《易筮通变(雷思齐)》

The Yishi Tongbian is a work by Lei Siqi, a Daoist priest from Linchuan, on the study of the Yi and the art of divination. It comprises three volumes and is included in the Tai Xuan section of the Zhengtong Daoist Canon. A copy in the Wenyuan Pavilion edition of the Complete Library of the Four Treasuries is also available for comparison.

“Yishi Tongbian” means “using the Book of Changes for divination and understanding transformations.” “Juan shang” means “upper volume,” and “bu shi” refers to using divination to foresee good or ill fortune.

The “Examining Doubts” chapter of the Great Plan says, “Choose the people responsible for divination by turtle shell and milfoil, and then instruct them to perform these divinations.” The Book of Songs says, “You divine with the turtle and cast with milfoil; neither the figures nor the cracks give an inauspicious sign. Turtle divination and milfoil casting are performed together, and everyone’s judgments say that their results are much the same.” The Monthly Ordinances in the Book of Rites also says that in the first month of winter, the Grand Scribe—a court official in charge of ritual and historical records—is ordered to sacrifice with the blood of an animal to the turtle shell and milfoil, then judge good and ill fortune from the signs. It seems, then, that turtle divination and milfoil casting should be used together.

The Great Commentary on the Changes says, “To trace the course of things, seek out what is hidden and subtle, probe the profound and reach the distant, and accomplish all the many affairs of the world—nothing is more important than milfoil and turtle shell.” It also says, “Those who perform divination should give due weight to the judgment.” This suggests that the Changes should serve both purposes: turtle divination and milfoil casting.

The Great Announcement records, “King Wen left me his precious sacred turtle, so that I might receive Heaven’s clear mandate.” The Metal-Bound Coffer records, “Then they divined with three turtles, and the signs of one repeatedly showed good fortune.” Neither passage mentions milfoil casting. The Book of Rites also says, “The Son of Heaven does not use milfoil casting; the feudal lords have officials specifically in charge of it.” Yet the “Explaining the Trigrams” chapter of the Zhou Changes says that the ancient sages created the Changes: through spiritual inspiration, they devised milfoil divination; taking Heaven and Earth’s numerical patterns as a model, they established the numbers; observing the transformations of Yin and Yang, they created the trigrams; and extending the transformations of firmness and yielding, they formed the line statements. In the end, this enabled people to accord with De and act in keeping with what is right, to probe the principles of things and human nature, and to reach the Mandate of Heaven. These statements speak only of milfoil casting and say nothing about turtle divination.

The Changes centers on milfoil casting. The “Appended Statements” explains the Great Expansion method—the numerical procedure for divining with milfoil—in detail, yet contains not a word about turtle divination. Although another account calls the turtle method “divination” and the milfoil method “casting,” I grew up seeing people in folk divination toss coins to produce the lines of a hexagram, and I have heard that this method originated with Jing Fang, a Han-dynasty scholar of the Changes. Jia Gongyan, a Tang-dynasty scholar of the classics, also interpreted the solid, broken, doubled, and crossed line forms produced by coin casting as signs obtained through coin divination. I have also seen people arrange coins with the help of a cross-section of a turtle shell.

Later miscellanies and biographies often call the casting of a primary and changing hexagram with the Yi “divination.” People are also accustomed to speaking of “casting hexagrams,” so I, too, once confused tortoise-shell divination with milfoil divination and gave the distinction little thought.

It was only later, when I read the “Spring Offices” chapter of the Rites of Zhou, that I noticed the Grand Diviner was in charge of three methods of tortoise-shell divination, called the jade cracks, the tile cracks, and the field cracks. Each method had its own fixed crack patterns and corresponding divinatory statements. The diviners were responsible for splitting open the tortoise shells and examining the crack patterns, while the tortoise keepers managed six kinds of tortoise and identified them by the orientation, color, and form of their shells.

The Grand Diviner was also in charge of the methods of the Three Yi: the Lianshan, the Guicang, and the Zhouyi. All three were based on the Eight Trigrams (Bagua) and developed into sixty-four hexagrams. The milfoil diviners used the nine methods of casting described in the Three Yi to judge good and ill fortune. When the state faced a major matter, it first consulted the milfoil and then performed tortoise-shell divination. A milfoil divination was also held at the beginning of each spring. In conducting state affairs, the milfoil diviner likewise cast first, then considered whether tortoise-shell divination was also needed.

From this we can see that tortoise-shell divination judged by crack patterns and their accompanying statements, of which there were many, while the Yi’s milfoil method always remained within the bounds of sixty-four hexagrams. Tortoise-shell divination had its own method, and milfoil divination had its own; originally, they were not used interchangeably.

The Great Plan also distinguishes between the results of tortoise-shell and milfoil divination: both agree; the tortoise-shell agrees while the milfoil disagrees; or both go against what people wish. This shows that the difference between the two forms of divination is perfectly clear, like black and white. I was deeply puzzled that later writers on divination discussed them in such confusion. I therefore examined the accounts of successful predictions in works such as the Zuo Tradition and came to understand clearly the distinct principles of tortoise-shell and milfoil divination.

Those who practice divination never cite the methods of milfoil divination in the Classic of Changes, and those who practice milfoil divination never cite the methods of turtle-shell divination. Here are several examples of each.

Some accounts use turtle-shell divination alone, without milfoil divination. When Duke Hui of Jin was still in the state of Liang, the Earl of Liang gave his daughter in marriage to him. Liang Ying became pregnant and passed her due date, so the diviner Zhao Fu and his son performed turtle-shell divination for her. Zhao Fu’s son said, “She will give birth to a boy and a girl.” Zhao Fu said, “Indeed. The boy will one day serve as another man’s minister, and the girl will one day become someone’s concubine.” They named the boy Yu and the girl Qie. Later, Yu was sent as a hostage to Qin, while Qie became a palace servant.

Duke Wen of Lu used turtle-shell divination to ask whether the capital should be moved to Yi. The official in charge of records said, “Moving the capital will benefit the people but harm the ruler.” Duke Wen replied, “If it benefits the people, we should move. Heaven brings the people into being and provides for them, then establishes a ruler to benefit them. Once the people have benefited, I too will naturally benefit.” After the capital was moved, Duke Wen died.

The Marquis of Qi set a date to send out troops and prepare to attack Lu, but then fell ill. The physician said, “You will die before autumn.” When Duke Wen of Lu heard this, he used turtle-shell divination to ask whether the Marquis of Qi would live until the agreed date for the campaign. Shuzhong Huibo ordered a turtle-shell divination, and the diviner Chuqiu interpreted it: “The Marquis of Qi will not live until the agreed date, but his death will not be caused by this illness. The ruler will not hear this news either, for the turtle-shell divination shows disaster.” Later, Duke Yi of Qi was killed, Duke Wen of Lu died first, and Shuzhong Huibo also died.

The King of Chu and the Lord of Ye repeatedly used turtle-shell divination to ask whether Ziliang should become chief minister, the highest official in Chu. Shen Yin Zhu said, “The omen is auspicious, but the outcome will exceed his expectations.” The Lord of Ye replied, “If the prince becomes chief minister, what outcome could exceed his expectations?” Later, the King of Chu instead used turtle-shell divination to ask whether Ziguo should become chief minister.

These four examples show that turtle-shell divination did not involve the hexagrams produced by milfoil divination in the Classic of Changes.

There are also examples that use milfoil divination alone, without turtle-shell divination. Bi Wan used milfoil stalks to ask about his prospects for holding office in Jin, and obtained the hexagram Zhun, which changed into Bi. Xin Liao interpreted it: “Auspicious. Zhun signifies things newly beginning and meeting with obstruction; Bi signifies closeness and adherence. What omen could be more auspicious than this? He is certain to prosper and grow in power. Zhen signifies a chariot, with horses harnessed to it. The people will adhere to him, elders will support him, his mother will shelter him, and the people will turn toward him. None of the six lines changes; joined together, they will be firm. In times of peace he can bring stability to the people, and in action he can eliminate harm. This is a hexagram of a duke or marquis.” These words are an interpretation based on a milfoil divination hexagram.

The descendants of the feudal lords will eventually return to the place where their ancestors began. When Taibo attacked Jin, the diviner Butufu performed an oracle and said, “It is auspicious. After crossing the Yellow River, the lords’ chariots will suffer three defeats.” Taibo explained, “This is in fact a great auspice. After three defeats, we will capture the ruler of Jin.” The resulting hexagram was Gu. Its statement says, “A thousand chariots depart three times; after the third departure, the male fox can be captured.” The fox symbolizes a ruler who brings confusion and disorder; it must refer to the ruler of Jin. The original form of the Gu hexagram is Wind, and its transformed form is Mountain. The season has reached autumn: I will gather the fruit and take the wood. The fruit has fallen and the wood has been cut down—if we are not defeated, when could it happen? The Qin army suffered three defeats. Then, at the Battle of Hanyuan, the Marquis of Jin confronted the Qin army, which captured him there and took him back to Qin.

The Marquis of Jin attacked Zheng, and the King of Chu came to its aid. The two sides met at Biling. The Marquis of Jin consulted the oracle, and the court historian said, “The army’s morale is in trouble.” The resulting hexagram was Fu. Its statement says, “The southern state acts without righteousness. Shoot the one who has no ruler, and the arrow will strike his eye. The state is trampled, and its ruler is wounded. If we are not defeated, when could it happen?” In the battle, Lü Qi shot King Gong of Chu in the eye. The king said, “Heaven intends Chu to perish. I cannot simply wait.” So he delayed his movements until nightfall.

Duke Xian of Jin consulted the oracle because he wanted to marry Bo Ji into the state of Qin. The resulting hexagram was Gui Mei, which changed into Kui. Shi Su interpreted it: “It is inauspicious. The statement says, ‘A man butchers a sheep, but there is no blood; a woman carries a basket, but brings back no harvest. The reproaches of the western neighbor cannot be repaid.’ Gui Mei changing into Kui means that the two sides cannot unite. Zhen changing into Li—that is, Li changing into Zhen—has Zhen as thunder and Li as fire. It foretells that the woman of the Ji clan will suffer gain and loss, defeat and ruin. The chariot’s shafts will come loose, fire will destroy the army’s banner, and the campaign will go badly; defeat will come at Zongqiu. Gui Mei changing into Kui also symbolizes an enemy drawing a bow and setting an arrow. The niece will follow her aunt; six years later…”

The nephew followed his aunt. Only after six years did he attain success; then he fled back to his own country, leaving his family behind. The following year, he died amid the ruins of Gaoliang. Like the four cases mentioned earlier, each was divined by yarrow stalks, producing a hexagram, but no turtle-shell omen or accompanying divination text was added.

