《大易象数钩深图(杨甲)》

The Taiji Diagram expresses the following teaching: Zhou Dunyi, whose courtesy name was Maoshu, passed this doctrine on to the two Cheng brothers. He said that the Supreme Ultimate is contained within the Non-Ultimate. The Supreme Ultimate moves and gives rise to Yang; when movement reaches its limit, it turns into stillness, and when stillness reaches its limit, movement begins again. Movement and stillness depend on each other, giving rise to Yin and Yang and forming the Two Principles.

As Yang Qi changes and Yin Qi combines with it, they produce the Five Phases: Water, Fire, Wood, Metal, and Earth. Each of the five kinds of Qi follows its own course, bringing about the succession of the four seasons. Ultimately, the Five Phases are Yin and Yang; Yin and Yang originate in the Supreme Ultimate, whose root is the Non-Ultimate. Once formed, the Five Phases each acquire distinct qualities. The original reality of the Non-Ultimate wondrously fuses and coalesces with the refined Qi of Yin-Yang and the Five Phases. The Qian principle gives rise to the male, and the Kun principle to the female. The two Qi of Yin and Yang interact and transform, bringing forth the myriad things. The myriad things reproduce without ceasing, and their transformations have no end.

An older explanation of the diagram says: Before the Supreme Ultimate has condensed into form, the Qian principle gives rise to the male and the Kun principle to the female. The two Qi of Yin and Yang interact and transform, bringing forth the myriad things. The myriad things flourish without end, and their transformations are boundless.

Another older explanation says: Before the Supreme Ultimate takes on concrete forms and numbers, it is simply one Qi. When this Qi divides, the light and pure part rises to become Heaven, while the heavy and turbid part descends to become Earth. This is the Supreme Ultimate giving rise to the Two Principles. Once Heaven and Earth are divided, Metal, Wood, Water, and Fire are arranged in the four directions. This is the Two Principles giving rise to the Four Images. Water is associated with the number six, occupies the Kan position, and gives rise to Qian; Metal is associated with the number nine, occupies the Dui position, and gives rise to Kun; Fire is associated with the number seven, occupies the Li position, and gives rise to Xun; Wood is associated with the number eight, occupies the Zhen position, and gives rise to Gen. This is the Four Images giving rise to the Eight Trigrams.

The diagrams that follow are titled “Diagram of the Supreme Ultimate Containing the Three Powers, with the Natural Odd and Even,” “Diagram Showing How Virtue and Affairs Are Interconnected and Rooted in Odd and Even,” and “Diagram of the Eight Directions in the Explanation of the Trigrams.” Here, “odd and even” refers to odd and even numbers, that is, Yang and Yin lines. The titles indicate that the Supreme Ultimate contains the Three Powers—Heaven, Earth, and humanity; that virtue and affairs are interconnected and rooted in Yin-Yang odd and even; and that the diagrams also show the directional positions of the Eight Trigrams.

The Qian hexagram consists of three lines and symbolizes Heaven because of the principle that “one contains three.” The Kun hexagram consists of six lines and symbolizes Earth because two lines form an even pair, and three such pairs together make six. The numbers of Heaven and Earth are one and two: these are the foundations of number. Heaven is represented by odd numbers and Earth by even numbers: these are the foundations of drawing hexagrams. These points are clear without comparison, but their subtlety lies in “one containing three, and two containing six.” Since Qian contains three, it gives rise to the three sons, whose lines are all Yang. Since Kun contains six, it gives rise to the three daughters, whose lines are all Yin. This is how Heaven and Earth generate the myriad things—a truly subtle principle.

Zhen symbolizes thunder. Thunder rises from beneath the ground, so its hexagram has one Yang line at the bottom. Kan symbolizes water. Water gathers within the earth, so its hexagram has one Yang line in the middle. Gen symbolizes a mountain. A mountain emerges above the earth, so its hexagram has one Yang line at the top. Yang governs movement, and Yin governs stillness. Zhen is grounded in movement, while Gen is grounded in stillness. Movement occupies the middle: it is neither inside nor outside. Thus it sometimes flows and sometimes stops, sometimes moves and sometimes rests. This is also why Kan symbolizes water.

Xun symbolizes wood. Wood grows up from beneath the ground, so its hexagram has one Yin line at the bottom. Li symbolizes fire. Fire kindles within wood, so its hexagram has one Yin line in the middle. Dui symbolizes a marsh, with one Yin line at the top. Yin is yielding, while Yang is firm; wood therefore begins soft and gradually grows strong, with a Yang line at its end. Yang is bright, while Yin is dark; fire is therefore bright on the outside and dim within, with Yang on the outside. Yang is dry, while Yin is moist; a marsh is therefore moist on the outside and dry within, with Yang on the inside.

Someone asked, “Why is a marsh dry within?” I replied, “Only when it is dry within can it generate metal; only when it is moist on the outside can it gather water. The principles that metal generates water and earth generates metal can also be understood through the symbolic meaning of Dui, the marsh. When the sages established images and drew meanings from them, they did not do so arbitrarily.”

Qian governs the initial beginning of all things.

Yang Qi begins to sprout in the Zi month. By the Chou month there are two yang lines; in the Yin month, three; in the Mao month, four; in the Chen month, five; and in the Si month, six. The Qian trigram lies in the northwest, before the Zi position. Thus it is said, “Qian knows the Great Beginning”: through the way of the father, Qian initiates Heaven and Earth.

Kun brings forth all things and brings them to completion.

Yin Qi begins to sprout in the Wu month. By the Wei month there are two yin lines; in the Shen month, three; in the You month, four; in the Xu month, five; and in the Hai month, six. The Kun trigram lies in the southwest, which corresponds to the Shen position. All things mature in the heart of autumn, at the time of You. Kun therefore begins bringing forth all things at Shen and brings them to maturity at You. Thus it is said, “Kun brings forth and completes all things.”

Heaven is honored, while Earth is lowly.

In the numerical order from one to ten, Heaven is above and honored, while Earth is below and occupies the lower position. Qian occupies the honored position, and so symbolizes the ruler, father, and husband; Kun occupies the lower position, and so symbolizes the subject, mother, and wife. These ideas all arise from the understanding that Heaven is honored and Earth is lowly. Thus it is said, “Heaven is honored and Earth is lowly; Qian and Kun are thereby established.”

Three in relation to Heaven and two in relation to Earth determine the numbers.

Qian’s primal force uses nine, symbolizing the number of Heaven as three; Kun’s primal force uses six, symbolizing the number of Earth as two. Thus it is said, “Take three from Heaven and two from Earth, and determine the numbers accordingly.” Here, nine and six refer to the generating numbers used in transformation.

The meaning of Yin and Yang can be illustrated through their correspondence with the sun and moon. The seal-script form of the character Yi (“Change”) is composed of “sun” and “moon,” indicating the sun’s course and the moon’s succession. Thus the meaning of Yin and Yang corresponds to the sun and moon.

The numerical diagram of the Yellow River Chart

Nine is at the top, one at the bottom, three on the left, and seven on the right. Two and four stand on either side like shoulders, while six and eight are below like feet; five occupies the center, like the heart and abdomen. The sum of all the numbers in the diagram is forty-five, and each horizontal and vertical line adds up to fifteen. The number of Heaven, five, lies at the center. The sages observed this diagram and thereby established the forms symbolized by the Eight Trigrams.

The numbers in the Yellow River Diagram (Hetu), an ancient chart showing the relationships among Yin-Yang, the Five Phases, numbers, and directions, add up to forty-five. According to tradition, a sage subtracted two, the numbers of Heaven and Earth, and placed five at the center; the total still came to forty-five. Whether added vertically or horizontally, each line sums to fifteen. The number five, belonging to Heaven, lies at the center. Observing this numerical pattern, the sage established the forms of the Eight Trigrams (Bagua).

The Number Chart of the Luo River Writing

The numbers in the Yellow River Diagram add up to forty-five. According to tradition, a sage subtracted the number one of Heaven, the number two of Earth, the number three of Heaven, and the number four of Earth—a total of ten—leaving only the number five of Heaven at the center.

The number five of Heaven lies at the center and governs Earth. In the Luo River Writing (Luoshu), the completed number of Earth, ten, also appears, and Water, Fire, Metal, and Wood are thereby formed.

The Diagram of the Four Images in the Yellow River Diagram

The Appended Statements says: “The Changes contains the Supreme Ultimate (Taiji). The Supreme Ultimate gives rise to the Two Modes; the Two Modes give rise to the Four Images; the Four Images give rise to the Eight Trigrams.”

The Four Images referred to here are the number one of Heaven, the number two of Earth, the number three of Heaven, the number four of Earth, and the number five of Heaven. The number one of Heaven occupies the Kan position in the north and belongs to Water; the number two of Earth occupies the Li position in the south and belongs to Fire; the number three of Heaven occupies the Zhen position in the east and belongs to Wood; and the number four of Earth occupies the Dui position in the west and belongs to Metal. These four numbers occupy the cardinal directions and are called the generating numbers.

The number five of Heaven lies at the center and represents the number five of Earth. Earth has no fixed direction. It is then distributed among the four directions, governs the four cardinal positions, and can generate the myriad things. Thus, adding Earth’s number five to Water’s generating number one in the north gives the completed number six; adding five to Fire’s generating number two in the south gives seven; adding five to Wood’s generating number three in the east gives eight; and adding five to Metal’s generating number four in the west gives nine. These are the “Four Images” mentioned in the text.

Diagram of the Yellow River Diagram’s Generating Numbers Added to the Luo River Writing’s Completed Numbers

In the Yellow River Diagram (Hetu), which represents the numbers by which Heaven and Earth generate things, the number of Heaven is one and the number of Earth is two; the number of Heaven is three and the number of Earth is four. These are the starting points for the images taken by the myriad things. When the number of Heaven reaches five, it occupies the center and governs the transformations of Earth. At this point, the myriad things have not yet taken on concrete form, so they are called the Four Images. The Luo River Writing (Luoshu), which represents the directions and numerical principles of the Five Phases (Wood, Fire, Earth, Metal, Water), contains the completed number ten for Earth. Thus Water, Fire, Metal, and Wood each pair odd numbers with even numbers to form concrete images.

By combining the numbers of the Four Images, the Yellow River Diagram can establish the positions of the eight directions. By containing the numbers of the Five Phases, the Luo River Writing can embody the images and completed numbers of the Eight Trigrams (Bagua). For images to generate trigrams, they must await the changes of Heaven’s timing and rely on Earth’s completed number, ten, in the Luo River Writing to become complete. Only then can the Eight Trigrams take shape. The Yellow River Diagram and the Luo River Writing must work together for the trigrams to form.

Diagram of the Yellow River Eight Trigrams

These eight trigram images were first derived from the Four Images. Fuxi first arranged the positions of the Eight Trigrams according to the eight directions shown in the Yellow River Diagram. He then drew on Earth’s completed number, ten, in the Luo River Writing to construct the trigrams’ images. He observed Yin and Yang, setting out odd and even lines; he also observed Heaven, Earth, and humanity, setting out the upper, middle, and lower lines of each trigram.

When all three lines are yang, the result is the Qian trigram; when all six lines are yin, the result is the Kun trigram. A single yang line beneath two yin lines cannot be subdued by their yielding force, so it rises and moves, forming the Zhen trigram. A single yin line beneath two yang lines does not contend with their strength, but withdraws and follows their course, forming the Xun trigram. A single yang line between two yin lines is weak above and below, unable to help itself, and so presents an image of danger, forming the Kan trigram. A single yin line between two yang lines is strong above and below, able to stand on its own, and thus attaches and becomes visible, forming the Li trigram. A single yang line above two yin lines is strong, but its downward movement comes to a halt, forming the Gen trigram. A single yin line above two yang lines gently pacifies what lies below, and so appears joyful, forming the Dui trigram.

Diagram of Qian’s Origin Using Nine and Kun’s Origin Using Six

The Qian symbolizes Yang strength and has twelve lines in total: the Qian hexagram’s three lines, plus one line each from Zhen, Kan, and Gen, and two lines each from Xun, Li, and Dui. When a Yang line sits above two Yin lines, its firm strength moves downward, forming Gen, which symbolizes stillness. When a Yin line sits above two Yang lines, it gently soothes what lies below, forming Dui, which symbolizes joy.

“Diagram of Qian’s Origin Using Nine and Kun’s Origin Using Six”

The Yang side of Qian has twelve lines: the Qian hexagram’s three lines, one line each from Zhen, Kan, and Gen, and two lines each from Xun, Li, and Dui. The Yin side of Kun has twenty-four lines: the Kun hexagram’s six lines, one line each from Xun, Li, and Dui, and two lines each from Zhen, Kan, and Gen. Together, the two sides have thirty-six lines.

Yang lines symbolize the way of the ruler, so they may include the number of Yin lines as well, giving thirty-six lines in all. Four times nine is thirty-six, which is why a Yang line is called “nine.” Yin lines symbolize the way of the minister and cannot overstep their position to take the upper place, so they total twenty-four. Four times six is twenty-four, which is why a Yin line is called “six.” The three lines of the Qian hexagram combine with the six lines of the Kun hexagram to form the Yang number “nine.” Yang Qi advances, so it is said, “Qian’s Origin uses nine”; Yin Qi withdraws and holds its position, so it is said, “Kun’s Origin uses six.” The numerical principles of nine and six express the firm and yielding qualities of Heaven and Earth.

The Numbers of Heaven and Earth

The Stalk Counts of Qian and Kun

Diagram of the Fifteen Numbers of Heaven and Earth in the Yellow River Chart

The numbers of Heaven and Earth together make fifteen. Viewed from different angles, these numbers have six meanings, all of which accord with the numbers of nature.

First, according to the vertical and horizontal sums in the River Chart (Hetu), the numbers in every vertical and horizontal line add up to fifteen.

Second, the numbers of Heaven—one, three, and five—and the numbers of Earth—two and four—add up to fifteen.

Third, before the Supreme Ultimate (Taiji) divides, it is undifferentiated and whole as one: this is “one.” The single Qi divides into the two modes of Yin and Yang, and the number becomes three. The two modes then divide into the Four Images, and the number becomes seven. The Four Images unfold further to generate the Eight Trigrams (Bagua), bringing the number to fifteen.

Fourth, the generating numbers of the Five Phases (Wood, Fire, Earth, Metal, Water) are: Water one, Fire two, Wood three, Metal four, and Earth five. Together they total fifteen.

