《易象图说内篇(张理)》

The hexagrams of the Changes correspond to Heaven and Earth, so there is no principle between Heaven and Earth that they cannot encompass. Yin and Yang interweave and transform; odd and even numbers divide and combine in correspondence, and all things are interconnected.

The three versions of the Changes mentioned in the Rites of Zhou each have eight basic trigrams, which combine to form sixty-four hexagrams. With the Eight Trigrams as the framework and the sixty-four hexagrams as its details, the order in which the hexagrams are drawn and their positions in the Primordial Heaven diagram—the arrangement based on Fuxi’s sequence of trigrams—become clear. This suggests that the diagram already existed when Fuxi created the Changes, and was handed down through the Xia, Shang, and Zhou dynasties.

Confucius’s discussions of the Supreme Ultimate, the Two Modes, the Four Images, and the Eight Trigrams, as well as his account of doubled hexagrams, and the methods of Najia and hexagram Qi associated with Jing Fang, a Han-dynasty scholar of the Changes, all follow the sequence of the circular diagram. The Primordial Heaven diagram must therefore have circulated for a long time. Later interpreters of the Changes stopped investigating its original foundations. Although the diagram remained, scholars no longer passed it on, until Shao Yong rediscovered it. Earlier Confucian scholars said that Shao Yong transmitted the diagram to Li Mu, whose teachings came from Chen Tuan, known by the courtesy name Xiyi. This account of its transmission can hardly have been invented from nothing.

Some have also said that the Primordial Heaven diagram in An Introduction to the Study of the Changes came from the Cai family and was adopted by Zhu Xi. But Zhu Zhen, known by the courtesy name Hanshang, already had this diagram. This makes it beyond doubt that the diagram came down through Shao Yong’s line. Even if a sage were to return, this account would not be changed.

The principles of the Yi are vast and inexhaustible. Anyone who studies it and investigates on the basis of their own understanding can gain something from it. As long as an interpretation arises from a natural grasp of the text and is not forced, it can stand as a school of thought in its own right, even if no earlier scholar has explained it.

Zhang Zhongchun of Qingjiang (Zhang Li, courtesy name Zhongchun) was naturally intelligent and diligent in his studies. He mastered the classics of many kinds and devoted particular attention to the Yi. Drawing on the insights he had gained through years of study, he wrote a work called Illustrated Explanations of the Images of the Yi. Its diagrams explain the generation of Taiji (the Supreme Ultimate), the Two Modes, images, and hexagrams. Odd-numbered lines are placed above and even-numbered lines below; from this arrangement, the text derives Yin and Yang, firmness and yielding, inside and outside, and their transformations through interaction. It also gives a thorough account of the origins of the hexagram lines, the significance of the four seasons, the principles of nature and life, the numerical patterns of the Hetu and Luoshu diagrams, and the changes and methods involved in divination with milfoil stalks.

The circular diagram of the sixty-four hexagrams follows the repeating sequence Qian, Dui, Li, Zhen, Kun, Gen, Kan, and Xun. From it one can discern the movement and stillness of Heaven and Earth, the solar terms traced by the sun over the course of the year, and the moon’s course through each month. The square diagram arranges the hexagrams in the sequence Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun, proceeding from top to bottom and from left to right. It can therefore be used to derive the monthly hexagram Qi described in the Cantong qi and Shao Yong’s Song of the Great Change, as well as the numerical and symbolic changes of the twenty-eight lunar lodges.

Another diagram repeatedly derives one configuration from the interaction of Qian and Kun: Yang lines rise successively toward the upper left, while Yin lines descend successively toward the lower right. The twelve waxing-and-waning hexagrams, six Yin and six Yang, which show the growth and decline of Yin and Yang, can thus be clearly examined and used for further derivation. A further diagram follows the Later Heaven arrangement of the Eight Trigrams, with each of the eight palaces developing into seven hexagrams. The hexagrams opposite one another in the four cardinal and four intermediate directions are arranged in clear order.

These diagrams are ingeniously conceived and rigorously ordered. They require no deliberate effort at calculation; nothing can be added or removed, and nothing in them gives cause for doubt. This is precisely what it means to follow nature without forcing an interpretation. Zhang Zhongchun’s illustrated explanations can carry forward the diagrammatic approaches to the Yi developed by Shao Yong and Zhu Xi, while establishing a school of their own and showing how the images and principles of the Yi are connected throughout. Only when students rely on their own understanding and truly gain insight can they pass their teachings on to later generations without leading them astray.

Zhang Zhongchun is a man of great learning and insight, and I have known him for a long time. When he completed the Illustrated Explanations, he first sent me the manuscript to read. I was especially impressed by how seamlessly it brings images and numbers together, and by the precision of its reasoning. I have therefore presumed to write this preface and have kept the manuscript in my collection.

Written with due respect in the autumn, in the seventh month of the Dingyou year of Zhizheng, by Huang Zhencheng, a man of Ziyun Mountain in Zhaowu.

The Book of Changes says: “The Yellow River brought forth the River Chart, and the Luo River brought forth the Luo Writing; the sages based the Changes on them.” The River Chart and the Luo Writing depict the forms of Yin and Yang in Heaven and Earth. The Changes is the classic through which sages portrayed the wondrous transformations of Yin and Yang in Heaven and Earth.

Within Heaven and Earth, movement and stillness give rise to many forms. Odd and even numbers continually come into being, movement and stillness transform into one another, and the Four Images—the four basic states formed by the transformations of Yin and Yang—combine above and below and alternate from left to right. In this way, the hexagram figures of the Changes were drawn. These figures represent natural forms such as Heaven, Earth, Water, Fire, Lake, and Mountain; Wind corresponds to Lake, and Thunder corresponds to Mountain. Hexagrams represent forms; forms are given names; names make meanings clear; and meanings give shape to words. Once the words have been clearly expressed, the book of the Changes is thereby written.

The Changes serves to follow the principles of nature and life, investigate the origins of ritual and music, bring about transformations, and set the affairs of spirits in motion. In the end, all of this depends on the forms and numerical principles presented by the River Chart and the Luo Writing.

In the River Chart, the circle “○” representing Heaven is “one”; the figure representing Earth is …; the center of the chart is …; the Four Images … . The text here is damaged or missing, and its meaning cannot be determined.

The Yang numbers—one, three, and five—together make the number of “supporting Heaven”; among them, three is called “supporting.” The Yin numbers—two and four—together make the number of “establishing Earth”; among them, two is called “establishing.” The Yang numbers sum to nine, the number of Yang’s function; the Yin numbers sum to six, the number of Yin’s function.

Arranged horizontally, the diagram displays the structure of the three trigrams; arranged vertically, it displays the positions of the nine trigrams. Crossing the horizontal and vertical arrangements produces fifteen trigrams. The Qian trigram takes nine and the Kun trigram takes six, making fifteen. The Kan trigram takes seven and the Li trigram takes eight, making fifteen; the Zhen trigram takes seven and the Xun trigram takes eight, making fifteen; the Gen trigram takes seven and the Dui trigram takes eight, likewise making fifteen. The Yellow River Diagram and the Luo River Writing work together like warp and weft, forming a pattern of the order of Heaven and Earth.

“Fifty” is the pivot of the Yellow River Diagram and the Luo River Writing. When five and ten are superimposed, they form a layout with four directions—left and right, front and back. This is the structure of the four cardinal directions in the Yellow River Diagram. When five and ten are interlaced, they form the four cardinal directions and four corners, displaying the Luo River Writing’s nine-palace arrangement. Turning left in sequence expresses the circular motion of the celestial bodies; it also provides the basis for the armillary sphere, an instrument for observing the heavens, and for devising the calendar. Arranged in reverse, turning to the right, the pattern expresses Earth’s square layout; it is also the origin of systems such as enfeoffing feudal lords and dividing land into well-field plots. Enclose the square within a circle, then frame the circle with the square, and the changes of Heaven and Earth can be encompassed in full without exceeding their bounds; the generation and transformation of the myriad things can be traced in every detail, with nothing omitted.

Human beings receive the virtue of Heaven and Earth. They are where Yin and Yang join and the spirits converge, and they embody the concentrated essence of the Five Phases (Wood, Fire, Earth, Metal, and Water). The upper half of the body corresponds to Heaven and the lower half to Earth; the head is round and the feet square, the abdomen belongs to Yin and the back to Yang. The eyes, like the Li trigram, perceive outwardly with clarity; the ears, like the Kan trigram, hear inwardly with acuity. The forms of the mouth and nose resemble mountains and marshes, while the voice and breath resemble thunder and wind. Thus the principles of the world can be embodied in the human person, who thereby stands between Heaven and Earth.

From this we can understand that the Changes are within my heart, and my heart is in communion with the Changes. Therefore, if we develop these principles into diagrams, the six positions—the places of the Yin and Yang lines in a hexagram—can reveal the Three Powers of Heaven, Earth, and humanity. Arranged according to the six seasonal divisions, they can display the course of the four seasons. Joined as six bodily forms, they can correspond to the human body; running through the six vessels, they can make the spirit and Qi complete. Expressed through the six classics, they can establish governance and instruction; matched with the six Yang pitch pipes in the ancient system of twelve pitches, they can harmonize sound. Establishing the six codes can bring order to government, and commanding the six armies can secure the state.

Thus, the trigram positions can be used to elucidate the Dao; the sequence of the seasonal divisions, to explain De (Virtue/Power); the body, to investigate nature; and the vessels, to gather life. The classics can be used to examine ritual institutions, pitch to set music right, codes to govern public affairs, and the army to administer punishments with care. In this way, both the substance and function of the eight trigrams of the Changes are complete.

The eight diagrams above are included here as an appendix to the outer chapter. When the eight trigrams cross and interact, then combine to form hexagrams, transform and unfold, and are put to use, one can draw the circular and square diagrams of the sixty-four hexagrams, along with diagrams showing their transformations and applications. The circular diagram models Heaven; the square diagram takes Earth as its model. Transformation follows the Dao, while application harmonizes principle and rightness. Afterward, yarrow stalks and counting rods can be used to organize the hexagram numbers, and divination through changing lines can explain the results of an oracle. The stages of divination—dividing into two, setting one aside, counting by fours, and returning the remainder—as well as such transformations as changing lines, doubled hexagrams, and branch hexagrams, are all set out in diagrams to make the hexagram images clear, with explanations of their underlying meaning.

Although these ideas do not entirely follow the commentaries handed down by earlier Confucian scholars, they may still come close to the general intent of the sages who composed the Changes. I earnestly hope that like-minded people who aspire to this work will revise and correct them. Written by Zhang Li, a later scholar of Qingjiang, at the Gen Retreat in Sanshan, on the Shangsi day of the third month in the year Jiachen, the Azure Dragon year, of the twenty-fourth year of Zhizheng.

The preface to the first volume says: In his “Preface to the Dragon Chart,” Master Chen Xiyi explained that the dragon-horse first appeared bearing its patterned markings in ancient times, before the age of Fuxi. The numbers preserved today have already been arranged, and people still wonder about their meaning. How much more difficult, then, to explain the numerical principles before they were arranged and combined. How, then, can people understand them? The answer is to seek their intent in Confucius’s three discussions of the meaning of the Nine Hexagrams when speaking about the Changes; through this, one can gain some understanding.