Moreover, the hexagram statements for the three hexagrams mentioned earlier—Zhun, Fu, and Gu—were not originally from the Zhouyi. Later, when the hexagram Guimei changed into Kui, the attached divination text was close to the Zhouyi but was not its original wording. From this, we may infer that the divination methods of the two Changes texts, Lianshan and Guizang, were the same, but their hexagram statements differed.

There were also cases in which turtle-shell divination and yarrow-stalk divination were used together, with each method having its own divination text. When Ji, son of Cheng, was about to be born, Duke Huan of Lu sent the father of Bu Chu Qiu to divine for him. The turtle-shell text said: “It is a boy. Name him You. His rank will be second only to the ruler; he will stand between the two ancestral altars and assist the ruling house. If the Ji clan perishes, Lu will not prosper.” Yarrow-stalk divination was then performed, yielding Dayou changing to Qian. Its divination text said: “He will return to his father and be honored like a ruler.”

After the child was born, there was a pattern on his palm shaped like the character “You,” so he was given that name. This case shows that turtle-shell divination and yarrow-stalk divination each had its own divination text, and that the hexagram statements used in yarrow-stalk divination were not those of the Zhouyi.

There were also cases in which turtle-shell divination came first, followed by yarrow-stalk divination. When Duke Xian of Jin planned to make Li Ji his wife, he first divined with a turtle shell, and the result was inauspicious. He then divined with yarrow stalks, and the result was auspicious. Duke Xian said, “I will follow the yarrow divination.” The diviner advised him: “The judgments of yarrow divination are more general, while those of turtle-shell divination are more detailed. You should follow the more detailed result.”

He further pointed to the yarrow divination text: “Showing her exclusive favor will bring calamity. She will take the ruler’s robes; once smoked, then stored with aromatic herbs, they will still stink ten years later.” The meaning was that this course of action must not be pursued. Duke Xian ignored the warning and made Li Ji his wife. She gave birth to Xi Qi and later secretly pressured the heir apparent, Shen Sheng, until he hanged himself. Duke Xian then made Xi Qi the heir apparent, setting off turmoil in Jin.

In some cases, divination was first performed with yarrow stalks and then with a tortoise shell. The Marquis of Wei once dreamed in the Northern Palace that a man climbed Kunwu Terrace. His hair hung loose, and he cried out loudly, “Climb Kunwu Terrace: vines stretch far and wide, bearing a great gourd. I am Hun Liangfu, wrongfully accused.” The Marquis performed a yarrow-stalk divination himself. Xu Mi She interpreted it: “There will be no harm.” The Marquis then divined with a tortoise shell. The oracle read: “Like a fish peering at its tail, it wanders across the current. A great state from afar is about to destroy it; it is about to perish. Bar the gates and block the holes.” Xu Mi She interpreted it: “There will be no harm.” The Marquis divined again, and the oracle repeated: “Like a fish peering at its tail, it wanders across the current. A great state from afar is about to destroy it; it is about to perish. Bar the gates and block the holes.” The Marquis then fled through a rear gate. In the tenth month of winter, the state of Jin attacked Wei again and captured its capital. Wei expelled Duke Zhuang and made peace with Jin. Jin installed Banshi, a grandson of Duke Xiang, as ruler of Wei, then withdrew its troops.

In these two cases, whether the tortoise-shell divination came before or after the yarrow-stalk divination, the results differed: the yarrow-stalk divination had no written judgment, while the tortoise-shell divination had an oracle text, known as a yaoci, attached to it. Yet the results of the two methods did not agree.

In another example, Duke Xian of Jin divined whether to attack the Li Rong. Shi Su interpreted the result: “Though you can win, it will not be auspicious.” Duke Xian asked, “What does that mean?” Shi Su replied, “The cracks in the shell show: ‘Clutching a bone, its teeth are injured by it; the Rong and the Hua contend, and both sides win and both suffer harm.’ That is why I say this. I am also concerned that the deed will bring reproach, and that those in power will claim the people and the state as their private property.” Duke Xian said, “How could there be reproach? I am the one with the authority to speak. If I refuse to accept it, who can make it happen?” Shi Su answered, “Once you bring people from the Li Rong back with you, you are sure to welcome the fruits of victory. You do not know how impossible it will be to keep this matter under wraps.” Duke Xian ignored him and went ahead with the attack. He won and brought back Li Ji, ultimately plunging the state into turmoil.

In accounts of this kind, only tortoise-shell divination is accompanied by an oracle text; yarrow-stalk divination is not mentioned. The Discourses of the States (Guoyu) records the same pattern, and its oracle texts differ little from those in the Zuo Commentary (Zuozhuan). As for the Family Sayings of Confucius (Kongzi Jiayu), it says that Confucius once performed a yarrow-stalk divination himself and obtained the Bi hexagram, which symbolizes adornment and embellishment. His expression seemed troubled and unsettled. Zizhang stepped forward and said, “When diviners obtain the Bi hexagram, it is auspicious.”

Why was Confucius displeased? It is said that he obtained the Bi hexagram. In the Zhouyi, “fire beneath the mountain” is the Bi hexagram, which concerns adornment rather than emphasizing a thing’s natural character. The essence of things should remain clear, pure, and unmixed, like black and white kept distinct. Obtaining the Bi hexagram did not match the omen Confucius was seeking.

I have heard that cinnabar-colored lacquer needs no further patterning, and white jade needs no carving. Why? Because their qualities are already complete; they need no embellishment from outside. In light of this, the story is indeed doubtful. If Confucius personally performed divination with yarrow stalks, why did Zizhang call it “tortoise divination”? Moreover, the account does not resemble the statements attached to the hexagrams and lines in the Zhouyi.

The explanation of the Judgment and Image for the Bi hexagram says: “Bi means that a yielding line comes below and adorns the firm lines; then a firm line rises above and adorns the yielding lines. Thus, going somewhere brings a small measure of benefit.” This describes the patterned order of the heavens. When civilization is expressed with restraint, it describes the patterned order of human society. By observing the heavens, one can discern the changes of the seasons; by observing the rites and patterns of human society, one can educate the world. If Confucius valued “adornment” when explaining the Image, why did he prize simplicity alone in divination? The two accounts contradict each other so sharply that I cannot accept the record in the Kongzi Jiayu as reliable.

The Zuozhuan contains many examples of divination using the Zhouyi without resorting to tortoise divination; there are too many to list them all. In each case, the outcome is inferred from the statements attached to the Zhouyi hexagrams. The Zhouyi has survived on its own, and its contents are familiar to people. Apart from the one incident recorded in the Kongzi Jiayu, the distinction between the two methods has always been clear: tortoise divination uses cracks in a tortoise shell to judge good or ill fortune, while yarrow divination uses stalks to calculate the hexagrams. They have never been confused. The Lianshan, Guicang, and Zhouyi are collectively known as the “Three Changes.” Each of the three classics has eight basic trigrams, from which sixty-four hexagrams are derived. This point is also recorded in the Liji; it is no empty claim.

The Lianshan and Guicang are now difficult to find. At most, scattered sources let us form a rough idea of them. They were surely nothing like the versions described in popular accounts of later times. Yet people often use the broad term “divination” for all methods of casting with yarrow stalks and the like to ask about good and ill fortune.

Some say that the Classic of Changes survived the Qin book burnings because it had become entangled with divination and omen reading. There may be some truth in this. But the omen-reading methods said to have been administered by the Grand Diviner supposedly had 120 hexagram forms and 1,200 hexagram statements, none of which have been passed down. Did those books of omens fail to survive the Qin burnings too?

Before Emperor Wen of Han left Dai and entered the capital to take the throne, he once obtained the omen called “Great Crosswise.” Its statement read: “Great crosswise, firm and bright; I become Son of Heaven; Xia Qi brings radiance.” Commentators took “Great Crosswise” to refer to the straight crosswise markings on a tortoise shell, the sign obtained in the divination. Emperor Wen’s later possession of the realm was seen as matching that omen. It seems, then, that omen-reading methods were still preserved in the early Han, but were lost later. When Gao Yang of Northern Qi sought to seize power from Eastern Wei, he also consulted Li Mi and obtained the “Great Crosswise” omen. Li Mi said it was the sign of Emperor Wen of Han. I think Li Mi was merely flattering Gao Yang and helping him find grounds for usurpation. How could we take his words entirely at face value?

Most later books on omen reading are absent from the records. Why, then, are there still so many accounts of predictions that proved accurate? Alas, the hexagram forms used in omen reading totaled 360, and their separate statements numbered as many as 3,600. With such a vast body of material, it is hardly surprising that it could not all be passed down. Even if these books still existed, who could master them all?

How can we know this? The world has long had no access to the Lianshan and Guicang; only the Zhouyi has come down to us. It contains just 64 hexagrams and 384 lines—the yin and yang symbols that make up the hexagram images. It has been composed, transmitted, and handed down through three dynasties and by four sages, yet even now no one can say that its subtle transformations and wondrous, unfathomable workings have been fully exhausted. As for explaining the basic hexagrams and their changes, this has generally been done by using the hexagram statements and line statements to interpret them; most later commentaries follow the same approach.

When asked about the principle that, in casting the yarrow stalks, one should “follow only where the changes lead” and judge by the transformations of the hexagrams and their lines, he was utterly at a loss and could not explain what it meant. How could one possibly discuss the Yi with someone like that? I therefore spoke of how divination cannot be treated as though it were all of one kind, and could not help sighing deeply over it.

The sage observes the forms and traces of things in the world, then uses images to compare with and portray the distinctive qualities of each. This is called “image.” The sage observes how things in the world move and change, examines the principles by which they meet and connect, and on that basis establishes rites. Explanations are then attached to judge good and ill fortune. This is called “line.” What gathers the forms and traces of all things in the world is the hexagram; what sets the changes and movements of the world in motion is the wording of the hexagrams and lines. What changes things and regulates them is “transformation”; what develops transformation and sets it in motion is “continuity.” Thus, only by adapting to change and achieving continuity can things bring their benefits fully to fruition; only by grasping the principles that connect change can order and pattern take shape.

When the Eight Trigrams are arranged, their images appear within them; when the trigrams are stacked to form the sixty-four hexagrams, the lines appear within them. As Yin and Yang lines shift in relation to each other, change arises. When statements are attached beneath the hexagrams and lines to explain them, the course of things is contained within them. The Eight Trigrams express things through images; line images explain them through the circumstances of things; change and continuity are explained through benefit and harm, gain and loss; and good and ill fortune shift with the circumstances of things.

It is also said that changes in line images arise within, while good and ill fortune become visible without; achievements emerge from change, while the sage’s intention is embodied in the statements. Since it is said that the force that sets the changes and movements of the world in motion lies in the statements, and also that attaching statements to the hexagrams and lines to explain them encompasses the direction in which things are moving, and since the statements are said to judge good and ill fortune and distinguish between them, the statements are an indispensable part of the Dao of the Book of Changes (Yi Jing).