Fifth, the numbers of the Five Phases can be assigned to symbolize Yin and Yang: seven represents Lesser Yang, and eight represents Lesser Yin. Together they also make fifteen.

Sixth, if Lesser Yin and Lesser Yang do not move, change cannot occur. Lesser Yin has the number eight. When Yin Qi stirs and withdraws, Lesser Yin turns into Greater Yin; as it withdraws, it is therefore called six. Lesser Yang has the number seven. When Yang Qi stirs and advances, Lesser Yang turns into Greater Yang; as it advances, it is therefore called nine. Six and nine together also make fifteen.

In general, one, three, and five occupy Yang positions and add up to nine. Five lies at the center and corresponds with the four directions. Six, seven, eight, and nine combine and circulate, forming the Four Images.

The diagram of their operation uses forty-nine.

When the Heavenly numbers descend to Earth and join with the Earthly number six, Water is generated in the north. When the Earthly number two rises and joins with the Heavenly number seven, Fire is generated in the south. The Heavenly number three moves to the left and joins with the Earthly number eight, generating Wood in the east. The Earthly number four moves to the right and joins with the Heavenly number nine, generating Metal in the west. The Heavenly number five moves through the unseen realm and joins with the Earthly number ten, generating Earth in the center.

Things generated from odd numbers are ultimately brought to completion by even numbers; things generated from even numbers are ultimately brought to completion by odd numbers. Heaven belongs to Yang, so its numbers are odd; Earth belongs to Yin, so its numbers are even. When odd and even numbers join, the total of fifty-five is complete.

In the number of Great Expansion (used in divination), five is subtracted to represent the workings of the Five Phases, while one is left unused to represent the source of primordial Qi (the fundamental energy from which all things arise). The Heavenly number five marks the beginning of change and is distributed among the positions of the Five Phases; for this reason, the center has no fixed form. Heaven first generated one, opening the way for numbers to appear; only afterward came the numbers of the Four Images and the Five Phases. This number is now left empty and unused to show that primordial Qi is the root of creation, occupying the honored position and remaining unmoving.

Diagram of the Six Children of Heaven and Earth

Diagram of the Six Positions of the Revolving Heavens

The Six Positions

Diagram of the Three Powers

In the Six Positions, two, three, four, and five form the warp (the vertical framework), while seven, eight, nine, and six form the weft (the horizontal framework). This arrangement takes its images from astronomy. Heaven has the Dragon, Tiger, Crow, and Tortoise as its warp, and Zhenxing, Suixing, Yinghuo, and Taibai as its weft. Among the Six Positions, the warp does not include the number of the Black Warrior, because when facing north one can see only the pivot of the Northern Dipper and the Pole Star. The Dipper is therefore called the “Northern Dipper,” and the Pole Star the “Northern Pole.” Though named as stars of the north, they are in fact located at the center of Heaven. This reflects the principle that one and six combine as the number of the Taiji, concealed within five. In the Yellow River Chart, six and one are positioned above…

Hai and Zi lie in the north, while five occupies the center, so both the center and the north contain the number of Taiji. The six positions are arranged lengthwise and crosswise; their numbers are those of the Primordial Stabilizing Star (that is, Saturn). The Stabilizing Star completes one circuit of the heavens in twenty-eight years. The Year Star, the Fire Star, the Great White Star, and the Morning Star (Jupiter, Mars, Venus, and Mercury, respectively) all move along the stellar lodges passed through and governed by the Stabilizing Star. This is like the Yin-Yang specialists’ saying, “Earth dwells in the central palace and rules the four seasons”: Earth occupies the center and presides over the seasons. Thus, the Changes has 384 lines, corresponding to the number of celestial phenomena; changes in divining good and ill fortune depend on the four numbers seven, eight, nine, and six, just as the movements of the five planets change.

Fuxi’s Earlier-Heaven Diagram

The diagram above is Fuxi’s Bagua (Eight Trigrams) diagram. Wang Yu passed it on to Shao Kangjie (Shao Yong, whose courtesy name was Kangjie), and Yaofu (Shao Yong’s style name) received it. The first classic of the Returning-to-the-Storehouse (Guicang) is said to have originated when Fuxi, after first drawing the Eight Trigrams, doubled them in pairs. The “Initial Qian, Initial Kun, Initial Gen, Initial Dui, Initial Kan, Initial Li, Initial Zhen, Initial Xun” listed in the text are each six-line hexagrams: precisely these eight doubled trigrams. Once the Eight Trigrams are doubled, the lines are contained within the hexagrams.

Diagram of Mutual Generation Between the Square and the Circle

Zheng says that the ancient, innate diagrams appear only in works such as Yang Xiong’s Taixuan Jing, Guan Ziming’s Dongji, Wei Boyang’s Cantong qi, and Shao Yaofu’s Huangji jingshi. Sadly, Yang Xiong and Guan Ziming modeled their books on the Zhouyi and became bound by words. Later generations therefore neglected them, thinking they merely piled one roof upon another or added another head atop a head: needless repetition. Wei Boyang’s Cantong qi focuses on refining and cultivating, but later fell into the realm of esoteric arts. From the perspective of the sages’ Way, it too was regarded as heterodox. Shao Yaofu freed himself from words and minor techniques in writing his work, yet people across the land were unwilling to accept it and treated it only as a tool for calculating the calendar. This is truly regrettable.

The teachings of all four schools are based on the ancient innate diagrams. Might the innate diagrams be the very source of the Zhouyi? Because they contain no written explanations, people have come to regard them as useless. I have now drawn square and circular diagrams, with annotations that are clearer and easier to understand than those of all four schools. The essential points of their teachings are also contained in my diagrams. These diagrams are of the greatest importance for studying the Zhouyi.

Diagram of Looking Up to Observe the Patterns of Heaven

Fuxi looked up at the celestial phenomena and, on that basis, drew the Eight Trigrams (Bagua). Thus the movements and patterns of the sun, moon, and stars, along with the ten celestial stems, the four seasons, and other matters related to the heavens—all celestial phenomena—are encompassed by the Eight Trigrams.

Diagram of Looking Down to Examine the Patterns of Earth

Fuxi looked down at the patterns of the earth and, on that basis, drew the Eight Trigrams. Thus the four directions, the nine provinces, birds and beasts, plants and trees, the twelve earthly branches, and other matters related to the earth—all earthly things and geographical patterns—are encompassed by the Eight Trigrams.

Diagram Titles

Fuxi’s Eight Trigrams Diagram

Diagram of the Images Taken from the Eight Trigrams

King Wen’s Eight Trigrams Diagram

Diagram of the Images and Numbers of the Eight Trigrams

Diagram of the Four Trigrams in Harmony with the Rhythms

Diagram of the Eight Trigrams with the Heavenly Stems Assigned to Them

Diagram of Hardness and Softness Interacting: Qian represents Yang and hardness and occupies the upper position; Kun represents Yin and softness and occupies the lower position. Qian moves leftward from the position of Zhen, while Kun moves rightward from the position of Xun. Heaven turns left and Earth turns right. This is therefore called “hardness and softness interacting,” meaning that Yin and Yang act upon one another.

Diagram of the Eight Trigrams Agitating One Another: Zhen stirs up Gen, Dui stirs up Kun, Li stirs up Xun, and Kan stirs up Qian. The Eight Trigrams move back and forth, taking turns to shift and transform. Jing Fang said, “Yin lines stir and enter Yang positions; Yang lines stir and enter Yin positions.”

The Six Lines and the Three Poles: The classic lists this heading but provides no specific explanation.

The Five Positions in Combination: The classic lists this heading but provides no specific explanation.

Diagram of the Emperor Emerging from Zhen: The classic lists this heading but provides no specific explanation.

The Virtue of the Yarrow and Hexagrams: The number used in yarrow divination is seven. Seven multiplied by seven gives forty-nine, which is how the yarrow number is used; thus, the nature of the yarrow number is to move in a rounded, fluid way. The number of the hexagrams is eight. Eight multiplied by eight distinguishes the sixty-four hexagrams; thus, the nature of the hexagram number is square and fixed. What moves in a rounded, fluid way and has no end can reveal the future; what is square and has a definite form can help us understand the past. Thus, the circle symbolizes the wondrous transformations of spirit, while the square symbolizes the wisdom to discern things clearly.

Diagram of the Sequence of the Upper and Lower Classics: When the nine-second line of the Qian hexagram changes, it first becomes Tongren, then Wuwang, Yi, and Yi (Nourishment), continuing to change until it finally becomes the Li hexagram. When the six-second line of the Kun hexagram changes, it first becomes Shi, then Sheng, Heng, and Dagao, continuing to change until it finally becomes the Kan hexagram. Thus, the Upper Classic begins with Qian and Kun and ends with Kan and Li.

Starting from the Six Two line of the Xian hexagram, successive line changes produce, in order, Da Guo, Kun, Kan, Shi, and Meng, and finally arrive at Wei Ji. Starting from the Initial Six line of the Heng hexagram, successive line changes produce, in order, Da Zhuang, Feng, Zhen, Fu, and Tun, and finally enter Ji Ji. Thus, the lower section of the Zhouyi opens with Xian and Heng and closes with Ji Ji and Wei Ji. “16” is a marker in the original text.

Book I of the Diagram of Images and Numbers in the Great Changes, Probing the Hidden

The following are the collator’s notes on textual variants and supplied characters. On the basis of the Siku Quanshu edition, the omitted characters “Kun,” “and,” “to be,” “not yet,” “move,” and “withdraw” have been restored. “Dwelling position” has been changed to “determining position,” “speak” to “expound,” and “upper image” to “celestial image”; “Zheng Fu” has also been corrected to “Yao Fu.” Other variant readings include “mutually assisting” and “mutually requiring,” “self-record” and “self-reliance,” and “rush downward” and “rule those below.” The Siku Quanshu edition reads “initially flourishing” where other editions read “initially protruding.” The character “Zhen” is suspected to be an error; the Siku Quanshu edition reads “Chen.” “Before Completion” has been supplied on the basis of the meaning.

Book II of the Diagram of Images and Numbers in the Great Changes, Probing the Hidden

Diagram of the Completion of the Three Transformations

Diagram of the Six Lines of the Doubled Changes

Diagram of the Celestial and Terrestrial Numbers of the Sixty-Four Hexagrams

Diagram of the Numbers of the Myriad Things in the Sixty-Four Hexagrams

Diagram of the Pitch Standards of the Hexagram Lines

In the eleventh month, the Hexagram Fu (Return), in which the first Yang is born, corresponds to the beginning of Yang energy’s return to life. The energy of Huangzhong, the first of the Twelve Pitch Standards, responds in harmony. By the fourth month, all six lines are Yang, forming the Hexagram Qian (the Creative). Thus, the state of opening the gate is called “Qian.” In the fifth month, the Hexagram Gou (Coming to Meet), in which the first Yin is born, appears, and the energy of Ruibin, one of the Twelve Pitch Standards, responds to it. By the tenth month, all six lines are Yin, forming the Hexagram Kun (the Receptive). Accordingly, the Diagram of the Pitch Standards of the Hexagram Lines …

In the eleventh month, the hexagram qi reaches Fu (Earth over Thunder: Return), where one yang line begins to grow, corresponding to the qi of Huangzhong. By the fourth month, all six lines are yang, forming Qian (Heaven over Heaven: The Creative). This is why the opening gate is called “Qian.” In the fifth month, one yin line begins to grow in Gou (Heaven over Wind: Coming to Meet), corresponding to the qi of Ruibin. By the tenth month, all six lines are yin, forming Kun (Earth over Earth: The Receptive). This is why the closing gate is called “Kun.” The waxing and waning of yin and yang lines here illustrate the changing seasonal nodes over the course of the year.

Diagram of Cycles and Calendrical Numbers

Fu spans twelve generations; Lin, twenty-four generations; Tai, thirty-six generations; Dazhuang, forty-eight generations; Guai, sixty generations; and Qian, seventy-two generations. Gou spans eighty-four generations; Dun, ninety-six generations; Pi, one hundred and eight generations; Guan, one hundred and twenty generations; Bo, one hundred and thirty-two generations; and Kun, one hundred and forty-four generations. Here, “generation” is the unit used to count the period associated with each hexagram.

Diagram of Qian and Kun as the Great Parents

With each change, Qian becomes Gou after one transformation, Dun after two, and Pi after three. The sequence stops at the fifth transformation, when it becomes Bo. The myriad things do not continue until they are exhausted. When Bo reaches its peak, it turns back from above, and so Fu follows.

With each change, Kun becomes Fu after one transformation, Lin after two, and Tai after three. The sequence stops at the fifth transformation, when it becomes Guai. After Guai, there must be an encounter, and so Gou follows.

Diagram of Fu and Gou as the Lesser Parents

When one yang arrives in Fu, it becomes two yang lines in Lin, four in Tai, eight in Dazhuang, and fourteen in Guai. It finally transforms into Guimei, bringing the total to sixteen yang lines.

One yin first appears in Gou. It becomes two yin lines in Dun, four in Pi, eight in Guan, and fourteen in Bo. It finally transforms into Sui, bringing the total to sixteen yin lines.

Diagram of the Eight Trigrams Giving Rise to the Sixty-Four Hexagrams

Diagram of the Eight Trigrams Transforming into the Sixty-Four Hexagrams

Yang

The Sequential Generation of Yang Hexagrams

Yang hexagrams are generated in sequence: starting from “one,” proceed upward and join with “eight.” As the number of Yin lines increases to eight, the process reaches the Bo hexagram, with fourteen Yin lines, and finally changes to the Sui hexagram, making sixteen Yin lines in all.

Diagram of the Eight Trigrams Generating the Sixty-Four Hexagrams

Diagram of the Eight Trigrams Transforming into the Sixty-Four Hexagrams

The Sequential Generation of Yang Hexagrams

From “one,” rise upward and join with “nine,” returning to “five,” which serves as the ruler’s position. “Ten” descends and joins with “six,” returning to “two,” which serves as the minister’s position. This is called “the sequential generation of Yang hexagrams.”

The Inverse Generation of Yin Hexagrams

From “one,” descend and join with “nine,” returning to “five,” which serves as the ruler’s position. “Ten” rises upward and joins with “six,” returning to “two,” which serves as the minister’s position. This is called “the inverse generation of Yin hexagrams.”

Diagram of the Six Hexagrams Fu, Gou, Lin, Dun, Tai, and Pi Generating the Sixty-Four Hexagrams

Diagram of the Reciprocal Transformations of the Sixty-Four Hexagrams

A hexagram with one Yin line and five Yang lines can transform through reciprocal reversal into six hexagrams; likewise, a hexagram with one Yang line and five Yin lines can transform into six. A hexagram with two Yin lines and four Yang lines can transform into twelve hexagrams; likewise, one with two Yang lines and four Yin lines can transform into twelve. Eight hexagrams remain unchanged after reciprocal reversal.