The images revealed by Heaven are as clear as beads strung together. The slightest error makes their order impossible to establish. Thus, from one to ten thousand, everything is connected layer upon layer, as if threaded on a line. Had the Dragon Chart appeared already arranged into its final form, the sages could not have seen its original pattern. Heaven’s intent, therefore, was to reveal the numbers in an uncombined state first. The sages then observed their pattern and understood their function. Heaven scattered the Dragon Chart into view; Fuxi brought it together and put it to use; Confucius explained it with subtlety.

The Dragon Chart contains fifty-five numbers. The twenty-five numbers in its upper part belong to the numbers of Heaven. Three, five, and nine run through them, while fifteen surrounds them on the outside. These numbers show the positions of Heaven’s three, five, and nine, as well as ten and five. Next, one and six appear without fixed positions, further revealing the function of two, ten, and four. This is what is meant by “Heaven hangs forth its images.”

The thirty numbers in the lower part belong to the numbers of Earth. They too are divided into five positions to show the function of “five.” Dividing ten into six equal parts presents the image of Earth. Six is then divided into the Four Images, but Earth’s six is not paired with the other numbers. In the upper part, one has no assigned position, revealing the function of two, ten, and four. In the lower part, six does not participate in the operation, likewise revealing the function of two, ten, and four. Only afterward are the numbers of Heaven and Earth fully combined.

Heaven’s one occupies the upper position and is the foundation of the Dao; Earth’s six occupies the lower position and is the foundation of the vessel, or concrete things. Three then sets Earth’s two and four in motion, enabling them to function. The commentary says: “Three” adds the Heavenly numbers one and three to make nine, symbolizing the Qian hexagram, which takes nine as its operative number. “Two” adds the Earthly numbers two and four to make six, symbolizing the Kun hexagram, which takes six as its operative number.

When “three” is on the Yang side, it avoids lone Yin; when it is on the Yin side, it avoids solitary Yang. The commentary explains: Forming the Eight Trigrams requires three positions. In the upper part, one, three, and five make up the three positions. Two and four cannot form a trigram because they lack the proper central position, and so are called “lone Yin.” In the lower part, six, eight, and ten make up the three positions. Seven and nine cannot form a trigram because they lack the proper central position, and so are called “solitary Yang.” “Three” occupies none of these positions, as though avoiding them.

The transformations of the Dragon Chart are vast and boundless, branching into countless paths. Here, only its general outline has been presented.

Confucius used teaching without words to offer people guidance through three groups of hexagrams in the Book of Changes, comprising nine hexagrams.

The Lü hexagram is the foundation of virtue. It is tenth in the sequence, indicating that its function is “ten.” It teaches people to distinguish between higher and lower, and between those of noble and humble rank.

The Qian hexagram is the handle of virtue. It is fifteenth in the sequence, likewise indicating a function of “fifteen.” It teaches people to reduce what is excessive and supplement what is insufficient.

The Fu hexagram is the root of virtue. As the twenty-fourth hexagram, it reveals the beginning of change in the movement of Qi (vital energy).

The Heng hexagram represents the stability of virtue. It is the second hexagram of the Lower Canon, revealing the beginning of change in physical form.

The Sun hexagram represents the cultivation of virtue, while the Yi hexagram represents its enrichment. Together, these hexagrams explain where changes in flourishing and decline begin.

The Kun hexagram represents discernment in virtue, while the Jing hexagram represents the foundation on which virtue rests. Together, they explain how things shift and find a way through.

The Xun hexagram represents the restraint and application of virtue. To act through the Way of Xun and exercise flexibility is a vital method by which sages govern affairs: they devise appropriate measures for each situation and adjust them as circumstances change. All the principles involved are contained here.

First Diagram and Book

The diagram above presents the numerical principles of the “Dragon Diagram” before Heaven and Earth had come together.

The upper part represents the numbers of Heaven. Taking five as the center, the numbers of Heaven are arranged in five positions; five times five makes twenty-five. Adding one, three, five, and seven also gives twenty-five. Arranged vertically and horizontally, five positions reveal three and five; three positions arranged in the same way reveal nine and fifteen. The Preface says that three, five, and nine run through the pattern, while fifteen encloses it on the outside. This is what it means.

The lower part represents the numbers of Earth. Taking six as the center, the numbers of Earth are likewise arranged in five positions; five times six makes thirty. Adding two, four, six, eight, and ten also gives thirty. The Preface speaks of “dividing into ten parts to form six”: this presents the image of Earth, and that is what it means.

Second Diagram and Book

This diagram represents the arrangement in which Heaven and Earth have already joined within the Dragon Diagram.

The upper layer represents “image.” Combine one, three, and five to make the number of the “three heavens”; take the even number four as the number of the “two earths.” Their sum is fifteen, the generating numbers used when the Five Phases come into being. These are also the five numbers above in the previous diagram: subtract four from the five at the top to get one; subtract three from the five at the bottom to get two; subtract two from the five on the right to get three; subtract one from the five on the left to get four; the five in the center remains unchanged. The Preface says, “Heaven’s one dwells above; it is the root of the Dao.” This refers to this arrangement.

According to the Treatise on Pitch Pipes and the Calendar, combining the two initial numbers of Heaven and Earth makes it possible to determine Yin-Yang, hardness, and softness: one is the beginning of Yang, and two the beginning of Yin. In this diagram, Heaven above takes one as its image, and Earth below takes two as its image. Heaven and Earth join to form the Four Images and the Five Phases. The upper left is Greater Yang and belongs to Fire; the upper right is Lesser Yin and belongs to Metal; the lower left is Lesser Yang and belongs to Wood; the lower right is Greater Yin and belongs to Water. Earth is the Qi that harmonizes Yin and Yang. It occupies the center and moves through the four directions, impelling the beginnings and growth of all things. Earth therefore possesses both Yin and Yang qualities.

The three on the right symbolizes the Three Powers of Heaven, Earth, and humanity, which is why a hexagram line figure has three strokes. The four on the left symbolizes the four seasons, which is why divination uses four yarrow stalks as a group when dividing and counting them. Thus, the one, two, three, and four in the upper layer represent the system of yarrow stalk counts and hexagram lines.

The lower layer represents “form.” Nine, eight, seven, and six are the numbers used when Metal, Wood, Fire, and Water are flourishing; the ten at the center is Earth’s completing number. These are also the five positions below in the previous diagram: divide the six at the center and add one above it to make seven; add two to the left to make eight; add three to the right to make nine; the six below is not paired with any other number and remains six. This is what the Preface means by “dividing six to form the Four Images,” and by saying that Earth’s number six does not participate in the pairing.

According to this account, seven corresponds to the circular number of the yarrow stalks: seven times seven makes forty-nine. Eight corresponds to the square number of the hexagrams: eight times eight makes sixty-four. Nine is the number used for Yang lines, of which there are altogether one hundred and ninety-two; six is the number used for Yin lines, of which there are likewise one hundred and ninety-two. Ten is connected with the number of the Great Expansion: five times ten, or ten times five, gives fifty. Thus, the six, seven, eight, and nine in the lower layer represent the numbers used for yarrow stalks and hexagram lines.

The upper layer speaks of substance, the lower of function; the upper speaks of image, the lower of form. Images change, while forms are relatively stable. Once substance is established, function can operate. In this way, the transformations of Heaven and Earth continue to generate life without end.

If one, two, three, and four are taken as the numerical symbols of Heaven, their transformations appear above; if six, seven, eight, and nine are taken as the numerical forms of Earth, they take shape below. Superimposed, above and below form the Five Phases, corresponding to the left and right, the front and back, and the positions of generation. Interlaced, above and below form the Bagua (Eight Trigrams), corresponding to the four cardinal directions, the four corners, and the positions of the Nine Palaces.

Considered together with the preceding and following diagrams, this arrangement should resemble the Yin and Yang configurations of the Taiyi Dunjia system: one, two, three, and four are like the celestial plate in Dunjia, which revolves above in accordance with the changing times; six, seven, eight, and nine are like the terrestrial plate below, which remains fixed. This illustrates the principle that “Heaven moves, while Earth is still.” Earlier Confucian scholars did not reveal its essential meaning.

Thus, in the diagram, “one” is placed in the south, and the arrangement begins according to the laws of celestial patterns, rotating to the right in accordance with the rules of movement. At the first conjunction, “one” is in the southeast, “two” in the northwest, “three” in the southwest, and “four” in the northeast. The four yang numbers are arranged above, slightly to the right, while the four yin numbers are arranged below, slightly to the left. Yin and Yang are set apart, thereby establishing the positions of Heaven and Earth.

The upper part represents the numbers of Heaven. With “five” as the center, the numbers of Heaven are arranged in five groups, making twenty-five in all. Adding one, three, five, and seven also gives…

These are the numbers in the Dragon Diagram before Heaven and Earth have joined.

The positions above represent the numbers of Heaven. Five is the central number among the numbers of Heaven. They are arranged in five positions, and five times five makes twenty-five. Adding one, three, five, and seven also gives twenty-five. In the five positions, whether read vertically or horizontally, one can see three and five; adding the three positions vertically and horizontally gives nine, while adding the five positions vertically and horizontally gives fifteen. The Preface says that three, five, and nine run through the center, with fifteen surrounding them on the outside. This is the arrangement it describes.

The positions below represent the numbers of Earth. Six is the central number among the numbers of Earth. They, too, are arranged in five positions, and five times six makes thirty. Adding two, four, six, eight, and ten also gives thirty. The Preface says to divide ten parts into six, thereby depicting the form of the Earth. This is the arrangement it describes.

Two Diagrams

These are the positions in the Dragon Diagram—a schematic representing the numerical principles of Heaven and Earth—in which Heaven and Earth have already been brought together.

The upper section explains “image.” Add one, three, and five to obtain fifteen, called “joining Heaven.” Take the even number four as “the two Earths,” that is, Earth’s number. Fifteen is the generating number of the Five Phases.

Distribute the numbers according to the five upper positions in the diagram above: subtract four from the five at the top to get one; subtract three from the five at the bottom to get two; subtract two from the five on the right to get three; subtract one from the five on the left to get four; the five in the center remains unchanged. This is what the preface means when it says, “Heaven’s One resides above and is the root of the Dao.”

The Treatise on Pitch Pipes and the Calendar says, “The two root numbers of Yin and Yang are brought together to determine hardness and softness.” One is the beginning of Yang, and two is the beginning of Yin. In this diagram, the top represents Heaven and symbolizes one; the bottom represents Earth and symbolizes two; the central position of Heaven represents the Four Images and the Five Phases. The single dot at the upper left represents the sun and symbolizes Fire; the dot at the upper right represents Lesser Yin and symbolizes Metal; the dot at the lower left represents Lesser Yang and symbolizes Wood; the single dot at the lower right represents Greater Yin and symbolizes Water. Earth is formed when Yin and Yang Qi converge. It occupies the center and circulates through the four directions, bringing forth the life of all things; it partakes of both Yin and Yang.