The principles described in the Book of Changes thus shift and transform continually, moving without pause and flowing everywhere through the positions of the six lines. Above and below have no fixed pattern; Yin and Yang, firmness and softness, transform into one another. They cannot be captured by fixed rules, but adapt to change as it comes. Hexagram images differ in scale, and the statements range from difficult and perilous to plain and easy. Each statement in the Book of Changes points out the direction in which things are about to go.

Here, “to” in the phrase “the direction toward which it goes” specifically refers to the direction toward which change tends and to which it adapts. “Change” means transformation. The Book of Changes makes the movement and transformation of the world clear, and its principles for setting those changes in motion can all be observed in it. Thus, divination with the Book of Changes looks at a line that changes, moves the hexagram image, and tends in a particular direction; this is expressed by saying that one hexagram changes into another. When we say that the statements point out the direction, we mean that they explain the hexagram produced by the change. Han Kangbo offered no commentary after the words “point out the direction toward which it goes.”

Kong Yingda explained the phrase “each points to what it reaches” as follows: the line statements and hexagram statements point respectively to where the hexagram or line arrives after changing. Hence the phrase “the statements point to what they reach.” Han Kangbo offered no annotation under the words “what they reach.” Kong Yingda further explained that the line statements and hexagram statements refer to the hexagram or line reached after the change. If that destination is auspicious, the meaning of the statement is auspicious; if it is inauspicious, the meaning is inauspicious.

Interpreting zhi as “to go toward” or “to arrive at” is not wrong. But speaking only of changing hexagrams and moving lines does not yet explain what the hexagram and line statements actually point to. An account in the Zuo Tradition can also help illustrate this.

When Chen Jingzhong was young, a Zhou court historian visited the ruler of Chen, bringing the Zhou Yi. The ruler asked him to perform a divination, and the result was the Guan hexagram changing into the Pi hexagram: line six in the fourth place of Guan changed into line six in the fourth place of Pi. The historian then cited the line statement for Guan, line six in the fourth place: “Observe the splendor of the state; it is advantageous to serve as a guest at the king’s court.” From this, he inferred that Chen Jingzhong would one day replace the ruler of Chen and possess the state.

When Duke Wen of Jin escorted the Zhou Son of Heaven back to his capital, he also performed a divination. The result was the Great Possession hexagram changing into the Opposition hexagram: line nine in the third place of Great Possession changed into line nine in the third place of Opposition. The diviner Bu Yan therefore cited the line statement for Great Possession, line nine in the third place, and said it was an auspicious sign: Duke Wen of Jin would perform a feast offering before the Son of Heaven in his capacity as a feudal lord. What could be more auspicious than winning a military campaign and then receiving honors from the Son of Heaven? The word heng in the line statement for Great Possession, line nine in the third place, is also written as xiang in some versions of the Yi Jing. Heng could, in any case, also be used with the meaning of xiang.

Cui Shu of Qi wished to marry Dongguo Jiang, the widow of Tang Gong, and performed a divination. The result was the Oppression hexagram changing into the Great Exceeding hexagram: line six in the third place of Oppression changed into line six in the third place of Great Exceeding. The court historians all declared it auspicious, so Cui Shu showed the hexagram to Chen Wenzi. Chen Wenzi cited the line statement for Oppression, line six in the third place: “Oppressed by rocks, leaning on thorn bushes; returning home, he does not see his wife. Inauspicious.” He believed this foretold that Cui Shu would suffer misfortune because of the marriage.

Trapped among the rocks, he could not cross the peril even if he pressed on; leaning on flourishing flowers and trees, he was harmed because of them. When he returned to the palace and could not find his wife, this was an ill omen: he would have nowhere to go. Cui Zhu eventually married Tang Jiang. Later, his family fell into turmoil and was finally destroyed.

When Shusun Muzi was born, his father Zhuang Shu consulted the Zhouyi. The divination yielded Mingyi changing into Qian—that is, the first line of Mingyi changing into the first line of Qian. Zhuang Shu showed the hexagrams to Bu Chu Qiu. Bu Chu Qiu said, “The light has not yet fully emerged; perhaps it is just before dawn. The change to Qian suggests a bird in flight, hence ‘Mingyi in flight.’ The sky is bright, yet the light has not fully spread, hence ‘its wings droop.’ The hexagram shows a journey, hence ‘the noble person has somewhere to go.’ It is dawn, hence ‘for three days he does not eat.’ Li symbolizes fire; fire burns through the forests and causes them to wither. In human affairs, fire symbolizes speech, and speech that causes harm is slander. Hence ‘he has somewhere to go; his lord has something to say’—those words must be slander.” This was the line statement for the first line of Mingyi. Shusun Muzi later indeed encountered the Jian Niu rebellion. From this, it seems that none of these divinations failed to come true.

Lady Xiang of Wei had no sons, but Diao, the son of Bi Ren, gave birth to Meng Zhi. Kong Chengzi dreamed that Kang Shu said to him, “Set up Wu as ruler. I will have Yu, the grandson of Ji, assist him, and Shi Gou will assist as well.” Shi Chao also dreamed that Kang Shu said to him, “I command your son Gou to assist Wu together with Yu, the great-grandson of Kong Xu Niu.” When Shi Chao met Kong Chengzi, he told him the command he had received in his dream; the two dreams confirmed each other.

In the year Han Xuanzi took office and went on a mission to the feudal lords, Diao gave birth to a son, who was named Wu. Meng Zhi had a disabled foot and could not walk normally. Kong Chengzi consulted the Zhouyi, saying, “Wu will one day possess the state of Wei and preside over its state sacrifices.” The divination yielded Zhun changing into Bi. He then said, “I also wish to set up Meng Zhi as ruler, and hope he will receive approval.” So he divined with the Zhun hexagram and showed it to Shi Chao. Shi Chao said, “The judgment of Zhun says ‘great success.’ What is there left to doubt?”

Chengzi said, “The word ‘establish’ here does not mean to make someone older.” Someone asked, “When Kangshu received his mandate, could he not already be considered established?” That is why the Xian hexagram says, “It is favorable to establish a feudal lord.” If inheriting the throne is auspicious, what else is there to establish? Establishing a feudal lord is not the same as inheriting the throne. Both hexagrams say, “You should establish him.” This was the message conveyed by the two hexagrams when Kangshu received his mandate.

King Wu once consulted the oracle again by means of a dream and yarrow divination. Perhaps he encountered the Zhun hexagram once more; its judgment said, “Great success and free flow.” The first line of Zhun changed, transforming it into the Bi hexagram. The first line of Zhun reads: “Hesitation and delay. It is favorable to remain settled and upright; it is favorable to establish a feudal lord.” This means that when one hesitates over whether to advance or retreat, it is favorable to remain settled and upright, and favorable to establish a feudal lord. Thus King Wu was installed.

When Nankui was about to rebel, he consulted the oracle and obtained Kun changing into Bi. The line statement was: “Yellow lower garments. Great good fortune.” Nankui took this to be a sign of great good fortune, brought the result to Zifu Huibo, and asked, “What if I intend to take action?” Huibo replied, “I once studied this kind of divination. An undertaking can be auspicious only if it arises from loyalty and good faith; otherwise, it is bound to fail. Yellow is the color of the center, and a lower garment is worn below the waist. ‘Great’ means the foremost in goodness. If you occupy the center but do not follow the middle way, you do not deserve yellow; if you are in a low position but are not deferential, you do not deserve the lower garment; if what you do is not good, you cannot attain the highest good. None of these three conditions is met, so of course the outcome is inauspicious. Besides, the Yi must not be used to divine about wicked and dangerous undertakings.”

This was because the fifth line of Kun changed, producing the fifth line of Bi, so Huibo interpreted the result using the fifth line statement of Kun. Nankui ultimately perished in his rebellion.

A survey of the many divination accounts in the Zuo Commentary and other records shows that judgments were often explained by reference to the resulting hexagram and the line that changed. The “resulting hexagram” is the hexagram formed after the change. In its account of the Sages’ way, the Yi says that those who act give importance to change, while those who divine give importance to the judgment. Understanding change is called “affairs”; exhausting the principles of number to know what is to come is called “divination.” When one divines about a matter, a resulting hexagram appears.

Those in ancient times who studied the Changes (the Yijing) did not use it only for divination. In their daily lives, exemplary people grounded their conduct in the sequence of hexagrams; what they took pleasure in studying and pondering were the statements attached to the lines. At rest, they observed the hexagram images and reflected on the line statements; in action, they watched for changes and examined the results of divination. Yet the Changes was not limited to obtaining a particular hexagram through divination. Whenever someone had a thought in mind and considered a matter at length, encountered a particular situation, or wanted to express an idea, they could extend their reasoning from one thing to related things and use them as points of reference. In such cases, it was also possible to draw on the hexagram images in one’s thinking.

The ruler of Chu besieged Zheng and captured it. The Jin army went to its aid. When Xun Huanzi heard that Zheng had already made peace with Chu, he wanted to withdraw. He said, “We failed to arrive in time to aid Zheng, and now we would make our people suffer for nothing. Why send out the troops at all?” Sui Wuzi agreed with him. Ying Ji disagreed and led the deputy commanders of the central army into battle. Zhi Zhuangzi said, “This army is in danger. The Zhouyi teaches this: when the hexagram The Army changes into Approach, its line statement says, ‘An army must set out under discipline; without discipline, there will be misfortune.’” This refers to the first line of The Army changing into the first line of Approach.

You Ji of Zheng returned from Chu and told Zizhan, “The ruler of Chu is probably going to die. He does not put his government and virtue in good order, but covets the lands of the feudal lords merely to satisfy his own desires. How could he keep succeeding for long?” He obtained the hexagram Return changing into Nourishment. The line statement says, “Having lost the right way and failing to return brings misfortune.” You Ji believed this referred to the ruler of Chu. This refers to the top line of Return changing into the top line of Nourishment.

Gongzi Manman of Zheng spoke with Wangzi Boliao about his wish to become a high minister. Boliao told someone else, “He has no virtue, yet covets high rank. According to the Zhouyi, he will probably meet the fate shown by Abundance changing into Radiance.” This refers to the top line of Abundance changing into the top line of Radiance. The line statement says, “The house is lofty and overshadows the home; the gates and courtyard are shut, and within there is no one. For years no one comes to visit: misfortune.” A year later, the people of Zheng did indeed kill Manman.

In these three cases, those who used the Changes relied on the meaning of just one line statement to judge good or ill fortune.

If there are three such cases, they are simply outcomes produced when a single line changes and points to another hexagram. When Cai Mo answered Wei Xianzi’s question about a dragon appearing in the countryside outside Jiang, however, he quoted the Zhouyi directly: “When the Qian hexagram changes into Gou, it says, ‘The hidden dragon: do not act.’ When it changes into Tongren, it says, ‘The dragon appears in the field.’ When it changes into Dayou, it says, ‘The flying dragon is in the sky.’ When it changes into Guai, it says, ‘The overreaching dragon will have cause for regret.’ The Kun hexagram says, ‘When a host of dragons appears without a leader, good fortune.’ When Kun changes into Bo, it says, ‘Dragons battle in the wild.’”