A hexagram with three Yin lines and three Yang lines can, through reciprocal reversal, transform into six hexagrams with one Yin line and five Yang lines, six with one Yang line and five Yin lines, twelve with two Yin lines and four Yang lines, and twelve with two Yang lines and four Yin lines. Eight hexagrams remain unchanged after reciprocal reversal. The transformations total twenty-four hexagrams.

Diagram of the Simplicity of Qian and Kun

Here, “reversal and opposition” means viewing a hexagram by turning it upside down, or comparing it with its corresponding hexagram. “Yin” and “Yang” refer to the Yin and Yang lines within a hexagram.

Qian and Kun correspond respectively to the numbers one and two, the shapes square and round, Qi that is clear and turbid, and principle that is active and still. Qian therefore contains the meaning of the Two Modes (Yin and Yang), and divides into above and below. Kun contains the forms of the Four Images (young Yang, old Yang, young Yin, and old Yin), and divides into south, north, east, and west. The Two Modes and Four Images together make six numbers; adding Qian and Kun themselves completes the number of the Eight Trigrams. This is why Qian and Kun are not far removed from the Taiji (Supreme Ultimate).

Upholding correctness within while allowing change without is the principle of the Two Modes; Originating, Smooth Progress, Advantage, and Perseverance are the principle of the Four Images. Taking two, three, four, and five as the warp, and seven, eight, nine, and six as the weft, one forms the positions of the Eight Trigrams. Thus number proceeds from one to two, from two to four, and from four to eight, then develops from eight into sixteen, thirty-two, and sixty-four. When the sixty-four hexagrams are complete, the Way of Heaven is complete as well: the course of the year is fulfilled, and human affairs are all encompassed. This is why the Yi Jing has sixty-four hexagrams, with “Qian” and “Kun” placed first. If students can return from the sixty-four hexagrams to “one,” and from “one” grasp the Taiji, then the principles of Fuxi, King Wen, and Confucius will all be present within them. The ability to bring about change and set the affairs of spirits and gods in motion also lies in this Way.

Diagram of the Image of Zhun

Diagram of the Image of Nurturing Correctness in Meng

The young learner occupies the six in the fifth place, and is disciplined from above by the nine in the top place: this is learning sought outwardly. Things encountered through the ears and eyes may support me, but may also harm my innate nature, so they should not be treated as hostile intrusions. The nine in the second place embraces the young learner, while the six in the first place gives the learner guidance: this is learning sought inwardly. Constructions of the mind are best noticed before they begin to sprout. Once attachment and possessiveness arise, they remain in the heart and give rise to cunning schemes. When we speak of breaking free from bonds, are the bonds to be broken not those within my own heart?

Diagram of the Image of Xu and Waiting

The central line of the Kan trigram, which symbolizes water, is a yang line. It can assist the yang line of the Qian trigram, whose yang line seeks help above. A yang line that receives help can advance; when one yin line withdraws from it, its momentum grows, but when another yin line blocks it, it retreats. This is why the fortunes of the Xu hexagram change.

The Sage, however, does not lay the blame on the two yin lines, but on the three yang lines. Nor does he lay it on the three yang lines, but singles out the yang line in the Kan trigram. Since the benefit is concentrated in that line, greater demands are placed upon it, and so the image of food and drink is used to explain the matter. In the Xu hexagram’s statement, “food and drink” symbolize what nourishes people, as well as what they hope for and seek. Yet people can also be trapped or harmed by food and drink. Small-minded people often covet gain at first, only to suffer misfortune in the end. They must therefore understand the proper way to conduct themselves. This is why the Xu hexagram stresses “steadfastness brings good fortune.” “Steadfastness” means remaining centered and upright. When one’s heart is centered and upright, one can be firm outwardly; and when one is firm outwardly, one will not fall into difficulty.

Diagram of the Image of the Song Hexagram

The Qian trigram occupies the position of Hai, and the Kan trigram begins from the direction of Zi. Hai and Zi are both in the north and both belong to water, so at first there is no dispute. Once they separate, Heaven tilts toward the west while water rushes eastward; Heaven revolves above, and water moistens below. Thus the Song hexagram, which symbolizes dispute, is formed.

Diagram of the Shi and Bi Hexagrams in Governing the Multitude

The Kun hexagram symbolizes the multitude, as does the Shi hexagram, whose meaning includes leading many people. Leading the multitude is impossible without virtue. Thus, the Shi hexagram is formed by the Nine in the Second Place of the Qian hexagram entering the Kun hexagram, taking the virtue of that line in Qian.

Pitch standards are derived from numbers, and numbers arise from the central position. The pitch standard of Huangzhong, the first of the ancient twelve pitch pipes, begins here and serves as the basis for establishing measures of length, capacity, and weight. The slightest error makes precision impossible. The northern Kan trigram is the root of Huangzhong. That is why the Shi hexagram’s judgment mentions a “mature man,” while its line statements also mention pitch standards. Both the mature man and the pitch standard concern the establishment of laws and measures. Is this not a responsibility only a virtuous person can undertake?

The north symbolizes darkness, gloom, and military campaigns; the south symbolizes turning toward the light and receiving court audiences. Among the six lines, the second, third, fourth, and fifth each correspond to a direction and a number. The second line occupies the southern position, the bright position of the Li trigram, so the Bi hexagram takes the image of facing south to govern. The fifth line occupies the center, not the north. Looking up at the northern sky, one can see only the pivot of the Northern Dipper and the celestial pole where the North Star lies. The celestial pole is called the “Northern Culmen,” and the Dipper’s pivot the “Northern Dipper.” Though their names include “north,” both are actually at the center of the heavens. The Shi hexagram takes the image of facing north, and so conveys the idea of organizing five people into a squad. The Bi hexagram takes the image of facing south, and so conveys the distinction among the five ranks of nobility. The top line stands behind the ruler’s position and above the ruler, which is why it says: “The one who comes after will meet with misfortune.”

Diagram of the auspicious and inauspicious aspects of the Da Xu and Xiao Xu hexagrams.

Xun lies in the southeast. Qian Qi travels from the Zi position to the Si position, enters the Xun direction, and is stored and nurtured by Xun. This is called Lesser Accumulation. It is because Yin Qi first arises in the Xun position. Xun represents faint Yin Qi, hence “lesser.”

Qian Qi travels from the Zi position to the Yin position, enters the Gen direction, and is stored and nurtured by Gen. This is called Greater Accumulation. It is because Yang Qi reaches its end in the Gen position. Gen represents the culmination of Yang Qi, hence “greater.” The Qian hexagram’s movement from the Zi position to the Yin position symbolizes the three-line Qian trigram; its movement from the Zi position to the Si position symbolizes the six-line Qian hexagram. Thus, Gen stores and nurtures the lower (inner) trigram of Qian, while Xun stores and nurtures its upper (outer) trigram.

Greater Accumulation gains the leading position because the Nine at the fifth line of Lesser Accumulation changes to a Six at the fifth line. By remaining humble and showing respect to worthy people of lower rank, one can take the lead and nurture others. Lesser Accumulation loses the leading position because the Six at the fifth line of Greater Accumulation changes to a Nine at the fifth line. Complacency and arrogance lead to the loss of the leading position, leaving one instead subject to others.

Diagram of Treading on the Tiger’s Tail

Qian lies at the Hai position. Its first line corresponds to the constellations Shi and Bi, and its second line begins with Kui. Kui symbolizes striking, hence the image of treading on a tiger’s tail. Kun lies at the Shen position, and the Shen constellation corresponds to Kun’s first line. Connecting the Shen constellation with the Dui trigram depicts the tiger giving a low growl when its tail is trodden on. When Qian is beneath Dui, there is no image of treading on the tiger’s tail, nor of the tiger making or not making a sound. When Qian rests above Dui, the image of treading on the tiger’s tail becomes clear. The Treading hexagram moves from Dui into Qian, from the Xu position to the Hai position, symbolizing a person entering the Qian position. With Qian beneath Dui, there is no image of whether the tiger’s tail makes a sound; when Qian rests above Dui, the image of treading on the tiger’s tail becomes evident. The Treading hexagram moves from Dui into Qian, from Xu to Hai, expressing the principle of aligning oneself with the Way of Heaven.

Diagram of the Coming and Going of Denial and Peace

By observing the image of Peace, one can see how Denial arises; by observing the image of Denial, one can also see how Peace flourishes. This is because Yin and Yang Qi move up and down, rising and descending in relation to one another to form the hexagram images. For this reason, both Denial and Peace use “coming and going” to describe this change.

Diagram of the Tongren Hexagram

Qian is above and accounts for thirty-six stalks. If its middle line changes, it becomes the Li hexagram. Li is below and accounts for twenty-four stalks. If its middle line changes, it becomes the Qian hexagram. This is called two people being of one mind: their outward appearances differ, but their inner intentions are the same.

Diagram of Holding One’s Position in the Dayou Hexagram

The Dayou hexagram has many yang lines and is at the height of its flourishing, yet its sixth line, in the fifth place, is yin. A ruler should understand the primal energy of Heaven and Earth and remain upright in the position of rulership. How could a ruler fail to understand the principle of holding one’s position and practicing benevolence? Further interpretation shows that the ninth line in the fourth place represents attendants, hence the phrase “not relying on those nearby.” The ninth line in the third place represents the Three Dukes, hence “the duke makes an offering to the Son of Heaven.” The ninth line in the second place represents feudal lords and local officials, hence “a great cart for carrying.” The first yang line is farthest from the ruler’s position and represents remote regions and the non-Han peoples, hence “no mutual harm.” These all concern carrying out ordinances and putting the way of benevolence into practice. In this way, blessings extend to the ancestral temple, and the state can endure for generations.

The Symbolism of the Qian Hexagram

Gen occupies the Yin position and belongs to Wood among the Five Phases (Wood, Fire, Earth, Metal, Water), symbolizing benevolence. Kun occupies the Shen position and belongs to Metal, symbolizing righteousness. Therefore, the top line and the fifth line carry an association with killing. The Qian hexagram takes utmost sincerity as its foundation, because speech is the voice of the heart. Words that are not sincere cannot come from a sincere heart or express what is originally in the heart; they are therefore false. Thus, “modest in one’s declaration” in the middle of the hexagram signifies utmost sincerity. Outside the hexagram, it signifies words that do not come from the heart. In that case, modesty is only an outward display, while inwardly one is competitive.

The Symbolism of the Yu Hexagram

When Zhen is beneath Kun, this is called the Fu hexagram, in which one yang first emerges. It symbolizes the original heart of Heaven and Earth, which continually brings life forth. Now Zhen rises above Kun: this is the Yu hexagram, in which yang energy emerges from the earth, and it too symbolizes the original heart of Heaven and Earth. The middle line of Kun is still within stillness, so the text says, “firm as a rock.” The middle line of Zhen is still within movement, so it says, “upright amid illness, enduring and never dying.”

In the diagram of the Sui hexagram, Kun is above and is called “Kun lost.” This is the transformation from Chu Di to the Yu hexagram, and it also expresses the original nature of Heaven and Earth. The middle line of Kun is at rest, and is stillness within stillness; hence the phrase “standing firm as a rock,” meaning that one’s position is as steadfast as stone. The middle line of Zhen, by contrast, is stillness within movement; hence “steadfast through illness, never dying,” meaning that despite illness or adversity, one can uphold what is right and endure without perishing.

Diagram of the Sui hexagram

The movement from Zhen to Dui represents proceeding from east to west, like beginning to plow in spring and harvesting in autumn. This is the meaning of the Sui hexagram: Yang Qi rises from within Yin Qi, and Yin Qi moves in accordance with Yang Qi. Yin Qi comes forward to meet Yang Qi, bringing it joy; Yang Qi, in turn, joins with Yin Qi. Thus the top line of Dui carries the symbolism of restraint and constraint.

Diagram of the Gu hexagram

Xun corresponds to the Si position, where Metal Qi comes into being. At the You position, Metal Qi flourishes and Xun’s function is complete; hence the fifth line of Xun says “Geng.” Now Xun lies beneath Gen, as though it were at the Yin position, where Wood Qi flourishes; hence it says “Jia.” Jia and Geng correspond respectively to the directions of Zi and Wu. Their cycle turns without end: this is the principle of adaptive movement.

Metal can overcome Wood. Now Metal lies beneath Wood, like a worm born inside a tree. Thus “Gu” symbolizes decay that arises naturally from within things. The top nine line of the Gu hexagram stands at the summit of a mountain and holds lofty aspirations. It is capable of rousing the spirit against accumulated ills, enabling even the timid and weak to establish themselves.

Diagram of the Lin hexagram

The image of the Lin hexagram originally describes a ruler in a position of authority facing the people. The way to govern the people is to extend kindness downward while maintaining an upright heart above. Extending kindness downward is like the two Yang lines at the bottom, just as the Qi of Heaven responds to the Earth. Maintaining one’s heart above means acting with wisdom and putting honesty and sincerity first, like governing with firmness and clarity tempered by gentleness.

Dui speaks pleasingly in words alone: it can speak but cannot act. It is like a king who continually issues edicts and repeats his exhortations, while his benevolence and generosity are never truly put into practice. How, then, can this be called extending kindness to the people or keeping the heart upright?

Diagram of “Observing the Splendor of the State”

When four Yin lines arise, the image shows Yin energy gradually growing and beginning to press upon Yang energy. Compared with the case of Yang pressing upon Yin, this is precisely the principle of the Great Strength hexagram. It is not called the Lesser Strength hexagram but the Contemplation hexagram because Yin energy is compliant and gentle, with no intention of harming Yang. Since those below are compliant and gentle, those above must remain centered and upright; only then can people below look up to them and be transformed by their example. Once those below have been transformed, how could they harm Yang?

The Biting Through hexagram takes the mouth as its image, yet also connects it with the toes, nose, ears, and eyes, because the whole body depends on the mouth for nourishment.