On the right side of the diagram is “three,” symbolizing Heaven, Earth, and humanity—the Three Powers—and also providing the basis for forming a hexagram from three lines. On the left is “four,” symbolizing the four seasons of spring, summer, autumn, and winter, and also providing the basis for counting yarrow stalks in groups of four during divination. Thus, the images above are represented by one, two, three, and four, explaining the foundations of yarrow numbers and hexagram lines.

The lower section explains “form.” Nine, eight, seven, and six are the flourishing numbers of Metal, Wood, Fire, and Water; the Earth number ten shown in the center is Earth’s completing number. Following the five lower positions in the diagram above, take the six at the center as the base: add one at the top to get seven; add two on the left to get eight; add three on the right to get nine. The six at the bottom is not paired with the other numbers and stands alone as six. This is what the preface means by “dividing six to form the Four Images,” and what it means when it says that Earth’s number six does not participate in the pairings.

Seven is the circular number used in yarrow divination; seven times seven is forty-nine. Eight is the square number used for hexagram images; eight times eight is sixty-four. Nine is the number of Yang’s function, and there are one hundred ninety-two Yang lines in total. Six is the number of Yin’s function, and there are likewise one hundred ninety-two Yin lines. Ten is associated with the “Great Expansion number”: five times ten, and ten times five, both equal fifty. Thus, below, six, seven, eight, and nine represent the function of yarrow numbers and hexagram lines.

The above concerns substance, and the below concerns function; the above concerns images, and the below concerns concrete forms and numbers. Images are in flux, while forms are still. Once substance is established, function unfolds, and from this the transformations of Heaven, Earth, and all things arise.

One, two, three, and four represent the patterns of Heaven, with number and image moving and changing above. Six, seven, eight, and nine represent the forms of Earth, taking shape below. Heaven and Earth, layered above and below, together establish the relations of the Five Phases (Wood, Fire, Earth, Metal, Water)—that is, the directions of front, back, left, and right, and the positions from which things arise. When Heaven and Earth meet and interact, they form the Eight Trigrams (Bagua), arranged at the four cardinal points, the four corners, and the positions of the Nine Palaces.

Comparing the two diagrams, one can understand them as the Yin and Yang configurations of Taiyi Dunjia, a system of divination that uses Yin-Yang, the Nine Palaces, and the Heavenly Stems and Earthly Branches to model changes in time and space. One, two, three, and four are like the celestial plate of Dunjia, revolving above in accordance with the changing times; six, seven, eight, and nine are like the earthly plate, fixed below and unmoving. This illustrates the principle that “Heaven moves while Earth is still.” Earlier Confucian scholars had not disclosed its essential meaning.

At the beginning, therefore, one is in the south and begins its movement according to the patterns of the heavens, turning to the right. After the first change, one moves to the southeast, two to the northwest, three to the southwest, and four to the northeast. The four Yang numbers are arrayed above and on the right, while the four Yin numbers are arrayed below and on the left. Yin and Yang are thus separated, establishing the positions of Heaven and Earth. After the second change, one moves to the northeast, two to the southwest, three to the southeast, and four to the northwest. Yin and Yang now join, and the six subsidiary trigrams—Zhen, Kan, Gen, Xun, Li, and Dui, formed through the interaction of Qian and Kun—come into being. These two changes produce the natural pattern through which the Early Heaven Eight Trigrams arise.

Next, the positions of origin are paired: one with six, two with seven, three with eight, and four with nine, matching Yin and Yang respectively. This is the diagrammatic arrangement explained by Shaozi (Shao Yong) and Zhuzi (Zhu Xi). In the third change, one moves to the northwest, two to the southeast, three to the northeast, and four to the southwest. Hardness and softness then interweave, forming the four trigrams Kan, Li, Zhen, and Dui. In the fourth change, one moves to the southwest, two to the northeast, three to the northwest, and four to the southeast. Yang is on the right and Yin on the left, and the trigrams Qian and Kun take their arranged positions. These two changes establish the positions formed by the ordered arrangement of the Later Heaven Eight Trigrams. After one more cycle, one returns to the south.

The phrase “combine three and five in their changes, and interweave and reorder their numbers” in the Xici (“Appended Statements”) of the Yizhuan (“Commentary on the Changes”) describes precisely this process of reciprocal change and rearrangement of numerical positions. Liu Xin said, “The River Diagram and the Luo Writing serve as warp and weft to each other; the Eight Trigrams and the Nine Chapters are inner and outer aspects of one another.” He meant the same thing.

Master Jiang Heshan said: In the Yellow River Chart, the completed numbers are placed below, symbolizing the Earth, which remains still; the generating numbers symbolize Heaven, which moves and changes, thereby forming the trigrams. The Earlier Heaven Bagua depict the forms that arise naturally, while the Later Heaven Bagua show the positions of the things of Heaven and Earth after they have been arranged and brought to completion.

Observe how the trigrams combine. In the first union, the Two Modes (Yin and Yang) are established. In the second, the Six Children—the six trigrams generated by Qian and Kun, namely Zhen, Xun, Kan, Li, Gen, and Dui—appear. In the third, Zhen and Dui face one another, while Kan and Li each occupy one side. In the fourth, Qian and Kun stand on either side, while Gen and Xun occupy the corners. The sages placed Li in the south and Kan in the north, setting the four directions in order. They also placed Qian in the northwest and moved Kun to the southwest, thus revealing the further meaning that the eldest daughter takes her mother’s place. In this way, the Earlier Heaven Bagua present the forms of nature, while the Later Heaven Bagua present the arranged directions; the reasoning is quite clear.

Although this account does not follow the interpretations of earlier Confucian scholars, the trigrams and their numerical principles have been laid out, and the reasoning they contain is plain. It may therefore stand as one school’s interpretation. Zhu Xi once said that spending free time studying the numerical principles of the Yellow River Chart and the Luo River Writing can set one’s thoughts in motion. Reading Zhongchun’s explanation now makes me believe this even more.

Charts and Writings, Part Three:

The chart above is the Dragon Chart, which represents the numbers by which Heaven and Earth come into being.

In the previous diagram, one, two, three, and four represent the numerical symbols of Heaven and rotate to the right as they move. Six, seven, eight, and nine represent the numerical forms of Earth; they remain still, each in its place. Thus, when one rotates to the north, it joins with six; two rotates to the south and joins with seven; three rotates to the east and joins with eight; and four rotates to the west and joins with nine. Five and ten dwell at the center, serving as the pivot of Heaven and Earth’s movement.

The “interweaving and ordering of the numbers” described in the Great Treatise refers to this numerical pattern. “Interweaving” means crossing and exchanging, like left and right facing one another, with three and four passing back and forth. “Ordering” means linking and drawing together, like a lower and a higher position, with one and two corresponding above and below. If the diagram is viewed as two layers, the relationship between moving Heaven and still Earth becomes clear.

Diagram Book Four

The diagram above presents the numerical pattern of Heaven and Earth meeting in the Luo Shu.

Yang Xiong said, “One and six form a single lineage; two and seven are companions; three and eight are friends; four and nine follow the same path; five and five keep one another company.” This describes precisely the diagram above. Zhu Xi held that six, seven, eight, and nine should each be paired and assigned respectively to Qian, Kun, Kan, and Li, placed at the four cardinal points. Then, following the order of one, two, three, and four, Gen, Dui, Zhen, and Xun should be placed in the four corners. This accords with the numerical pattern in the diagram.

By examining how the numbers are generated and observing how they combine and separate, advance and withdraw, interweave and remain still, we can clearly see that this represents the meeting of Heaven and Earth. The “number of the Great Expansion is fifty” in fact uses forty-nine numbers. When yarrow stalks are used for divination, the steps of dividing the stalks, setting one aside, counting them, and gathering the remainder—as well as the resulting line values of seven, eight, nine, and six—all follow this numerical pattern.

Diagram Book Five

The diagram above shows the Luo Shu in which every row and column adds up to fifteen.

The first section of the Hongfan discusses the Five Phases; the second, the respectful use of the Five Affairs; the third, the proper implementation of the Eight Governmental Measures; the fourth, the coordinated arrangement of the Five Divisions of Time; the fifth, the establishment and use of the Supreme Norm; the sixth, the use of the Three Virtues; the seventh, careful discernment and consultation in resolving doubts; the eighth, attention to the various signs; and the ninth, the bestowal of the Five Blessings and warnings against the Six Extremes.

Han dynasty Confucian scholars held that these sixty-five characters were the original text of the Luoshu. The account passed down by Xiyi (Chen Tuan’s sobriquet) regarded them instead as the third transformation of the Longtu, and took the generation diagram as the original text of the Luoshu. Some suspected that a copying error had occurred, prompting debate over which diagram, the Longtu or the Luoshu, was arranged around nine and which around ten. Today, if the names of the two diagrams are switched, calling them the Longtu and the Guishu, their difference becomes clear without further effort.

The Commentary on the Changes says: “A diagram emerged from the Yellow River, and a writing emerged from the Luo River; the sages modeled their actions on their forms and principles.”

Kong Anguo says: The Hetu appeared during the reign of Fuxi, when a dragon-horse emerged from the Yellow River. Fuxi then drew the Eight Trigrams based on the markings on its body. The Luoshu appeared when Yu the Great was controlling the floods, borne on the back of a divine turtle. People used its markings and numbers to devise corresponding rules.

Kong Anguo also says: The numbers in the Hetu are arranged up to nine. Yu the Great followed this order and distilled nine categories of principles, known as the Nine Categories of the Hongfan. Liu Xin says: Fuxi received the Mandate of Heaven and became king. After obtaining the Hetu, he drew the Eight Trigrams in accordance with it. When Yu the Great controlled the floods, he obtained the Luoshu and arranged the Nine Categories in accordance with it. The Hetu and the Luoshu complement each other like warp and weft; the Eight Trigrams and the Nine Chapters correspond to each other like the outer and inner aspects.

Guan Ziming says: In the arrangement of markings in the Hetu, seven is in front, six behind, eight on the left, and nine on the right. The Luoshu is arranged with nine in front, one behind, three on the left, and seven on the right; four at the front left, two at the front right, eight at the rear left, and six at the rear right.

Shaozi (Shao Yong, a scholar of the Northern Song) said: “The circle represents the celestial patterns of the stars. Perhaps the principles of numbers used in the calendar and the reckoning of years began here. The calendar pairs the two beginning numbers to determine firmness and yielding; pairs the two middle numbers to determine musical pitches and the calendar; and pairs the two ending numbers to record the remainder that gives rise to intercalary months. This is what is called the reckoning of the calendar.

The square represents the land. Perhaps the methods of dividing provinces and laying out the well-field system also took their model from this. Each province is divided into nine well-fields, and each well-field contains nine hundred mu. This is what is meant by dividing provinces and laying out well-fields.

The circle embodies the numerical principles of the Yellow River Diagram, while the square embodies the writing and pattern of the Luo River Writing. Thus Fuxi and King Wen followed them in composing the Book of Changes, while Yu the Great and Jizi followed them in writing the Great Plan.