The dragon imagery and actual events involving dragons discussed here may not all be fully explained through the principles of meaning. Yet the six line statements from Qian and Kun that Cai Mo cites compare the statements associated with their mutual transformations, showing which hexagram a single changing line points to. The Zhouyi as a whole has sixty-four hexagrams and three hundred eighty-four lines; changes among its hexagrams and lines generally follow this principle.

This is enough to explain the Great Commentary on the Changes’ statement, “The statements each point to where [the change] is going”: the statements for the hexagrams and lines each indicate the hexagram toward which a change tends. They are not set up for some other purpose; they are made for the hexagrams that arise through change. In this way, one can observe how things under Heaven change and examine how they converge and connect, so as to apply principles and judge good or ill fortune. One can also adapt and act in step with change, so that one’s actions accord with where it leads. The outcome toward which change tends is what is called the resulting hexagram.

Thus it is said: “The hexagram and line images change within, while good and ill fortune appear without. Achievements emerge through change, while the sage’s intent is expressed in the statements for the hexagrams and lines. Hexagrams differ in scope, and their statements in danger or ease; the statements for the hexagrams and lines each indicate the outcome toward which change tends.”

Scholars use these principles to observe how things change and determine the hexagram images, and to derive the line images through numerical calculation. They probe deeply into what is subtle and profound, study the faint signs of change in things, and thereby reach a wondrous state. They follow the Dao and De, and handle affairs in accord with what is right. By exhausting the principles and changes of things, they determine the hexagram images; through numerical calculation, they derive the line images. They probe deeply into what is subtle and profound, study the faint signs of change in things, and thereby reach a wondrous state. They follow the Dao and De, and handle affairs in accord with what is right. They exhaust the principles of things and fully develop human nature, thus coming to understand Heaven’s mandate. When the body and function of the Changes are fully grasped within, one has perhaps reached this state.

End of Book One of The Comprehensive Changes in Divination.

The Comprehensive Changes in Divination, Book Two

Written by the Daoist Lei Siqi of Linchuan

Nine and Six

The Changes begins with the two kinds of Yin and Yang lines. A Yang line is drawn as one unbroken horizontal stroke and is called “odd”; a Yin line is drawn as two separated horizontal strokes and is called “even.” As the lines of the Qian hexagram divide and develop, they form the Zhen hexagram, the Kan hexagram…

The Changes (the Zhouyi) is based on two kinds of symbols: a yang line is one unbroken horizontal line, called “odd”; a yin line consists of two separated horizontal segments, called “even.” The yang lines of the Qian hexagram divide and combine to form the yang lines in the Zhen, Kan, and Gen hexagrams. The yin lines of the Kun hexagram divide and combine to form the yin lines in the Xun, Li, and Dui hexagrams. Thus it is said: “Yang hexagrams take odd; yin hexagrams take even. Yang hexagrams contain more yin lines, while yin hexagrams contain more yang lines.” Although odd and even, and more and fewer, may seem to be matters of counting, this does not mean that these hexagrams were originally called “nine” or “six.”

The sages composed the Changes by observing the transformations of yin and yang and establishing the hexagram images, thereby embodying yin and yang in the Way of Heaven. They also explained how the transformations of firmness and yielding give rise to the lines, thereby embodying yielding and firmness in the Way of Earth. Each hexagram consists of six strokes; the strokes are yin or yang, and yielding and firmness alternate. Arranged in six positions, they form the hexagram image. “Stroke” and “position” refer to the symbols and placements of the hexagrams and lines. These symbols themselves are not divided into nines and sixes.

Later, when the Qian hexagram was doubled, all six positions contained yang lines, and “nine” was attached before the line statements; there is also the example “use nine.” When the Kun hexagram was doubled, all six positions contained yin lines, and “six” was attached before the line statements; there is also the example “use six.” The line statements of the other hexagrams likewise bear the labels nine or six. Having seen this so often, scholars grew accustomed to regarding the lines as nines and sixes, without asking why. The author argues that this view deserves to be reconsidered.

Nine and six are numbers. The Commentary on the Changes says: “Exhausting the principles of number to infer what is to come is called divination; understanding transformations and putting them to use is called action.” Nine and six are numbers used in divination and in working out transformations. Such calculations begin with “combining three and five to bring about change, and interweaving and arranging their numbers”: Heaven has five numbers, and Earth also has five; the numbers of Heaven total twenty-five, those of Earth total thirty, and the numbers of Heaven and Earth together total fifty-five. These numbers bring about transformations and set the principles of spirits and spirits in motion. Yet here the numbers of Heaven and Earth themselves are not directly identified as nine or six.

Regard the numbers of Heaven as one, three, five, seven, and nine, whose sum is twenty-five; regard the numbers of Earth as two, four, six, eight, and ten, whose sum is thirty. The numbers of Heaven and Earth together make fifty-five. The ancients held that these numbers formed the basis for the transformations of all things and the movements of spirits and ghosts. This does not mean, however, that the numbers of Heaven and Earth are directly identified as nine and six.

The numbers of Heaven and Earth are paired across five positions, with each pair making a sum. Thus, numbers below five are called “generative numbers,” and those above five are called “complete numbers”: one pairs with six to form Water, two with seven to form Metal, three with eight to form Wood, four with nine to form Fire, and five with ten to form Earth. In this way, nine and six emerge through the pairing of numbers, but their use in divination still requires further explanation.

Numbers below five belong to the “numbers of substance,” while those above five belong to the “numbers of function.” Among the generative numbers that make up the numbers of substance, the numbers of Heaven—one, three, and five—add up to nine, while the numbers of Earth—two and four—add up to six. This is the meaning of “taking three from Heaven and two from Earth as the basis for numbers”: using three numbers of Heaven and two of Earth to establish the method of deriving numbers. The three numbers of Heaven add up to nine, and the two numbers of Earth to six. This is why nine and six stand out in particular as the numbers used in divination.

“To pair one with four to make five, and two with three to make five” means pairing numbers and combining them in alternating ways to produce five. Then pair five in turn with one, two, three, and four to obtain six, seven, eight, and nine; pairing five with five gives ten. Five and ten add up to fifteen, as do seven and eight, and nine and six. This is what is meant by “combining groups of three and five to bring about change, interweaving and rearranging the numbers”: the numbers are paired and combined with one another, then repeatedly rearranged to derive transformations.

The numbers nine, six, seven, and eight all make the generative numbers of Heaven complete by means of the complete numbers of Earth. This is what is called “forming images.”

Add five to one, two, three, and four respectively, and the results are six, seven, eight, and nine: six is old Yin, seven young Yang, eight young Yin, and nine old Yang. Among Yin and Yang lines, the young remain unchanged, while the old change. People are familiar with the nines and sixes marked beside the hexagram lines in the Yijing, but often do not know that the fixed number for a Yang line is seven and for a Yin line, eight. The phrase “the nines, sixes, sevens, and eights of the lines transform and serve as the basis for use” means that these four line values together provide the basis for judging change in divination.

The Yi concerns change. “Exhausting numerical patterns to infer what is to come is called divination; understanding change and acting accordingly is called action.” This describes the principles of change in divination. In the yarrow-stalk method, four rounds of calculation make one change, and eighteen changes form a hexagram. The results of every three changes combine to form one line; four and eight are then used to distinguish odd from even, that is, Yang lines from Yin lines.

When the three results are combinations such as one, four, two; one, two, four; two, four, one; or four, two, one, they symbolize hexagrams such as Zhen, Kan, and Gen and are drawn as Yang lines. When the results are combinations such as one, eight, two; one, two, eight; two, eight, one; or eight, two, one, they symbolize hexagrams such as Xun, Li, and Dui and are drawn as Yin lines. This expresses the idea that the intermingling of Yin and Yang gives rise to the six children. Only when all three results are four is the line drawn as Yang, symbolizing Qian; only when all three are eight is it drawn as Yin, symbolizing Kun.

The combinations of one, four, two, and eight add up to the fixed value seven for a Yang line; the combinations of one, eight, two, and four add up to the fixed value eight for a Yin line. These two kinds of lines do not change. When all three results are four, the Yang line has reached its extreme and is called a moving line, with the value nine. When all three results are eight, the Yin line has reached its extreme and is also called a moving line, with the value six. Both kinds of lines change.

The fixed Yin and Yang lines listed at the beginning of each hexagram indicate only whether the lines are moving or still, showing the substance of firmness and yielding. The lines that do not change form the fixed hexagram.

Moving lines such as nine and six are interspersed among the various hexagrams and are not listed at the head of each hexagram. They do not represent change, but serve specifically to mark the underlying nature of firmness and yielding. When no change occurs, they are drawn as fixed hexagrams. Moving lines such as nine and six are interspersed among the various hexagrams and are not included in the hexagram figures themselves; instead, they signify the operation of Yin and Yang. When change occurs, they are activated accordingly, forming the resulting hexagram—the hexagram produced when the original hexagram changes. This is precisely what “Using Nine” and “Using Six” are meant to explain.

The Duodu says: “Yang moves by advancing, while Yin moves by withdrawing and holding its position. Thus, seven is the image of Yang and eight the image of Yin; Yang changes from seven to nine, and Yin changes from eight to six.” Chao Shuozhi, whose courtesy name was Yidao, said: “When the ancients drew hexagrams, they used odd and even lines respectively to represent Yang and Yin. A hexagram had only six positions; the names seven and eight did not yet exist. Later, some adopted Cao Yan’s account of the Yi, calling changing lines of old Yang ‘nine,’ and changing lines of old Yin ‘six,’ while calling young Yang ‘seven’ and young Yin ‘eight.’ The seven and eight in the Zhouyi are what the ancients called odd and even.”

In Yi divination, when nine or six appears in the hexagram statement, it indicates that the corresponding line will change. For example, if all six lines are nines, Qian changes into Kun; if all six are sixes, Kun changes into Qian. These are examples of “Using Nine” and “Using Six,” and are sufficient to explain the principle. What I have observed is the same. The cases recorded in the Zuo Zhuan can further corroborate one another, and it is also necessary to examine the errors in their annotations.

After Lady Mu Jiang of Lu died, her body was initially taken to the Eastern Palace. A divination was performed, yielding the Gen hexagram, with an “eight” among its lines. The diviner said: “This is Gen changing into Sui. The Sui hexagram means following the ruler; you will surely leave here soon.” Mu Jiang replied: “That cannot be. The Zhouyi says that the Sui hexagram is primordial, prosperous, beneficial for upholding what is right, and free of misfortune. ‘Primordial’ means the beginning of all things; ‘prosperous’ means the gathering of goodness; ‘beneficial’ means consonant with what is right; and ‘steadfast’ means that things can hold to the right way.”