The Biting Through hexagram takes the mouth as its image and also involves the toes, nose, ears, and eyes, because the whole body depends on the mouth for nourishment. Eating in accordance with what is right is the blessing brought by Biting Through; eating contrary to what is right is the misfortune it brings. Misfortune is common and blessings are few because there are more petty people who crave the pleasures of the palate. In the image of Biting Through, lightning comes first and thunder follows: lightning shines, and thunder then shakes the air. It is like the tongue moving first and the teeth chewing afterward—this is the natural order. Both Biting Through and Adornment contain the image of something lodged between the upper and lower parts of the Nourishment hexagram. One becomes Adornment and the other Biting Through because Biting Through takes the image of movement in the lower part of Nourishment, while Adornment takes the image of stillness in its upper part. Only when the lower part moves does it become Biting Through.

The Li hexagram is formed by a yielding line attached between firm lines. Li symbolizes the sun. The sun moves across the sky, conveying openness and smooth progress. The Gen hexagram is formed by a firm line attached between yielding lines. Gen symbolizes a mountain. The mountain stands still, while clouds rise from it and turn into rain. Trees, too, can become useful timber after they are cut down. Hence the saying, “There is somewhere to go; a small benefit is gained.”

Yet when Confucius spoke of these things, he called them “heavenly patterns” and did not mention earthly forms. This is because, when the Xiang Zhuan was composed through observing the heavens, the images it drew upon included the sun and moon shining in turn. The sun and moon alternate in their courses and meet at the new moon—the moment when they lie in the same direction, marking the start of the lunar month. The cycle of the new moon and the dark moon, the end of the lunar month, repeats in turn, giving rise to the four seasons. This is why the Xiang Zhuan was composed through observing changes in the seasons. The Li hexagram conveys the idea of brightness succeeding brightness. The Bi hexagram arises when the fourth line of Li changes and symbolizes the sun and moon embracing one another; thus it can be said to reveal a key principle of heavenly patterns.

Diagram of Bo as the Seed of Yang Qi

The bottommost yang line of the Fu hexagram is the topmost yang line of the Bo hexagram, which has descended beneath the earth. Thus, Fu carries the image of “a large fruit left uneaten”: Yang Qi lies hidden within, like a seed. The Qian hexagram symbolizes a tree fruit. Wood begins to sprout at the time and position of Hai, which corresponds to Qian. Although the tree has begun to grow, it has not yet put forth buds. Once it does, it will bear seeds and reproduce. The root of a fruit that has not yet budded lies in the topmost yang line of the Bo hexagram, as though the fruit were still hanging from the treetop.

Diagram of Fu’s Seven Days

The positions of the lines are six actual numbers, while Taiji is six in the abstract. These abstract sixes originate in cumulative calculation using three as the base; this calculation, in turn, takes the diameter of a circular object as one. Thus all the numbers in the world—ten, a hundred, a thousand, ten thousand, and so on—can be derived from six.

When six advances, it becomes seven; when it retreats, it becomes five. Five is the state in which six is not yet complete; six is the state in which five has reached completion; beyond six comes seven. Six is the limit of a number. When one Yang is born, there is “return after seven days”; when two Yang lines are born, there is “misfortune in the eighth month.” Seven belongs to lesser Yang, and eight to lesser Yin. The sun corresponds to the Zhen trigram, and the moon to the Dui trigram. Although the Lin hexagram represents the gradual growth of Yang energy, it in fact contains the number eight of the Dui trigram, which is why it says that misfortune will come in the eighth month.

In the Fu hexagram, the return of one Yang line is called “seven days” because the Yin energy of Kun reaches its limit at the Hai position, where the cycle of six is exhausted. Yang energy reappears from the Kan position, making seven altogether. A full circuit of number is six Jia; a full turn of the cycle is three unifications. Returning to the starting point again becomes the “Origin.” This, too, is the meaning of “return after seven days.”

Diagram: Wu Wang rooted in Zhong Fu

Zhong Fu speaks of trustworthiness, and Wu Wang also speaks of trustworthiness. The trustworthiness of Zhong Fu arises from natural sincerity; that of Wu Wang seems to take shape through some prompting. Thus the scripture says that a firm line comes from outside, occupies the center of the inner trigram, and becomes its guiding force. The way of trustworthiness should naturally arise from within the heart; “center” also means that the central position is taken as the governing one. If a firm line comes from outside and instead governs what is within, how can this be called natural? This is precisely the difference between Wu Wang and Zhong Fu.

Diagram: The Spirit Tortoise of Yi

The center of the Yi hexagram is empty. The scripture then goes on to discuss taking the center as the governing principle, along with the situation in which a firm line comes from outside and governs what is within, using this to explain the distinction from Zhong Fu.

Hexagram Yi has an empty center and thus symbolizes the numinous tortoise. When a noble person sees this hexagram, they use the numinous tortoise to caution themselves. A petty person, however, sees it and drools greedily for food, like someone with mouth agape and cheeks puffed out. Nine Third symbolizes the lower teeth: once the teeth move, they are ready to bite and eat. This makes its danger greater than that of Six Second and Six Fifth. Nine Third is set in motion because Initial Nine carries the image of the Zhen trigram.

Diagram of the Ridgepole Rising and Bending in Hexagram Da Guo

In Hexagram Da Guo, the decisive lines for good or ill are the Initial and Top lines. The ridgepole rising symbolizes acting with care and solemnity, like laying down rushes to receive offerings during a sacrifice. The ridgepole bending, by contrast, symbolizes waters rising so high that they submerge trees, an image of excess. Thus, the judgment of Hexagram Da Guo concerns the Nine Third line.

When Yang Qi grows arrogant and excessive, the situation becomes one of “the great exceeding.” Nine Second pairs with young Yin, so the withered poplar can still send out new shoots. This is like laying down a thick bed of rushes during a sacrifice, signifying care. Nine Fifth pairs with old Yin, and the principle of growth has reached its limit. Hence the image of a withered poplar blossoming: though the tree flowers, it cannot bear fruit and can only put forth flower buds.

The Image Commentary on the Kan hexagram says, “The heart can attain free passage.” Here, “heart” means a heart free of thoughts of good and evil and undisturbed by joy, anger, sorrow, or pleasure. Once it is shaped by acquired habits, the nature that was originally the same becomes different. Thus, from beginning to end, the Kan hexagram uses the image of petty people repeatedly cultivating danger and evil until they bring themselves into difficulty. It warns people not to harbor evil thoughts.

Yin and Yang can also explain the beginnings of good and evil and the distinction between movement and stillness. When the heart moves, an evil thought may arise. Yang governs movement and Yin governs stillness; Yang symbolizes good, Yin evil. The Six in the Third place is a Yin line in a Yang position, so its ill intent is at its strongest. It is also caught between two Yin lines and is therefore shaped only by evil influences. The Six in the Fourth place is a Yin line in a Yin position: stillness has reached its extreme, symbolizing a return to one’s original nature and to sincerity. It is also between two Yang lines and is shaped only by good influences. Thus the line text for the Six in the Fourth place—“a goblet of wine and two bowls, using earthenware”—conveys simplicity and sincerity. Although the Nine in the Second and Fifth places are both Yang lines and occupy central positions, they remain trapped within a group formed by two Yin lines and cannot avoid being influenced by their habits. Confucius therefore points out that they have not truly escaped danger and that their inner centrality and correctness have yet to fully shine forth.

Diagram of the Li Hexagram’s Successive Brightness

The lower Li represents the beginning of the hexagram, while the upper Li represents what follows and transforms. The lower trigram is brightness at the outset; the upper is brightness continuing from it. The moon follows the sun and gains its light. At the new moon, the moon is in conjunction with the sun, and only afterward does it gradually become visible. The overlapping upper trigram encloses the lower one, giving the image of the sun and moon following one another and moving toward brightness.

Li originally symbolizes the sun, not the moon. But when two Li trigrams are joined, an image of the moon arises. This is why the text says “twofold brightness”: brightness succeeds itself, one phase following another. The Commentary on the Changes also says, “The sun and moon are attached to the heavens,” meaning that they move in dependence on the sky. The hexagram as a whole, too, suggests the sun and moon following one another and moving toward brightness.

The “yellow radiance” in the line for the Six in the Second place symbolizes brightness appearing from inner centrality and correctness—that is, the natural radiance of an honest nature. The Six in the Fifth place, by contrast, symbolizes grief and sorrow, like the moon after the full moon, beginning to move away from the sun. It also symbolizes how darkness begins to arise once brightness has reached its utmost fullness.

The Diagram of Friends Joining in Xian

All things are linked through a single Qi (vital energy). Thus, moisture rises from the waters in a marsh and forms clouds and mist among the mountains, while springs on the mountains flow down into the marsh. This is how mountain and marsh respond to one another. The Xian hexagram has three yang lines, with Nine in the Fourth Place at the center, symbolizing the heart. Yet it forms a faction with the other two yang lines, so it cannot avoid partiality and stubbornly holding to its own views; as a result, it hesitates when coming and going.

Nine in the Fifth Place connects upward with Six at the Top, directing its influence toward that line. Six at the Top symbolizes the cheeks and tongue, while Nine in the Fifth symbolizes the spleen. Nine in the Third Place connects downward with Six in the Second, directing its influence toward that line. Six in the Second symbolizes the calves, while Nine in the Third symbolizes the thighs. The thighs move with the calves, but the spleen does not speak along with the cheeks and tongue. The situations represented in these two cases therefore differ, as do their auspicious and inauspicious outcomes.

The Diagram of Enduring Constancy

Of the six lines, only Nine in the Second Place combines the qualities of firmness and yielding while also occupying the central position. Confucius held that it symbolizes someone who can maintain the middle course and remain unchanged over time.

Six in the Fifth Place also combines firmness and yielding and occupies the central position. But the line that joins it in carrying the authority of the heavenly position is also yielding. It therefore symbolizes a woman who remains chaste and faithful to one partner throughout her life, and differs from Nine in the Second. Nine in the Third Place is firm and yang, and occupies a yang position. Its actions go too far and stray from the middle course, symbolizing what cannot endure. It therefore fails from the outset to accord with the way of lasting constancy. The first and top lines—one sinking deeply downward, the other striving forcefully upward—both show a loss of direction. Neither keeps to the middle course, so both are inauspicious.

Nine at the second place embodies the centered, correct, gentle, and yielding qualities of the yellow ox. An ox can bear heavy loads because its hide is strong. Without its hide, an ox would be no different from a piece of meat on a chopping board—how could it accomplish anything? Nine at the third place is a firm, vigorous line in an outer position, and thus carries the image of change. If Nine at the third place follows the Qian hexagram and withdraws, Nine at the second place will meet with misfortune. Hence the advice here is to hold firmly to it.

Six at the fourth place occupies a Yin position but is filled by a Yang line, and it corresponds with the initial Six; hence the word “good.” “Good” means forming friendly relations: a Yang line occupies a Yin position and engages with the Yin line below. Nine at the fifth place occupies a Yang position and corresponds with Six at the second place; hence the word “fine.” “Fine” refers to a spouse: a Yang line occupies a Yang position and is paired with the Yin line in the Yin position below. The Yin line is paired with me and associates with me; a petty person, however, must not be befriended. Since a petty person must not be befriended, one should sever relations with them, and this is auspicious. A spouse is my proper partner and cannot be cast aside, so I can only make my own intentions upright. When my intentions are upright, licentious and deviant things cannot intrude. This is what is meant by “steadfast and auspicious”: upholding what is right brings good fortune.

The Great Strength: The Ram at the Fence

In the Great Strength hexagram, four solid Yang lines are arranged consecutively at the bottom, firm like a ridge beam and the foundation of a house; hence it is called “Great Strength.” The upper trigram is Zhen, and the lower is Qian. Zhen is associated with green bamboo, and so suggests a fence. When Nine at the third place in Qian changes, it becomes Dui, which suggests a ram. Dui is in the west and Zhen in the east; Mao and You lie directly opposite one another, giving the image of a ram butting against a fence.

The initial line is like the ram’s toes. When a ram butts a fence with its horns, its toes must also brace against it; if its horns are injured, its toes are hampered as well. Nine at the fourth place and Nine at the second place are both Yang lines. If Nine at the fourth place breaks through the fence and opens a broad path, allowing the ram to advance and smash through the obstacle, then the three Yang lines below will instead become the shafts of a powerful carriage. Therefore, both Nine at the second place and Nine at the fourth place are auspicious when they remain steadfast.

In the Jin hexagram, the Nine in the Fourth Place and the Nine in the Second Place are both genuine yang lines of the same kind. Once the fences are opened and a broad road cleared so that the flock can enter and multiply, the three yang lines below will in turn become the shafts that strengthen the carriage. This is why the Nine in the Second Place and the Nine in the Fourth Place are considered upright and auspicious.

Diagram of the “Kang Marquis” in the Jin Hexagram

In the symbolic imagery of the Eight Trigrams (Bagua), the Qian trigram represents the horse. The Jin hexagram is centered on Kun as its inner trigram, and its yin line occupies the fifth place, which would not ordinarily signify a horse. The horse mentioned here is one bestowed by the Qian trigram. Bestowing a horse means that a feudal lord has been given the means to flourish and develop, making the symbolism of the lord clear. The Book of Changes uses the sun rising above the earth to depict a feudal lord because fire in the heavens symbolizes the Great Possession hexagram, which represents the Son of Heaven. The Son of Heaven and the feudal lords are both rulers who face south to govern. They must possess clear and discerning virtue so that the people may live in peace; when the people are at peace, the ruler’s position can be secure. Hence the term “Kang Marquis”—a ruler who brings well-being to the feudal lords and stability to the realm.

Diagram of “Jizi” in the Mingyi Hexagram

The hexagram and line images of Mingyi are especially clear in their depiction of human affairs. The fifth line symbolizes Jizi, the worthy minister of the late Shang; the top line symbolizes King Zhou. The statement in the Nine in the Third Place about hunting to the south and capturing the enemy leader—could it refer to King Wu of Zhou? And does “rescuing a strong horse” not refer to the ministers who assisted King Wu and brought order to the chaos? The Six in the Fourth Place is a yin line of the Kun trigram. It occupies a human position and, like the Nine in the Third Place, is also in a human position. Could this symbolize Weizi and the Grand Duke, who joined the Zhou?

The Initial Nine and the Top Six both correspond to the water image of the Kan trigram: like a bird about to fly but lowering its wings, like a horse ready to set out but lacking strength. One wishes to rescue them but lacks the power to do so. Could this refer to people such as Boyi and Shuqi? They refused to attach themselves to the Zhou and were ultimately unable to save the Shang from its fall.