The numbers of Heaven and Earth are matched in sequence: Heaven one, Earth two; Heaven three, Earth four; Heaven five, Earth six; Heaven seven, Earth eight; Heaven nine, Earth ten. There are five numbers of Heaven and five of Earth. The five pairs correspond to one another, each pair combining to make a whole. The numbers of Heaven total twenty-five, those of Earth total thirty, and the numbers of Heaven and Earth together total fifty-five. These numbers give form to change and set the affairs of spirits and gods in motion.”

This section explains the numerical principles of the Hetu and Luoshu. Odd numbers belong to Yang and are the numbers of Heaven; even numbers belong to Yin and are the numbers of Earth. The numbers of Heaven—one, three, five, seven, and nine—sum to twenty-five. The numbers of Earth—two, four, six, eight, and ten—sum to thirty. Together they make fifty-five. The changes between Heaven and Earth, and the waxing and waning of Yin and Yang, all fall within the scope of these numbers.

Through different combinations and deductions, these numbers can generate various systems. Divided into pairs, they form the Two Principles (Yin and Yang); divided into three, they form the Three Powers (Heaven, Earth, and humanity); grouped into five categories, they form the Five Phases (Wood, Fire, Earth, Metal, and Water); arranged in combinations, they form the Eight Trigrams; and extended to nine directions, they form the Nine Palaces. These are the main principles.

Zhu Xi said that between Heaven and Earth there is only one Qi. This Qi divides into two forms: Yin and Yang. The movement and transformation of the Five Phases, and the generation and ending of the myriad things, are all governed by them. The Inner Canon says that the numbers of Yin and Yang can be extended to ten, a hundred, a thousand, ten thousand, and beyond counting. Yet when governed by the principles of the Yi, they can encompass everything without omission or excess, and connect all things.

Through mutual comparison and interweaving change, numerical principles become intelligible, revealing the patterns of Heaven and Earth. By fully investigating these numbers, one can determine the forms of all things under Heaven. Without profound insight into the changes of the world, who could take part in this process of deduction?

This section further explains the patterns of change in the Yellow River Chart and the Luo River Writing. “Can” means placing numbers in relation to two groups and arranging them in an interlaced pattern. In the Mei diagram, this means pairing one, two, three, and four with six, seven, eight, and nine. “Wu” means arranging numbers in five positions, as in the terms “ten and five” or “ranks and files.” In the Mei diagram, it means pairing one, two, three, and four with six, seven, eight, and nine, then distributing them among five positions. “Cuo” means exchanging elements in an interlaced pattern, so that they lie one to the left and one to the right; in the Mei diagram, this appears as three and four switching places. “Zong” means gathering and interweaving elements so that one position is lower and the other higher; in the Mei diagram, this appears as one and two being placed above and below each other. Through these changes of can, wu, cuo, and zong, the patterns between Heaven and Earth become visible, and the forms of all things under Heaven are established. Might the Yellow River Chart and the Luo River Writing, then, be the very foundation that unlocks the myriad transformations of the world?

In ancient times, when the sages composed the Book of Changes (Yijing), they drew on subtle revelations from the spirits to devise the method of divination with milfoil stalks. They took Heaven as three and Earth as two to calculate and establish the numbers. They observed the transformations of Yin and Yang and set up the hexagrams; they explained the changes of the firm and yielding lines, giving rise to the individual lines. They harmonized Dao and De, ordering them according to what was fitting; they explored the principles of things and the nature of human beings, and ultimately arrived at an understanding of Heaven’s mandate.

This chapter explains the sages’ central purpose in composing the Classic of Changes (Yi Jing), and the foundations of its numerical principles for hexagrams and lines. “Quietly assisting the workings of the spirits” means that the sages fasted and purified their minds, withdrawing to a secluded, tranquil place, while the spirits secretly aided and protected them. Using forty-nine yarrow stalks—the stems used in ancient divination—they performed the procedures of dividing, setting aside, counting, and gathering the stalks to derive the numerical values of Yin and Yang, firmness and yielding. The numbers of Heaven and Earth worked together, revealing the hexagram and line forms represented by nine, eight, seven, and six.

The sages observed the Yin-Yang changes of the Way of Heaven and established the hexagram images. They explained the changes of firmness and yielding in the Way of Earth, giving rise to the meanings of the lines. They brought these principles into accord with Virtue, arranging each thing according to its proper place. By probing the patterns of Yin, Yang, firmness, and yielding throughout Heaven and Earth, fully realizing their own nature, and thereby understanding the nature of all things, they could assist Heaven and Earth in nurturing and transforming the myriad things, becoming one with the workings of natural transformation. This is the highest state reached through the sages’ utmost sincerity.

In ancient times, the sages composed the Classic of Changes to follow the principles governing nature and life. Accordingly, the Way of Heaven takes Yin and Yang as its fundamental principles; the Way of Earth takes yielding and firmness; and the human way takes benevolence and righteousness. Combining the two principles belonging to each of the Three Powers—Heaven, Earth, and humanity—produces the six-line hexagram of the Classic of Changes. Arranging Yin and Yang and alternating yielding and firmness establishes the order of the six line positions within a hexagram.

The sages composed the Classic of Changes to follow the principles of nature and life; ultimately, they composed it for people. They observed the changes of Yin and Yang and used them to establish the laws of the Way of Heaven. The workings of Heaven are expressed in changes such as the alternation of cold and heat.

The sages created the Yi Jing to accord with the principles of nature and life; ultimately, it was made for human beings. Thus, by observing the changes of Yin and Yang, they established the Way of Heaven. The Way of Heaven consists of the alternation of cold and heat, day and night. By examining the changes of hardness and softness, they established the Way of Earth. The Way of Earth consists of flowing water and standing mountains, of grasses and trees growing and trees rising upright. By taking benevolence and righteousness as their foundation, they established the Way of Humanity. The Way of Humanity consists of honoring one’s parents, loving one’s siblings, being loyal, and keeping faith.

Human beings receive Qi from Yin and Yang and so come to life; they are endowed with the qualities of hardness and softness and so take bodily form; and they possess the principles of benevolence and righteousness. In this way, their nature, temperament, and physical form are formed. With temperament and physical form in place, their nature can come to completion, and the principles of the Three Powers—Heaven, Earth, and Humanity—are complete.

In the Bagua, the bottom line of a trigram represents Earth, the middle line represents Humanity, and the top line represents Heaven. Each of the three lines has its own distinction between Yin and Yang, odd and even. When the Bagua are doubled to form six-line hexagrams, each of the Three Powers is represented in two layers. In a doubled hexagram, the first and second lines belong to Earth, the third and fourth to Humanity, and the fifth and top lines to Heaven. Considered separately, the first, third, and fifth lines occupy Yang positions, while the second, fourth, and top lines occupy Yin positions. Yang represents hardness, Yin softness. Yin and Yang, hardness and softness, alternate and intermingle across the six lines of a hexagram, thereby forming its pattern and order.

The Yi Jing is vast and complete in scope, encompassing the Ways of Heaven, Humanity, and Earth. It draws on all Three Powers, dividing each into two layers, and thus has six lines. What the six lines express is precisely the Way of the Three Powers. The Way undergoes change, hence the term “line”; lines have different ranks, hence the term “things”; and the images of various things interweave, hence the term “pattern.” When these patterns and positions do not correspond, good fortune and misfortune arise.

The “Way” referred to here means the Ways of Heaven, Earth, and Humanity. The Way of Heaven is formed through the union of Yin and Yang, giving rise to “five”; the Way of Earth is formed through the union of softness and hardness, giving rise to “ten.” Five and ten are doubled to form the lines; changes in the lines are what is meant by movement, and from this arise good fortune and misfortune.

The Dao is the principle followed in common by Heaven, Earth, and humanity. In the Way of Heaven, Yin and Yang join to form “five”; in the Way of Earth, softness and firmness join to form “ten.” When five and ten are layered together, they form the yao lines, whose images express change and movement. A “yao” is a symbol that models the changes of Heaven and Earth, and a symbol used to represent the movement of the myriad things under Heaven.

“Deng” means different ranks and orders. The author explains the form of the character, linking it to counting rods made of bamboo: the “ten” and “one” within it represent numbers from beginning to end. In the author’s view, the traditional explanation of the character’s form does not fit its meaning, and so he corrects it.

As yao lines change between movement and stillness, they occupy six ranked positions—initial, second, third, fourth, fifth, and top—and have four distinct numerical values: seven, eight, nine, and six. For this reason they are called “things.” Here, “things” refers to yao images that change over time. Seven and nine are odd numbers, symbolizing Yang and firmness, and belong to the Qian hexagram; six and eight are even numbers, symbolizing Yin and softness, and belong to the Kun hexagram. More specifically, nine belongs to Yang and six to Yin, while seven represents firmness and eight softness. Yin and Yang are the images adopted; firmness and softness are the forms they take. Thus nine and six change, while seven and eight do not. The yao statements “use nine” and “use six” emphasize their function in change.

It can also be said that the number of the yarrow stalks is seven, while the number of the hexagrams is eight. Firmness and softness make up the form of the hexagrams and yao lines. Thus the Qian yao lines use nine and the Kun yao lines use six, expressing the function of Yin and Yang. Yin and Yang join to form their De (Virtue/Power); firmness and softness each take shape, and as they cross one another, they create patterns and adornment. When these patterns are arranged appropriately, they bring good fortune: positions are correct, actions are measured, and things accord with their principles. Good fortune arises from this.

The author also explains “good fortune” through the form of its written character. The “ten” represents Yin turning into Yang, while the “mouth” represents the joining in which Yang turns into Yin. The sound of the character is indicated by “one.” Because Yin and Yang can return to the right course amid change, good fortune follows. The author cites the Book of Documents: “When De acts in unity, nothing is not auspicious,” and the Commentary on the Changes: “The movements under Heaven are made correct through unity.” Though the changes under Heaven are many, keeping to what is correct and returning to unity leads toward good fortune. Wang Luzhai of Jinhua, meanwhile, interprets “good fortune” as the image of old Yang rising from the earth.

When patterns are arranged improperly, danger and misfortune follow: positions lose their proper balance, actions become incorrect, and one falls into the peril of the Kan trigram. The author also interprets the written form of “misfortune,” taking it to symbolize a fall amid change, like an action sinking into a pit and losing its proper balance. Wang Luzhai of Jinhua interprets “misfortune” as the image of old Yin sinking beneath the earth. Thus good fortune, misfortune, regret, and distress all arise from changes in action.

This volume’s record is now complete.

The diagram on the right shows the Supreme Ultimate (Taiji) — the origin of the cosmos — giving rise to the Two Modes (Yin-Yang). At first, the Book of Changes had neither the Qian nor the Kun hexagram; it had only a single horizontal line. After the Supreme Ultimate differentiated, the light, clear Qi rose and formed Heaven, while the heavy, turbid Qi gathered below and formed Earth. The sages looked up to observe the patterns of the heavens and down to examine the forms of the earth, taking the Yellow River Diagram as their model for drawing the trigrams: a circle represented Heaven, and a horizontal line represented Earth. Among the lines, an unbroken line was called “odd” and represented Yang; a broken line was called “even” and represented Yin. Yang above and Yin below symbolized Heaven and Earth each settled in its proper place. The “five” in the middle symbolized the meeting of Heaven and Earth’s Qi, the foundation from which the Four Symbols, the Eight Trigrams, and all things arise.