Treat people with benevolence and kindness, and you can become an elder to the community. Gather people through beautiful and proper ritual, and they will observe the rites and laws. Let all things obtain their benefit, and you will accord with what is right. Hold fast to the way of uprightness, and you can accomplish your work. Yet uprightness must not be twisted at will. Thus even the hexagram Sui, “Following,” can be said to bring no blame.

I am a woman, yet I have taken part in disorder; I cannot claim to be without fault. I cannot bring peace to the state, so I cannot claim to be flourishing. My actions instead bring harm upon me, so I cannot claim they are beneficial. I have abandoned my position to pursue beauty, so I cannot claim to be following the right way. Only when these four virtues are present can following in one’s actions bring no blame. I possess not one of them. How, then, can I call this proper following? I am bringing punishment upon myself. My conduct must not continue, and it will cause harm besides. How could I escape blame? I will surely die in this palace, with no way out.

For this reason, I once used the hexagram Gen, “Keeping Still,” to divine on this matter. It especially shows that seven and eight are used to determine the hexagram lines, rather than treating nine and six as changing lines; the commentary got this wrong. The Rites of Zhou says that the Grand Diviner was in charge of the three Changes and carried out nine methods of divination. The three Changes are the Lianshan, Guicang, and Zhouyi. All are based on the eight trigrams, which are combined to form the sixty-four hexagrams. This shows that although the Changes have three names, their methods of divination are the same: seven and eight determine the hexagram lines, while nine and six indicate the action of the lines. This is what is meant by “Gen changing into eight.”

When Gen changes, its first line becomes the hexagram Bi, “Adornment”; its third line becomes Bo, “Stripping Away”; its fourth becomes Lü, “Travel”; its fifth becomes Jian, “Gradual Progress”; and its top line becomes Qian, “Modesty.” Thus, the divination yields Gen: five of its six lines change, each transforming in turn into a different hexagram. The official historian considered these changes all together and was left unable to judge. Only the second line, a yielding line, remains unchanged and does not transform into another hexagram. It should therefore be examined through the hexagram’s reverse and inverse forms, and the judgment should be made on the basis of Gen changing into Sui, “Following.”

He then examined the divination record from that time and said, “Obtaining the Hexagram Sui indicates a journey; the ruler should set out at once.” Jiang then examined himself and concluded that he was unworthy of receiving the virtue and meaning shown by this hexagram. Next, he quoted the hexagram statement from the Zhouyi: “Sui: beginnings, success; it is fitting to remain correct; there will be no misfortune.” He then explained again, “The Hexagram Sui indicates a journey; the ruler should set out at once.” Jiang again reflected on himself and concluded that he was unworthy of receiving the hexagram’s virtue and meaning. The explanation that follows merely repeats these points.

How could this passage have quoted the two Changes texts Lianshan and Guicang? And how could it have performed another divination? Du did not understand the divination method of the Zhouyi. He mistook the fact that there are only eight kinds of paired hexagram lines for the basis on which Lianshan and Guicang made their judgments, using seven and eight. He also claimed that the court diviner suspected that obtaining an “eight” in a Zhouyi divination was inauspicious, and then explained it using the Zhouyi method of divining changing lines. This was a grave error. A closer examination makes clear that seven and eight are simply the formed hexagram lines within a hexagram structure; they are not called “nine” or “six,” the numbers used to mark yang and yin lines and their changes.

The Discourses of the States (Guoyu) records that Chong’er, a prince of Jin, consulted the oracle to ask whether he would ever again possess Jin. The primary hexagram was Zhun and the resulting hexagram was Yu; the lines in both hexagrams were numbered “eight.” Wei Zhao’s commentary explains that the inner trigram of Zhun is Zhen, and its two yin lines do not change; the outer trigram of Yu is also Zhen, and its two yin lines likewise do not change. That is why the account says “both are eight.” This is evidence for the method of divination. Dong Yin later divined for him as well and obtained the hexagram Tai, which also contained an eight. Wei Zhao explains that Tai has no changing lines; its unchanging yin lines are all numbered eight. This, too, serves as evidence.

We can therefore see that an unchanging yin line is recorded as “eight,” and an unchanging yang line as “seven.” This is clear. Yet the Zhouyi contains no “seven” or “eight”; it shows only “nine” and “six.” Scholars often mistake the phrases “using nine” and “using six” as referring to a distinction between these two line numbers, without understanding how nine and six are used. As explained above, they refer to the lines’ changing states and were established to show how hexagrams and lines transform.

The Zuo Tradition makes clear that whenever it speaks of “one hexagram changing into another,” it means that a line moves and transforms, producing a different hexagram. In other words, change leads to different outcomes. Diviners therefore focus on the judgment, while changing lines reveal the transformation; the term “line” refers precisely to change. The sages observed how the myriad things under Heaven moved and changed, examined their convergences and pathways, and on that basis established enduring norms and ritual systems. They also attached judgments to the hexagrams and lines to determine good and ill fortune; hence the term “line.” Though the changes under Heaven are many, they follow an order. Thus the text says, “The meaning of the six lines is easy to make manifest”: the six lines clearly reveal the meaning of change.

From this we may infer that before a line moves, its number is fixed as either seven or eight. Once it moves, a yang line advances from seven to nine, containing a yin element; a yin line recedes from eight to six, containing a yang element.

When the Zhuan discusses the lines that change during divination, it generally follows the rules outlined earlier. Cai Mo makes this especially clear when answering Wei Xianzi’s question about dragons.

Cai Mo says that the Zhouyi gives examples of this. When the Qian hexagram changes into Gou, the corresponding line statement in Gou is “Hidden dragon: do not act.” When it changes into Tongren, the corresponding statement is “Dragon appearing in the field.” When it changes into Dayou, it is “Flying dragon in the heavens”; when it changes into Guai, it is “Arrogant dragon will have cause for regret.” Kun contains the statement “See a host of dragons without a leader. Auspicious.” When Kun changes into Bo, it has “Dragons fight in the wild.” These examples show that only after lines such as seven and eight change and bring about a transformation can they be called nine and six.

Otherwise, each line of Qian already has its own statement, such as “Hidden dragon: do not act,” and the statement for the top six in Kun is already “Dragons fight in the wild.” Why, then, would one need to list each transformation, such as Qian changing into Gou and Kun into Bo, and cite the corresponding line statements to explain the rule? In particular, beneath “Use nine” in the Qian hexagram is written “See a host of dragons without a leader. Auspicious.” Yet Cai Mo specifically says this is a line statement from Kun, and only then explains it according to his interpretation. This further shows that “Use nine” refers to a situation in which the line pattern changes.

Each time, he first identifies the hexagram that results from the change, then cites that hexagram’s line statement to explain that a yang line changes from seven to become nine, while a yin line changes from eight to become six. Thus, examining the hexagram and line statements cited in the Yizhuan, we can see that a line must change from seven or eight in order to become nine or six.

That is why there are the expressions “using nine” and “using six”: they refer to how nine and six are used in divination. In the Qian hexagram, from the first line through the top line, a yang line is based on seven and is called “nine” only after it changes. In the Kun hexagram, from the first line through the top line, a yin line is based on eight and is called “six” only after it changes.

Chao says that when nine and six appear in the lines of a hexagram, this means that all six line positions have changed. If all six lines are nines, Qian changes into Kun; if all six are sixes, Kun changes into Qian. The Duodu of the Qian (Qian Zuo Du) makes this point repeatedly as well: yang lines change forward, from seven to nine, symbolizing the growth of Yang Qi; yin lines change backward, from eight to six, symbolizing the decline of Yin Qi. It also says that the Qian hexagram wanes over thirty-two generations, while the Kun hexagram waxes over thirty-two generations.

Thus the Great Commentary on the Changes says, “Are Qian and Kun perhaps the gateways of the Changes?” All things enter into transformation through this gateway of Qian and Kun. The other hexagrams, too, can be understood according to this principle: only after a hexagram changes are its lines called nine or six. That is why “using nine” and “using six” appear only in the Qian and Kun hexagrams, and not in the others. [The phrase “sheng min” in the original appears to be a textual corruption. The general meaning seems to be that the relevant method was not established solely for Qian and Kun, but should also be applied to the other hexagrams.]

In divination, if none of the six lines change, one judges by the statement of the original hexagram. If five lines change and only one remains unchanged, one judges by the image statement for that unchanged line in the resulting hexagram, rather than by the line statement. Since this line has not changed, it cannot be called nine or six.

Ouyang Yongshu asked, “What does it mean that the Qian hexagram says ‘using nine’ and the Kun hexagram says ‘using six’?” The reply was, “This explains why seven and eight are not used.” The lines of the Qian hexagram are represented by seven or nine; nine changes; …

Some explain that seven and eight are not used as changing lines because the line numbers in the Qian hexagram include seven and nine, with nine changing, while those in the Kun hexagram include eight and six, with six changing. Divination with the Yi determines good and ill fortune through changes in the lines, so the lines are named using the numbers that change. Zhu Xi strongly agreed with this explanation. He also explained what “using nine” in the Qian hexagram and “using six” in the Kun hexagram mean: in divination, a Qian line may be seven or nine, and a Kun line may be six or eight. Nine and six change, while seven and eight do not. The Yi examines change, so lines are named according to the line images obtained through divination; this does not mean that all six lines are nine or six.

In actual divination, sevens and eights are usually more common than nines and sixes, and sometimes no nines or sixes appear at all. Each of these outcomes therefore needs interpretation. This applies to all sixty-four hexagrams, though the point is stated more clearly for Qian and Kun, from which the other hexagrams can be understood by extension. The author considers this explanation a significant contribution, clarifying what earlier scholars had not fully explained. The claim that sevens and eights are common while nines and sixes are rare also shows that the divination method of the time formed a hexagram through three transformations, as Yi Xing said. On this basis, the author examines Zhu Xi’s account and concludes that Zhu Xi had seen only Ouyang Xiu’s explanation, or perhaps the explanation by the Master Chao; he had probably not encountered these other interpretations.

As for works such as the Qian Zao Du, Confucian scholars often look down on them, considering them part of the Weft texts on the Yi—that is, texts that interpret the Yi Jing. They not only reject them, but some do not read them or have never even seen them, unaware that they contain material useful for comparison and textual verification. In the author’s view, Ouyang Xiu’s and the Master Chao’s explanations mentioned above were probably both unknown to Zhu Xi.

As for books such as the Qian Zao Du, Confucian scholars often looked down on them, regarding them as works of the Yiwei—texts that explain and supplement the Classic of Changes. They not only declined to accept them; some did not read them or had never even seen them. Yet they did not realize that these books, too, contain material worth consulting. When we examine records from ancient and more recent times, we find that some accounts, though not deliberately made alike, naturally correspond. Still, none explains clearly why the numbers nine and six are what they are.

