fire. Heaven, through the number three, gives rise to Wood, and Earth, through the number eight, brings it to completion; thus three and eight are in the East and belong to Wood. Earth, through the number four, gives rise to Metal, and Heaven, through the number nine, brings it to completion; thus four and nine are in the West and belong to Metal. Heaven, through the number five, gives rise to Earth, and Earth, through the number ten, brings it to completion; thus five and ten are at the center and belong to Earth. Earth connects the Qi of the four directions and becomes the pivot of their movement.

The forms of the Five Phases are therefore manifested in Heaven, while their substance is embodied in Earth. Human beings are born by modeling themselves on Heaven and Earth: they possess the five kinds of Qi, which form the body, and receive five qualities, which form their De (virtue). Thus, discussions of human nature and the Dao cannot be separated from the Five Phases. Those who receive upright and open Qi become sages and worthies; those who receive crooked and obstructed Qi become foolish and unworthy.

Yet local customs may also develop biases because people see different things, and what they like and esteem varies from place to place. The East is the place of growth, where the sun rises; people there often witness the growth of all things, so Laozi speaks of seeking long life. The West is the place of decline, where the sun sets; people there often witness the passing away of all things, so Buddhism speaks of quiescent extinction. In the South, brightness flourishes, Yang Qi extends, and spirits appear; in the North, darkness and concealment prevail, Yin Qi contracts, and ghosts and strange beings appear.

Only the sage stands at the center of the world, bringing peace to the people of the four seas and governing the realm while facing the light. Free of selfish intentions and reckless action, the sage remains inwardly still and unmoving, yet responds to changes in the world and understands its underlying principles. This is the highest and most wondrous state of spiritual clarity in the world. Zhou Dunyi said, “The sage brings peace to the world through centrality, correctness, benevolence, and righteousness; takes stillness as the guiding principle; and establishes the highest standard for human conduct.”

Images and Numbers IV

Zhouzi says: When Yang Qi changes and Yin Qi gathers, they generate Water, Fire, Wood, Metal, and Earth. The five kinds of Qi move in a set sequence, and the four seasons change in turn. The Five Phases are, at their root, one whole. The sage takes centrality, uprightness, benevolence, and righteousness as guiding principles, and makes purity and stillness primary, thereby establishing the highest standards for conducting oneself in the world.

Zhouzi says: When Yang Qi changes and Yin Qi gathers, they generate Water, Fire, Wood, Metal, and Earth. The Qi of the Five Phases moves in sequence, bringing about the change of the four seasons. The Five Phases all arise from Yin-Yang; Yin-Yang arises from Taiji (the root of all things in the universe), and Taiji is rooted in Wuji (the formless, imageless source). The true nature of Wuji and the vital essences of Yin-Yang and the Five Phases unite and coalesce in a wondrous way. The Way of Qian (the principle governing the movement of Yang) generates men, and the Way of Kun (the principle governing the movement of Yin) generates women. The two Qi, Yin and Yang, respond to each other and transform to produce the myriad things. The myriad things continue to grow and multiply, and their transformations have no end.

Only human beings receive the finest endowment between Heaven and Earth, and so they are the most intelligent and perceptive. Once the human form takes shape, the spirit develops awareness. The five dispositions are stirred by external things, and good and evil become distinct; from this, all kinds of affairs arise. The sage disciplines himself through centrality, uprightness, benevolence, and righteousness, and makes purity and stillness primary, thereby establishing the highest standards for conducting oneself in the world. When the noble person cultivates himself in accordance with these standards, he will meet with good fortune; when the petty person goes against them, he will meet with misfortune. The principles contained in the Yi Jing are truly vast and profound, reaching the utmost limit.

Images and Numbers V

The five and ten described above meet at the center and form the sequence of the Nine Palaces—that is, the numbers of the Luo Shu (an ancient legendary numerical diagram). One, three, nine, and seven belong to the numbers of Heaven; the numbers of Heaven are odd.

The passage on the right describes the sequence in which five and ten converge in the Nine Palaces. This is the numerical pattern of the Luo Writing (Luoshu).

One, three, nine, and seven belong to the numbers of Heaven. The numbers of Heaven are odd, and odd numbers symbolize the circle. Multiplying by three makes the sequence turn to the left, beginning with one in the north. One times three is three, so three comes next in the east. Three times three is nine, so nine comes next in the south. Three times nine is twenty-seven; taking the final digit, seven comes next in the west. Three times seven is twenty-one; taking the final digit, one brings the sequence back to its beginning.

Two, four, eight, and six belong to the numbers of Earth. The numbers of Earth are even, and even numbers symbolize the square. Multiplying by two makes the sequence turn to the right, beginning in the southwest. Two times two is four, so four comes next in the southeast. Two times four is eight, so eight comes next in the northeast. Two times eight is sixteen; taking the final digit, six comes next in the northwest. Two times six is twelve; taking the final digit, two brings the sequence back to its beginning. This is the natural rule by which Yin-Yang moves in leftward and rightward directions. The directions associated with two, seven, four, and nine differ from those in the River Diagram (Hetu).

The Inner Canon (Neijing) says: “The numbers of Heaven begin with one and end with nine. One belongs to Heaven, two to Earth, and three to humanity. Heaven, Earth, and humanity each divide into three; three times three makes nine. Nine, in turn, divides into nine regions, known as the Nine Fields.” The north is called Ji Province, roughly encompassing what are today Dadu, Yannan, Hejian, and Pingyang circuits. The east is called Qing Province, including what are today the prefectures of Yidu, Yimi, and Deng-Lai. The south is called Yang Province, including what are today the Two Huai regions, the Two Zhe regions, Jiangdong, Jiangxi, and Oumin. The west is called Liang Province, including what are today Sichuan and Yun-Yao. The center is called Yu Province, including what are today Henan and Xiangyang. The northeast is called Yan Province, including what are today Jinan, Dongping, Dongchang, and Jining. The southeast is called Xu Province, including what are today the prefectures of Xu, Qiong, Su, and Bo. The southwest is called Jing Province, including what are today the Jing-Tan region and Huguang. The northwest is called Yong Province, including what are today Shaanxi and Gansu.

Thus the divine Yu divided the land into nine provinces and compiled the Tribute of Yu (Yugong), while Jizi developed these principles and wrote the “Nine Categories” in the Great Plan (Hongfan). In addition, theories of cyclical influences, the art of Taiyi, Yin-Yang techniques, and the learning of physicians differ in their approaches and vary in substance and quality, yet none extends beyond the numerical pattern of the Nine Palaces.

In the diagram on the right, 1, 3, 5, 7, and 9 are Yang numbers. They encompass the Two Modes (the classification of Yin and Yang Qi), the Four Images (the four forms arising from further changes in Yin and Yang), and the Eight Trigrams. Yang Qi leads, while Yin Qi responds; Yang is substantial, and Yin is insubstantial. Although the Two Modes are said to comprise two kinds, they in fact include three states. The Four Images, though four in number, actually include five forms. And the Eight Trigrams, though there are eight, actually include nine. This shows that between Heaven and Earth, nothing can come into being without Yang Qi, and nothing can be brought to completion without Yin Qi. This is the foundation of nature’s creative process.

Image and Number, Part Six

The diagram on the right shows how the numbers from one to fifteen in the Yellow River Chart and the Luo River Writing generate one another.

The Commentary on the Changes says, “The Yellow River brought forth the Yellow River Chart, and the Luo River brought forth the Luo River Writing; the sages modeled themselves on them.” To “model oneself on them” means to follow their images and numerical principles. Number begins with one: by tracing its patterns on a small scale, it forms five; on a larger scale, it forms ten. Five and ten together summarize the principles of number. The Yellow River Chart and the Luo River Writing are important foundations grounded in these principles, and they also provide the basis for the line drawings that make up the Trigram images.

In this diagram, the numbers add up to fifteen in both the vertical and horizontal directions. Arranged in their proper positions, they correspond precisely to the image of the Yellow River Chart’s center, where the celestial number five is multiplied by the terrestrial number ten.

“Central” refers to the Changes, that is, to the Five at the center of the diagrams. Yang Qi stirs and rises, joining with Heaven; its image is Yang. Yin Qi rests and descends, joining with Earth; its image is Yin. Yin and Yang arise in Heaven, while the yielding and the firm arise on Earth. This corresponds to the upper, lower, left, and right positions around the fifth place in the diagrams. In number, Yang is one and Yin is four; the firm is three and the yielding is two. Extending this pattern gives one and six, two and seven, three and eight, and four and nine, corresponding respectively to the four directions in the diagrams. From this the Eight Trigrams (Bagua) differentiate, and the Five Phases (Wood, Fire, Earth, Metal, Water) come together. As the Five Phases arise, each takes on its own distinct nature.

This diagram shows the source from which the myriad things arise. The River Chart (Hetu) arranges the Five Phases according to the directions in which they flourish; the Luo Writing (Luoshu) encompasses transformation, while the number of the Great Expansion reveals its practical pattern. In the River Chart, Wood is in the east, Fire in the south, Metal in the west, and Water in the north: this is the regular order. In the Luo Writing, Metal and Fire exchange places, with Metal in the south and Fire in the west: this is the order of transformation.

In terms of the sequence in which things first arise, Kan and Xun are born from Earth’s firmness. These are what Zhu Xi called “Lesser Yang,” the weaker Yang Qi. Lesser Yang corresponds to the Yin position, belongs to spring, and has the number three. Adding the Lesser Expansion brings the total to five: add two to three. Adding the Great Expansion brings the total to ten: add seven to three. Two and seven belong to Fire, so Fire begins to arise at the Yin hour and flourishes at the Wu hour. Looking at the River Chart, seven and one are in the south, where Qian and Dui occupy the corresponding positions: Qian is in the seventh place and Dui in the second. Qian and Dui are born from Yang in Heaven. They are what Zhu Xi called “Greater Yang,” the most abundant Yang Qi. Greater Yang corresponds to the Si position; Si is when the six Yangs reach their peak. It belongs to summer and has the number one. Adding the Lesser Expansion brings the total to five: add four to one. Adding the Great Expansion brings the total to ten: add nine to one. Four and nine belong to Metal, so Metal begins to arise at the Si hour and flourishes at the You hour. Looking at the River Chart, four and nine are in the west, where Xun and Kan occupy the corresponding positions: Xun is in the fourth place and Kan in the ninth. Qian intermingles with Kan, and Kan in turn intermingles with Qian; Xun and Dui exchange places, and Dui in turn exchanges places with Xun.