Diagram of the Jia Ren Hexagram

Someone asked, “Does the image of the Family hexagram mentioned by Wen Zhongzi (Wang Tong) mean that one should discern what is happening within and bring order to what is outside?” This should be the hexagram formed by Li and Xun. In the diagram, Yin and Yang lines are paired and occupy the central positions, suggesting parents and husband and wife. This interpretation is based on Confucius’s Commentary on the Images. Jiao Yanshou regarded the top line as the ancestral temple and the fifth line as the ruler. If we apply that interpretation to the Family hexagram, the ruler’s position corresponds to the father. Confucius said, “There is a stern authority in the household”; this refers to the parents.

In the Opposition hexagram, the six lines are mutually at odds, as Yin and Yang fail to harmonize. Yang lines occupy Yin positions, so the line positions are at odds with one another. The second and fifth lines correspond, but the fifth is also linked with the top line; the top and third lines correspond, while the third is also linked with the second. Thus the lines’ mutual responses also seem at odds. When they are at odds, they separate and cannot come together. Therefore, in explaining the statements attached to the six lines of the Opposition hexagram, the sages resolve this discord and enable Yin and Yang to each rest in their proper place. The Opposition hexagram presents a richer array of images than the other hexagrams in order to express its meaning fully.

The diagram of movement to and from the Obstruction hexagram.

In Jian (one of the sixty-four hexagrams of the Book of Changes, symbolizing difficulty and danger), the two yang lines are both trapped between yin lines, hence the name “Jian.” In the hexagram, four lines concern coming and going, while the other two do not take movement as their image. The first four lines are not in central positions; the last two are.

The sages cultivate themselves by holding to the Way of centrality and correctness. Thus, even when facing hardship, they remain at ease and carry on as usual amid adversity, without needing to rush back and forth. Nine at the Fifth occupies the central position in the upper trigram, gaining the middle Way while also holding a high position. Skilled at dealing with difficulty, he does not oppress those below him, so people willingly turn to him. Friends therefore come to his aid, and he does not remain isolated in danger.

Six at the Second occupies the central position in the lower trigram, gaining the middle while holding a low position. Skilled at dealing with difficulty, she does not seek support from those above her. Though the matter is not her own, she is willing to take responsibility. In the end, she is without fault and receives a response from those above.

Nine at the Third does not occupy a central position, so the text urges him to reflect on himself and cultivate his virtue. Six at the Fourth is also not in a central position, so she is urged to join with the two yang lines. Initial Six is at the very bottom of the hexagram, so she is urged to build a good reputation and not set out rashly. Top Six is close to Nine at the Fifth, so she is encouraged to strengthen herself and follow a virtuous great person, joining with the yang line as Six at the Fourth does.

An Explanation of the Diagram of the Kan Hexagram of Danger

The Kan hexagram, which symbolizes falling into danger, has a yang line in its middle. Initial Six is at the very bottom, so she is urged to build a good reputation and not set out rashly. Top Six is close to Nine at the Fifth, so she is encouraged to strengthen herself and follow a virtuous great person, joining with the yang line as Six at the Fourth does.

The yang line in the middle of the Kan hexagram is the yang line at the bottom of the Zhen hexagram. At first it is concealed within Kan; later it rises above Kan, sets things in motion, and becomes Zhen’s bottom line. This is like the kernel inside a fruit transforming and growing into a tender shoot. Hence the phrase “obtaining the yellow arrow.” “Arrow” refers to a straight shaft, symbolizing being centered and upright. When centered and upright, the tender shoot can grow and extend.

In the Jie hexagram, which symbolizes release from hardship, Yin and Yang are disordered and the lines occupy unsuitable positions. Thus the top line symbolizes release from discord: Zhen is situated within Kan. A gentleman in a low position, when petty people hold power, may humble himself, endure hardship, and move among them, yet never forget his great resolve to rise and act. Some also say that once a gentleman escapes his constraints and leaves, he can extend his aspirations. This is the reason the fourth nine and third six lines have the image of a “toe” (the great toe, symbolizing entanglement or attachment).

Diagram of the Center in Decrease and Increase

The images of the Decrease and Increase hexagrams both say to act in accord with the times. The line statements of both hexagrams mention “a turtle worth ten sets of cowries,” a precious instrument for divination. To act in accord with the times means to decrease when decrease is called for, without people under Heaven judging it stingy, and to increase when increase is called for, without people under Heaven judging it extravagant. The turtle signifies that both turtle divination and yarrow divination show compliance, and that the subjects and people offer no resistance.

Diagram of Resolving the Decisive

Five yang lines resolve against one yin line; five gentlemen remove one petty person. This should not be difficult. But the yin line is attached to five positions, entangling both the fifth nine and the fourth nine. This produces the situation of the Dui hexagram. The yin line conceals the yang, and the petty person constrains the gentleman; hence it is difficult to make a decisive break and remove the obstacle.

In the Great Strength hexagram, the ram exerts its firm strength through the Zhen trigram; Zhen and the ram belong to the same category. In the Resolving hexagram, the ram exerts its firm strength through the Dui trigram. Dui and the ram do not belong to the same category, but once change occurs, they become alike. This is why the fourth nine line has the image of leading a ram, and why the third nine line, after changing, takes on the image of a ram.

The Diagram of the Gou (Encounter) Hexagram

Looking at the first and central lines, the diagram contains the image of a pig, while the Nine in the Third position stands out as the rump. Looking at the first, second, and fourth lines, there is also the image of a fish: yang lines surround a yin line. The Fifth Nine shows a vine spreading and growing.

The Gou Hexagram derives from the Qian Hexagram: when its first line changes from yang to yin, the image of the dragon is transformed into a fish. Once the dragon becomes a fish, its horns are no longer of use; this is why the image of the “horn” in the Gou Hexagram reaches its end. The yang Qi of the Qian Hexagram begins at the zi position and ends at the si position. The si position lies in the Xun direction and symbolizes the flourishing of vines. Thus, the six yang lines of the Qian Hexagram meet the Xun Hexagram at the si position, and the single yin line within Xun begins to emerge. Since this yin line has arisen, the hexagram is called “Gou,” or “Encounter.”

The Diagram of the Cui (Gathering) Hexagram

Once the Cui Hexagram has formed, all things gather according to their respective kinds. The yang lines occupy the position facing south: one line symbolizes the Son of Heaven and another the feudal lords. Below them are the Three Ministers, the twenty-seven senior officers, and the eighty-one gentlemen, all serving under their authority. They uphold the ancestral temple to preserve its dignity. The first line conveys the principle of preventing the people from falling into disorder, while the top line offers a warning about losing the people’s support.

“Cui” means that all things gather after reaching maturity in autumn. Autumn belongs to the Dui Hexagram, whose top line was originally dominant. Now the Qi of the Kun Hexagram moves from the southwest to the west, and yin lines increase, so the two yang lines take the lead. Yet the top line has lost the people’s support.

The one Yin line below Xun (the Xun hexagram, symbolizing wind and wood) joins with the three Yin lines of Kun to form a whole. Yin Qi is heavy and still, while Yang Qi rises upward; the two Yang lines are what ascend. The first line attaches itself to these two Yang lines and rises with them, while the three Yin lines also join them as one. This creates the image of “permitted ascent”: rising smoothly and successfully. “Permitted” means gaining the trust of others.

Kun governs the Hai position. Hai is also the time when the Qi of wood begins to grow but has not yet taken shape. At the Zi position, the Zhen hexagram lies beneath Kun. Zhen, too, belongs to wood and symbolizes wood just beginning to sprout and take root. If Xun lies beneath Kun, it has two Yang lines, unlike Zhen, which has only one; this is why the resulting hexagram is called Sheng (“Ascent”). Sheng corresponds to the Chou position. By the Mao position, the Qi of wood has become vigorous.

The outer trigram explains one’s position. The fifth line occupies the position of Heaven and cannot ascend step by step as if climbing a staircase. Yet “steadfastness” means acting rightly. Yao, Shun, Yu, and Tang each rose to the position of Son of Heaven by following the right Way, as though climbing steps. If one does not follow the right Way, how could one avoid falling?

Collation notes for the middle volume of Gou Shen Tu of the Images and Numbers of the Great Change. The following entries explain differences between the original wording and various editions, and record the grounds on which the editor amended or supplied characters.

For example, “zu zhi” originally read “zu zhi”; it was changed on the basis of the Siku edition. “Fu tui” originally read “bi tui” and was likewise changed according to the Siku edition. Some words and phrases were supplied or corrected from the context: the character “ju” was added based on the meaning, while “zheng chong,” originally “zheng heng,” was corrected with reference to the context and the middle volume of Zhouyi Tu in the Daoist Canon.

The collation notes also list variant readings across editions. For example, “san yang” appears as “er yang” in the Siku edition. The original character “di” was “zhi” and was corrected on the basis of the middle volume of Zhouyi Tu in the Daoist Canon. “Bian wo” appears as “bian kan” in the Siku edition, while “zhen xia” appears there as “zhen shang.”

Some readings remain uncertain. For example, at “ji bei,” the Siku edition reads “ji zhao.” The editor considers that it may instead be “ji zhi,” but cannot yet determine which reading is correct. At “yuan shang,” the original wording is erroneous and was also emended to “yuan shang” on the basis of the Siku edition. These entries mainly document variant readings and the grounds for the editor’s corrections.

The Kun hexagram symbolizes distress and obstruction. It corresponds to the ninth lunar month, when the seasonal Qi of Dui (the Qi of autumn) is dominant, and to the Earthly Branch Xu. Earth blocks the waters of the marsh, so the Great Image says, “There is no water in the marsh: this is Kun.”

Kun is formed by Dui above Kan: Dui symbolizes autumn, and Kan symbolizes winter. The yin line in Dui represents the beginning of autumn, when creeping plants have not yet withered. The predicament is therefore likened to a tangle of kudzu vines that is difficult to escape. The Six in the Third Position falls at the transition from autumn to winter, when the leaves have fallen from the creeping plants and only their thorns remain; the predicament is likened to a thicket of brambles. The Initial Six lies at the very bottom of Kan, symbolizing the bitter cold of the Great Cold season. Frost has killed nearly all the creeping plants, leaving only trees, so the predicament is likened to a tree stump. The three yin lines of Kun are thus each represented by plants or trees.

Diagrams of the two uses of water and fire in the Jing and Ding hexagrams

In the Jing hexagram, yang lines symbolize spring water, because water arises from the yang of Heaven’s First (the yang energy that represents the source of water in the Yin-Yang conception).

In the Jing hexagram, yang lines symbolize spring water because water arises from the yang Qi of Heaven’s First. The central yang line of the Kan trigram symbolizes the cold spring in the direction of Kan (the north). The saying “the north gives rise to cold, and cold gives rise to water” expresses this principle; hence it is also called “Taiyang Cold Water.”

The Xun trigram contains two yang lines. One is in the Earth position and tends downward, symbolizing a valley rather than a well. The other is in the Human position, but lies beneath the “fan,” so water drawn from the well cannot reach it. It is inferior to the fifth line, which rises above the “fan.” A well is best when its water is abundant, whereas a cauldron must not be filled to the brim. This shows that the well and the cauldron, as vessels, each have their own distinct qualities.

The Ding hexagram has symbolic images for the cauldron’s crossbar, ears, and feet, though one of the feet is missing. Thus the first line says, “The cauldron is overturned, its feet upward.” The yin line below instead takes the form of two cauldron ears, so the fifth line is called “yellow ears,” distinguishing it from the first.

Diagram of the Furnace and Bellows Forging Metal in the Ge Hexagram

Although the Ge hexagram evokes a cauldron or li vessel transforming raw food into cooked food, its primary images are the furnace and the wheel. The fire power of the Li trigram (symbolizing fire) is used to forge the metal of the Dui trigram (symbolizing metal), transforming it into shape. Metal thus “follows change,” altering its form through forging. Change comes first, and the cauldron follows, since a cauldron is made by smelting and casting with bellows. The Xia ruler Hou once cast a cauldron, and Tang of Shang and King Wu of Zhou also used cauldrons as treasured vessels. The Ge hexagram therefore also contains the symbolism of the revolutions of Tang and Wu.

Diagram of the Movement and Traces of the Heart

The six lines of the Zhen hexagram first counsel people to remain cautious and alert, so that they can then speak and laugh with ease. The second line warns that when money is lost, one should not pursue it. This means that the mind should not stir recklessly, and outwardly one should not covet profit. The third line says “quaking and trembling,” urging people to correct hidden faults and distinguish what is confusing, so they do not ultimately stray onto the wrong path. These are all important principles for calming the mind.

The outer trigram concerns a situation in which action is imminent. Thus the fourth line says “bogged down in the mud,” indicating that matters are obstructed and one hesitates, unable to decide. The fifth line says “no loss,” indicating that something has been accomplished. The top line says “going forth brings misfortune,” indicating that matters ultimately fail.

Diagram of the Image of the Back in the Gen Hexagram

The image of the Gen hexagram mentions the cheeks but not the mouth; the body but not the abdomen; and the back and waist, but not the navel. It presents the figure as standing with its back toward someone, hence the phrase “keeping the back still” (stopping at the back). Viewed as a whole, the hexagram does not distinguish the lower legs from the toes, or the body from the cheeks above. Its four yin lines appear together, as if forming the shape of the backbone. The top yang line symbolizes the shoulders, and the middle yang line symbolizes the spine. This image draws on the idea of the spine running down the body’s center line.

The Nine in the Third Place of the Gen hexagram is the hexagram’s governing line. As a yang line in a yang position, it has an impulsive nature and is like the waist. Bending and stretching, sitting and standing, walking and moving all depend on the waist; yet movement is in fact directed by the mind. Therefore, the sage uses the image of “fumigating the heart” to explain this line.

The Six in the Second Place is a yin line in a yin position, with a quiet nature, and symbolizes the lower leg. The mind wants to move, but the lower leg cannot take a step; naturally, the heart cannot feel at ease. The sage therefore describes it as “the heart is not pleased.”

The lower trigram of the Gradual Progress hexagram is Gen, and the upper is Xun. The season is just after the Beginning of Spring in the first lunar month, when wild geese return north, so all six lines use geese as metaphors. Wild geese migrate in response to the rising Yang energy. Gen and Xun also correspond respectively to the Yin and Yang directions represented by Zi and Wu, making the use of geese to explain this hexagram apt.

Line Six in the Third place lies at the top of the Gen trigram, while the top line, Nine, lies at the top of the Xun trigram. They symbolize the southern and northern shores respectively. Line Six in the Third place is a Yang line among Yin lines. It coincides with the season when wild geese return north and birds and beasts are about to mate and reproduce. This is why the hexagram evokes a husband setting out on a campaign and a wife becoming pregnant. Line Six in the Third place and Line Nine in the Fourth place occupy the human positions; their Yin and Yang energies meet, giving rise to the image of pregnancy. Line Nine in the Fifth place and Line Six in the Second place, by contrast, occupy the positions of Heaven and Earth. Separated from each other, they can only respond from afar, with the male and female each in their own place; thus, there is no image of pregnancy.