The “one movement and one stillness” described in the Record of Music refers to the changing operation of Yin and Yang between Heaven and Earth. Zhou Dunyi said: “The Supreme Ultimate moves and produces Yang; when movement reaches its extreme, it turns to stillness. Stillness produces Yin; when stillness reaches its extreme, movement resumes.” Movement and stillness depend on each other, and Yin and Yang differentiate from this interaction, thereby forming the Two Modes.

The diagram on the right shows the Two Modes giving rise to the Four Symbols. Yang Qi moves until it reaches its extreme, then turns to stillness; stillness produces Yin, and when stillness reaches its extreme, movement resumes. Movement and stillness depend on each other, and Yin and Yang differentiate, thereby establishing the Two Modes.

The “Two Modes” refers to Yin and Yang, from which the Four Images arise. The author holds that the Yijing originally had no Eight Trigrams, only the two trigrams Qian and Kun.

Zhu Xi said: The Yang Mode gives rise to a single yang line, forming the Greater Yang; it gives rise to a single yin line, forming the Lesser Yin. The Yin Mode gives rise to a single yang line, forming the Lesser Yang; it gives rise to a single yin line, forming the Greater Yin. Earlier diagrams depicted the Four Images in a row, showing the ceaseless generation and transformation of all things. This diagram instead shows the Yang Mode branching downward into Yin and Yang, and the Yin Mode branching upward into firmness and yieldingness. The Four Images cycle endlessly and interact with one another: firmness joins with Yin, Yin joins with firmness, Yang joins with yieldingness, and yieldingness joins with Yang. Through their interplay above and below, to the left and right, all things come into being. Zhou Dunyi said that the transformations of Yang Qi and the union of Yin Qi produce the Five Phases—Water, Fire, Wood, Metal, and Earth. The five kinds of Qi move in sequence, and the four seasons take shape along with them. The Yizhuan says that the pattern of Heaven is established through Yin and Yang, and the pattern of Earth through yieldingness and firmness. This is the principle being described.

The passage explains how the Two Modes give rise to the Four Images: the Yin Mode gives rise upward to a single yang line. This is precisely what the Yizhuan means when it says that Heaven has Yin and Yang, while Earth has yieldingness and firmness.

When the Yin Mode gives rise upward to a single yang line, it becomes the Lesser Yang, or Yang within Yin. The Lesser Yang corresponds to the East, the stage when Yang Qi begins to emerge and bring forth the myriad things; among the seasons, it corresponds to spring. The word “spring” carries the sense of stirring into life. Only after the myriad things sprout can they become active, so the form of the Lesser Yang accords with the circle drawn by a compass. In the heavens it corresponds to wind; on Earth, to Wood; among the constellations, to the Year Star (Jupiter); and among the virtues, to Yuan, the foremost of the good virtues. In the human body it corresponds to the sinews, among the organs to the liver, and it is linked to the eyes. In the emotions it corresponds to anger; among the sounds, to exhalation; in color, to blue-green; in taste, to sourness; among the five notes, to Jue; among domestic animals, to the chicken; and among grains, to wheat. Its number is three, the generating number of Wood—the number associated with Wood’s generation within the Five Phases.

The yang configuration, an image formed from yang lines, generates an odd-numbered line below, forming Greater Yang. Greater Yang is yang within yang. In the south, yang Qi is abundant and nourishes all things; it corresponds to summer among the four seasons. “Summer” means growth: all things grow and flourish through the aid of yang Qi, unfolding in calm balance. It therefore corresponds to “central measure.” In the heavens it corresponds to heat, on earth to fire, among the stars to Yinghuo (Mars), and in virtue to flourishing. Flourishing means the gathering of beautiful things. In the human body it corresponds to the channels and network vessels; among the organs, to the heart, which connects with the tongue. In the emotions it corresponds to joy; its sound is laughter, its color red, its flavor bitter, and its musical note zhi. Its domestic animal is the sheep, its grain is millet, and its number is seven, the completed number of fire.

The yang configuration generates an even-numbered line below, forming Lesser Yin. Lesser Yin is yin within yang. In the west, yin gathers in all things; it corresponds to autumn among the four seasons. “Autumn” carries the sense of gathering and yielding: only after all things have gathered in can they mature. It therefore corresponds to “central square.” In the heavens it corresponds to dryness, on earth to metal, among the stars to Taibai (Venus), and in virtue to what is beneficial. Being beneficial means bringing things into accord with what is right and enabling them to harmonize with one another. In the human body it corresponds to the skin and hair; among the organs, to the lungs, which connect with the nose. In the emotions it corresponds to sorrow; its sound is weeping, its color white, its flavor pungent, and its musical note shang. Its domestic animal is the horse, its grain is rice, and its number is four, the generating number of metal.

The yin configuration, an image formed from yin lines, generates an even-numbered line above, forming Greater Yin. Greater Yin is yin within yin. In the north, yin stores away all things; it corresponds to winter among the four seasons. “Winter” carries the sense of ending: all things cease growing and are stored away, allowing them to be nourished and take shape. It therefore corresponds to “central authority.” In the heavens it corresponds to cold, on earth to water, among the stars to Chenxing (Mercury), and in virtue to steadfast integrity. Steadfast integrity is the foundation for bringing things to completion. In the human body it corresponds to the bones; among the organs, to the kidneys, which connect with the ears. In the emotions it corresponds to fear; its sound is groaning, its color black, its flavor salty, and its musical note yu. Its domestic animal is the “burden-bearing animal,” its grain is beans, and its number is six, the completed number of water.

The center lies between Yin and Yang and within the four directions. Only when the Qi of Yin and Yang converge can things become straight, like a carpenter’s ink line; this is why the center is called “true to the line.” Among the four seasons, it corresponds to the transition between them; in the sky, to dampness; on earth, to soil; among the stars, to the Stellar Ruler (Saturn); and in moral qualities, to sincerity. Zhou Dunyi said, “Yuanheng is sincerity flowing freely; Lizhen is sincerity returning to its source.”

In the human body, it corresponds to the muscles; among the organs, to the spleen, which is connected to the mouth. In the mind, it corresponds to reflection. Its sound is singing, its color is yellow, its flavor is sweet, and its musical note is Gong. The animal it nourishes is the ox, the grain it corresponds to is millet, and its number is five. This is the generating number of Earth.

The Three Diagrams of the Trigrams

The diagram above shows how the Four Images generate the Eight Trigrams. The foundation of the Changes is the sixty-four hexagrams, but only the Eight Trigrams are shown here.

In ancient times, when Fuxi ruled the world, he looked up and observed the patterns of the heavens, looked down and examined the forms of the earth, and studied the markings of birds and beasts and the conditions on the land. Taking images from himself when things were near and from the myriad things when they were far away, he began to create the Eight Trigrams, using them to make the virtues of the spirits intelligible and to classify the conditions of the myriad things. (In the phrase “between … and earth,” some editions include the word “heaven” before “earth.”)

This explains why the sage created the trigrams. The Changes says: “The Taiji generates the Two Modes; the Two Modes generate the Four Images; the Four Images generate the Eight Trigrams. The Eight Trigrams determine good and ill fortune, and good and ill fortune bring great undertakings to completion.”

This explains the purpose behind the sage’s drawing of the trigrams.

The Four Images described above arise when a Yang line intersects with yielding Yin below, and yielding Yin intersects with a Yang line above. From these come Qian and Kun, symbolizing the fixed positions of Heaven and Earth, and Gen and Dui, symbolizing the intercommunication of mountain and lake Qi. When a firm line above intersects with a Yin line, the Yin line…

Among the four images above, a yang line meets yin softness below, while yin softness meets yang firmness above. This forms Qian and Kun, symbolizing Heaven and Earth each settled in its proper place; Gen and Dui symbolize the breath of the mountain and the marsh flowing into one another. When yang firmness meets a yin line above and a yin line meets yang firmness below, this forms Zhen and Xun, symbolizing thunder and wind stirring one another; Kan and Li symbolize water and fire not harming one another through opposition.

Heaven receives yang Qi and suspends the sun, moon, and stars. Li symbolizes the sun, and Dui symbolizes the stars. To observe the celestial patterns, one looks upward and then reasons downward from above. Thus the four images of Heaven—Qian, Dui, Li, and Zhen—are generated from top to bottom. Earth receives yin Qi, with mountains, rivers, and openings distributed across it. Gen symbolizes mountains, and Kan symbolizes rivers. To observe the terrain, one looks downward and follows the contours of the land. Thus the four images of Earth—Kun, Gen, Kan, and Xun—are generated from bottom to top.

When the Eight Trigrams interweave, the upper trigrams cross to the left and the lower trigrams to the right. This produces the arrangement with Qian in the south, Kun in the north, Li in the east, and Kan in the west, revealing the circular diagram of the Earlier Heaven Eight Trigrams. Next, compare Zhen and Gen: when Zhen is turned around, it becomes Gen; when Gen is turned around, it becomes Zhen. In this arrangement, Qian, Kun, Gen, and Xun occupy the four corners, while Kan, Li, Zhen, and Dui occupy the centers of the four sides, revealing the square diagram of the Later Heaven Eight Trigrams. From this we can see that movement and stillness depend on one another, and Earlier Heaven and Later Heaven embody one another. The circular and square diagrams each have their own transformations and functions, and the principles by which Heaven and Earth bring things into being unfold without end.

Shaozi (Shao Yong, a Song dynasty scholar of the Classic of Changes) said, “Qian and Kun are the great parents,” as shown in the Four Images diagram; “Fu and Gou are the small parents,” as shown in the Eight Trigrams diagram. The Classic of Changes takes Qian and Kun as its foundation, yet the process of generation and transformation begins again from the Gou and Fu hexagrams: yang firmness meets yin softness to form the Fu hexagram, and yin softness meets yang firmness to form the Gou hexagram. From there, transformations continue without limit.

He also said that among the forms of the Eight Trigrams, four remain unchanged: Qian, Kun, Kan, and Li. The other four form two pairs that reverse into one another: Zhen reverses to become Gen, and Dui reverses to become Xun. Through six transformations, the Eight Trigrams are formed.

The four hexagram diagrams.

The diagram above was formed by developing the preceding diagram of the Four Images into the Eight Trigrams. The lines above the yang symbols cross and extend to the left, while the lines below the yin symbols cross and extend to the right, forming this diagram.

The arrangement described by Shao Yong, known as Master Kangjie—“Kun in the north, Qian in the south, Li in the east, Kan in the west, Zhen in the northeast, Dui in the southeast, Xun in the southwest, and Gen in the northwest”—is the one shown here. The circle represents Taiji (the Supreme Ultimate); the two corresponding symbols represent the yin and yang symbols, that is, the two Qi of Yin and Yang.