Li and Zhen are born from Yin in Heaven. They are what Zhu Xi called “Lesser Yin,” the weaker Yin Qi. Lesser Yin corresponds to the Shen position, belongs to autumn, and has the number four. Adding the Lesser Expansion brings the total to five: add one to four. Adding the Great Expansion brings the total to ten: add six to four. One and six belong to Water, so Water begins to arise at the Shen hour and flourishes at the Zi hour. Looking at the River Chart, one and six are in the north, where Kun and Gen occupy the corresponding positions: Gen is in the first place and Kun in the sixth. Kun and Gen are born from Earth’s yieldingness. They are what Zhu Xi called “Greater Yin,” the most abundant Yin Qi. Greater Yin corresponds to the Hai position; Hai is when the six Yins reach their peak. It belongs to winter and has the number two. Adding the Lesser Expansion brings the total to five: add three to two. Adding the Great Expansion brings the total to ten: add eight to two. Three and eight belong to Wood, so Wood begins to arise at the Hai hour and flourishes at the Mao hour. Looking at the River Chart, three and eight are in the east, where Li and Zhen occupy the corresponding positions: Zhen is in the third place and Li in the eighth. Kun intermingles with Li, and Li in turn intermingles with Kun; Zhen and Gen exchange places, and Gen in turn exchanges places with Zhen.

We can therefore see that the Earlier Heaven trigrams are based on the diagram: Qian in the seventh place and Dui in the second occupy firm positions; Li in the eighth place and Zhen in the third occupy yielding positions. The four images of Heaven intermix with those of Earth. Kun in the sixth place and Gen in the first occupy Yin positions; Kan in the ninth place and Xun in the fourth occupy Yang positions. The four images of Earth intermix with those of Heaven.

The Later Heaven trigrams, too, are based on the diagram. Qian and Dui are born from Yang in Heaven; Qian one and Dui nine add up to ten, so Qian occupies the first place and Dui the ninth. Li and Gen are born from Yin in Heaven; Zhen transforms into Gen, and Li seven and Gen three add up to ten, so Li occupies the seventh place and Gen the third. Kun and Zhen are born from Earth’s yieldingness; Gen transforms into Zhen, and Kun two and Zhen eight add up to ten, so Kun occupies the second place and Zhen the eighth. Kan and Xun are born from Earth’s firmness; Kan six and Xun four add up to ten, so Kan occupies the sixth place and Xun the fourth. In the Later Heaven arrangement shown in the diagram, Xun occupies the second place and Kun the fourth. This corresponds to what Shao Yong called “the eldest daughter taking the mother’s place”: Xun, the eldest daughter, takes Kun’s position as mother. The Earlier and Later Heaven trigrams and their numbers run through one another, showing that there was a purpose behind drawing the diagrams and forming the trigrams.

End of Volume One of the Outer Chapters on Diagrams and Explanations of the Images of the Changes.

“Composed by Zhang Li, style name Zhongchun, a later scholar of Qingjiang” means that Zhang Li, style name Zhongchun, a later scholar from Qingjiang, wrote the text.

Trigrams and Lines (I)

The diagram above shows the Four Images, the Eight Trigrams, and the six positions. The Commentary on the Changes says: “In ancient times, the sages created the Changes in order to…”

The diagram above illustrates the relationship between the Four Images, the Eight Trigrams, and the six positions. The “Appended Statements” says: “The sages of old created the Changes to accord with the principles of nature and life. They established Yin and Yang as the laws of Heaven, yielding and firm as the laws of Earth, and benevolence and righteousness as the laws of humanity.” Dividing Heaven, Earth, and humanity—the Three Powers—into two categories each gives rise to a hexagram of six lines. Yin and Yang lines are arranged within it, while yielding and firm lines alternate. Thus each of the six lines occupies its position, forming the hexagram image.

In the diagram, the Yin and Yang of Heaven divide into the four trigrams Qian, Dui, Li, and Zhen; the yielding and firm qualities of Earth divide into Kun, Gen, Kan, and Xun. The Two Forms, the Four Images, and the Eight Trigrams together form the six positions. Qi from above, below, left, and right meets and exchanges: Qian descends to join with Kun; Xun rises to join with Zhen; Li descends to join with Kan; and Gen rises to join with Dui. Humanity stands at the center where the Qi of Heaven and Earth converges. By observing Heaven and Earth, the Four Images, and the Qi of the Eight Trigrams, people form their bodies and receive the corresponding principles.

The human body also embodies these trigram images. The head is round and above, taking its image from Qian. The abdomen is hollow and able to contain, taking its image from Kun. The legs and arms can move, taking their images from Zhen and Xun. Li corresponds to the eyes and governs sight; Kan corresponds to the ears, which are skilled at hearing sounds; Dui corresponds to the mouth, which can speak; and Gen corresponds to the nose, which remains still. The eyes and mouth belong to Yang and receive the Qi of Heaven, so they are active. The ears and nose belong to Yin and receive the Qi of Earth, so they are still. This is what is meant by receiving a particular kind of Qi and thereby forming a corresponding bodily shape.

Wisdom follows the Yang quality of Heaven and corresponds to Kan in the trigram images, because water symbolizes wisdom. Benevolence follows the Yin quality of Heaven and corresponds to Gen, because mountains symbolize benevolence. Ritual propriety follows the yielding quality of Earth and corresponds to Li, because fire symbolizes ritual propriety. Righteousness follows the firm quality of Earth and corresponds to Dui, because metal symbolizes righteousness. This is what is meant by receiving the corresponding principles and thereby forming a corresponding nature.

Since people possess these bodily forms and principles, they naturally have desires as well: the eyes crave colors, the ears crave sounds, the mouth craves flavors, the nose craves scents, and the limbs crave ease. When desires arise and emotions take over, likes and dislikes come into conflict, and good or ill fortune follows.

The sages created the Changes in accord with the principles of nature and life, teaching people to strengthen their De (virtue) and broaden their endeavors. They looked up to observe the movements of the sun, moon, and stars, and the changes of cold and heat, day and night. They looked down to examine the forms of mountains, rivers, and plants, and the transformations of water, fire, earth, and stone. Rain and dew, wind and thunder, and moving currents of Qi interweave in great variety; living creatures and all things take shape, while the things between Heaven and Earth move up and down, sometimes flowing freely and sometimes becoming obstructed. The sages used the “Five Cycles”—principles for governing and recording the seasons and calendar—to bring these into harmony, and the “Five Matters”—five principles for self-cultivation and governance—to set them right. The Changes, the Documents, the Odes, the Spring and Autumn Annals, the Rites, the Music, and other classics were all used by the sages to connect the Dao of Heaven and Earth and assist the transformation and nurturing of all things.

Hexagrams and Their Lines, Chapter Two

Above is the diagram of the “Four Images, Eight Trigrams, and Six Periods.”

The changes in the qi of the four seasons arise together from the opening and closing of Qian and Kun, movement and stillness, the waxing and waning of Yin and Yang, and their rising and descending. At the winter solstice, Yin reaches its extreme and Yang begins to emerge; at the summer solstice, Yang reaches its extreme and Yin begins to emerge. This is how Qian and Kun, and Yin and Yang, join and interact. At the autumn equinox, Yin is at the midpoint, and the Kun hexagram closes; at the spring equinox, Yang is at the midpoint, and the Qian hexagram opens. The winter and summer solstices are times when Yin and Yang unite, while the spring and autumn equinoxes are times when they separate. Compare these points with the diagram, and the underlying pattern becomes clear.

Thus, one can infer the pattern from the hexagram figures and verify it against the changes of the seasons. The period extending thirty days on either side of the winter solstice forms one section, from Minor Snow to Great Cold. The sixty days before the spring equinox form one section, from Great Cold to the spring equinox; the sixty days after it form another, from the spring equinox to Grain Buds. The period extending thirty days on either side of the summer solstice forms one section, from Grain Buds to Great Heat. The sixty days before the autumn equinox form one section, from Great Heat to the autumn equinox; the sixty days after it form another, from the autumn equinox to Minor Snow. The six sections together amount to 360 days.

Among the outer trigrams, Xun represents warmth, Qian heat, Zhen freezing cold, and Kun severe cold. These are the normal seasonal qi of Heaven and Earth. The four trigrams at the center—Kan, Li, Gen, and Dui—are associated respectively with rain, clear skies, warmth, cold, and wind. They represent the shifting qi that circulates through the seasons of Heaven and Earth. This circulating qi changes in complex ways and is often uneven. When the five kinds of weather—rain, clear skies, warmth, cold, and wind—each occur at the proper time, the grains ripen and plants flourish, and auspicious signs appear in response. When the weather is excessive or deficient, the grains fail to ripen and signs of calamity emerge.

Only when a sage occupies the throne and brings the affairs of Heaven, Earth, and humanity into harmonious balance can he secure the myriad things and nourish the people. In this way, the Five Affairs—the principles to be cultivated in governing—are put in order. Heaven and humanity then respond to one another, and the first signs of their response appear in subtle ways.

The Inner Canon says: Responding to the Qi of Heaven means moving without cease. Cold, heat, dryness, dampness, wind, and fire are the Yin-Yang Qi of Heaven; the human body responds upward to them through the three Yin and three Yang categories, which classify the meridians and the Qi transformations of the organs and viscera. Responding to the Qi of Earth means remaining still in a fixed place; the human body responds downward to it through the five organs and six viscera.

The Five Movements—Wood, Fire, Earth, Metal, and Water—circulate, with variations of excess and deficiency. The Six Qi—wind, cold, heat, dampness, dryness, and fire—rise and descend, undergoing changes described as reversal, compliance, dominance, and counteraction. “Remaining still and holding to one’s place” refers to the dominant Qi that governs the seasons in each year at fixed times; that is, the Qi of Earth. The text goes on to say, “One day is the Qi of Earth; another name for it is the original Qi.” This phrase repeats what came before, and its meaning is not entirely clear.

Each Qi governs a period of sixty days and eighty-seven and a half ke. From Great Cold to the Spring Equinox, Jueyin, one of the Yin categories, governs. It belongs to Wind-Wood and is the first Qi; wind prevails, and all things begin to grow. From the Spring Equinox to Lesser Fullness, Shaoyin governs. It belongs to sovereign Fire, a term for the Qi transformation of Heart Fire, and is the second Qi. The text below is omitted.

Hexagram and Line Texts, Three

The diagram above shows the Four Images, Eight Trigrams, and Six Bodies.

The Book of Changes says, “Once Heaven and Earth are set apart, the principles governing the changes of the Yi are established within them.” Applied to the human body, this means that people receive the Qi of Heaven and Earth, Yin-Yang, and the Five Phases, and from it take shape. In general, the human body corresponds to Heaven and Earth.