The Sleeves of the Ruler and Her Younger Sister in the Marrying Maiden Hexagram

Zhen symbolizes green bamboo: solid at the bottom and hollow at the top, like a basket. The Marrying Maiden hexagram resembles the Peace hexagram. In both, the two lines in the human positions are interchanged, creating the image of sleeves overlapping. The left side of the human body belongs to Yang, and the right to Yin. When Yin and Yang unite, it is like two sleeves crossing over one another.

“Yimei” refers to the younger sister who accompanies a bride in marriage. She is in the lower position, and her line is Yang. “Jun” refers to the principal wife. She is in the upper position, and her line is Yin. The Changes regards Yang as good and Yin as bad, and Yang as noble and Yin as lowly. Accordingly, this interpretation holds that the ruler’s sleeve is inferior to the younger sister’s.

The hexagram Marrying Maiden (Guimei) symbolizes a woman marrying, but this journey does not accord with the right way. In the hexagram, Zhen (Thunder), which represents Yang Qi and Wood, moves to the eastern Yang position to join the western Yin position. This signifies the Qi of Zhen Wood entering Dui Metal, where Wood is subdued by Metal. It is therefore auspicious only to wait until the moon is nearly full. When the moon is full, Yin Qi is strong enough to contend with Yang Qi, and the weak may overcome the strong, while the lowly may rise above the noble. For this reason, the judgment of Marrying Maiden says only, “Going forth brings misfortune; there is nothing favorable.” Acting contrary to the right way is not what a sage would do.

Fuxi placed the Zhen trigram, symbolizing the Qi of Lesser Yang, in the east, and the Li trigram, symbolizing the sun’s brightness, in the south. This shows the Qi of Lesser Yang stirring in the east and the sun’s radiance reaching its height in the south. King Wen placed Zhen above Li and named the resulting hexagram Abundance (Feng). The name signifies the Qi of Lesser Yang moving southward and joining Li’s brightness to form an image of abundance. In the judgment of Abundance, King Wen explains that when brightness reaches its peak, it begins to decline; hence the statement, “It is favorable to act at noon.” In the line statements, he explains that when brightness reaches its peak, it turns to darkness; hence the reference to seeing the Northern Dipper and dim stars at noon.

King Wen’s statements for the hexagram and its lines mention only the sun and the Northern Dipper. Why, then, does Confucius’s Image Commentary, which explains the hexagram’s image, also speak of the moon? Because Abundance corresponds to the transition between the fifth and sixth lunar months. At that time, the sun moves through the region of the Willow lunar mansion, and the handle of the Northern Dipper points toward the Wu and Wei directions. The region traversed by the Willow mansion actually spans three earthly-branch directions, so it is possible for the Northern Dipper to be seen during the day.

Diagram of the traveler’s lodgings in the hexagram Traveling (Lü).

Six Two relies on a centered and even tempered way of dealing with affairs, allowing him to travel with goods and servants. Nine Four combines firmness with yielding and is aided by a corresponding line, so he obtains resources and an axe. Both gain only in the short term; in the end, neither is as good as Six Five.

The Li hexagram is bright because it uses wisdom in accordance with the moment. Thus it says, “Raising a cow brings good fortune.” The “cow” here symbolizes a yielding and gentle nature. The top Nine loses the cow, symbolizing the loss of brightness and clear discernment.

The Travel hexagram comes after the Fu hexagram and before the Qian hexagram. When Yang energy is flourishing, people are often only temporary guests in the places they occupy; hence the name “Travel,” meaning to lodge or reside somewhere temporarily. The top Nine of the Travel hexagram gains influence and holds power, yet entrusts himself to the flames, unaware that disaster will come when his nest is burned. Nine Three is eager to attach himself to power and advance recklessly, also unaware that disaster will come when the lodging house is burned.

Six Two and Nine Four both travel in a yielding manner, carrying goods or obtaining an axe, and gain something for the time being. But Six Two must first give of himself to avoid disaster, while Nine Four is not at peace within. Does this not warn people against pursuing profit single-mindedly while away from home?

As for Six Five, he initially hunts pheasants by means of the cultured refinement symbolized by the Li hexagram. But his arrows are lost, and he catches no prey. This shows that the path he follows is obstructed and that he cannot obtain any benefit.

The image of the Xun hexagram beneath the bed.

In the hexagram Xun, the yang lines represent the lungs and internal organs, while the yin lines represent the roots and feet of trees. This is because the image of feet lies below the lungs and internal organs. The four yang lines arranged together also resemble a bamboo basket. The second nine represents the eastern wall of the trees, and the top nine represents their western wall. Hence both are said to lie beneath the trees, with the roots and feet of the trees used to support this interpretation.

The fifth nine represents a flying dragon and also the tiger’s transformation. The flying dragon corresponds to Jia, and the tiger’s transformation to Geng; together they symbolize the changing Qi of Yin and Yang. The top nine “loses its axe” because its firmness is excessive. The second nine “employs the scribe and the shaman” because, though firm and centered, it is not in a fitting position. The third nine “frowns repeatedly” because it is both out of position and away from the central place. From this, it follows that the one able to wield authority must be a line that occupies the honored position and is also centered. Who could that be, if not the fifth nine?

Diagram of the Images of Dui

The first six of the hexagram Kan governs the winter solstice, and the first nine of Li governs the summer solstice. The first lines of Zhen and Dui govern the spring and autumn equinoxes, respectively. Thus, the lower two lines of Dui have stronger yang energy and symbolize the seventh month; the middle two lines contain equal shares of yin and yang and symbolize the eighth month; and in the upper two lines, yin exceeds yang, symbolizing the ninth month.

The fourth nine of Dui speaks of “trading in Dui,” using this to explain that Zhen corresponds to the musical note Jue, Li to Zhi, and Kan to Yu. The fifth nine speaks of “trust in stripping away,” using this to explain the patterns of change embodied in Zhen, Yang, Li, Shen, Kan, and Fu.

Diagram of Huan’s Body

At the beginning of the Zi hour, one Yang is born; by the Si hour, the Qi of the six Yang lines has reached its height. Zi corresponds to the Kan trigram, and Si to the Xun trigram. When Xun is placed above Kan, they form the Huan hexagram. This explains the principles expressed by the Huan, Yang, Li, Zhen, Kan, and Fu hexagrams.

Diagram of Huan and the Body

At the beginning of the Zi hour, one Yang is born; by the Si hour, the Qi of the six Yang lines has reached its height. Zi corresponds to the Kan trigram, and Si to the Xun trigram. When Xun is placed above Kan, they form the Huan hexagram. “Huan” means dispersal. According to the theory of hexagram Qi, which uses hexagram images to describe the changing solar terms, Huan corresponds to the period after the summer solstice and before Major Heat. At this time, Yang Qi disperses outward. Yet even as it spreads, Yang Qi retains a source that continues to grow: the single Yang line in the middle of the Kan trigram. This is the primordial Qi, the original vital energy from which all things under Heaven and Earth arise.

Yang governs Qi; Yin governs form. Because Yang Qi disperses outward, sweat and blood are used to describe it. The two Yin lines occupy the middle of the hexagram, so the terms “group” and “body” are used to describe them. “Body” refers to the physical form, which is divided into the limbs; “group” refers to parts gathered together into a form, corresponding to the five viscera and six bowels. These bodily forms all differentiate from primordial Qi. The basis of human life is primordial Qi, which comes from Kan water—that is, the “essence of Heaven’s One,” the vital essence symbolized by Kan water. It is transformed by steaming into sweat, then circulates through the body as blood, nourishing the limbs and the five viscera.

Diagram of the Solar Terms

The top line of the Xun trigram (the line at the very top of the hexagram)… The basis of human life is primordial Qi. Primordial Qi comes from Kan water, that is, the “essence of Heaven’s One.” It is transformed by steaming into sweat, then circulates as blood, nourishing the limbs and the five viscera.

When the top line of Xun (Wind) and the bottom line of Dui (Lake) change, both become Kan (Water). The Qi of Kan water rises as vapor, nourishing the branches and leaves of Xun wood. As it seeps downward, it nourishes the water plants growing in Dui’s lake. When the lake dries up, it becomes the Kun hexagram, symbolizing water flowing away below.

The single Yang line of Dui drains downward, symbolizing a warning against desire. The single Yin line of Kan is deficient upward, symbolizing a warning against indulgence. To guard against desire, one must twice “not leave the courtyard gate”; to guard against indulgence, the flavors of sweetness and bitterness serve as reminders. The first line says, “Not leaving the courtyard gate brings no blame,” while the second says, “Not leaving the courtyard gate brings misfortune.” Both express the intention of restraining desire.

When the first line changes, it becomes Kan. The “Water of Heavenly Unity” within it is regarded as the source of true Jing (essence). If a noble person understands the principles of opening and closing, guards carefully and discreetly against the outward loss of Jing and Qi, and keeps the gates through which they enter and leave closed, this is an important method of nourishing life. The second line of Kan belongs to Fire. The “gate and courtyard” symbolize the openings of the body—in other words, the heart. The heart’s Fire should nourish Water below, while the mind should discern things clearly beyond. To keep everything closed and let nothing out is to lose the way of balance and centrality; this too is a warning to restrain desire.

The sixth line of the third position says “sighing,” expressing regret over a failure to exercise restraint. The sixth line of the fourth position says “at ease,” expressing contentment with restraint. Both lines explain the benefits and harms involved. The way of nourishing life is fully contained in these two hexagrams.

A diagram of the eggs and wings that give rise to life in the Zhongfu and Xiaoguo hexagrams.

“Inner Confidence” (Zhongfu) symbolizes the first stirrings of Yang Qi, like a bird hatching from an egg. “Conjoining” (Xian) symbolizes the first stirrings of Yin Qi, like a warm-blooded animal conceived and born from its mother. Thus, “Inner Confidence” represents the beginning of Yang Qi’s emergence, while “Small Exceeding” (Xiaoguo) represents its completion. Crows, sparrows, and other birds lay eggs throughout the year, especially abundantly in spring, so bird eggs can symbolize the Beginning of Spring. At the winter solstice, they also symbolize Yang Qi first arising within Yin.

“Inner Confidence” evokes the image of a crow laying eggs. The crow’s nature belongs to Fire, whose tendency is to rise. The hexagram text says, “The pig and fish bring good fortune,” because pigs and fish—animals that live in water—belong to things that moisten and descend, and so can balance Fire’s upward tendency. The north belongs to the position of Zi, and is also the direction symbolized by pigs and fish. “Small Exceeding” says that a bird flying away brings danger because it flies from the east toward the center and encounters the net symbolizing the south. The net corresponds to Yang Qi in the “Clinging” (Li) hexagram. When Yang Qi reaches the south represented by “Clinging” and becomes excessive, Yin Qi arises in response.

The pitch standards (lü lü), established by the Yellow Emperor to coordinate musical tones with the seasonal nodes, are assigned to Qian and Kun, and paired with Kan and Li. Qian and Kun represent the six Yang lines and six Yin lines respectively; Kan and Li, in turn, form the “Already Fulfilled” (Jiji) and “Not Yet Fulfilled” (Weiji) hexagrams.

Diagram of the Pitch Standards Corresponding to “Already Fulfilled” and “Not Yet Fulfilled”

In the changes of the pitch standards corresponding to “Already Fulfilled” and “Not Yet Fulfilled,” the Yang line in Kan is about to rise. When it reaches Zhonglü, the corresponding governing hexagram is “The Creative” (Qian). This is called “Qian is full at nine, yet its head is not seen,” meaning that Qian Yang has moved to the position of nine, with its leading end concealed from view. The Yin line in Li has already entered Kan. When it reaches Yingzhong, the corresponding governing hexagram is “The Receptive” (Kun). This is called “Kun is empty at ten, with Qian,” meaning that Kun Yin is at the position of ten, guiding the hidden Dragon Qi—the latent Yang Qi that has not yet appeared.

The beginning of “Already Fulfilled” corresponds to the beginning of “The Creative”; the end of “Not Yet Fulfilled” corresponds to the end of “The Receptive.” The end of “The Creative” continues into the end of “The Receptive,” in the order of nine followed by ten. The beginning of “The Receptive” takes up from the beginning of “The Creative,” in the order of two preceding one.

The Twelve Inner Months and the Twelve Pitch Standards

Diagram of the Qi of the Hexagrams: The Sun and Moon’s Courses, and the Alternation of Cold and Heat

Diagram of Mutual Generation: annotated “Yang arises below; Yin ascends above”

Diagram of the Thirteen Hexagrams and Their Symbolic Images

The Li and Xun trigrams together symbolize ropes and mesh. The mesh is called a gu: connect two mesh openings and weave them together with rope, and they form a net. Li symbolizes the pheasant and also hunting; Dui and Xun symbolize fish and fishing.

In the Yi hexagram, Qian symbolizes metal and Xun symbolizes wood. Metal cuts wood, representing the cutting of timber to make tools. When the fourth line changes into the top line, it forms the Kan trigram. Kan symbolizes bent timber, representing the first step in making tools from curved wood. Zhen symbolizes bending the timber. Inserted into the earth, which is symbolized by Kun, the timber bends forward; cut into shape, it becomes a si, a tool for turning the soil. Bent backward, it becomes a lei, the wooden shaft used in farming.

In the Shihe hexagram, multiple Li images appear above. Li also symbolizes the sun, so this represents midday. Kun symbolizes the people and is below, representing the crowds at a market. The Li trigram contains a hidden image, while Dui symbolizes goods. Kun symbolizes people coming together, so this represents drawing people from across the realm and gathering goods from across the realm. Kun and Qian join, symbolizing exchange.

Qian symbolizes Heaven and Kun symbolizes Earth. When Heaven and Earth remain still, each of their six children—the Zhen, Xun, Kan, Li, Gen, and Dui trigrams—has its own function. The ruler lets his robes hang and folds his hands, and the realm is governed. Qian is above, symbolizing clothing.

Kun is below, symbolizing the lower garment. A skirt is clothing worn on the lower body.

In the Huan hexagram, Qian symbolizes metal and Xun symbolizes wood. Metal splits wood, and the wood floats on water, symbolized by Kan, representing the making of a boat from split timber. The pointed shape of a flame symbolizes carving wood to make an oar.