The preceding diagram uses odd and even lines to determine the upper and lower positions, progressing from Heaven and Earth through the Four Images to the Eight Trigrams, and finally converging at the center. This is what is meant by “gathered together, it fits in one hand”: although the myriad things in the world are all different, they have only one source.

This diagram, by contrast, places Yin and Yang on the left and right and unfolds outward step by step through movement and stillness, the four seasons, and the eight directions. This is what is meant by “spread out, it fills the four quarters of Heaven and Earth”: although the myriad things each differ, they still all come from one source.

The Announcement of Tang says, “The great God bestowed upright nature on the people, so that each has a constant nature.” Liuzi says, “People are born by receiving the balanced and upright Qi of Heaven and Earth.” Confucius says, “Of all the natures bestowed by Heaven and Earth on the myriad things, the human nature is the most noble.” Master Zisi says, “What Heaven bestows on people is called nature.” The principle of balance and uprightness is human nature; it is what Heaven has bestowed on me.

By examining the Diagram of Generation, which shows how the myriad things come into being and change, we can see that the principles of Heaven and Earth, the Four Images, the Eight Trigrams, and the myriad things are all present within my mind. The principle that Chengzi called “the balance and uprightness naturally present from the beginning,” what Mencius called “the principles of the myriad things are all present in me,” what Zengzi called “fidelity,” and what Confucius called “the One” all come down to this same principle.

The Diagram of the Earlier Heaven, which depicts the order in which Heaven, Earth, and the myriad things come into being, unfolds from “One” to “Two,” from “Two” to “Four,” and from “Four” to “Eight.” Its progress can continue, expanding to hundreds, thousands, millions, and billions without end. Earlier Confucian thinkers said, “The mind is the Taiji (Supreme Ultimate), containing all principles and responding to all things.” Mencius said, “Strive to put the way of reciprocity into practice”; Zengzi said, “Reciprocity”; and Confucius said, “The One runs through it all.” The principles behind these expressions, too, come down to this same idea.

Learners should contemplate these principles carefully with an empty, tranquil mind, then return to themselves and put them to the test in lived experience. When they truly see the principles and truly grasp the Dao, they can accomplish something through silent contemplation. The substance of Dao, De, nature, and life, as well as the foundations of ritual and music, punishments, and government orders, all lie within this principle.

The fifth section of the hexagram diagrams.

On the right is the “Diagram of the Four Images Giving Rise to the Eight Trigrams Before the Former Heaven.” Viewed in reverse from the center, the four trigrams are Zhen, Dui, Kan, and Li. Viewed forward from the sides, they are Qian, Kun, Gen, and Xun. Thus Kan, Li, Zhen, and Dui occupy the central positions of the four cardinal directions, while Qian, Kun, Gen, and Xun occupy the four corner positions.

According to the Hetu, an ancient diagram used to explain the numerical principles and directions of Heaven and Earth, one and six belong to Water in the north and correspond to the Kan trigram, which symbolizes water. Two and seven belong to Fire in the south and correspond to Li, which symbolizes fire. Three and eight belong to Wood in the east and correspond to Zhen, which symbolizes thunder and represents the stirring of spring. Four and nine belong to Metal in the west and correspond to Dui, which symbolizes marsh and represents the scene of autumn. Qian lies in the northwest and symbolizes cold and ice; it is associated with Dui and belongs to Metal. Xun lies in the southeast and symbolizes rising force and wind; it is associated with Zhen and belongs to Wood. Five and ten belong to Earth at the center and correspond respectively to Kun, the Earth, and Gen, the mountain. Kun is Yin, so by the principle that like follows like, it withdraws to the southwest. Gen is Yang, so by the same principle it is placed in the northeast. This is how the directions of the Later Heaven Bagua (Eight Trigrams) are determined. By relating them to the seasons, examining the advantages of the land, and consulting human affairs, one can understand the sequence of the four seasons’ movements.

The “Explanation of the Trigrams” says that Gen is where the myriad things come to an end and begin anew. Since the myriad things cannot be without a ruler, the bearing of an emperor begins with the Zhen trigram. Zhen is in the east, the direction from which the sun rises. The eldest son is best suited to oversee matters such as the ritual vessels. With the eldest son in charge, the eldest daughter is his counterpart; accordingly, the text next speaks of Xun, which embodies the eldest son of the principal line and the senior consort, the eldest son’s wife. Once the family is in order, the state can be governed, so Li comes next. Li symbolizes brightness. The sage faces south to govern all under Heaven, bringing clarity to the realm like the sun moving to the center of the sky. Once the sun reaches noon, it begins to decline toward the west, so Kun comes next. Kun symbolizes compliance: the myriad things follow the Way of Kun in their labor. When it is time to rest, Dui follows. Dui is in the west, the direction of the setting sun. As darkness falls, people return home to rest; thus the air of joy is said to appear in the Dui trigram.

Next comes Qian. Qian belongs to Yang, yet lies in the northwest, a Yin direction. Yin and Yang press against one another there, so the text says that Yin and Yang do battle in the direction of Qian. Kan follows. Kan symbolizes water and lies due north, representing the dim, sunless scene of midnight. Hence the text says that the myriad things labor in the time of Kan. Only through labor can things be accomplished, so accomplishment is said to appear in the Gen trigram, which also brings the sequence to its end.

Hexagram Diagram Six

The diagram above is based on the previously described pattern in which the “Four Images generate the Eight Trigrams.” Only the positions of the four trigrams on the left and right have been switched. Qian, Li, Kan, and Kun are placed in the center, symbolizing the head, eyes, heart, and abdomen respectively. Zhen, Gen, Xun, and Dui are arranged on the left and right, symbolizing the hands, feet, thighs, and arms. Master Xiyi (Chen Tuan) held that this arrangement matches the trigrams with the human body.

Human beings come into being through the convergence of the Qi of Heaven and Earth. Heaven grants people their innate endowment, giving them an enduring nature. This is therefore where the study of the Dao begins its search for the source. The Miscellaneous Hexagrams says: “Qian is firm and strong; Kun is yielding and compliant. Li is above, Kan below. Dui is manifest, Xun concealed. Zhen sets things in motion; Gen keeps them still.” By examining these statements, we can understand the meanings of the hexagram images.

The Cantong qi (Token for Joining the Three), a Daoist alchemical classic, says: “Qian and Kun are the gateways of the Yi, the parents of the myriad hexagrams. Kan and Li are like the outer frame; in their movement, they are like the hub and axle of a cart. The four hexagrams Kan, Li, Zhen, and Dui are like the key to the union of female and male.” This, too, is an insight drawn from these hexagram images. They are therefore set out here and passed on to later generations.

Hexagram Diagram Seven

The diagram above shows the cyclical transformations of the sixty-four hexagrams.

The Discussion of the Trigrams says: “Heaven and Earth establish their positions above and below; the forces of mountain and marsh communicate; thunder and wind stir one another; water and fire do not clash. The Eight Trigrams interweave and combine. To calculate what has already happened, one proceeds forward; to understand what is yet to come, one reasons backward. Thus the Yi uses reverse counting to discern the future.”

The passage above explains the images represented by the circular diagram of the sixty-four Later Heaven hexagrams. Heaven and Earth each occupy their proper place: the Qian hexagram is in the south, and the Kun hexagram in the north. Heaven is high above, and Earth lies below. The qi of mountains and marshes flows between them: mountains guard the northwest, while waters of the marshes flow southeast. Thunder and wind stir one another: thunder issues from the northeast, and the wind is strongest in the southwest.

Water and fire each follow their own course and do not intrude upon one another. The Li hexagram descends, symbolizing the sun rising in the east and its light gradually growing brighter. The Kan hexagram ascends, symbolizing the moon appearing in the west, its light comparatively faint. This describes the images within the hexagram diagram, emphasizing its stillness and the way each trigram guards its own direction.

The Eight Trigrams interlace with one another. Here, “interlace” means that they alternate and exchange places: Qian and Xun switch places, Kan and Dui switch places, Li and Gen switch places, and Kun and Zhen switch places. Qian, Dui, Li, and Zhen belong to the Yang Mode—the trigrams formed from Yang qi. Originally on the left, they move to the right, above the Yin Mode. Kun, Gen, Kan, and Xun belong to the Yin Mode—the trigrams formed from Yin qi. Originally on the right, they move to the left, above the Yang Mode. In this way, hard and soft rub against each other, and the Eight Trigrams shift and transform one another, so change has no end. A fuller explanation follows below.

This explains matters through the outer changes in the hexagram images, focusing on movement and change and on following the seasons. The Eight Trigrams revolve and develop into the sixty-four hexagrams. Arranged around the eight directions, they are like the twenty-eight lunar lodges (the twenty-eight star groups of ancient astronomy) distributed among the twelve earthly branches, the twelve positions used to mark direction and the passage of time.

Thus, counting from the right, the Eight Trigrams are Qian, Dui, Li, Zhen, Kun, Gen, Kan, and Xun. They cycle from the inside outward, as if arranged in a ring with neither beginning nor end.

“Counting what has passed proceeds in order” means that to calculate the hexagram images of the past, one counts in the sequence of the Eight Trigrams. For example, looking back from today to the preceding days, or counting back from the Winter Solstice to the Start of Winter and the Autumn Equinox, one proceeds from the Kun hexagram through Gen, Kan, Xun, and Qian, following the sequence.

“Knowing what is to come proceeds in reverse” means that to calculate the hexagram images yet to come, one counts against the sequence of the Eight Trigrams. For example, looking ahead from today to the coming days, or moving from the Winter Solstice toward the Start of Spring and the Spring Equinox, one proceeds from the Kun hexagram through Zhen, Li, Dui, and Qian, inferring what is to come in reverse order.

However, the Yi Jing’s method of counting is rooted in reversal: the lines that form a hexagram develop from the bottom upward, while the hexagrams are counted from right to left. That is why the Yi Jing is said to “count in reverse.”

This diagram is based on the Earlier Heaven Bagua, with one arrangement upright and the other inverted: the lower Bagua remains still in its positions, while the upper Bagua rotates clockwise. The upper and lower trigrams join, firm and yielding lines rub against each other, and the eight trigrams shift in relation to one another. In this way, one “root hexagram” (the primary hexagram) gives rise to eight “changed hexagrams” (hexagrams transformed from the primary one). Each palace thus forms a group of eight hexagrams, and the eight palaces together make up the sixty-four hexagrams, interwoven across the left and right sides.

In the eight hexagrams of the Zhen palace, Zhen joins with Kun. Beginning with Fu, the sequence continues through Zhen, Shihe, Sui, Wuwang, Yi, and Tun, and ends with Yi. This presents the root hexagram and its changed hexagram as opposites: Zhen is below and Gen above, with the two trigram images facing one another vertically.

In the eight hexagrams of the Li palace, Li joins with Gen. Beginning with Bi, the sequence continues through Mingyi, Feng, Li, Ge, Tongren, and Jiaren, and ends with Jiji, forming a hexagram in which Yin and Yang join and are centered. Li is below and Kan above; three Yang lines and three Yin lines each take up half, like day and night divided equally.