In this diagram, the back is Yang and the abdomen is Yin. The head is round, symbolizing the odd numbers associated with Yang; the body’s openings belong to Yin, symbolizing the even numbers associated with Yin. The upper half of the body corresponds to Heaven, and the lower half to Earth. The Governing Vessel, the Yang channel along the back, begins at the Shuyu point at the lower extremity, travels upward along the spine to the Fengfu point, and then enters the brain. The Thoroughfare Vessel, an important channel associated with Yin, begins at the Qichong point and rises alongside the Foot Shaoyin channel, passing beside the navel before spreading through the chest. Thus, on the right side of the diagram, the line from the middle line of the Xun trigram to the top line of the Qian trigram represents the Governing Vessel’s course from the body to the crown of the head. The line from the middle line of the Zhen trigram to the bottom line of the Kun trigram represents the Thoroughfare Vessel’s course from the chest to the lower abdomen.

The Inner Classic says that the back belongs to Yang. Yang within Yang is the heart, which corresponds to the Li trigram and Fire; Yin within Yang is the lungs, which correspond to the Dui trigram and Metal. Since the heart and lungs are located in the upper body, they correspond to Li and Dui. The abdomen belongs to Yin. Yin within Yin is the kidneys, which correspond to the Kan trigram and Water; Yang within Yin is the liver, which corresponds to the Gen trigram. Gen is also opposite to and paired with the Zhen trigram, symbolizing the Wood of the liver. Since the kidneys and liver are located in the lower body, they correspond to Kan and Gen. The spleen lies at the center of the body and is called the “central province”; it is the most Yin within Yin. The internal organs and their outer counterparts are connected and resonate with one another, so they too correspond to the changes of Yin and Yang between Heaven and Earth.

The Three Burners, the upper, middle, and lower functional regions described in Chinese medicine, have names but no fixed physical form. They extend throughout the body and regulate its Qi. The Scripture of the Numinous Pivot says: the upper burner is like mist, irrigating the channels; the middle burner is like bubbling and fermenting, digesting food and drink; the lower burner is like a drainage ditch, directing fluids into the bladder and storing them there.

If people preserve life by following the Five Qis, care for the body by harmonizing the five flavors, safeguard their Virtue by understanding the five qualities of human nature, and practice the Dao by following the five constants, they can take part in Heaven and Earth’s transforming and nurturing work, allowing all things to find their proper place. This is called “treading one’s form”: fully realizing the nature carried by one’s bodily form. Hence it is said that human beings are exceptional creatures, formed from the Virtue of Heaven and Earth, the union of Yin and Yang, the gathering of spirits and ghosts, and the condensed vital essences of the Five Phases.

Cheng Yi said that people often devote themselves to investigating the principles of the myriad phenomena of Heaven and Earth, yet do not know to turn their attention inward. They fail to understand the conditions of their own five viscera and six bowels, hair, tendons, and bones. Those who truly know how to learn should begin with themselves. To understand Heaven and Earth by observing one’s own body: this is the principle set out here.

The climatic influences of summer heat, warmth, and dryness reach upward to Heaven and belong to Fire. Those of dampness, cold, and wind reach downward to Earth and belong to Water. Summer heat is a manifestation of flourishing Yang Qi and corresponds to the Qian trigram. Qian symbolizes bright red, the color of Fire. Warmth arises through the transformation of Fire Qi and corresponds to the Li trigram. Dryness arises through the transformation of Yang Qi and corresponds to the Zhen trigram. Zhen symbolizes rupture and dryness, expressing the formation of dry Qi. Dampness is a manifestation of flourishing Yin Qi and corresponds to the Kun trigram. Cold arises through the transformation of Water Qi and corresponds to the Kan trigram. Wind arises through the transformation of Yin Qi and corresponds to the Xun trigram.

The heart, lungs, and pericardium (the organ that encloses and protects the heart) are located in the upper body and belong to the hand meridians. From the hour of Wu to the hour of Hai, the six Yin influences arise in the upper body and travel downward along the meridians. The liver, spleen, and kidneys are located in the lower body and belong to the foot meridians. From the hour of Zi to the hour of Si, the six Yang influences arise in the lower body and travel upward along the meridians. To examine the upper body, one observes the body’s exterior; a floating pulse reveals Qi. To examine the lower body, one observes the interior; a deep pulse reveals blood. From this, one can understand the essentials of pulse diagnosis.

Cold, summer heat, dryness, dampness, wind, and fire are the six climatic influences of Heaven. Pungent, sweet, salty, bland, sour, and bitter are the six flavors of the things produced by Earth. The hands and feet each have three Yin and three Yang channels, making up the body’s six meridians. People are born by receiving the balanced Qi of Heaven and Earth, and take shape through the generating and transforming activity of the Five Phases. Yin and Yang, hardness and softness, converge within a single body, enabling people to connect Heaven and Earth and become one of the Three Powers.

The Qi of life has its root within the body. Its function of sustaining life and governing change is called the “spirit mechanism.” When the six climatic influences remain balanced outside the body and the six flavors nourish it within, regular daily routines and moderation in eating and drinking help keep the body in harmony. When a person’s spirit and Qi are settled, the vital functions operate normally, and the body remains healthy and rarely falls ill. But if emotions are stirred by external gains and losses, depleting the body’s Jing and Qi, the six influences and six flavors can throw the body into disorder, bringing on illness.

Cold and dampness belong to Yin. Cold pathogens injure nutritive Qi, and illness often affects the lower body, so the meridians of the feet are affected first. Heat and fire belong to Yang. Heat pathogens injure the body’s Qi, and illness often affects the upper body, so the meridians of the hands are affected first. Wind is Yang within Yin: it moves readily and changes quickly. When wind becomes excessive, it can affect the liver, which governs the sinews; tight sinews and spasms of the hands and feet are therefore often associated with wind pathogens. Dryness is Yin within Yang: it readily contracts and desiccates things. When dryness becomes excessive, it can affect the lungs, which govern the skin and body hair; dry, rough, and cracked skin is therefore often associated with dryness pathogens.

Different pathogens can be treated with corresponding flavors. The general principles of treatment are these: for illness in the upper body, use emetic methods; for illness in the lower body, use purgative methods; for illness in the middle body, use harmonizing methods. Tonify deficiency and drain excess. When an illness is neither deficient nor excessive, treat it according to the corresponding meridian. These are only broad outlines; the detailed teachings are fully set out in the Yellow Emperor’s medical writings. They are recorded here to show that the principles of the Yi extend everywhere.

Hexagram and Line Texts, Five

The above is the “Diagram of the Four Images, Eight Trigrams, and Six Meridians.”

In the Han dynasty, Yi Feng heard his teacher say: “Heaven and Earth have each been set in their proper place; the sun and moon are hung in the sky, the stars are arrayed, Yin and Yang are distinguished, the four seasons established, and the Five Phases—Wood, Fire, Earth, Metal, and Water—set in order. Through these, the Way known to the sages is made manifest. This is called the Dao (the Way).

“When sages see the Dao, they understand the principles for governing the world. So they divided the land into provinces, established the relations between ruler and minister, set musical pitch and the calendar, and explained success and failure, gain and loss. In this way, they presented these teachings to the worthy. This is called the Jing (scriptures and classics). Those who understand the classics can then grasp the principles of how to conduct themselves in the world. These classics are the Book of Songs, the Book of Documents, the Book of Changes, the Spring and Autumn Annals, the Book of Rites, and the Book of Music.

“So the sages composed the Book of Music to symbolize Heaven and established the rites to accord with Earth. Music has its source in Yang, and ritual has its source in Yin; ritual and music are like the Yin and Yang of Heaven. The Book of Changes, the Book of Documents, the Book of Songs, and the Spring and Autumn Annals correspond to the four seasons. When the seasons move in harmony and the four teachings are put into practice in the state, the system of ritual and music can flourish.”

Shaozi (Shao Yong) said: “The Book of Changes arose in the age of the Three Sovereigns and corresponds to spring; the Book of Documents arose in the age of the Five Emperors and corresponds to summer; the Book of Songs arose in the age of the Three Kings and corresponds to autumn; the Spring and Autumn Annals arose in the age of the Five Hegemons and corresponds to winter.”

I once heard Master Du Qingbi say: “The Book of Changes reveals the foundations of ritual and music; the Book of Documents records the institutions of their flourishing; the Book of Songs carries through their transformations; and the Spring and Autumn Annals seeks to rescue a world in which ritual has collapsed and music has fallen into disarray. Once the principles of the Six Classics are understood, the ways of Heaven and humanity are both fully present.

“Thus, the Book of Changes explains Yin and Yang; the Book of Documents clarifies affairs of government; the Book of Songs gives voice to nature and feeling; and the Spring and Autumn Annals draws a solemn distinction between good and evil. Musical pitch, the calendar, divination, inquiry and verification, and calculation and inference all extend from the Book of Changes. Rhapsodies, panegyrics, encomia, ballads, and remonstrances flow from the Book of Songs. Edicts, proclamations, memorials, formal submissions, treatises, and discussions continue the work of the Book of Documents. Biographies, records, tables, and inscriptions are genres derived from the Spring and Autumn Annals. Though dynasties have risen and fallen and gifted people have appeared in every age, no kind of writing has gone beyond the scope of these four classics.

“Therefore, honoring ritual, valuing music, cherishing benevolence, and following righteousness are the teachings of the former kings. Defying the constant ways, altering proper principles, seeking what is hidden, and acting strangely are the harms brought by heterodox teachings. When the teachings of the Six Classics are put into practice, the dangers of heterodoxy recede.

“In the flourishing ages of the Xia, Shang, and Zhou, the Way of the sage kings shone brightly. How could there have been harm from heterodox teachings then? Later, when learning from the classics grew obscure, deviant doctrines and strange practices spread rapidly. Alas, how can students fail to devote themselves to the foundations, yet freely indulge in tangled disputes? It is truly lamentable that learning should remain unclear.”

The “Image Commentary” on the Yu hexagram says, “Thunder emerges from within the earth, shaking all things: this is Yu.” Thus the sage kings of antiquity created music to make their virtue manifest, and made grand offerings to the Lord on High, with their ancestors sharing in the sacrifice. Once a ruler had completed his achievements and brought order to the state, established its guiding principles and laws, and brought harmony among the people, he would compose music. Its purpose was to spread the customs of the eight directions, in keeping with the varied climates and generative Qi of Heaven and Earth.