For example, the Zuo Tradition records many cases in which divinations came true. These accounts help fill gaps in the meaning of the Classic of Changes, so I have included the relevant details here. But I have also carefully considered the view of Master Chao, who argues that the hexagram and line statements use only nine and six, never seven and eight. He is merely raising a question; that does not mean he truly understands the principle behind nine and six.

I respectfully note that the Discussion of the Trigrams says: “In ancient times, the sages created the Changes and secretly assisted the spirits; thus the milfoil stalks came into being.” This clearly describes the method of divination using milfoil stalks. The phrase “taking three from Heaven and two from Earth to establish the numbers” means that Heaven’s number is divided into three: three multiplied by three gives nine, called “three from Heaven.” This corresponds to the Qian hexagram’s “Qian’s primal power uses nine.” Earth’s number is divided into two: three multiplied by two gives six, called “two from Earth.” This corresponds to the Kun hexagram’s “Kun’s primal power uses six.” This is the origin of the use of nine and six.

“Observing the changes of Yin and Yang to establish the trigrams” refers to establishing Yin and Yang as the way of Heaven, yielding and firmness as the way of Earth, and benevolence and righteousness as the way of humanity. Taking together the Three Powers—Heaven, Earth, and humanity—and dividing each into two gives the Changes’ six-line hexagram. We can therefore see that the symbols at the head of a hexagram mark odd and even numbers. When no change is underway, the lines remain fixed, with seven and eight implicit within them.

As for “developing firmness and yielding to produce the lines,” a line differs from a stroke. A stroke that has not yet changed and remains still is called a “stroke”; once it begins to change, it is called a “line.” The Changes uses six positions to form the pattern of a hexagram. From the initial position to the top position, Yin and Yang each have their fixed places, while firmness and yielding alternate in their operation. Change is ceaseless, moving through the six positions. Above and below, nothing remains constant; firmness and yielding transform into one another, each tending in its own direction as change unfolds. Sometimes the number taken is nine, from Heaven; sometimes it is six, from Earth. The use of nine and six is precisely what allows them to change within the lines and thereby produce changing hexagrams. What is there to doubt about nine and six?

The sages observed the traces and transformations of the myriad things under Heaven, modeled the forms of different things, and examined how they meet and connect. They then attached statements to the hexagrams and lines to judge good and ill fortune. That is why it is said that the hexagram images form an ordered pattern. The words of the Changes are concise, yet its principles are complete; its way of making those principles clear to the world and to later generations is already plain. Scholars know the terminology but not what lies behind it, and follow these teachings all their lives without realizing it. Instead, they let their doubts lead them to make their own conjectures, imagining that they alone have discovered something, and write up their own accounts. This is truly lamentable. For this reason, I have taken care to explain these principles.

The Middle Volume of Yishi Tongbian ends here.

1. The character “jin” was originally written as “que”; it has been corrected on the basis of the Siku edition.

2. The term “gua wen” appears as “gua yao” in the Siku edition.

3. The author developed his own interpretation and set it down in writing, which is all the more lamentable. For this reason, it is explained here in detail.

The Middle Volume of Yishi Tongbian ends here.

1. The character “jin” was originally written as “que”; it has been corrected on the basis of the Siku edition.

2. The term “gua wen” appears as “gua yao” in the Siku edition.

3. The two characters “men yan” were originally written as “wei”; they have been corrected on the basis of the Siku edition.

4. “Mu Jiang” was originally written as “Mu Hua”; it has been corrected on the basis of the Siku edition.

The Lower Volume of Yishi Tongbian

Written by the Daoist Lei Siqi of Linchuan

Numerical derivation (working out numerical principles)

The total number of Heaven and Earth is fifty-five: the numbers of Heaven are one, three, five, seven, and nine, adding up to twenty-five; the numbers of Earth are two, four, six, eight, and ten, adding up to thirty. In principle, these numbers should not increase or decrease. Yet the “Great Expansion number” subtracts five and gives fifty. As a result, attempts to infer the underlying principle yield no answer, and checks of the numbers do not add up. No one has ever been able to grasp the fundamental meaning. People have offered different explanations, each seemingly plausible in some respects, but no one has truly understood what it means. This has been the case since antiquity.

Because they are bound by traditional doctrines, Confucian scholars probably did not wish to accept or read the book Liezi, and so they were especially unaware of its discussion. The book opens by saying that sages use Yin-Yang to govern Heaven and Earth. Since things with form arise from what is formless, where, then, did Heaven and Earth themselves come from? The book therefore describes four stages: Great Change, Great Beginning, Great Origin, and Great Substance. Great Change is the stage before Qi has appeared; Great Beginning is the stage when Qi first arises; Great Origin is the stage when form first takes shape; and Great Substance is the stage when material substance first emerges. When Qi, form, and substance are all present but have not yet separated from one another, this state is called “undifferentiated wholeness”: all things are mixed together and remain undivided. Hence it is called “Change.”

“Change” transforms into “One”; “One” marks the beginning of the transformation of form. This account also appears in Qianzaodu, a text in the Weft of the Changes, where the view is essentially the same. From this we can see that the “Supreme Ultimate” spoken of in the Changes is simply a name for the state of undifferentiated wholeness. Before this state, one can speak of Great Change, Great Beginning, Great Origin, and Great Substance; together with undifferentiated wholeness, there are five names. Thus calling undifferentiated wholeness the Supreme Ultimate is what is meant by the “Five Great Stages.”

This means that the “Five” are already contained within Taiji (the Supreme Ultimate, the source from which all things arise and change). The numbers of Heaven and Earth therefore add up to fifty-five, while the Great Expansion number, used in the calculations of the Changes, is fifty. It sets aside the Five contained within Taiji and uses fifty to bring the subtleties of divination into play.

The Commentary on the Changes says: “Unceasing generation and transformation is called Change; taking form is called Qian; modeling forms and establishing patterns is called Kun; carrying numerical calculation to its limit and thereby knowing what is to come is called divination; carrying transformation through is called action; and the unfathomable transformations of Yin and Yang are called spirit.” This is precisely the principle at work here.

From this we can see that the Changes takes Taiji as the One, and that the One is the beginning of changes in form. The text says that the Changes has Taiji, and that “unceasing generation and transformation is called Change.” It then says, “taking form is called Qian,” without mentioning Taiji again. Why? Because Taiji is the shared source of Yin and Yang, and Taiji itself is the root where their transformations converge. Thus, the Changes transforms and manifests as the One; the One is the beginning of changes in form. The Changes uses Taiji to signify this One, corresponding to “taking form is called Qian”—that is, the beginning of changes in form. The One is also the root that encompasses all things.

Qian divides from the One into Two; only then is it called Kun. Of the fifty Great Expansion numbers, the One that is set aside symbolizes the Changes’ Taiji. The One dividing into two aspects symbolizes the formation of the Two Modes (the two aspects of Yin and Yang). They are called the Two Modes rather than simply “Two” to show that they derive from the One. Thus, in the Great Expansion number of fifty, the unused One, Taiji, is given primacy and regarded as the root from which all things are ceaselessly generated.

The passage says that divination uses forty-nine stalks of milfoil and begins by dividing them into two bundles, symbolizing the Two Modes (Yin and Yang). One stalk is then set aside to symbolize the Three Powers (Heaven, Earth, and humanity). The stalks are next counted in groups of four, symbolizing the four seasons. From this, the four directions—north, south, east, and west—the order of the four seasons—winter, summer, spring, and autumn—and the four directional correspondences of Water, Fire, Wood, and Metal all become apparent. Counting by fours therefore symbolizes the four seasons; on this basis, the numbers in the River Chart (Hetu) are said to total forty.

Yet the numbers of Heaven and Earth total fifty-five, while the number of Great Expansion (Dayan) is fifty. The “five” among the numbers of Heaven has no place among the Four Images, and the “ten” among the numbers of Earth has no place among the Eight Trigrams. Why, then, is there such a great difference between them?

The “five” among the numbers of Heaven exists as a number but has no fixed position. The ancient form of the character “five” symbolized vertical and horizontal lines crossing, like Yin and Yang meeting. Its modern form depicts Yin and Yang alternating within “two”; the shape of “ten” also emerges from this. Five belongs to Earth, and the form of the character “earth” likewise contains the idea of beginning with one, residing at five, ending at ten, and then returning to one. Earth has no fixed central position, so “five” is not listed among the Four Images, nor is “ten” listed among the Eight Trigrams.

I once investigated the origin of the fifty-five ascribed to the numbers of Heaven and Earth. When the numbers one, two, three, and four among the Four Images are used to form the Eight Trigrams, one need only use one, two, three, and four again, adding five to each to obtain six, seven, eight, and nine. The total is therefore only forty-eight.

In the numbers of the trigrams, one and nine, two and eight, three and seven, and four and six intersect in pairs, and each pair sums to ten. Calculated this way, the total is only forty; the numbers “Heaven five and Earth ten” have not been treated as fixed numbers assigned to particular directions. It is precisely because Heaven’s number five and Earth’s number ten are paired that multiplying five by ten yields the Great Expansion’s number, fifty.

How can this be explained? The function of “five” is to pair the Eight Trigrams so that Yin and Yang can transform into one another. The number of the northern Kan trigram is one; add five and it becomes six, corresponding to the northwestern Qian trigram. The number of the eastern Zhen trigram is three; add five and it becomes eight, corresponding to the northeastern Gen trigram. This first takes the numbers of the cardinal directions, then shifts them to the diagonal directions. The number of the southwestern Kun trigram is two; add five and it becomes seven, corresponding to the western Dui trigram. The number of the southeastern Xun trigram is four; add five and it becomes nine, corresponding to the southern Li trigram. This first takes the numbers of the diagonal directions, then shifts them to the cardinal directions. Thus, adding five to an odd Yang number turns it into an even Yin number; adding five to an even Yin number turns it into an odd Yang number. Yin and Yang differentiate in this way, and the Eight Trigrams are thereby arranged and formed.

The function of “ten” is to bring together the numbers of opposing trigrams. Li, in the south, has the number nine; opposite it is Kan in the north, with the number one, and together they make ten. Dui, in the west, has the number seven; opposite it is Zhen in the east, with the number three, and together they make ten. These are Yang numbers joining with one another, each returning to a cardinal direction. Gen, in the northeast, has the number eight; opposite it is Kun in the southwest, with the number two, and together they make ten. Qian, in the northwest, has the number six; opposite it is Xun in the southeast, with the number four, and together they make ten. These are Yin numbers joining with one another, each returning to a diagonal direction.

Next, a space of five is left empty at the center of each position, so each group becomes another transformation of fifteen. Firmness and yielding grind against one another; the Eight Trigrams stir and interlace with one another, transforming and connecting, then unfolding further. From this we can see that Heaven five and Earth ten each govern the functions of five and ten respectively.