In the eight hexagrams of the Dui palace, Dui joins with Kan. Beginning with Jie, the sequence continues through Sun, Lin, Guimei, Kui, Dui, and Lü, and ends with Zhongfu. This too presents the root hexagram and its changed hexagram as opposites: Dui is below and Xun above, with the two trigram images facing one another vertically.

In the eight hexagrams of the Qian palace, Qian joins with Xun. Beginning with Xiaoxu, the sequence continues through Xu, Daxu, Tai, Dazhuang, Dayou, and Guai, and ends with Qian, reaching a pure Yang hexagram with all six lines Yang. This is the image of the root and changed hexagrams facing one another, and it forms the left side of the diagram.

In the eight hexagrams of the Xun palace, Xun joins with Qian. Beginning with Gou, the sequence continues through Xun, Jing, Gu, Sheng, Heng, and Ding, and ends with Dagua. This presents the root hexagram and its changed hexagram as opposites: Xun is below and Dui above, with the two trigram images facing one another vertically.

In the eight hexagrams of the Kan palace, Kan joins with Dui. Beginning with Kun, the sequence continues through Song, Huan, Kan, Meng, Shi, and Jie, and ends with Weiji, forming a hexagram with equal parts firm and yielding. Kan is below and Li above; three firm lines and three yielding lines are evenly divided, like day and night in balance.

In the eight hexagrams of the Gen palace, Gen joins with Li. Beginning with Lü, the sequence continues through Xian, Dun, Jian, Jian, Gen, and Qian, and ends with Xiaoguo. This presents the root hexagram and its changed hexagram as opposites: Gen is below and Zhen above, with the two trigram images facing one another vertically.

In the eight hexagrams of the Kun palace, Kun joins with Zhen. Beginning with Yu, the sequence continues through Jin, Cui, Pi, Guan, Bi, and Bo, and ends with Kun, reaching a pure Yin hexagram with all six lines Yin. This forms the right side of the diagram.

Viewed as a whole, the sixteen hexagrams Qian, Kun, Tai, Pi, Kan, Li, Jiji, Weiji, Sui, Gu, Jian, Guimei, Yi, Dagua, Zhongfu, and Xiaoguo are arranged in alternating sequence through relationships of exchange and opposition. They are like beads strung together, or like the main lines and divisions of a net: their order is clear and without confusion. The subtlety of their natural formation is not something human effort could arrange. The author therefore goes on to use the solar terms of a year to explain this pattern.

Viewed through the changing solar terms of the year, Zhen, the trigram in which Yang Qi begins to stir, first joins with Kun, the purely Yin trigram. At the winter solstice, the image of a single Yang line beginning to arise appears. Kun transforms into Fu, the trigram that signifies Yang Qi returning to life. Thus, Qian, the pure Yang force, is said to begin emerging from the bottom nine line of Fu. This process is like pearls strung on a thread, or a net’s main cord drawing its meshes along: each part follows a clear and orderly pattern. Observing the subtlety of these natural changes shows that no human effort could have arranged them.

Likewise, over the course of the year’s solar terms, Qian and Kun establish the positions of above and below. At the winter solstice, Kun changes into Fu. Yin Qi still predominates, the weather is cold, the day is shortest, and the night longest. Yang Qi gradually grows from Fu’s bottom nine line, reaching its peak at noon. At the summer solstice, Xun, the trigram in which Yin Qi begins to wane, starts to join with Qian, and the image of a single Yin line beginning to arise appears. Qian transforms into Gou, the trigram that signifies Yin Qi beginning to arise. Thus, Kun Qi is said to begin from Gou’s bottom six line and gradually develop, reaching its peak at midnight. At the summer solstice, Yang Qi is abundant, the weather is hot, the day is longest, and the night shortest.

The Winter Solstice and Summer Solstice are the times when Yin and Yang unite. The Qian and Kun hexagrams join in the middle, forming Kan and Li; Kan and Li then join to form Ji Ji and Wei Ji. Ji Ji and Wei Ji join between north and south. At the Spring Equinox, Ji Ji transforms into Jie. Thus Kan begins at the time corresponding to the second nine line of Jie and ends at the hour of You (dusk).

At the Autumn Equinox, Wei Ji transforms into Lü. Thus Li begins at the time corresponding to the second six line of Lü and ends at the hour of Mao (dawn). At the Spring and Autumn Equinoxes, each hexagram has three Yang lines and three Yin lines; the climate is neither too warm nor too cold, and day and night are equal in length. At these two seasonal turning points, Yin and Yang separate from one another.

At the Beginning of Spring, Yi transforms into Bi. Yi has two Yang lines on the outside and four Yin lines within. At the Beginning of Summer, Zhong Fu transforms into Xiao Xu. Zhong Fu has four Yang lines on the outside and two Yin lines within. This shows that in spring and summer Yang Qi is on the outside and Yin Qi within. It is what the sages mean when they say that one should nourish Yang in spring and summer.

At the Beginning of Autumn, Da Guo transforms into Kun. Da Guo has two Yin lines on the outside and four Yang lines within. At the Beginning of Winter, Xiao Guo transforms into Yu. Xiao Guo has four Yin lines on the outside and two Yang lines within. This shows that in autumn and winter Yang Qi is within and Yin Qi on the outside. It is what the sages mean when they say that one should nourish Yin in autumn and winter.

In this way, the whole pattern of the year’s seasonal cycles is contained in this diagram. The spring, summer, autumn, and winter, and the changing lengths of day and night described by Shaozi (the Song dynasty scholar of the Changes, Shao Yong), all arise from it.

Now consider the cycle of a month. The period corresponding to the doubled Kun hexagram falls at the transition between the end and beginning of the month; after that, the moon gradually appears. Xiao Guo corresponds to Zhen, and the two Zhen hexagrams doubled symbolize the evening of the third day, when the moon appears in the west at the Geng position. Da Guo corresponds to Dui, and the two Dui hexagrams doubled symbolize the first quarter moon on the eighth day, at the southern Ding position. On the fifteenth day, the image of Qian corresponds to the full moon: the moon is round and bright, rising in the east at the Jia position, after which its light gradually wanes.

Zhong Fu corresponds to Xun, and the two Xun hexagrams doubled symbolize the morning of the eighteenth day, when the moon can be seen in the west at the Xin position. Yi corresponds to Gen, and the two Gen hexagrams doubled symbolize the last quarter moon on the twenty-third day, at the southern Bing position. The pattern of the moon’s movement through the month is also contained in this diagram. The new moon, first quarter, full moon, and last quarter described by Shaozi, along with the degrees of the moon’s movement and its waxing and waning, are all reflected in it.

As for the Gen hexagram, it lies in the northeast and symbolizes where all things end and begin. Thus the hexagram corresponding to the Winter Solstice ultimately falls on Yi, Mountain over Thunder, within Gen; the seasonal period of the Beginning of Spring starts with Bi, Mountain over Fire, within Gen. This is the natural course of things. Hence it is said, “The Changes accords with Heaven and Earth.”

Shao Yong said, “Although this diagram has no text, I discuss the principles of the Changes all day long and have never departed from it, because the principles of Heaven, Earth, and all things are contained within the diagram.”

Zhu Xi said, “The Xiantian Diagram can be explained through the course of a year. Viewed on a grand scale, the changes across 129,600 years, from antiquity to the present, unfold within this single circle. Viewed on a small scale, the changes over the twelve double-hours of a single day unfold within it as well. These changes are all derived from the Returning hexagram, which symbolizes Yang energy beginning to grow again.”

The Commentary on the Changes says, “Heaven is high and Earth is low; thus the positions of the Qian and Kun hexagrams are established. As high and low are arranged, so too are the positions of the noble and the humble. Movement and stillness each have their regular patterns, and the qualities of firmness and yielding become distinct. Things gather according to their kinds, and the myriad things are distinguished according to their classes; thus good fortune and misfortune arise. In Heaven, images take shape; on Earth, concrete forms take shape, and change becomes apparent. Thus firmness and yielding interact, and the Eight Trigrams push and shift against one another. Thunder stirs things into motion, and wind and rain nourish them; the sun and moon move through their courses, bringing the alternation of cold and heat. The Dao of Qian generates men, and the Dao of Kun generates women.”

The passage above is chapter one of the “Appended Statements, Part One.” It explains the meaning of the circular diagram of the sixty-four Xiantian hexagrams. The phrase “Heaven is high and Earth is low; Qian and Kun are established” means that clear, bright Heaven is above, while substantial, weighty Earth is below. Because Heaven occupies the upper position, it is called honored; because Earth occupies the lower position, it is called humble. Accordingly, the Daos of Qian and Kun each have their own place. The Dao of Kun governs Yin and yieldingness and symbolizes women.

The passage on the right is the first chapter of the Shangxi (“Appended Statements,” Part One, of the Zhouyi). It explains chiefly the meaning of the circular diagram of the sixty-four precelestial hexagrams.

Heaven is above and Earth below; thus the positions of Heaven and Earth, represented by the Qian and Kun hexagrams, are established. Heaven is clear and dwells above, while Earth is turbid and dwells below. The upper position is honored and the lower position is humble, and so the places of Qian and Kun are determined. Once the order of high and low is set out, the ranks of honor and lowliness become apparent. Yang is honored and Yin is humble; ruler is honored and subject is humble. Each occupies its proper place, and the distinction between the honored and the lowly is thereby drawn. Movement and stillness each have their regular pattern, and the qualities of firmness and yielding are made clear. Yang Qi moves outward, while Yin Qi remains still within. Yang governs movement and Yin governs stillness; each follows its regular pattern, and the meanings of firmness and yielding are thus established.

Things above are close to Heaven, and things below are close to Earth. The four hexagrams Qian, Dui, Li, and Zhen belong to the southeast, while Kun, Gen, Kan, and Xun belong to the northwest. All kinds of things are likewise assigned according to the hexagram categories to which they belong, just as horses, cattle, sheep, and pigs each have their own category: things of the same kind gather together, while different things belong to separate groups. Zheng of Hesha says: “Animals belong to Yang, and plants belong to Yin. Animals cannot take root and grow, so they incline toward Yang; plants cannot move of themselves, so they incline toward Yin.” Thus things with different Yin-Yang qualities are sorted into groups. Human beings alone can both move and grow upright. They have the capacity for movement as well as the upright form of plants, and thus possess the qualities of both Yin and Yang. Their spiritual nature surpasses that of other things.

Qian belongs to Yang within Yang and represents creatures such as birds and beasts. Gen, Kan, and Zhen belong to Yin within Yang and represent creatures such as insects and fish. Kun belongs to Yin within Yin and represents things such as earth and stone. Xun, Li, and Dui belong to Yang within Yin and represent things such as grasses and trees. When Yin and Yang, firmness and yielding, and good and evil come together or separate, good fortune and misfortune arise. Good fortune and misfortune are signs of gain and loss. When the five climatic influences—rain, clear skies, warmth, cold, and wind—appear at the proper times and in due measure, this is an auspicious sign. If any one of them is excessive or entirely absent, it is an inauspicious sign. Things bring gain or loss, and good fortune, misfortune, calamity, and blessing appear accordingly, in much the same way.