The winds of the eight directions correspond respectively to the Eight Trigrams and the seasonal nodes. The Beginning of Spring corresponds to Gen and the Tiao wind, also called the Rong wind; the Spring Equinox to Zhen and the Ming Shu wind, also called the Gu wind; the Beginning of Summer to Xun and the Qingming wind; the Summer Solstice to Li and the Jing wind, also called the Kai wind; the Beginning of Autumn to Kun and the Liang wind; the Autumn Equinox to Dui and the Changhe wind; the Beginning of Winter to Qian and the Buzhou wind; and the Winter Solstice to Kan and the Guangmo wind. Music follows these patterns to express the different dispositions of the myriad things. When the Qi of Heaven and Earth respond to one another, wind takes shape. As Yin and Yang harmonize, all things undergo corresponding changes, each in its proper time.

To establish the pitches, one first sets the central pitch as the foundation, then applies the principles of generation, diminution, and increase in sequence until all twelve pitch standards are complete. In this way, the principle of the “Three Unities” is expressed. Heaven opens at the hour of Zi, which belongs to the Heavenly Unity. Yang Qi gathers to form Heaven; the yang numbers begin with one and reach their limit at nine, so the Yellow Bell pitch pipe is nine inches long. The Yellow Bell is diminished by one part and generates downward, producing the Lin Bell at the position of Wei, opposite Chou. Earth opens at the hour of Chou, which belongs to the Earthly Unity. Yin Qi gathers to form Earth; the yin numbers begin with two, and six is their central number, so the Lin Bell pitch pipe is six inches long. The Lin Bell is increased by one part and generates upward, producing the Great Bush at the position of Yin.

Humanity is born at Yin, which belongs to the Human Unity. Human beings stand where Yin and Yang meet, participate in the number three, and accord with eight; therefore the Great Bush pitch pipe is eight inches long. Eight also symbolizes Fuxi’s drawing of the Eight Trigrams, through which he aligned himself with Heaven and Earth and communicated with the spirits. The Three Unities of Heaven, Earth, and humanity connect with one another, while the three kinds of calendrical year beginnings take turns being used. The yang and yin pitch standards combine according to their generative sequence; the six yang pitches and six yin pitches govern the twelve zodiacal positions, revolving through the modes with inexhaustible significance.

The Rites of Zhou records that the Grand Music Master was in charge of the six yang pitches and the six yin pitches, using them to harmonize the sounds of Yin and Yang. The Yellow Bell, Great Bush, Washing Vessel, Flowering Guest, Worn Robe, and Without Excess are yang sounds; the Great Lü, Responding Bell, Southern Lü, Lin Bell, Lesser Lü, and Lesser Bush are yin sounds. The Sun and Moon join in the twelve stations and move to the right; the sages established the six yin pitches to symbolize this movement. The handle of the Dipper passes through the twelve zodiacal positions and turns to the left; the sages established the six yang pitches to symbolize it. The six yang pitches turn left to accord with Yin, while the six yin pitches turn right to accord with Yang. Pitch standards occupying the same position symbolize husband and wife; those in different positions symbolize mother and child. The six yang pitches derive from the line images of the Qian hexagram, while the six yin pitches derive from those of the Kun hexagram. The six yang pitches turn left and generate the six yin pitches; when they occupy the same position, they pair as husband and wife. The six yin pitches turn right and generate the six yang pitches; because they occupy different positions, they pair as mother and child. The derivation of pitches also takes its images from the Eight Trigrams and the Three Powers.

Yang Qi moves from Zi to Si, growing strong, and its pitch pipes are longer. Yin Qi moves from Wu to Hai, gradually increasing, and its pitch pipes are shorter. These differences in length distinguish the five notes: a longer pipe produces a lower sound, while a shorter pipe produces a higher one. Low sounds are weighty and unhurried; high sounds are light and clear, and move quickly.

The palace note is like a ruler: it occupies the center, governs the four directions, and initiates and leads the other four notes. Thus the palace note is the guiding principle of the five notes. The commerce note is firm and weighty, its sound descending from a higher register and returning to the center. The wood note is rounded, sustained, clear, and balanced. The fire note rises and falls with fluidity, ascending from below and returning to the proper center. The water note is fine and high, distant and pure.

An ancient text says that hearing the palace note makes people gentle and at ease, with open hearts; hearing the commerce note makes them upright and principled, and fond of what is right; hearing the wood note awakens compassion and care for others; hearing the fire note makes them glad to do good and willing to give; and hearing the water note makes them disciplined in their conduct and fond of ritual. The five notes also symbolize ruler, minister, people, affairs, and things. The palace note acts through Wuwei (non-action) and shelters all things, so it symbolizes the ruler. The commerce note acts and connects all things, so it symbolizes ministers. The wood note readily sets things in motion and is difficult to restrain, so it symbolizes the people. The fire note makes the invisible show its signs, so it symbolizes affairs. The water note expands and contracts in keeping with the seasons, so it symbolizes things. In this order, the ruler governs ministers, ministers administer the people, the people advance affairs, affairs bring things to completion, and things ultimately serve human use.

The principles of the five notes are grounded in the Five Phases—Metal, Wood, Water, Fire, and Earth. They are tested with five tools: the compass, the square, the steelyard weight, the balance, and the measuring line. They follow five standards of conduct: appearance, speech, sight, hearing, and thought. They are performed on eight kinds of instruments: metal, stone, silk, bamboo, gourd, earth, hide, and wood. And they are linked through the Eight Trigrams. In this way, the workings of Heaven, the transformation of Earth, and the guiding principles of human affairs are all made complete.

The Yellow Bell pitch pipe also serves as the standard for measures of length, capacity, and weight. For length, ten fen make one cun, and ten cun make one chi; these units are then converted in sequence into zhang and yin, making the five measures—fen, cun, chi, zhang, and yin—precise. For capacity, the Yellow Bell pipe is nine inches long and holds 1,200 millet grains. This quantity is called one yue. Ten yue make one ge, ten ge make one sheng, ten sheng make one dou, and ten dou make one hu, establishing consistent standards for the five measures of capacity: yue, ge, sheng, dou, and hu. For weight, the 1,200 millet grains held by the Yellow Bell pipe weigh twelve zhu. Two yue equal twenty-four zhu, or one liang. Sixteen liang make one jin; 384 zhu also correspond to the 384 lines of the sixty-four hexagrams. Thirty jin make one jun, and four jun make one shi. These standards—zhu, liang, jin, jun, and shi—make it possible to measure weight.

Thus the pitch standards accord with Heaven and Earth and have their roots in Yin and Yang; they also correspond to human relationships and arise from human nature and feeling. When the people are transformed through virtue and their hearts moved by music, they can be brought into harmony, and the whole world can be guided and settled. The Book of Music says that people receive the balanced Qi of Heaven and Earth at birth. They all contain the essence of the Five Phases and possess the virtues of the Five Constant Virtues. To educate the people is simply to use the harmonious five notes to awaken the nature of the Five Constant Virtues: hearing the palace note can awaken sincerity; hearing the fire note can awaken reverence; hearing the commerce note can awaken discernment between shame and wrongdoing, thereby fulfilling righteousness; hearing the water note can awaken discernment between right and wrong, thereby fulfilling wisdom; and hearing the wood note can awaken compassion, thereby fulfilling benevolence. When music is put into practice, human relationships become clear. People’s ears and eyes grow more perceptive, and their bodies, minds, Qi, and blood become more balanced. Customs are transformed, and the world can then be at peace.

The diagram shows the correspondences between the Four Images, the Eight Trigrams, and the six ministries.

The six ministries in the Rites of Zhou correspond to Heaven and Earth and the four seasons. Their officials numbered 360, symbolizing the 360 days of the year and corresponding to the 360 degrees of the celestial circuit. The Book of Documents says that Tang Yao and Yu Shun examined ancient institutions and established about a hundred official posts. At the center were the Chief Minister and the Four Peaks; in the regions were provincial governors and lords.

Tradition holds that, beginning in the time of Zhuanxu, Chong of the Southern Corrector was appointed to oversee affairs of Heaven, and Li of the Northern Corrector to oversee affairs of Earth. Together, they were called Xihe. Tang Yao continued this system, instructing Xihe to reverently follow Vast Heaven, carefully determine and announce the seasons for farming, and resume their former posts to manage the affairs of Heaven and Earth. Later, Xi Zhong, Xi Shu, He Zhong, and He Shu were separately appointed to preside over the four seasons and perform the duties of the six ministers.

After Shun served as Chief Minister, he renamed the Minister of Earth as Minister of Instruction, the Minister of Autumn as Minister of Justice, the Minister of Winter as Minister of Works, and the Minister of Spring as Director of Ceremonies. Under the Yin dynasty, the Son of Heaven established five ministries, and offices such as Minister of War and Minister of Justice also came into use. King Cheng of Zhou drew on Yin institutions to compile the Rites of Zhou, dividing official posts into six systems governing Heaven and Earth and the four seasons. The Minister of Heaven, the Grand Steward, oversaw state affairs, led the officials, and governed the four regions. The Minister of Earth, the Minister of Instruction, oversaw education, promoted the Five Constant Virtues, and cared for the people. The Minister of Spring, the Director of Ceremonies, oversaw ritual and harmonized relations among spirits, people, and those of higher and lower rank. The Minister of Summer, the Minister of War, oversaw military affairs, commanded the armies, and kept the feudal states at peace. The Minister of Autumn, the Minister of Justice, oversaw penal prohibitions and punished wrongdoing and rebellion. The Minister of Winter, the Minister of Works, oversaw land and construction, enabled the people to live in security, and developed the land’s resources in keeping with the seasons. Each of the six ministers had distinct responsibilities and led the officials under them, so that the people could prosper and the affairs of the state could be properly managed.

The Zhou also established the Grand Preceptor, Grand Tutor, and Grand Guardian, collectively called the Three Dukes. They deliberated on the principles of governance, administered the state, and harmonized Yin-Yang. The Junior Preceptor, Junior Tutor, and Junior Guardian were collectively called the Three Assistants. They helped the Three Dukes promote education and reverently aid Heaven and Earth. These posts were not named after any particular task; their purpose was to embody the principles of Heaven and Earth, Yin-Yang, and the passage of the seasons.

After the Zhou declined, the system of official posts fell into disorder, and the various duties of government gradually lapsed. During the Warring States period, the feudal lords fought one another and each state altered the old institutions. Under the Qin, the old system was abandoned: feudal domains were abolished and commanderies established, and offices such as Chancellor, Imperial Secretary, and Grand Commandant were created. The Han and later dynasties followed the Qin system. The official structure gradually became disordered, with orders issued from many different centers and no clear chain of responsibility.