Therefore, when divining with yarrow stalks, the stalks must be handled in groups of four, symbolizing the four seasons. This is where the functions of five and ten are expressed.

The “manipulation” (separating and counting the yarrow stalks in divination) described here involves adding five to one, two, three, and four, yielding six, seven, eight, and nine respectively, and then multiplying each result by four. Six gives twenty-four, the stalk count for old Yin, the Kun hexagram; seven gives twenty-eight, the count for the young Yang hexagrams Zhen, Kan, and Gen; eight gives thirty-two, the count for the young Yin hexagrams Xun, Li, and Dui; and nine gives thirty-six, the count for old Yang, the Qian hexagram.

The seven and eight of young Yin and young Yang do not change. Added together, they make fifteen, representing the unchanging lines in a doubled hexagram—a six-line hexagram made up of an upper and a lower trigram. The six and nine of old Yin and old Yang do change. Added together, they also make fifteen, representing the changing lines in a doubled hexagram. The transformations of the Classic of Changes correspond to the four seasons, so yarrow stalks are manipulated in groups of four to symbolize transformation. The “four operations that bring about change” in the Classic of Changes—the four steps of yarrow-stalk divination—derive from this.

The actual number of the Yellow River Chart is forty. Remove two fives from the heavenly number five, then use the earthly number ten to extend the calculation, and the result is fifty. Each line requires three rounds of yarrow-stalk manipulation. In each round, the stalks are divided into left and right groups, and the remainders from both sides are added together. The left side may have one remaining and the right three, or the left three and the right one; alternatively, each side may have two remaining. In every case, the total is four. If four remain on the left first, then four must also remain on the right afterward. The two fours combine to make eight, which is recorded as a number and shows that odd numbers must be paired with even numbers. Four is odd and eight is even; this also shows that adding eight to the Yellow River Chart’s forty forms the Eight Trigrams.

However, the remainder from each round of yarrow-stalk manipulation described here is four; it is never five or nine. Those who use the yarrow-stalk method today, however, hold that the remainder in the first round is either five or nine. This view comes from the explanation in the Commentary on the Classic of Changes that “the remainder in the first change is either five or nine.”

The remainder obtained in the second and third rounds is initially always four or eight. The source of this claim appears to be a mistaken belief that the “one stalk set aside” before the first round—taking one stalk from the bundle and placing it apart, before dividing the stalks into two piles—was also included in the count. This led people to say that the first round’s remainder was five or nine, and that only the second and third rounds yielded remainders of four or eight. In fact, they have mistakenly counted the one stalk set aside, thereby confusing the numbers used in the stalk-counting procedure.

The remainder from the stalk counting is originally four; add one to it and it becomes five. Originally eight; add one and it becomes nine. This is how the figures five and nine came about. But no one noticed that this “adding one” merely miscounts a remainder that was originally four stalks. It has no practical effect and only creates confusion. Besides, setting aside one stalk has its own place: it is one of the “four operations” in the stalk-counting method. It should be done after dividing the stalks to symbolize the two powers of Heaven and Earth, and before counting them in groups of four; it is not part of the count itself. If the single stalk set aside had not been mistakenly included, how could anyone claim that the second and third rounds always yield remainders of four or eight?

A change consists of counting the stalks once on each side, left and right. The Commentary on the Changes says, “Eighteen changes form a hexagram.” If a hexagram is formed through eighteen changes, then the procedure for counting the stalks should be the same each time. How, then, can one say that in every set of three rounds, only the first round yields a remainder of five or nine? On this account, only six of the eighteen changes would be special. If those six differ from all the others, how can they collectively be called eighteen changes?

This error originated in the commentary by Kong Yingda in his Correct Meaning of the Zhou Changes. Later scholars failed to examine the matter carefully, and either accepted the claim blindly or remained uncertain. Their explanations only deepened the confusion, and no one ever corrected it—a real pity. If the single stalk set aside should indeed be added to the remainder in the count, then how is this to be explained when the stalk is set aside only after the step called “gathering the odd stalks between the fingers”?

The errors discussed earlier probably arose from clinging to the saying, “The Great Expansion has a number of fifty, of which forty-nine are used.” This led to the mistaken belief that the one stalk “set aside” (taken from the yarrow stalks and hung up during divination) was included among the forty-nine actually used. But the point is that the stalk set aside marks the forty-eight stalks that actively take part in the calculations at each change. Only when the number of calculations performed with those forty-eight stalks is included do we arrive at the actual number in use. How could this one stalk be mixed in with the forty-eight and thereby disrupt the calculation?

Thus, the forty-eight yarrow stalks take part in the derivation and undergo actual changes; the stalk set aside records the number of changes. Together they make the “number in use,” forty-nine. Add the one stalk that was unused from the outset in the Taiji (Supreme Ultimate, the undifferentiated source of all things), and the result is the Great Expansion’s number of fifty.

“Fifty” refers to the yarrow stalks’ De (Virtue/Power), which is complete and wondrous. In the system of yarrow numbers, seven is the number of the round: seven times seven is forty-nine. In the system of hexagram numbers, eight is the number of the square: eight times eight is sixty-four. Seven and eight together make fifteen, a number already embodied in the numerical principles of the yarrow stalks and the hexagrams. The meaning of the six lines appears through change and is expressed separately in the nine in use of the Qian hexagram and the six in use of the Kun hexagram; nine and six together also make fifteen. As for five, and the numbers seven, eight, nine, and six below it, each has its own significance and none is without purpose. That is why five multiplied by ten is called the Great Expansion’s number of fifty.

Seen this way, the significance of all fifty-five numbers—from Heaven and Earth, and from one through ten—has a basis. Both the Great Expansion’s number of fifty and the actual number in use, forty-nine, can be fully explained. The ceaseless generative process of the Yi, the images presented by Qian, the principles embodied by Kun, divination that explores numerical patterns to discern what is to come, and the principles that enable us to understand change can all be understood from this. As for the unfathomable changes of Yin-Yang, called “spirit,” how to apprehend and put this wondrous power to use is up to the person.

The “Discussion of the Trigrams” says: In ancient times, when the sages created the Changes, they secretly assisted the way of the spirits and devised the method of divination with yarrow stalks. They established the numerical system by taking three as the number of Heaven and two as the number of Earth; observed the changes of Yin and Yang and created the images of the hexagrams; and, by fully revealing the transformations of firmness and yielding, called this the miraculous. How to grasp and explain this mystery depends on people.

Since yarrow stalks—the stems used in ancient divination—arose in this way, the numerical system was not invented out of thin air, the hexagram images were not made arbitrarily, and the lines that compose the hexagrams were not arranged at random. Hexagrams are formed from lines; the hexagrams display the divination numbers; and divination is performed with yarrow stalks. In this way, one can fully apprehend the signs of all things under Heaven and set their changes in motion. This is the basis for selecting and applying the Changes. The “Great Treatise” says: The virtue of the yarrow is round and wondrous; the virtue of the hexagrams is square and discerning; and the meaning of the six lines appears through change. This is the basis for using the number of the Great Expansion in yarrow divination.

The number of the Great Expansion is fifty, but only forty-nine stalks are used in divination. One stalk is set apart and honored as a number that takes no part in the procedure, symbolizing Taiji (the Supreme Ultimate), the undivided whole before the myriad things separate. This is what is meant by “The Changes contains Taiji.” The forty-nine stalks are then divided and placed in two groups, left and right, symbolizing the Two Modes—the two basic forces of Yin and Yang. This is what is meant by “Taiji gives rise to the Two Modes.” Yin and Yang each have an old and a young aspect, so the Two Modes already contain the Four Images: old Yang, young Yang, old Yin, and young Yin.

Next, one stalk is taken from the left group and placed between the fingers, symbolizing “three,” the Three Powers of Heaven, Earth, and humanity. Each of the Eight Trigrams consists of three lines, so drawing a trigram with three lines also symbolizes the way of the Three Powers. The author explains that the stalk set aside, together with the two groups on the left and right, makes three; taking one stalk from the divided groups and placing it between the fingers symbolizes humanity standing between Heaven and Earth. This is the meaning of “taking Heaven as three and Earth as two, and relying on these numbers”: the single stalk placed between the fingers symbolizes three, while the two divided groups symbolize two.

Thus, by observing the changes of Yin and Yang, the images of the hexagrams can be established. The stalk that does not take part in the procedure is not used directly in the calculations, yet it symbolizes the original One of Qian’s Yang. The signs of the myriad things begin from this, and so practical use also proceeds from it. When the One of Qian’s Yang differentiates into the Two of Kun’s Yin, the Yin and Yang that symbolize the Two Modes take shape. Each has an old and a young aspect, so the Two Modes contain the Four Images. Then, by dividing Yin and Yang and alternating firmness and yielding through the three lines that symbolize the Three Powers, the Four Images give rise to the Eight Trigrams. Each trigram has three lines; at this point the initial formation is complete, and the way of the Three Powers is revealed.

In general, the Yi describes the Taiji (Supreme Ultimate) giving rise to the Two Modes, the Two Modes to the Four Images, and the Four Images to the Eight Trigrams. This is a process in which the root of all things gradually becomes manifest as specific functions and forms. However, the number of the Great Expansion—the numerical system used in divination with yarrow stalks—is only touched on in the initial steps, such as “dividing into two” and “hanging one,” and has not yet been fully developed.

The unused number represented by the Taiji is one; the number of the Two Modes is two; and the number for hanging one is three. Although these three are listed in sequence, the yarrow stalks actually used in divination are only two: the one set aside as unused and the one hung up. Starting with fifty stalks and first using two in this way leaves forty-eight. This can be understood as drawing on the number forty in the Hetu to derive the Eight Trigrams. Each of the Eight Trigrams has six lines, making forty-eight line positions in all.

When the Eight Trigrams are paired and stacked, they form the sixty-four hexagrams. The sixteen Wandering Soul and Returning Soul hexagrams are not included among the six line positions of the standard Eight Trigrams, so the number considered here is limited to forty-eight. These sixteen hexagrams are then conceptually set aside from the forty-eight hexagram positions. The stalks are counted in groups of four, thereby forming the sixty-four hexagrams.

By observing changes in Yin and Yang, the hexagram images were established; by further revealing changes between firmness and yielding, the lines were produced. Lines represent the movement and transformation of things under Heaven. The Way of Heaven is expressed through Yin and Yang, the Way of Earth through yielding and firmness, and the Way of humanity through benevolence and righteousness. Since the Three Powers—Heaven, Earth, and humanity—are all included, and each has two aspects, the Yi uses six lines to form each hexagram.