In the Sui hexagram, Kun symbolizes an ox and Zhen symbolizes a foot, representing driving an ox and putting it to work under a yoke. Zhen also symbolizes a horse’s feet, which the top line six draws along. It is drawn along to carry a load. The inner trigram is near and the outer trigram far away; the top line six lies beyond the outer trigram, so it symbolizes transport to a distant place.

The Yü hexagram and the Qian hexagram have opposite images. In the Qian hexagram, Gen symbolizes a gate. When line nine in the third position changes into line nine in the fourth position, it forms another Gen image, representing a double gate. Gen symbolizes the hand, Kan symbolizes hardness, and Zhen symbolizes sound. Striking hard wood with the hand makes a sound, representing the beating of wooden clappers as a warning. Kun symbolizes a closed gate, and Kan symbolizes approaching bandits, representing raiders attacking.

In the Xiaoguo hexagram, Dui symbolizes metal and Xun symbolizes wood. Metal cuts wood to make a pestle, a wooden tool for pounding. The wood symbolized by Xun enters the earth symbolized by Kun, representing digging into the ground to make a mortar from stone or wood. Kan symbolizes a hollow, just like the shape of a mortar. The pestle moves above while the mortar remains fixed below. The fourth line corresponds to them, representing striking to make a sound and beating clappers as a warning. Kun symbolizes a closed gate, and Kan symbolizes approaching bandits, representing raiders attacking.

In the Xiaoguo hexagram, Dui belongs to Metal and Xun to Wood. Metal from Dui cuts through the Wood of Xun, forming a pestle. The Wood of Xun enters the Earth of Kun, which is dug out to make a mortar. Kan carries the meaning of sinking in, just like a mortar dug into the ground. The pestle moves above while the mortar remains fixed below. The fourth line corresponds to the first, and the third to the top line; this response between upper and lower is precisely what makes the pestle and mortar convenient to use together. When Kan changes into Xun, it symbolizes the movement of the thighs, and so the people are able to receive aid.

The Kui and Jia Ren hexagrams have opposite configurations. In Jia Ren, Xun symbolizes wood; Xun together with Li symbolizes silk, and Kan symbolizes a bow. Bending wood into a bow is the making of a bow. Dui belongs to Metal and is used to carve the wood into a sharp point, making an arrow. Dui symbolizes granaries, while Qian symbolizes strength and vigor; together they represent governing the world through authority.

The Dazhuang hexagram develops from the Fu hexagram and, after one change, becomes the Zhongfu hexagram. Gen symbolizes a dwelling, and the image of Dui resembles an opening; a cave, too, is a place to live. After another change, it becomes the Daxu hexagram, with Qian above, symbolizing the horizon and also the open country. Xun enters and changes into Gen, indicating stopping to live in the wilderness. A third change produces the Dazhuang hexagram: Zhen symbolizes strong timber above, like a roof beam, while Qian symbolizes Heaven and also a roofed dwelling. Xun symbolizes hidden wind, and Dui symbolizes flowing marsh water, indicating waiting for wind and rain. When the Dazhuang hexagram is reached, the roof beam no longer bends.

The Great Exceeding hexagram derives from the Retreat hexagram. Its first transformation produces the Conflict hexagram. Qian appears and Kun recedes, indicating that nothing is enclosed. Its next transformation produces Xun, which symbolizes wood; Dui symbolizes metal, and metal destroys wood, so there are no trees. Its third transformation produces the Cauldron hexagram. Li symbolizes the eyes, and Dui symbolizes marsh water; when the water drains away, this signifies mourning. The top nine line changes and corresponds with the third line. Kan and Dui signify restraint; if one does not observe the mourning period, there is no fixed measure.

Wood lies beneath the marsh, with the person symbolized by Qian inside: this is a coffin and its outer casing. At burial, the coffin is used; Dui, associated with metal, also symbolizes the destruction of wood, so no trees are planted afterward. The third transformation produces the Cauldron hexagram. Li symbolizes the eyes, and Dui symbolizes marsh water; when the water drains away, this signifies mourning. The top nine line changes and corresponds with the third line. Kan and Dui signify restraint; if one does not observe the mourning period, there is no fixed measure. Wood lies beneath the marsh, with the person symbolized by Qian inside: this is a coffin and its outer casing. At burial, the coffin surrounds the body, the outer casing surrounds the coffin, and earth surrounds the casing. This is precisely what the Great Exceeding symbolizes: going beyond the ordinary measure, with layers enclosing one another.

The Breakthrough hexagram derives from the Coming to Meet hexagram and, after four transformations, becomes the Great Possession hexagram. In the Coming to Meet hexagram, Xun symbolizes a cord, and thus the tying of knots to record events. Xun transforms into Li and Kun; Li symbolizes documents, while Dui symbolizes metal. Metal is used to engrave wood and make tally certificates.

Diagram of the Three Presentations of the Nine Hexagrams

First Part

The Treading hexagram is the foundation of De; the Modesty hexagram is its handle; the Return hexagram is its root.

The Duration hexagram makes De steadfast; the Decrease hexagram cultivates De; the Increase hexagram makes De more abundant.

The Oppression hexagram puts De to the test of discernment; the Well hexagram is where De finds its place; the Gentle Penetration hexagram is the method by which De is put into practice.

Second Part

The Treading hexagram achieves its aims through harmony; the Modesty hexagram is noble and bright; the Return hexagram distinguishes things from their earliest, subtle signs.

The Duration hexagram encompasses variety without becoming tiresome; the Decrease hexagram brings hardship first, after which things become easier; the Increase hexagram continually grows and enriches De, making it a rule for conduct.

The Oppression hexagram remains able to make progress despite hardship; the Well hexagram stays in its place while benefiting those who move elsewhere; the Gentle Penetration hexagram weighs things and conveys its principles subtly.

Third Part

The Treading hexagram means acting with a harmonious attitude; the Modesty hexagram is used to establish ritual and law; the Return hexagram is used to understand oneself.

The Duration hexagram is used to hold steadfastly to De; the Decrease hexagram is used to keep misfortune at a distance; the Increase hexagram is used to undertake beneficial endeavors.

The Oppression hexagram is used to lessen resentment and blame; the Well hexagram is used to clarify what is right; the Gentle Penetration hexagram is used to act flexibly and adapt to the times.

The three lines of the upper canon are arranged in three pairs, forming nine hexagrams in all; the six lines of the lower canon are arranged in three pairs, forming eighteen hexagrams. The numerical values are: Lü (Treading), ten; Qian (Humility), fifteen; Fu (Return), twenty-four; Heng (Duration), two; Sun (Decrease), eleven; Yi (Increase), twelve; Kun (Oppression), seventeen; Jing (The Well), eighteen; and Xun (Gentle Penetration), twenty-seven. The nine hexagrams have a combined value of 136. Deriving this number through three iterations gives 408.

The number of the celestial cycle is 360, known as the completed number. The value 408 exceeds 360 by 48, representing the pattern of Yin and Yang waxing and waning, advancing and withdrawing. Yang Qi moves forward toward the Qian hexagram, advancing by 48 each month from Fu to Qian. Yin Qi withdraws toward the Kun hexagram, also retreating by 48 each month, from Gou to Kun.

Diagram of Change through Threefold Arrangement and Fivefold Coordination

Heaven’s One descends to generate Earth’s Six; Earth’s Two rises to generate Heaven’s Seven. Heaven’s Three moves left to generate Earth’s Eight; Earth’s Four moves right to generate Heaven’s Nine.

“Threefold arrangement” means bringing things together; “coordination” means matching them in pairs. The numbers of Heaven and Earth come together and pair off, interweaving and moving back and forth, generating one another. In this way, the numbers of generation are completed, and the patterns and order between Heaven and Earth are revealed. The Xici says: “Through threefold arrangement and fivefold coordination, change occurs; their numbers are interwoven and combined. By mastering their changes, the patterns of Heaven and Earth are formed.” This is the principle being described.

Diagram of the Eighteen Changes

When male and female unite, the upper and lower scriptures together contain only twelve positions. The proper positions are the eight hexagrams Qian, Kun, Kan, Li, Xian, Heng, Sun, and Yi, divided into eighteen positions. Qian and Kun transform into Yi and Daguo; Yi and Daguo transform into Kan and Li; Kan and Li transform into Zhongfu and Xiaoguo; and Zhongfu and Xiaoguo transform into Xian and Heng. From this, human relationships in the world take shape.

Diagram of One Yin and One Yang

The sixty-four hexagrams are composed of two kinds of lines, Yin and Yang. They begin with Qian, the pure Yang hexagram, and end with Kun, the pure Yin hexagram. Starting with Qian and Kun, the sixty-four hexagrams are arranged according to combinations of one Yin and one Yang. Combinations of two Yang and two Yin, four Yang and four Yin, sixteen Yang and sixteen Yin, and thirty-two Yang and thirty-two Yin are then arranged in sequence, thereby forming the sixty-four hexagrams. Hence the saying: “One Yin and one Yang are called the Dao.”

Diagram of Before Jia and After Jia

The thirty days from Jiawu to Guihai, extending from the Shen hour to the Si hour, are called “Before Jia” and are represented by a black halo.

The thirty days from Jiazi to Guisi, extending from the Yin hour to the Hai hour, are called “After Jia” and are represented by a white halo.

Yin and Yang as Ruler and People

Yang hexagrams take odd numbers as their governing principle. Thus, in a hexagram with one Yang line and two Yin lines, the Yang line symbolizes the ruler and the Yin lines symbolize the people. Yin hexagrams take even numbers as their governing principle. Thus, in a hexagram with two Yang lines and one Yin line, the Yin line symbolizes the ruler and the Yang lines symbolize the people. In a Yang hexagram, one line stands for the ruler and two for the people; this order accords with the natural principle and is therefore called “the way of the noble person.” In a Yin hexagram, two lines stand for the ruler and one for the people; this order is reversed and is therefore called “the way of the petty person.”

Yin-Yang Odd and Even

Zhen, Kan, and Gen are classified as Yang trigrams. Why, then, do they contain more Yin lines? This comes from changing the line positions of Kun one by one. Each of the three trigrams has one Yang line and two Yin lines; together, they make five forms. Hence they are called “odd-numbered Yang trigrams.” Xun, Li, and Dui are classified as Yin trigrams. Why, then, do they contain more Yang lines? They arise through changes to Qian. Each of the three has one Yin line and two Yang lines; together, they make four forms. Hence they are called “even-numbered Yin trigrams.” Here, “odd” refers to Yang numbers, and “even” to Yin numbers.

Odd and Even in Yin and Yang

Zhen, Kan, and Gen are Yang trigrams, yet they contain more Yin lines because they come from changing the lines of Kun one by one. Each has one Yang line and two Yin lines; together they make five forms, which is why they are called the “odd” Yang trigrams. Xun, Li, and Dui are Yin trigrams, yet they contain more Yang lines because they arise through changes to Qian. Each has one Yin line and two Yang lines; together they make four forms, which is why they are called the “even” Yin trigrams.

The Ten Changes Derived from the Two Modes

The title indicates that the Two Modes—Yin and Yang—give rise to ten changes.

The Generative Cycle of the Ten Heavenly Stems and Five Phases

The title indicates the generative relationships between the Ten Heavenly Stems and the Five Phases (Wood, Fire, Earth, Metal, and Water).

Diagram of the Number of the Great Expansion

The title indicates that this section presents a diagram of the “Number of the Great Expansion,” a number used to derive hexagram images in the divination method of the Zhouyi.

Diagram of the Yarrow-Stalk Divination Method

The title indicates that this section explains divination using yarrow stalks. During divination, the stalks are divided into groups and counted; the remainder is then used to determine the line image. The term die means to divide and count the yarrow stalks.

The first, second, and third counts are performed between the little finger, middle finger, and index finger, respectively. The remainder from each count is either five or nine, or four or eight.

The combination “four, four, five” belongs to the “three small” group and totals thirteen stalks. Subtracting thirteen from the forty-nine stalks leaves thirty-six, or four groups of nine, giving old Yang.

The combination “nine, eight, eight” belongs to the “three large” group and totals twenty-five stalks. Subtracting twenty-five from the forty-nine stalks leaves twenty-four, or four groups of six, giving old Yin.

“Five, eight, eight” gives young Yang.

The combination “nine, four, eight” consists of two large counts and one small count, totaling twenty-one stalks. Subtracting twenty-one from the forty-nine stalks leaves twenty-eight, or four groups of seven, giving young Yang.

The combination “nine, eight, eight” belongs to the “three large” group and totals twenty-five stalks. Subtracting twenty-five from the forty-nine stalks leaves twenty-four, or four groups of six, giving old Yin.

“Five, eight, eight” gives young Yang.

The combination “nine, four, eight” consists of two large counts and one small count, totaling twenty-one stalks. Subtracting twenty-one from the forty-nine stalks leaves twenty-eight, or four groups of seven, giving young Yang.

“Nine, eight, four” gives young Yang.

“Nine, four, four” gives young Yin.

The combination “five, eight, four” consists of two small counts and one large count, totaling seventeen stalks. Subtracting seventeen from the forty-nine stalks leaves thirty-two, or four groups of eight, giving young Yang.

“Five, four, eight” gives young Yin.

The Number 106 in the Yellow River Diagram

The title indicates that this section discusses the “Number 106” in the Yellow River Diagram.

Multiply each of the fifteen numbers associated with Heaven and Earth by three, five, and seven, giving forty-five, seventy-five, and one hundred and five. The numbers of the Nine Palaces end at one hundred and five, so one hundred and six is the extreme number. Three, five, and seven are chosen because they are Yang numbers, and these particular numbers are used from among them.

Diagram of the Eight Trigrams Governing Transformation

The Qian trigram governs the generation and nurturing of all things and covers them. The Kan trigram governs the transformations of cold, the Gen trigram those of moisture, the Zhen trigram those of thunder, the Xun trigram those of wind, and the Li trigram those of heat. The Kun trigram governs the forming and bearing of all things, while the Dui trigram governs the transformations of dryness.

Diagram of Gathering by Kind and Dividing into Groups

The Kan trigram is in the north, Zhen in the east, Qian in the northwest, and Gen in the northeast. These four trigrams are all Yang. Li is in the south, Dui in the west, Xun in the southeast, and Kun in the southwest. These four trigrams are all Yin. Hence the saying, “Directions gather things according to kind”: things in the same or nearby directions gather according to their similar natures.