Heaven and Earth have four seasons, and the officials have six kinds of responsibility; together, these encompass the affairs of the realm. This system is like the main cord of a net or the collar of a robe: it should not be altered lightly from one generation to the next. If rulers of later ages wish to examine ancient institutions and set titles and duties in order, what source can they rely on besides the Zhouguan—that is, the Rites of Zhou?

Hexagrams and Lines VIII

The diagram above shows the “Four Symbols, Eight Trigrams, and Six Armies.”

The Commentary on the Changes says that “army” means a large group of people. When a group grows, its members need to be organized into units, hence such terms as squad, platoon, company, battalion, army corps, and army. The Son of Heaven commanded six armies, while a great state maintained three. The ways armies were arranged and maneuvered largely took their models from the images of the Changes.

During the Han dynasty, the chancellor Zhuge Wuhou (Zhuge Liang) mastered these principles and developed them further into the Eight Formations. Heaven, Earth, Wind, and Cloud represent the four directional positions among the Later Heaven Eight Trigrams; Dragon, Tiger, Crow, and Snake correspond to the four cardinal directions. Regular formations establish the basic layout, while extraordinary troops respond to changing circumstances. Extraordinary and regular forces transform into one another, and the formation’s front and rear support each other. When arranged in a circle, its ranks connect like the spokes of a wheel; when squared, they are as orderly as a chessboard. It can conceal itself deep from view, as though lying beneath the nine layers of Earth, or strike swiftly, as though moving above the nine heights of Heaven. It circulates without obstruction. It moves freely like water, yet stands firm and unshaken like a mountain. Its strength and decisiveness embody the meaning of Dui Metal; its stern authority, resolve, and strict discipline express the nature of Li Fire. Its sudden movement is like thunder, its surging force; its dense, rapid maneuvers are like wind, its speed of deployment. These eight formations are all available to a commanding general, who may employ them as circumstances require.

The Wuji Text says: four formations are regular and four are extraordinary; the commander keeps the remaining extraordinary troops in reserve for flexible use. The formation is based on the number nine: a central position is left open as a mobile reserve under the great general’s command, serving as the coordinating center for all eight directions. A formation can contain another formation, and a unit can contain another unit; the front can become the rear, and the rear can become the front. An advance must not turn into a headlong rush, and a withdrawal must not become a panicked rout. Any side of the formation can serve as its front, and any of the eight directions as its rear. It can respond where it stands to an attack from any direction; if enemy forces break into its center, reinforcements can come to the rescue from either end.

In the unit structure, five men make a squad, and five squads make a company. The formation begins with groups of five and expands to eight companies: five is the number used to organize a squad, while eight is the number by which the formation expands. A small formation has eight companies, a medium formation sixty-four, and a large formation five hundred and twelve.

Under the Zhou military system, five men made a squad, and five squads made a platoon; four platoons made a company of one hundred men. From there, each expansion multiplied the force by five: a battalion of five hundred, then an army corps of two thousand five hundred, then an army of twelve thousand five hundred. This is three successive expansions by a factor of five. In the Eight Formations, five men make a squad and five squads make a company; the number of companies then multiplies by eight at each step. A small formation has two hundred men, a medium one sixteen hundred, and a large one twelve thousand eight hundred. This is three successive expansions by a factor of eight.

Sunzi says, “Managing a large army is like managing a small unit: the key is to define its organization and chains of command clearly.” With clear levels of command, even a very large force can be deployed effectively. The mobile troops under the commander’s control respond to the eight directions. Here, “pivot” refers to the authority to coordinate from the center, like the concealed hinge of a gate: it turns at the center without revealing its movement.

Thus the Eight Formations consist of eight positions around the perimeter and one central hub, making nine in all. The great general occupies the center, with the eight directions arrayed around him. The formation’s ranks cross lengthwise and crosswise, with large formations containing smaller ones. At rest, it becomes a fortified camp; in motion, it becomes a battle formation. The Crow Formation is in the south, the Snake Formation in the north, the Dragon Formation in the east, and the Tiger Formation in the west; Heaven, Earth, Wind, and Cloud are placed at the four corners. Regular formations occupy the four cardinal directions, and extraordinary formations the four intercardinal directions. Regular and extraordinary forces transform into each other, and their variations are inexhaustible.

This concludes the middle volume of Yixiang Tushuo Waipian. The editions differ in their wording of phrases such as “ju zao” and “zhi wu.” The editor has revised the text in accordance with the editions and the usage suggested by the context.

The lower volume of Yixiang Tushuo Waipian, written by Zhang Li, a later scholar from Qingjiang, whose courtesy name was Zhongchun.

On Measures and Numbers, Part One

The diagrams above illustrate the movement of the celestial sphere, the calendar and celestial phenomena, and the seasonal nodes.

The Image Commentary on the Hexagram Ge says, “There is fire within the lake; this is Ge.” From this, the noble person orders the calendar and clarifies the seasons.

The Image Commentary on Hexagram Ge says, “Fire in the marsh: this is Ge. Thus the noble person establishes the calendar and clarifies the seasons.” The changing of the four seasons is one of the most conspicuous forms of change. Establishing a calendar and calculating its cycles means observing changes in the positions of the sun, moon, and stars, in order to clarify the sequence of the seasons. Why, then, is this explained through “fire in the marsh”?

The Discussion of the Trigrams says that Li symbolizes fire and also the sun, while Dui symbolizes a marsh and also water. Shao Yong’s Book of Supreme Principles Governing the World further takes Dui to symbolize the moon and Li to symbolize the stars. The stars may be understood as lights formed by the scattering of sunlight. In this way, the trigrams Li and Dui encompass the three celestial bodies: sun, moon, and stars.

Another Image Commentary says, “Water and fire bring one another to an end.” Water symbolizes the moon, and fire symbolizes the sun; their alternating courses produce light. Water symbolizes cold, and fire symbolizes heat; the alternation of cold and heat forms the year. Nothing in the heavens shines more brightly than the sun and moon. Heaven displays celestial signs, and the sages observe and take them as their model.

When observing the courses of the sun and moon over the year, the places where they meet are called “chen,” of which there are twelve. Calendars have often changed over the generations. Here, following the Shoushi Calendar, the twelve places where the sun and moon meet are listed as follows: in the first month of spring, they meet in Xuanyiao; in the second month, in Juxu; in the third month, in Jianglou; in the first month of summer, in Daliang; in the second month, in Shishen; in the third month, in Chounshou; in the first month of autumn, in Chounhuo; in the second month, in Chounwei; in the third month, in Shouxing; in the first month of winter, in Dahuo; in the second month, in Ximu; and in the third month, in Xingji.

According to the Monthly Ordinances, in the first month of spring the sun is in Ying Shi, and the earthly branch indicated by the handle of the Big Dipper is Yin; Yin therefore corresponds with Hai. In the second month of spring, the sun is in Jianglou and the handle points to Mao; Mao therefore corresponds with Xu. The remaining months follow the same pattern. Today, the positions along the courses of the sun and moon have shifted, and the earthly branches indicated by the Dipper’s handle no longer correspond to these directions. If one still observes the seasonal nodes and establishes musical pitches according to ancient methods, those methods may no longer apply fully.

The regions of the sky through which the sun and moon pass are called “lodges.” There are twenty-eight lodges, also known as the Twenty-Eight Mansions. The seven mansions of the Azure Dragon in the east are Jiao, Kang, Di, Fang, Xin, Wei, and Ji; the seven mansions of the Black Tortoise in the north are Dou, Niu, Nü, Xu, Wei, Shi, and Bi; the seven mansions of the White Tiger in the west are Kui, Lou, Wei, Mao, Bi, Zui, and Shen; and the seven mansions of the Vermilion Bird in the south are Jing, Gui, Liu, Xing, Zhang, Yi, and Zhen.

The positions of the sun and moon as they pass through the sky are measured in “degrees.” One circuit of the heavens is about 365 and one-quarter degrees. The sky has no divisions of its own; people divide it into degrees by following the sun’s path. The twenty-eight mansions each cover a different number of degrees, also in relation to the sun’s position in the sky: the seven eastern mansions cover seventy-five degrees, the seven northern mansions ninety-eight, the seven western mansions eighty, and the seven southern mansions one hundred and twelve, totaling 365 degrees.

By following changes in the celestial signs, one can divide the year into four seasons, determine the eight seasonal nodes, and arrange the twelve months; these can then be further divided into the twenty-four solar terms and seventy-two pentads. With 365 and one-quarter days as a complete cycle, the year is brought to its full measure.

The Changes encompasses the transformations of Heaven and Earth without exceeding their bounds. It aligns the Four Images with the four seasons: Lesser Yang with spring, Greater Yang with summer, Lesser Yin with autumn, and Greater Yin with winter. It aligns the Eight Trigrams with the eight seasonal nodes: the Start of Spring with Gen, the Spring Equinox with Zhen, the Start of Summer with Xun, the Summer Solstice with Li, the Start of Autumn with Kun, the Autumn Equinox with Dui, the Start of Winter with Qian, and the Winter Solstice with Kan.

The twelve sovereign hexagrams, which correspond to the twelve months according to the waxing and waning of Yin and Yang, align with the twelve chen: Fu corresponds to the eleventh month, Lin to the twelfth month, Tai to the first month, Dazhuang to the second month, Guai to the third month, Qian to the fourth month, Gou to the fifth month, Dun to the sixth month, Pi to the seventh month, Guan to the eighth month, Bo to the ninth month, and Kun to the tenth month.

The twenty-four lines of the Eight Trigrams correspond to the twenty-four solar terms; the seventy-two lines of the twelve sovereign hexagrams correspond to the seventy-two pentads; the twenty-eight hexagrams formed by reversing hexagrams correspond to the twenty-eight mansions; and the 384 lines of the sixty-four hexagrams correspond to the days of the year and accord with the 365 degrees of the circuit of the heavens.

Therefore, when establishing a calendar, one begins calculations at the start of the year, adjusts the positions of the sun and moon and the seasonal markers midway through the year, and calculates the remainder at year’s end. The solar terms, the new moons (the first day of each month), and the gains and losses in the calendar’s count of days are then calculated together, and from this the intercalary month arises.

The Commentary on the Changes says that the movements of the sun and moon bring winter’s cold and summer’s heat. The Great Plan says that a calendar arranging their movements must first establish the beginning of the year, then correct the midpoint of the year, and finally calculate the remaining days at year’s end. By aligning these calculations with the solar terms, the new moons (the first day of each month), and the waxing and waning of the moon, one can determine when to insert leap months.