Earlier, the unused one, the two symbolizing the Two Modes, and the three for hanging one were listed in sequence, leading from three to four. The stalks divided to the left are then counted in groups of four to symbolize the four seasons. The four seasons have eight solar terms, just as the Four Images give rise to the Eight Trigrams. Deriving eight from four explains how the sixteen hexagrams each have four line positions; deriving further from eight then forms the sixty-four hexagrams.

The “four-four remainder”—the number left over when the yarrow stalks are counted in groups of four—is used to represent Qian; the “eight-eight remainder” is used to represent Kun. Although eight is called “even,” it is also made up of two fours, so it can still be called “odd.” Groups of four are used to match the numbers formed in the process, which is why this step is also called “gathering the odd remainder.” In divination, counting by fours corresponds to the sixty-four hexagrams, while counting by eights corresponds to Kun’s symbolic numbers.

When yarrow stalks are used for divination, the remainder from counting will be one, two, three, or four. Gathering these remainders is called “gathering the odd remainder”; “placing the odd remainder at the notches” symbolizes the intercalary month in the calendar. An intercalary month accommodates the extra days in the calendar’s count, so the leftover “odd remainder” is used as its symbol; “odd” also carries the sense of something left over.

Next, count the stalks on the right in groups of four. The remainder will be either four or eight. Then consider the remainders from both sides together: if the right side has one left, the left side must have three, making four in all; if the right side has three left, the left side must have one, again making four; if the right side has two left, the left side also has two, making four; and if the right side has four left, the left side also has four, making eight. When the left has one and the right three, or the left three and the right one, the total is four and is treated as “odd.” When both sides have two left, they also total four, but under this system of numbers they are treated as a doubled four, making eight, and thus belong to the “even” category. If each side has four left, the total is likewise eight and is treated as “even.” Though called eight, it is still formed by combining two fours. Likewise, the Yin line in the Kun hexagram is explained as having branched off from a line in the Qian hexagram, so the whole is still collectively called “odd.”

Then return the remainder counted from the right, along with the corresponding stalks, to the left, and hang up the remainders counted from both sides to use in the second and third changes. This is called “notching again, then hanging.” The initial “hanging one” means taking one stalk from the forty-nine and hanging it separately; the later “hanging” means hanging up the remainders left after counting.

Then gather together the yarrow stalks that were previously divided into two parts, the single stalk set aside, and the stalks already counted in groups of four, restoring them to the initial state of the Great Expansion number. This is called “the four operations complete the Changes,” and it completes one round of divination for the first line.

The “four operations” are: dividing into two parts as the first step, setting aside one stalk as the second, counting by fours as the third, and collecting the remainder as the fourth. Once these four steps are complete, set aside the remaining stalks; the first change is then finished.

After the first change, retain the remainder that was set aside. Gather the other stalks together, then repeat the first change’s procedure: divide into two parts, set aside one, count by fours, and collect the remainder. This completes the second change. Set aside its remainder as well, combine it with the remainder from the first change, and prepare for the third change. The third change follows the same sequence: divide into two parts, set aside one, count by fours, and collect the remainder.

After all three changes are complete, add together the remainders from the three rounds and use their total to determine the resulting line image. A total of twelve is called “small”; a total of twenty-four is called “large.” If all three rounds yield small remainders, their total is twelve, leaving thirty-six stalks: the stalk count for Qian. If all three yield large remainders, their total is twenty-four, leaving twenty-four stalks: the stalk count for Kun. If two rounds yield large remainders and one yields a small remainder, their total is twenty, leaving twenty-eight stalks: the stalk count for Zhen, Kan, and Gen. If two yield small remainders and one yields a large remainder, their total is sixteen, leaving thirty-two stalks: the stalk count for Xun, Li, and Dui.

Here, “stalk count” refers to the number of yarrow stalks obtained through this method of divination. A “change” is one complete operation of dividing into two parts, setting aside one stalk, counting by fours, and collecting the remainder.

Only after three such changes is the complete result for one line of a hexagram obtained. When recording it, write down the remainder from each change in order, from the first to the third, building upward from the bottom, just as the lines of a hexagram are drawn.

A remainder of four belongs to Yang; a remainder of eight belongs to Yin. This follows the method of taking images used in the Eight Trigrams (Bagua). When two of the three results are eight and one is four, the resulting line is a Yang line:

• If the first result is four and the second and third are eight, this is the lower position of the Yang line, taking the image of Zhen, which represents young Yang, seven.
• If the first result is eight, the second is four, and the third is eight, this is the middle position of the Yang line, taking the image of Kan, which represents young Yang, seven.
• If the first and second results are eight and the third is four, this is the upper position of the Yang line, taking the image of Gen, which represents young Yang, seven.

When two of the three results are four and one is eight, the resulting line is a Yin line:

• If the first result is eight and the second and third are four, this is the lower position of the Yin line, taking the image of Xun, which represents young Yin, eight.
• If the first result is four, the second is eight, and the third is four, this is the middle position of the Yin line, taking the image of Li, which represents young Yin, eight.
• If the first and second results are four and the third is eight, this is the upper position of the Yin line, taking the image of Dui, which represents young Yin, eight.

When Zhen, Kan, or Gen is obtained, draw a Yang line; when Xun, Li, or Dui is obtained, draw a Yin line. These are all called “young,” indicating that Yin and Yang have not yet changed immediately.

If all three results are four—that is, four, four, four—regard the result as pure Yang, taking the image of Qian, the old Yang nine, and draw a Yang line. In the notation commonly used at the time, this old Yang line was called “double.” If all three results are eight—that is, eight, eight, eight—regard the result as pure Yin, taking the image of Kun, the old Yin six, and draw a Yin line. This old Yin line was called “crossing.”

Qian is old Yang: it is originally the odd-numbered Yang line, nine, and contains the possibility of transforming into the even-numbered Yin line, six. Kun is old Yin: it is originally the even-numbered Yin line, six, and likewise contains the possibility of transforming into the odd-numbered Yang line, nine. The lines of Qian and Kun are called “old” because Yin and Yang have reached maturity and can therefore change. A line must be determined through three changes to show that Yin-Yang change can be established only through a process of derivation and deliberation.

For each line, the remainder obtained through its three changes is distinguished according to the relation between four and eight. This embodies the idea that Qian and Kun interact to give birth to their six children. In every change, the stalks must be divided, set aside, and counted in the same way. First add together the remainders, then combine them with the stalks left over from the previous step. This process is called “three changes”; only when it is complete is one line formed.

Repeat the three changes to form the second line, then repeat them again to form the third. The three lines undergo nine changes in all. Once the nine changes are complete and all three lines are in place, they make one of the Eight Trigrams. Each trigram has three strokes, and arranging the three strokes in eight possible combinations produces the Eight Trigrams. These are called the inner trigram, lower trigram, three subtle lines, and inner correctness. Since the Eight Trigrams are now formed in their preliminary state, this is called the “Small Completion.” This is what the three versions of the Changes mean when they say that each has eight basic trigrams.

Next, carry out the same procedure: spread the stalks, divide them, set some aside, and count them, beginning by tallying the total number of remainder stalks. Group the changes in threes, accumulating them into nine changes; then complete three lines to form the outer trigram, also called the upper trigram, the three stalks, or outer regret. Combine it with the three lines formed by the previous nine changes, and the hexagram is complete with six lines. These are the sixty-four distinct hexagrams described in the three versions of the Changes. The hexagram is formed only after all eighteen changes are complete, and its six positions are thereby arranged in order.

Eighteen changes are required because Zhen, Kan, and Gen each have five strokes, making fifteen in total; add the three strokes of Qian, and the sum is eighteen. In the Qian hexagram, the first, third, and fifth lines are selected, which likewise add up to eighteen. Xun, Li, and Dui each have four strokes, making twelve in total; add the six strokes of Kun, and the sum is eighteen. In the Kun hexagram, the first line is selected and the fourth is not, which also adds up to eighteen.

Taking eighteen from each of the two counts and combining them gives thirty-six, corresponding to the number of stalks for the Qian hexagram: four times nine equals thirty-six. This is because in the first nine changes, each line undergoes four operations, making thirty-six operations across the nine changes. Doubling thirty-six gives seventy-two, the number of stalks used in turtle divination.

Earth, one of the Five Phases, governs eighteen days in each of the four seasons. Four sets of eighteen also make seventy-two days. Each season has ninety days; after subtracting the eighteen days governed by Earth, seventy-two days remain in each season. Thus, eighteen changes with four operations each also amount to seventy-two operations. Seventy-two multiplied by five equals three hundred and sixty, approximately the number of days in a year. This is why stalk divination uses eighteen changes and seventy-two operations, with forty-nine yarrow stalks.

In the first nine changes, the three lines are each determined as Yin or Yang and arranged into one of the Eight Trigrams; the hexagram image thereby takes shape. In the next nine changes, the Yin and Yang lines among the three alternate, and the Eight Trigrams are successively doubled to form six-line hexagrams. Across these eighteen changes, Yin and Yang, softness and firmness, are alternately put to use. They interact, shift, and transform, allowing change to flow through. Extending this process to the sixty-four hexagrams lets one follow the tendencies of change. In this way, change is contained within the hexagram images.

By extending this reasoning from the sixty-four hexagrams to the three hundred and eighty-four lines and beyond, there is no principle in the world that cannot be investigated. Can the function of the yarrow stalks not be called all-encompassing and wondrous, yet governed by a constant method? Can the function of the hexagrams not be called orderly and capable of illuminating the principles of things? Can the meaning of the six lines not be said to reveal change as they receive Heaven’s mandate, like an echo answering a call? Is this not precisely what is meant by “still and unmoving, yet when stirred, it penetrates the causes of all things under Heaven”? Thus, divination with the Changes can connect with the intentions of people everywhere, accomplish the affairs of the world, establish its undertakings, and resolve its doubts. It assists and supports the spirits, responding with certainty as it receives Heaven’s mandate and revealing itself through change.

Thus, the Changes can reach the intentions of all under Heaven, accomplish the affairs of all under Heaven, bring stability to the undertakings of all under Heaven, and discern the difficulties of all under Heaven. It subtly assists the spirits and generates numbers; it takes Heaven and Earth as its models to establish the numbers of the hexagrams, observes the changes of Yin and Yang to set out the hexagram images, and brings forth the qualities of firmness and yielding to generate the line figures. Could these have arisen arbitrarily? Could the numbers of the hexagrams depend on nothing at all? Could the images of the hexagrams have been set up at random? And could the line figures have been arranged haphazardly? If one can follow this method and bring one’s Virtue to a wondrous, spirit-like state, one can indeed make the Great Dao manifest, render one’s Virtue numinous, and thereby repay the spirits for their protection. The number of the Great Expansion is fifty, but in practice forty-nine are used. Perhaps this is the principle behind it.

End of Volume Two of The Changes: Divination and Transformation

Editorial note: Several characters and phrases in the text have been emended or supplied on the basis of the Siku Quanshu edition.