The number six corresponds to the Kan and Qian trigrams, nine to Kun and Dui, seven to Li and Xun, and eight to Zhen and Gen. Hence the saying, “Things divide into groups according to kind.” Receiving help from those of the same kind brings good fortune; acting against those of the same kind brings misfortune. From this arise good and ill fortune.

Diagram of Understanding the Passage of Day and Night

The Zi hour marks the beginning of the Qian trigram, and the movement of Yang Qi ends at the Si hour. The Wu hour marks the beginning of the Kun trigram, and the movement of Yin Qi ends at the Hai hour. There are 292 Yang lines, the number of daytime, totaling 1,728; there are 192 Yin lines, the number of nighttime, totaling 1,152. Together, the two parts of day and night give a stated total of 2,889 lines; calculated fourfold, the total is 11,520. Thus, by understanding the way day and night move, one can understand the origins of Yin-Yang transformation.

Yin within Yang

Yang within Yin

The “Chart of Hexagram Sequence” is divided into the Upper Classic, with thirty hexagrams, and the Lower Classic, with thirty-four.

The “intermingled hexagrams” in the “Chart of Miscellaneous Hexagrams” are arranged in a crisscrossing pattern. Their meanings are explained through the relationships between hexagrams, revealing the limitless functions of their images. The chart explains the meanings of the hexagrams chiefly in terms of firmness and yielding, ascent and descent, and movement back and forth. This differs from the “Sequence of Hexagrams,” which explains their order. Han Kangbo said that the Miscellaneous Hexagrams sometimes group identical hexagrams together and sometimes use different hexagrams to clarify one another. This is what it means to arrange all sixty-four hexagrams in an interwoven pattern to express their meanings.

The passage on the “Ruan Xuanzhun” also explains that the Miscellaneous Hexagrams clarify meaning through interwoven arrangement, using firmness and yielding, ascent and descent, and movement back and forth to reveal the hexagrams’ functions. It cites Han Kangbo on the method of arrangement.

The “Chart of Hexagram Names in the Ruan Xuanzhun’s Commentary on the Changes” sets out quantities that increase by successive levels: one Xuan generates three directions; the three directions generate nine regions; the nine regions generate twenty-seven divisions. The sequence then expands to eighty-one families, 243 tables, and 729 praises, finally reaching 26,244 measures. In general, each level is derived by multiplying the previous one by three; the increase from 729 praises to 26,244 measures is calculated by multiplying by thirty-six. The passage also states that one Xuan corresponds to one year, seventy-two measures to one day, and that the cycle begins in the eleventh month.

The “Chart of Hexagram Qi in the Taixuan’s Commentary on the Changes” states that the calendar begins at the winter solstice and that hexagram qi begins with the Zhongfu hexagram. Hexagram qi is a system of inference that maps hexagram images onto seasonal changes.

The “Chart of the Complete Numbers in the Huangji Jingshi” lists the correspondences between the units yuan, hui, day, and month, and hexagram images. One-one corresponds to “yuan of yuan, day of day, Qian of Qian,” and has the value one. Two-one corresponds to “hui of yuan, month of day, Dui of Qian,” and has the value twelve. One-two corresponds to “yuan of hui, day of month, Qian of Dui,” and has the value twelve. Two-two corresponds to “hui of hui, month of month, Dui of Dui,” and has the value 144.

This passage pairs time levels such as “three yuan,” “three hui,” “four yuan,” and “four hui” with the sun, moon, stars, celestial bodies, and the Bagua (Eight Trigrams) directions to represent different cycles and their numerical values. Here, “yuan,” “hui,” “yun,” and “shi” are units or names of time periods; “Qian, Dui, Zhen, Xun, Kan, Gen, Kun, and Li” are the symbols of the Eight Trigrams. The word “zhi” indicates a pairing: for example, “Qian zhi Li” means pairing the Qian trigram with the Li trigram.

As listed in the original, the first part proceeds as follows: the first three-yuan yun pairs the sun with the stars, matching Qian with Li, for a value of 360; the second three-hui yun pairs the moon with the stars, matching Dui with Li, for a value of 4,320. Next, the first four-yuan shi pairs the sun with the celestial bodies, matching Qian with Zhen, for a value of 4,320; the second four-hui shi pairs the moon with the celestial bodies, matching Dui with Zhen, for a value of 51,840.

The passage then lists correspondences at further levels: the first five-yuan year pairs the sun with stone, matching Qian with Xun, for a value of 119,600; the second five-hui year pairs the moon with stone, matching Dui with Xun, for a value of 1,555,200. The first six-yuan month pairs the sun with earth, matching Qian with Kan, for a value of 1,555,200; the second six-hui month pairs the moon with earth, matching Dui with Kan, for a value of 18,662,400. The first seven-yuan day pairs the sun with fire, matching Qian with Gen; the second seven-hui day pairs the moon with fire, matching Dui with Gen. The first eight-yuan star pairs the sun with water, matching Qian with Kun; the second eight-hui celestial body pairs the moon with water, matching Dui with Kun. The numerical values following these entries are copied as given in the passage, though some characters and numbers appear to be corrupt.

At the end, another set of pairings is listed: the third one-yun yuan pairs the stars with Li and the sun with Qian, for a value of 360; the fourth one-shi yuan pairs the celestial bodies with the sun and Zhen with Qian, for a value of 4,320; the third two-yun hui pairs the stars with the moon and Li with Dui, for a value of 4,320; the fourth two-shi hui pairs the celestial bodies with the moon and Zhen with Dui, for a value of 85,140; the third three-yun yun pairs the stars with themselves and Li with Li, for a value of 129,600.

These entries mainly use a numerological system to lay out correspondences among cycles, celestial terms, trigram images, and numerical values.

The four-three cycle of circulation corresponds to the earthly branch Chen and to the stars. Its hexagrams are Zhen and Li, and its number is 1,555,200.

The three-four cycle of circulation corresponds to the age, the stars, and Chen. Its hexagrams are Zhen and Zhen, and its number is 1,555,200.

The four-four age corresponds to the age and Chen. Its hexagrams are Zhen and Zhen, and its number is 18,862,400.

The three-five cycle of circulation corresponds to the year, the stars, and stone. Its hexagrams are Li and Xun, and its number is 46,656,000.

The four-five age corresponds to the year, Chen, and stone. Its hexagrams are Zhen and Xun, and its number is 599,872,000.

The three-six cycle of circulation corresponds to the month, the stars, and earth. Its hexagrams are Li and Kan, and its number is 5,598,720,000.

The four-six age corresponds to the month, Chen, and earth. Its hexagrams are Zhen and Kan, and its number is 60,184,640,000.

The three-seven cycle of circulation corresponds to the day, “Gao” (the character used in the original), and fire. Its hexagrams are Li and Gen, and its number is one.

The three-six cycle of circulation corresponds to the month, the stars, and earth. Its hexagrams are Li and Kan, and its number is 5,598,720,000.

The four-six age corresponds to the month, Chen, and earth. Its hexagrams are Zhen and Kan, and its number is 60,184,640,000.

The three-seven cycle of circulation corresponds to the day, Gao, and fire. Its hexagrams are Li and Gen, and its number is 16,796,160,000.

The four-seven age corresponds to the day, Chen, and fire. Its hexagrams are Zhen and Gen, and its number is 201,553,920,000.

The three-eight cycle of circulation corresponds to Chen, the stars, and water. Its hexagrams are Li and Kun, and its number is 201,553,920,000.

The four-eight age corresponds to Chen, Chen, and water. Its hexagram is Kun; the original has “nong.” Its number is 2,418,664,704,000.

The five-one year corresponds to the origin, stone, and the day. Its hexagrams are Xun and Qian, and its number is 129,600.

The six-one month corresponds to the origin, earth, and the day. Its hexagrams are Kan and Qian, and its number is 1,555,200.

The five-two year corresponds to the conjunction, stone, and the month. Its hexagrams are Xun and Dui, and its number is 1,555,200.

The six-two month corresponds to the conjunction, earth, and the month. Its hexagrams are Kan and Dui, and its number is 18,662,400.

The five-three year corresponds to the cycle of circulation, stone, and the stars. Its hexagrams are Xun and Li, and its number is 46,656,000.

The six-three month corresponds to the cycle of circulation, earth, and the stars. Its hexagrams are Kan and Li, and its number is 5,598,887,200.

Here, images and numbers are arranged by levels such as years, months, days, periods, yuan, and hui. The categories and correspondences are marked by symbols such as stone, earth, fire, and water, and by the trigrams Xun, Zhen, Kan, Li, Gen, Kun, Qian, and Dui. The number following each entry is the value assigned to that level.

Expressions such as “the age-cycle of four years,” “the age-cycle of four months,” and “the fortune-cycle of three months” refer to units of time at different levels. “Xun corresponding to Zhen” and “Kan corresponding to Li” indicate correspondences between two successive trigrams. The text then lists levels such as “year within a year,” “month within a month,” and “day within a year,” showing how the system derives relationships and assigns numbers across its various levels.

“Yuan of seven-one days,” “yuan of eight-one periods,” and “hui of seven-two days” move to the larger time levels of yuan and hui, again pairing trigrams with numbers. The passage is primarily a tabulation of images and numbers, setting out the names and categories of each level, its trigram, and its assigned value.

“Eight-two, the meeting of Chen; the month of Water; Kun corresponding to Dui” is paired with the number “six thousand seven hundred and eighteen thousand four hundred and sixty-four thousand.” “Seven-three, the cycle of the day; the star of Fire; Gen corresponding to Li” is paired with “1,679,616 ten-thousands.” “Eight-three, the cycle of Chen; the star of Water; Kun corresponding to Li” is paired with “10,155,392 ten-thousands.” “Seven-four, the age of the day; the Chen of Fire; Gen corresponding to Zhen” is paired with the same number, “10,155,392 ten-thousands.” “Eight-four, the age of Chen; the Chen of Water; Kun corresponding to Zhen” is listed with the number “24,185 thousand 3,392 ten-thousands.”

It then lists “Seven-four, the age of the day; the Chen of Fire; Gen corresponding to Zhen,” with the same number as before, followed by “Eight-four, the age of Chen; the Chen of Water; Kun corresponding to Zhen,” with the number “24,186 ten-thousands 4,704 ten-thousands.” Next, “Seven-five, the year of the day; the stone of Fire; Gen corresponding to Xun” is paired with “60,466 ten-thousands 1,760 ten-thousands,” and “Eight-five, the year of Chen; the stone of Water; Kun corresponding to Xun” with “725,594 ten-thousands 1,120 ten-thousands.” “Seven-six, the month of the day; the earth of Fire; Gen corresponding to Kan” is listed with the same number as the preceding item, while “Eight-six, the month of Chen; the earth of Water; Kun corresponding to Kan” is paired with “8,707,129 ten-thousands 3,440 ten-thousands.”

At the end, it lists entries such as “Seven-seven, the day of the day; the Fire of Fire; Gen corresponding to Gen,” accompanied by their respective numbers; one entry also includes the characters “corresponding to Kan.” The final groups are “Eight-seven, the day of Chen; the Fire of Water; Kun corresponding to Gen,” “Seven-eight, the Chen of the day; the Water of Fire; Gen corresponding to Kun,” and “Eight-eight, the Chen of Chen; the Water of Water; Kun corresponding to Kun,” each followed by a number. The end of the text is marked “Shao’s Diagram of the Supreme Ultimate’s World-Ordering Classic” and “Wen Gong.”

Here, “day,” “Chen,” “year,” “month,” and the other terms are categories of images and numbers arranged at different levels. “Kun corresponding to Dui” and “Gen corresponding to Li” indicate correspondences between the Eight Trigrams (Bagua). The numbers are the calculated values given in the diagram.

Latent Emptiness

Diagram Imitating the Profound Mystery (a diagram modeled on the Taixuan)

Diagram of the Nature Principle in Latent Emptiness

When arranging the sequence of “nature,” begin by listing ten states of complete unity. Once these ten states have been fully set out, reduce by one level, then by two, three, and four levels. Finally, pair five kinds together, and the principle of nature is complete. Beginning with unity and ending with pairing: this is the pattern by which Heaven and Earth operate.

Diagram Matching the Trigrams with Directions

The primordial Qi of the workings of creation is like the heart of a sage. The Qi of creation takes bringing forth life as its foundation, and the sage’s heart likewise aims to rescue and benefit the people. It must therefore turn from stillness to movement, and pass from nonbeing into being, so that the myriad things may grow and flourish in harmony and each may settle into its own work.

People throughout the world have never perceived the subtle workings of creation or the sage’s intent. Why is this? Although the Qi of creation and the sage’s heart turn and act, they never depart from stillness; although they appear as being, they never relinquish nonbeing. They nurture the myriad things and bring well-being to the people, allowing all things and people to grow and live within them. The myriad things pass through the stages called “alignment, appearance, service, delight, struggle, and toil,” yet are unaware of it. This is why the sequence of the Eight Trigrams begins with Zhen and is completed with Gen. Does the term “Emperor” not refer precisely to the unity of the Qi of creation and the sage’s heart?

Diagram of the Transmission of the Yijing Learning from Antiquity to the Present

End of Volume Two of Diagram of Hooking the Profound in the Images and Numbers of the Great Changes.

The character “ling” is the same as in the Siku Quanshu edition; it is suspected that the original text mistakenly wrote “ling” as “ling” (with a different character).

The original text has “mu” for the character “mo”; this has been corrected according to the Siku Quanshu edition.

The original text has “yan ci” for the two characters “fen ci”; these have been corrected according to the Siku Quanshu edition.

The character “zhi” has been supplied according to the Siku Quanshu edition.

The original text has “four branches” for “four limbs”; this has been corrected according to the Siku Quanshu edition.

The Siku Quanshu edition has “gate and courtyard” for “door and courtyard.”

The original text has “wu kan” for the two characters “cheng kan”; these have been corrected according to the Siku Quanshu edition.

The original text has “fu yi” for the two characters “hou yi”; these have been corrected according to the Siku Quanshu edition.

The original text has “bian yi” for the two characters “bian yi”; these have been corrected according to the Siku Quanshu edition.

The original text has “chang” for the character “dan”; this has been corrected according to the Siku Quanshu edition.

The original text has “yong” for the character “qiu”; this has been corrected according to the Siku Quanshu edition.

The Siku Quanshu edition has “and knows” for the two characters “and begins.”

The character “three” has been supplied according to the Siku Quanshu edition.

The Siku Quanshu edition reads “those myriad things and myriad beings have already…” for the sentence “embracing the myriad things and myriad people.”