At the winter solstice, the sun travels through the northern part of the sky, bringing cold weather; at the summer solstice, it travels through the southern part, bringing heat. In spring and autumn, the sun passes through the western and eastern parts of the sky respectively. Day and night are then equal, and the climate is milder. Fengxiangshi, the official responsible for observing celestial phenomena and establishing the calendar, therefore measured the sun’s position in winter and summer and observed the moon in spring and autumn to determine the boundaries of the seasons.

To measure the sun, an eight-foot gnomon was set upright on the ground, and the length of its shadow was measured in different directions. The scripture also divides the paths along which the sun and moon travel into the Yellow Path—the sun’s apparent annual path—and the moon’s paths, known as the Blue, White, Red, and Black Paths. In different seasons the moon sometimes deviates from the Yellow Path and follows these other routes. The ancients believed that when the sun and moon followed the Yellow Path, they were proceeding correctly. A deviation from a yang path might portend drought, while a deviation from a yin path might portend rain.

Zheng Kangcheng said that at the spring equinox the sun is in the Lou mansion, and at the autumn equinox it is in the Jiao mansion; at the moon’s first and last quarter, it passes through mansions such as Qianniu and Dongjing. By observing the shadows and positions of the sun and moon, the ancients could tell whether a solar term had arrived. The Account of Divinatory Signs also says that one need not observe the solar terms associated with the Eight Trigrams only when the moon is full: around the eighth day of the month, one can observe the first-quarter moon, and near the end of the month, the last-quarter moon. This suggests that the moon’s position could also be used to identify the solar terms. For example, according to the ancient positions of the lunar mansions, at the spring equinox the first-quarter moon was in Dongjing and the last-quarter moon in Qianniu; at the autumn equinox, the positions were reversed. Because of the precession of the equinoxes—the slow change in celestial positions over time—the mansions associated with the spring and autumn equinoxes today differ from those in the ancient account. The mansions through which the first- and last-quarter moons pass have changed as well.

The following section lists the sun’s position at each solar term of the year, along with the times of sunrise and sunset recorded in the Shoushi Calendar. At the winter solstice, the sun is at the eighth degree of the Ji mansion, and sunrise is later while sunset is earlier. As the seasons progress, sunrise gradually comes earlier and sunset later. Daylight is longest at the summer solstice, after which the days gradually shorten. At the autumn equinox, day and night are equal once more; as winter sets in, the nights grow longer. The text also specifies the sun’s mansion and the times of sunrise and sunset for each of the other solar terms, illustrating the changing lengths of day and night throughout the year.

The Qi of Heaven and Earth flows through the six directions: above, below, and the four quarters. The sun travels westward as the moon comes from the east; cold recedes as heat arrives. The circular and square diagrams shown earlier are based on the Eight Trigrams. The trigrams interweave and move in both forward and reverse directions, depicting Yin and Yang as they push and yield to each other, advancing and retreating. Yang corresponds to daylight, warmth, and heat; yin corresponds to darkness, cold, and frost. The alternation of day and night allows all things to grow, while the succession of cold and heat forms the four seasons. Five days make one pentad, three pentads make one solar period, six solar periods make one season, and four seasons make one year. The year has twenty-four solar terms, so the twenty-four lines of the Eight Trigrams each correspond to one term. The lower trigram is called “zhen,” and the upper trigram “hui.” The first and fourth lines, the second and fifth lines, and the third and top lines correspond to one another.

The winter solstice begins with the first nine in the Fu hexagram: Zhen is below and Kun above, symbolizing one yang beginning to emerge beneath the depths of yin. The author uses the proportions of yin and yang to explain the changing solar terms: around the winter solstice, yin is strong and yang weak, the nights are long and the days short, and the cold reaches its height. During Minor Cold and Major Cold, yin cold grows more intense, but the first signs of spring are also beginning to gather.

The Beginning of Spring begins with the first nine in the Bi hexagram. Yang Qi gradually increases and the weather warms; Rain Water and the Waking of Insects follow. The spring equinox corresponds to the Jie hexagram, when yin and yang are balanced, the weather is mild, and day and night are equal. During Clear and Bright and Grain Rain, warmth accumulates and the Qi of summer begins to appear.

The Beginning of Summer begins with the first nine in the Small Accumulation hexagram. Yang Qi gradually grows stronger and the weather turns hot; during Grain Buds and Grain in Ear, the summer heat intensifies. The summer solstice corresponds to the first six in the Gou hexagram, symbolizing one yin first emerging beneath flourishing yang Qi. Daylight is longest and the weather hottest at this time. During Minor Heat and Major Heat, the heat builds, and the Qi of autumn begins to stir.

The Beginning of Autumn begins with the first six in the Kun hexagram. Yin Qi gradually increases and the weather turns cool; End of Heat and White Dew follow. The autumn equinox corresponds to the Lü hexagram, when yin and yang are balanced once more, day and night are equal, and the weather is cool and clear. During Cold Dew and Frost’s Descent, the chill deepens and the Qi of winter begins to appear.

The Beginning of Winter begins with the first six in the Yu hexagram. Yin Qi gradually strengthens and the weather turns cold. During Minor Snow and Major Snow, yin reaches its height, and one yang is born again below. This cycle repeats without end, like a ring with no beginning or end. The Eight Trigrams interweave: one “zhen hexagram” combines with eight “hui hexagrams” to form the sixty-four hexagrams. The sixty-four hexagrams circulate and change in the circular diagram, representing the cycles of celestial movement.

Fu, Gou, Jie, Lü, Bi, Xiao Xu, Kun, and Yu are all “first-generation hexagrams” in the eight-palace system of hexagram transformation—that is, hexagrams formed by changing the first line of the hexagram in their original palace. Fu and Gou correspond to the Winter Solstice and Summer Solstice, respectively, and arise from changing the first line of Qian and Kun. Jie and Lü correspond to the Spring Equinox and Autumn Equinox, and arise from changing the first line of Kan and Li. Bi corresponds to the Beginning of Spring and arises from changing the first line of Gen; Xiao Xu corresponds to the Beginning of Summer and arises from changing the first line of Xun; Kun corresponds to the Beginning of Autumn and arises from changing the first line of Dui; and Yu corresponds to the Beginning of Winter and arises from changing the first line of Zhen.

The Winter Solstice, Summer Solstice, Spring Equinox, and Autumn Equinox correspond to Qian, Kun, Kan, and Li. These are the four cardinal hexagrams, whose directions are fixed and do not change. The beginnings of spring, summer, autumn, and winter correspond to Gen, Xun, Dui, and Zhen. These are the four corner hexagrams, whose directions shift relative to one another. These eight hexagrams share another feature: the first and fourth lines correspond in Yin-Yang, while the second and fifth lines, and the third and sixth lines, do not. Thus, although the year has twenty-four solar terms, only eight hexagrams can serve as markers for them.

Degree Two

The diagram above covers an area of ten thousand li in every direction and shows the division of territories among feudal lords.

The Image Commentary on the Bi Hexagram says, “There is water upon the earth: this is the Bi Hexagram.” The early kings took this as a model when establishing the many states and drawing the feudal lords near. To be a king meant dividing and governing the territories of the realm, enfeoffing lords to establish states, and having them guard and remain close to the royal house, so that all under Heaven would become attached to it.

The systems of the Xia and Shang dynasties can probably no longer be verified. We can now rely on the Rites of Zhou—its accounts of determining directions and selecting the site of the capital, and of laying out the capital and its fields—to diagram and arrange the system of the royal domain (the area directly ruled by the Son of Heaven, extending a thousand li in each direction), together with its districts: the xiang, sui, du, bi, dian, shao, and xian. We also mark the Nine Regions of feudal enfeoffment, arranged by distance: Hou, Dian, Nan, Cai, Wei, Yao, Yi, Zhen, and Fan. In this way, the relative distances of the various regions are shown together.

The Commentary says that in an age of great peace the realm extended ten thousand li, of which the Central Plains covered seven thousand. When society was still relatively stable, the realm, including its adjoining territories of the Yi and Di peoples, covered seven thousand li, while the Central Plains covered five thousand. In the declining age, the territory adjoining the Yi and Di covered five thousand li, while the Central Plains covered three thousand. The Commentary repeats this account elsewhere.

Thus the Mencius says that the land within the Four Seas was divided into nine regions, each a thousand li square. The fiefs of dukes and marquises were each a hundred li square; those of earls, seventy li; and those of viscounts and barons, fifty li. Land was divided into three grades. This was probably the system of the Xia and Shang, which the early Zhou continued. When the Duke of Zhou assisted King Cheng, he expanded the territory of the Nine Provinces and enlarged the fiefs of meritorious lords: a duke received five hundred li square, a marquis four hundred, an earl three hundred, a viscount two hundred, and a baron one hundred. A territory smaller than a hundred li, attached to a feudal lord, was called an “appanage”—a small state dependent on a lord.

The Rites of the King says that each province contained 210 states, and that the eight provinces together contained 1,680. These are only approximate figures.

The Rites of Zhou, in the section “Grand Minister of Education,” also says that a territory smaller than a hundred li and attached to a feudal lord was called an appanage. The Rites of the King says that each province contained 210 states, and that the eight provinces together contained 1,680. This, too, is only an approximation.

The Rites of Zhou records that the Grand Minister of Education, an official responsible for land and instruction, used a tugui, a device for measuring the sun’s shadow, to survey the land and compare the lengths of shadows in search of the center of the realm. At places farther south, the shadows were shorter and the heat more intense; farther north, the shadows were longer and the cold more severe. Farther east, evenings were often windy; farther west, mornings were often overcast. The place where the shadow measured one foot and five inches at the summer solstice was called the “center of the land.” It was regarded as the place where Heaven and Earth met, the seasons turned, wind and rain gathered, and Yin-Yang came into balance. Because all things flourished and prospered there, the royal capital was established at this site.

This passage explains how to find the “center of the land,” a place suited to establishing a capital. The ancients believed this central location had a balanced climate, with harmonious Yin-Yang, wind, and rain. They used the sun’s shadow to determine directions and distances.

The tugui, a jade measuring tool for gauging shadows and comparing distances between places, was one chi and five cun long. It was used to survey land and measure the length of the sun’s shadow. According to tradition, the Duke of Zhou identified the center of the land at Yangcheng in Yingchuan. He set up an eight-chi gnomon. Around noon on the summer solstice, if its shadow extended one chi and five cun to the north—exactly matching the tugui—the place was considered the center of the land. The gnomon there was called the “central gnomon.”

Starting from the central gnomon, another gnomon was set up one thousand li to the south. Around noon on the summer solstice, if its shadow was one chi and four cun long, one cun shorter than the tugui, this showed that the sunlight was stronger and the climate hotter there. One thousand li to the north, the shadow measured one chi and six cun, one cun longer than the tugui, indicating a colder climate. One thousand li to the east, because the place was closer to where the sun rises, a shadow pointing toward the sunset could be seen after more than half the day had passed on the summer solstice; this meant the region was windier. One thousand li to the west, because the place was farther from the sunrise, a shadow pointing toward the sunrise did not appear until more than half the day had passed; this meant the region had more overcast weather. The ancients therefore held that when cold or heat, clear or cloudy weather, and winds were too pronounced in one direction, conditions were not well balanced. Only around Yangcheng, where Yin-Yang, wind, and rain were in harmony, could a place be called the “center of the land.”

The ancients also believed that a difference of one cun in shadow length corresponded to a distance of about one thousand li. According to San Guang Kao Ling Yao, the sun, moon, and stars rose and set within a range of thirty thousand li, and the place where the shadow measured one chi and five cun was the center of the land. Half of thirty thousand li is fifteen thousand li, corresponding to the measurement made with the tugui. From this they derived the rule that a one-cun difference in shadow length meant a distance of one thousand li; the calculation method yielded the same result.

The later passage describes how to survey a site when building a capital: “The builder establishes the capital and levels the ground with suspended instruments.” This means that when constructing a city, one uses a hanging device to determine whether the ground is level. A gnomon is then erected, and the sun’s shadow is used to establish direction. The shadows at sunrise and sunset are recorded and compared with the midday shadow; at night, the North Star is observed to correct the directions and positions of east, west, north, and south, as well as the orientations of day and night.

When craftsmen build a capital city, they use suspended cords and water to determine whether the ground is level. They also use suspended cords to align the measuring rods. By observing the shadows at sunrise and sunset, they identify the east-west direction. They then compare the shadows at noon during the day and observe the North Star at night to determine the north-south direction and align the city.

The capital is planned as a square, nine li on each side, with three gates on every side. Inside the city are nine north-south roads and nine east-west roads, each wide enough for nine carts to travel abreast. The ancestral temple is placed on the left and the altar to the soil and grain gods on the right; the court is in front and the market behind. The market and the court each occupy one fu, or one hundred mu of land.

This describes how to build a capital city and determine its orientation. To measure the ground with water, posts are set at the four corners of the planned city, and the water’s surface is used as a level to measure differences in elevation. To set the rods and measure them with suspended cords, an eight-foot wooden post, called a nie, is erected. Eight cords are hung around it at corresponding points and laid against the post to check that it stands straight.

Once the post is aligned, observing the shadows at sunrise and sunset establishes the east-west direction. Comparing the shadow at noon during the day and observing the North Star at night establishes the north-south direction. In this way, the city’s orientation is aligned and its directions determined.

The capital is nine li on each side and can be divided into nine squares on a grid. The north-south roads are called “warp,” and the east-west roads “weft.” The nine roads in each direction intersect; each of the four sides has three gates, making twelve gates in all, corresponding to the twelve earthly branches. The roads in both directions must be wide enough for nine carts to travel abreast. Allowing for the space on either side of each cart, a single cart lane is about eight feet wide. Nine lanes together measure seventy-two feet, or twelve paces.

Each gate has three passageways: men use the left, women the right, and carts the middle. The ancestral temple and the altar to the soil and grain gods stand on either side of the central passageway. The ancestral temple belongs to Yang, so it is on the left; the altar belongs to Yin, so it is on the right. The three courts are where ruler and ministers conduct affairs of state. They belong to Yang and are therefore placed in front. The three markets are places for trade, profit-seeking, and the administration of punishments. They belong to Yin and are therefore placed behind. The market and the court each occupy one fu, or one hundred mu of land. This is how the capital’s layout and orientation are determined.

The Zaisi, an official responsible for dividing land and administering taxes and labor service, prescribed how land was to be allocated: within the city, land was administered by the Chen and the Li; garden plots were designated as fields and gardens; in the near suburbs, land was assigned as residential plots, farmland, and commercial plots; in the outer suburbs, it was assigned as palace land, cattle land, reward land, and pasture; in the Dian area, it was assigned as land for public towns; in the Shao area, as land for household towns; in the Xian area, as land for small capitals; and in the Hua area, as land for great capitals.

The above describes the system of villages, districts, capitals, and outlying territories within the royal domain—the area directly governed by the Son of Heaven. The royal domain extended a thousand li in every direction. The capital stood at its center, with five hundred li from the capital to each boundary. Each hundred li formed a district: the land within fifty li of the city was the near suburb, and the land within a hundred li was the outer suburb.

The outer suburbs comprised four tong. At their center were the six xiang, with a total of seventy-five thousand households; the remaining land was allocated to nine grades of farmland. By Zhou calculations, the four tong of the outer suburbs contained ten thousand jing and thirty thousand households, for a total of one hundred and twenty thousand households. Of these, seventy-five thousand were assigned to the six xiang, leaving forty-five thousand households for the nine grades of farmland.

Beyond the outer suburbs lay the Dian area, comprising twelve tong. At its center were the six sui, also with seventy-five thousand households; the remaining land was allocated as farmland for public towns. The ditches and canals that irrigated and drained the fields were managed by the Suiren. By calculation, the twelve tong of the Dian area contained three hundred and sixty thousand households. After deducting the seventy-five thousand households of the six sui, the remaining two hundred and eighty-five thousand households were assigned to farmland for public towns.

Beyond the Dian area lay the Shao area, comprising twenty tong, where farmland for household towns was allocated. Beyond the Shao area lay the Xian area, comprising twenty-eight tong, where farmland for small capitals was allocated. Beyond the Xian area lay the Hua area, comprising thirty-six tong, where farmland for great capitals was allocated.

The Xiaositu was responsible for planning the division of farmland into the well-field system and the division of pastureland. The Simafa records: within the first hundred li around the royal city lay the suburbs; at two hundred li, the province; at three hundred li, the wilds; at four hundred li, the counties; and at five hundred li, the capitals.

The Grand Minister of Education oversaw the founding of states, the division of land, and the counting of the people. He defined the boundaries of each state, its capital, and its outlying districts. He grouped five households into a “bi,” so neighbors would watch over and protect one another; five bi into a “lü,” so members would welcome and look after one another; four lü into a “zu,” so members would help one another with funerals; five zu into a “dang,” so members would come to one another’s aid; five dang into a “zhou,” so members would visit one another; and five zhou into a “xiang,” so members would treat one another with the courtesies due to guests.

When laying out the capital and outlying districts, he marked their boundaries and established borders and ditches, then allocated land according to the number of households under his jurisdiction. Where land was cultivated every year, each household received one hundred mu. Where fields lay fallow every other year, each household received two hundred mu. Where they lay fallow for two years at a time, each household received three hundred mu. These allocations took account of the land’s fertility and the needs of crop rotation to ensure a harvest.

“Du” and “bi” were fiefs granted to royal clansmen, high ministers, and officials, providing them with income. They were divided into three grades: a duke’s fief was established in a large capital and covered a radius of one hundred li; a minister’s fief was established in a small capital and covered a radius of fifty li; and a senior official’s fief was established in a family town and covered a radius of twenty-five li. Royal clansmen most closely related to the king held fiefs equal in grade to those of dukes; those one degree more distantly related held fiefs equal to those of ministers; and those a further degree removed held fiefs equal to those of senior officials.

The Lesser Minister of Education was responsible for organizing the people into military and labor units: five men formed a “wu,” five wu formed a “liang,” four liang formed a “zu,” five zu formed a “lü,” five lü formed a “shi,” and five shi formed an “army.” This organization was used to mobilize troops, arrange fieldwork and other corvée labor, apprehend thieves, and collect tribute.

The soldiers in the six armies were recruited from the six townships. Within each township were local units called the bi, lü, zu, dang, zhou, and xiang. Five households made a bi. When laborers were conscripted, each household supplied one person, so five men formed a wu. Five bi made a lü, comprising twenty-five households; twenty-five men formed a liang. Four lü made a zu, comprising one hundred households; one hundred men formed a zu. Five zu made a dang, comprising five hundred households; five hundred men formed a lü. Five dang made a zhou, comprising 2,500 households; 2,500 men formed a shi. Five zhou made a xiang, comprising 12,500 households; 12,500 men formed an army.

Armies were raised to campaign against an enemy. Laborers were conscripted for work in the fields, whether for hunting or other labor. Recruiting people through units such as the bi and lü also made it possible to pursue and capture bandits: “pursue” means to chase down hostile raiders, while “investigate” means to scout for and apprehend bandits. These units could also be used to collect tribute and taxes. “Tribute” refers to the nine grains and products from mountains and marshes; “tax” refers to the requisitioning of carts and laborers to supply the county’s public service needs.

The Suiren administered the state’s suburban and rural districts. Using maps of the land, they surveyed and laid out the fields, and established rules for dividing counties and districts. Five households made a lin, five lin made a li, four li made a zan, five zan made a bi, five bi made a xian, and five xian made a sui. Each unit had defined boundaries, with ditches and trees marking its limits, and its own administrative regulations and criminal prohibitions. The Suiren inspected the population by season, assigned farmland and dwellings, checked weapons, and taught the people to sow and harvest.

Here, “the countryside” refers to the suburban districts called dian, shao, xian, and du. According to the Dasi Tu, the six township units—bi, lü, zu, dang, zhou, and xiang—correspond respectively to the countryside units lin, li, zan, bi, xian, and sui. Thus Zheng Xuan says in his commentary on “sui”:

“The military organization of the six townships was the same as that of the six suì, and the system of farmland in the six townships likewise corresponded to that of the six suì.”

The superior, middle, and inferior grades of countryside land also had to be distinguished, so that farmland and homesteads could be assigned according to grade. Under the allotment system for superior land, each husband received one plot, and administration was organized through the levels of zan, bi, xian, and sui.

The organization of the army was like the “Six Townships,” a system of settlements arranged by region. The system for dividing farmland in the townships was like the “Six Suburban Districts,” the administrative areas beyond the townships and their land system. The two systems were connected.

First, the soil quality of the lands beyond the suburbs had to be assessed, and the land classified as upper, middle, or lower grade. Farmland and residential plots were then allotted accordingly. On upper-grade land, each adult man received a holding consisting of one hundred mu of farmland and fifty mu of vegetable plots; the other adult men were allotted land in the same way. On middle-grade land, each man received one hundred mu of farmland and one hundred mu of vegetable plots. On lower-grade land, each received one hundred mu of farmland and two hundred mu of vegetable plots.

On upper-grade land, each person had one hundred mu of farmland and fifty mu of vegetable plots. The “Treatise on the Offices of the Earth” in the Rites of Zhou says that where the land did not need to lie fallow in rotation, each household had one hundred mu of farmland and no fifty mu of vegetable plots. The vegetable plots mentioned here were land left uncultivated temporarily during fallow periods. On land cultivated in alternate years, each household had two hundred mu of farmland: one hundred mu was cultivated and the other hundred left fallow. It was cultivated again after lying fallow for one year, hence the term “alternate-year cultivation.” On land cultivated once every three years, each household had three hundred mu: one hundred mu was cultivated and the other two hundred left fallow. It was cultivated again after lying fallow for two years, hence the term “two-year rotation.” Upper-grade land had no areas that needed to lie fallow, so no separate vegetable plots of this kind were allotted.

The land described above is a holding for ten thousand men: each household had three hundred mu, of which one hundred mu was cultivated and the other two hundred left fallow. It was cultivated again after lying fallow for two years, hence the term “two-year rotation.” Upper-grade land had no areas that needed to lie fallow.

A holding for ten thousand men covered approximately a square whose sides measured thirty-three and one-third li. In the diagram, each square represents land for one hundred men, with a “field ditch” (xu), a major channel between the plots. A row of such squares represents land for one thousand men, with a “main drainage and irrigation channel” (hui), a still larger canal; nine waterways run around the perimeter.

In a diagram of land for one hundred men, the waterway at the center is the “field channel” (sui). If the field ditch is treated as a field channel, each square represents one man and a row represents ten men, with a “ditch” (gou) between each man’s plots. If the main drainage and irrigation channel is treated as a ditch, nine ditches lead into a field ditch. The same arrangement can be understood by treating a river (chuan) as a field ditch. Zheng Xuan’s commentary on the width and depth of ditches and main channels broadly accords with the well-field system. However, the ditches and main channels in the well-field system are spaced farther apart, while the ditch-and-channel system described here is denser. The river here is broad and deep, and should be twice the size of a main channel. It differs from a naturally formed river: in the well-field system, there is only one major river for every hundred li.

In the system for governing the fields in the countryside, each fu of farmland had a sui watercourse, with a small path beside it. The fields of ten fu had a gou ditch, with a zhen track beside it; those of a hundred fu had a xu canal, with a tu road beside it; those of a thousand fu had a hui channel, with a dao road beside it; and those of ten thousand fu had a chuan river, with a main road beside it, providing access to the royal domain—the territory around the capital directly governed by the Son of Heaven.

The farmland cultivated by ten fu was grouped into two lin; that of a hundred fu formed one cheng; that of a thousand fu formed two bi; and that of ten thousand fu formed four xian. The sui, gou, xu, and hui were all waterways that carried water into the chuan. The jing, zhen, tu, dao, and lu were roads for carts and travelers heading toward the capital. Oxen and horses could pass along a jing; large carts along a zhen; a tu was wide enough for one carriage, a dao for two side by side, and a lu for three side by side.

The fields of ten thousand fu covered a little more than thirty-three li on each side. The fields of ninety thousand fu together covered one tong on each side, an ancient unit of land division. In a plan laid out with the fields running north to south, the sui ran lengthwise and the gou crosswise; the xu ran lengthwise and the hui crosswise. Nine hui channels flowed into a chuan, which surrounded the farmland.

The Commentary on the Image for the Shi hexagram says, “Water within the earth: this is the image of the Shi hexagram.” From this, the exemplary person learns to settle the people and sustain the multitudes. Water does not leave the earth; soldiers, too, do not leave the farmers. To sustain the people and keep them settled, places such as du and bi must have appropriate organizations, households must be grouped into lü and jing, and boundaries and ditches must be laid out among the fields. The Mencius says that putting benevolent government into practice must begin with defining the field boundaries. Accordingly, drawing on the image of “water within the earth” and the account in the Zhouguan, a diagram of the well-field system is presented to explain the meaning of the Yi.

The diagram above shows farmland ten li on each side, called one cheng. If it is understood as a tong measuring one hundred li on each side, then yi may be treated as dian, qiu as xian, and dian as du. This diagram of the well-field system, too, draws on the account in the Zhouguan to explain the meaning of the Yi.

As stated above, an area ten li square is called a cheng. Considered within the area a hundred li square called a tong, an yi corresponds to a dian, a qiu to a xian, and a dian to a du. The channel formerly called a gou corresponds to a hui, while the channel formerly called a xu corresponds to a chuan.

According to the regulations on gouxu (field irrigation channels) in “The Artificers” chapter of the Kaogong ji, a si (a tool for turning soil) is five cun wide. Two si working side by side are called a ou. The ridge of land turned by one ou is one chi wide and one chi deep, and is called a mu. The channel at the end of the fields is twice those dimensions: two chi wide and two chi deep, and is called a sui. Nine fu make one jing; the channel between jing is four chi wide and four chi deep, and is called a gou. An area ten li square is called a cheng; the channel between cheng is eight chi wide and eight chi deep, and is called a xu. An area a hundred li square is called a tong; the channel between tong is two xun wide and two ren deep, and is called a hui. The xun and ren are ancient units of length. The sui between mu run lengthwise, while the gou run crosswise. The xu run lengthwise and the hui crosswise; natural rivers, in turn, flow crosswise.

The Xiao Situ chapter of the Rites of Zhou records that the junior minister of lands and populations demarcated territories and laid out the countryside according to the well-field system. Nine fu made one jing, four jing made one yi, four yi made one qiu, four qiu made one dian, four dian made one xian, and four xian made one du. Land was allocated for different uses according to this scheme, which also determined tribute and the administration of various taxes.

This passage concerns the fief system and well-field divisions in the capital and its surrounding territories, which differed from the system in the xiang and sui districts. The same divisions were also used for flat, fertile land: nine fu made one jing, four jing made one yi, four yi made one qiu, four qiu made one dian, four dian made one xian, and four xian made one du. Land was then allocated for different uses, tribute was set, and taxes were collected accordingly.

This passage describes the ancient well-field system and the method of raising war chariots, soldiers, and laborers according to the size of the land. The land system in the capital’s outer districts and in fief lands differed from that in the rural and frontier regions: fertile low-lying land was laid out as well-fields, while higher, sunnier land was used for pasture. Nine fu—with fu serving as a unit for measuring both land and the cultivators who worked it—made up one pasture unit; ordinarily, two pasture units equaled one well-field.

A square li of land was divided into nine sections, each of one hundred mu. Each fu was allotted one hundred mu, so nine fu made one well-field. Four well-fields made one settlement, which was two li square; four settlements made one qiu, four li square; and four qiu made one dian, eight li square. Adding one li around each side of the dian created a square cheng, ten li across, comprising one hundred well-fields and nine hundred fu. Of these, 64 well-fields, or 576 fu, paid land tax, while the 36 well-fields around the perimeter, or 324 fu, were responsible for clearing the field channels.

Four cheng made one county, twenty li square; four counties made one du, forty li square. Four du formed a region eighty li square. Adding ten li around each side made a square tong, one hundred li across, comprising ten thousand well-fields and ninety thousand fu. Of these, 6,400 well-fields, or 57,600 fu, paid land tax, while 3,600 well-fields, or 32,400 fu, were responsible for maintaining the channels. The well-field system was complete only at the scale of a tong.

However, those granted fiefs in the outer lands actually enjoyed the use of only one quarter of all the land. Fiefs came in three sizes: a state one hundred li square had four du, and gave the king the tax revenue from one du; a state fifty li square had four counties, and gave the king the tax revenue from one county; a state twenty-five li square had four dian, and gave the king the tax revenue from one dian.

The Simafa records that six chi made one bu, one hundred bu made one mu, and one hundred mu made one fu; three fu made one household plot, three household plots made one well-field, and ten well-fields made one tong. Here the calculation uses the area of one cheng: each side is divided into ten sections, forming a row of ten well-fields, which together make one tong. Each tong was said to contain thirty households and to supply one horse, one soldier, and two laborers—people assigned to manual work or support in battle—making ninety fu in all. The figure of thirty households is calculated after excluding land occupied by official residences, roads, and the like. Because the land was managed with fallow periods, the average ratio was three fu cultivating the land of six fu. Thus, the land of sixty fu corresponded in practice to thirty households. Each tong therefore supplied one horse, one soldier, and two laborers.

Ten tong made one cheng, ten li square, with one hundred well-fields and three hundred households; it supplied one leather-covered war chariot, ten soldiers, and twenty laborers. Ten cheng made one zhong, comprising one thousand well-fields and three thousand households; it supplied ten war chariots, one hundred soldiers, and two hundred laborers. Ten zhong made one tong, one hundred li square, with ten thousand well-fields and thirty thousand households; it supplied one hundred war chariots, one thousand soldiers, and two thousand laborers. Ten tong made one feng, with one hundred thousand well-fields and three hundred thousand households; it supplied one thousand war chariots, ten thousand soldiers, and twenty thousand laborers. Ten feng made one ji, one thousand li square, with one million well-fields and three million households; it supplied ten thousand war chariots, one hundred thousand soldiers, and two hundred thousand laborers. The Lu Hymns says, “The lord’s army had a thousand chariots and thirty thousand men on foot.” In this figure, the foot soldiers are included among the laborers.

This concludes the lower volume of Explanations of the Diagrams of the Yi (Yixiang Tushuo Waipian).

1. The original text has “zheng” (“upright”); this has been changed to “zhi” (“stop”) based on the Siku Quanshu edition.

2. The original text mistakenly has “gua jian”; this has been corrected to “fengjian” (“enfeoffment”) based on the Siku Quanshu edition.

3. The phrase “a territory of one hundred li” is absent from the Siku Quanshu edition and may have been omitted there.

4. The Siku Quanshu edition also has the name “Yingchuan.”

5. The Siku Quanshu edition has “Zhongguo” where this text has “within the state.”

6. The Siku Quanshu edition has “no more than one person in each household” where this text has “no more than one household.”

7. The Siku Quanshu edition has “bi” (“outlying district”) where this text has “bu” (“department”).

8. The Siku Quanshu edition has “jian” (“simple”) where this text has “jian.”

9. Judging from the wording conventions in the preceding passage, the original text should read “tong wen” (“ask the same question”).

10. The character “xiao” (“small”) was missing from the original text and has been supplied based on the Siku Quanshu edition.

11. The Siku Quanshu edition has “shui lian” (“tax levies”) where this text has “shui yin.”