In Heaven, the sun, moon, and stars appear as images; on Earth, water, fire, wood, and metal take shape. The images of Heaven appear and the forms of Earth arise, making the traces of change clearly visible.

Firm and yielding lines rub against one another and alternate in their changes: one, seven, three, and nine belong to firmness; two, six, four, and eight belong to yielding. The repeated interweaving of firmness and yielding forms the Eight Trigrams. As the Eight Trigrams stir and transform one another, Qian, Kun, Kan, Li, Zhen, Gen, Xun, and Dui interact to form the sixty-four hexagrams.

Thunder shakes all things, expressing the images of the Zhen and Gen hexagrams. Wind and rain nourish all things, expressing the images of Xun and Dui. The movements of the sun and moon express the images of Kan and Li. Cold and heat alternate, expressing the changes of Yin and Yang: when the sun moves south, away from its farthest point, the weather is cold; when it moves north, toward its farthest point, the weather is hot. These are images of change appearing in Heaven. The Qian Dao brings forth men, and the Kun Dao brings forth women; this is an example of change taking form in concrete things. Compare these with the hexagram diagram and reflect on the principles of the Yi, and you will already have understood most of them.

Hexagram Diagrams Eight

The sixty-four hexagrams shown above are formed by pairing and stacking the eight trigrams.

The Shuogua says: Thunder sets all things in motion, and wind scatters them. This describes the images through which change appears. The Way of Qian, represented by the Qian hexagram, gives rise to the male; the Way of Kun, represented by the Kun hexagram, gives rise to the female. This describes the forms shaped by change. Compare these words with the diagram, and you will already understand more than half the principles of the Yi.

Hexagram Diagrams Eight

The sixty-four hexagrams shown above are formed by pairing and stacking the eight trigrams.

The Shuogua says: Thunder sets all things in motion, wind scatters them, rain nourishes them, and sunlight warms and brightens them. Gen, which represents mountains and stillness, brings all things to rest; Dui, which represents marshes and joy, delights all things. Qian governs all things, and Kun contains them.

The diagram on the right shows the hexagrams in the square arrangement of the sixty-four Later Heaven hexagrams. Shaozi said, “All hexagram diagrams begin at the center.” As we see here, Zhen represents thunder, which sets all things in motion, while Xun represents wind, which disperses all things. They lie precisely at the center of the diagram and each also occupies the midpoint of four directions. Kan represents rainwater, which nourishes all things, and Li represents the sun, which shines on all things. Thus Kan follows Xun, and Li follows Zhen. Gen represents stillness, and Dui represents joy, so Gen follows Kan, and Dui follows Li. Qian governs all things, while Kun gathers them in; therefore Qian follows Dui, and Kun follows Gen. These hexagrams all unfold outward from the center of the diagram. In this way, the left and right, above and below, and the vertical and horizontal are interconnected, determining the positions of the sixty-four hexagrams.

The southeast belongs to Yang, and Qian lies in the southeast. Qian corresponds to the fourth lunar month, so it occupies the Si position. The northwest belongs to Yin, and Kun lies in the northwest. Kun corresponds to the tenth lunar month, so it occupies the Hai position. Tai corresponds to the first month and lies in the Yin position; Pi corresponds to the seventh month and lies in the Shen position. These are the four corner positions: Yin, Shen, Si, and Hai.

At the winter solstice, one Yang begins to emerge at the center of the Zi position, corresponding precisely to the Fu hexagram, the hexagram of the eleventh month. At the summer solstice, one Yin begins to emerge at the center of the Wu position, corresponding precisely to the Gou hexagram, the hexagram of the fifth month. The spring equinox falls at the center of the Mao position, and the Dazhuang hexagram corresponds to the second month; the autumn equinox falls at the center of the You position, and the Guan hexagram corresponds to the eighth month. These are the four cardinal positions: Zi, Wu, Mao, and You. The hexagrams for the months of Chen, Xu, Chou, and Wei lie off to the side, attached to the four corners.

Lin corresponds to the twelfth month and is adjacent to Tai. Thus, in the Later Heaven arrangement, the Chou and Yin positions belong to Gen, in the northeast. Guai corresponds to the third month and is close to Qian, so the Chen and Si positions belong to Xun, in the southeast. Dun corresponds to the sixth month and is close to Pi, so the Wei and Shen positions belong to Kun, in the southwest. Bo corresponds to the ninth month and is adjacent to Kun, so the Xu and Hai positions belong to Qian, in the northwest. This arrangement accords with the directions of the earth.

If we look at the arrangement with Qian above and Kun below, the Eight Trigrams form a vertical trunk, while the other fifty-six hexagrams are distributed to either side like horizontal branches. This is what the Commentary on the Changes means when it says, “Heaven and Earth establish their positions, and the Changes move between them.” If we look at the arrangement with Pi above and Tai below, the Eight Trigrams are laid out in sequence, while the other fifty-six hexagrams interweave above and below. This is the pattern described in the Commentary on the Changes: “Qian and Kun form the rows, and the Changes take their place between them.”

The twenty-eight hexagrams around the square correspond to the twenty-eight lunar mansions, the twenty-eight groups of stars in the sky. The seven hexagrams from Qian to Daxu correspond to the seven mansions of the Azure Dragon in the east: the Horn mansion begins at Qian, Chen corresponds to the Neck mansion, and Mao to the Root mansion. The seven hexagrams from Tai to Qian correspond to the seven mansions of the Black Tortoise in the north: Chou corresponds to the Ox mansion, and Zi to the Emptiness mansion. The seven hexagrams from Kun to Cui correspond to the seven mansions of the White Tiger in the west: Xu corresponds to the Bond mansion, and You to the Hairy Head mansion. The seven hexagrams from Pi to Lü correspond to the seven mansions of the Vermilion Bird in the south: Wei corresponds to the Ghost mansion, and Wu to the Star mansion.

Hence the saying: “In heaven, things appear as celestial patterns; on earth, they take shape as the myriad things.” The Commentary on the Judgement of the Classic of Changes, hexagram Bi, also says that observing celestial patterns reveals the changes of the seasons, while observing human institutions and customs enables one to transform the world.

The Cantong qi (The Seal of the Unity of the Three, a classic that uses the images and number patterns of the Yijing to explain the Way of alchemy) says: “In heaven, things appear as images; on earth, they take shape as the myriad beings.” The Commentary on the Judgments of the Bi hexagram also says that observing celestial phenomena reveals changes in the seasons, while observing the rites and institutions of human society can educate the world.

The Cantong qi says:

Dawn on the first day of the lunar month corresponds to the Fu hexagram, which symbolizes the first emergence of Yang Qi. Yang Qi begins to circulate, moving back and forth freely without obstruction. It is like setting up a gnomon to measure the sun’s shadow: Yang Qi makes its first faint appearance. The Zi month, the eleventh lunar month, corresponds to the Huangzhong pitch. Signs of growth gradually become clear. Mild Yang Qi spreads widely, allowing plants and the five grains to grow as they should.

When cultivation is carried out beside the furnace, it is like spreading out branches and clearing a path, so that brightness can emerge in an upright and orderly way. Sunlight grows stronger, and the days become longer one by one. The Chou month, the twelfth lunar month, corresponds to the Dalu pitch. The rising and descending of Yin and Yang tend toward balance.

Look up at the celestial patterns, and one enters the Tai hexagram, which symbolizes the harmonious union of Heaven and Earth. The firm and the yielding flourish together. Yin and Yang interact: Yin gradually recedes while Yang grows. The myriad beings gather in the Yin month, the first lunar month, and move in accord with the season.

As the cycle advances through the Dazhuang hexagram, which symbolizes flourishing Yang Qi, Yang Qi extends side by side in the Mao month, the second lunar month. Elm seeds fall and return to their source. Punishment and virtue—terms used in antiquity for the two forces governing the waxing and waning of Yin and Yang—restrain one another, and day and night begin to grow equal in length.

With the Guai hexagram, which symbolizes resolution, Yin Qi withdraws and Yang Qi rises forward. At this time, one should cleanse the wings and shake off the old dust: that is, clear away accumulated habits and renew one’s state of cultivation.

In the Qian hexagram, which symbolizes pure Yang and strength, Yang Qi is full and bright, reaching in every direction. In the Si month, the fourth lunar month, Yang Qi reaches its peak; then Yin and Yang begin to alternate again.

The Gou hexagram, which symbolizes the first emergence of Yin Qi, begins a new cycle. Its earliest sign is like the first touch of frost beneath one’s feet. The cold spring at the bottom of a well symbolizes the Wu month, the fifth lunar month, which corresponds to the Ruibin pitch. Yin Qi gradually gains the upper hand and becomes dominant.

With the Dun hexagram, which symbolizes retreat, Yang Qi withdraws from its former position. One gathers one’s essence, nourishes De, and waits for the right moment, dwelling in quiet seclusion.

In the time of the Pi hexagram, which symbolizes obstruction, Yin and Yang do not communicate, and sprouts cannot grow. Yin Qi extends while Yang Qi bends back; Yang Qi lies hidden, as if it had vanished without a trace.

Observe the light and setting, and attend to the character of mid-autumn. At this time, one should nurture tender, subtle signs of life, so that what is old and withered may come alive again. Young shoots of plants such as shepherd’s purse and wheat also sprout and grow together.

Physical form gradually breaks down and decays, until at last it disappears. Qi is transformed and depleted, and even the most refined Shen (spirit) is lost with it. When the Dao (the Way) reaches its limit, it turns back, returning to the primal source of Kun—the earth that gives life to all things. All things continually follow the earth’s patterns, receiving Heaven’s will and putting it into practice, making it manifest. The process is deep and mysterious, beyond grasp, yet all things are connected. Following the seasons, it brings forth the myriad kinds of life and is the source of Yin-Yang transformation. Heaven and earth are vast and open; their changes are elusive and unpredictable, and no one knows where they begin. At first, they lose their way and stray from their course, yet later they become masters. What is level will eventually become uneven: this is the natural course of the Dao. Change and succession, flourishing and decline, waxing and waning, all depend on one another. The cycle ends with the Kun hexagram and begins with the Fu hexagram, like links in a ring. If rulers can follow and guide this pattern, their rule can endure for a long time.

Shao Yong, a Northern Song scholar of the Changes, writes in “Ode to the Great Changes”: Heaven and earth each take their place, corresponding to the Pi and Tai hexagrams, whose qualities are opposed. Mountain and marsh share their qi, expressed in the meanings of the Sun and Xian hexagrams. Thunder and wind stir one another, giving rise to the intent of the Heng and Yi hexagrams. Water and fire interact, corresponding to the Ji Ji and Wei Ji hexagrams. The four pairs of images combine with one another to form sixteen relationships; the Eight Trigrams doubled in pairs make the sixty-four hexagrams.

Zhu Xi held that this passage explains the hexagrams on the two crossing lines of the square diagram: Qian is at the southeast corner, with Kun opposite it in the northwest. An older edition places Kun at the southeast corner, making Qian its opposite in the northwest. Qian and Kun facing one another is precisely “Heaven and earth take their places.” Pi at the southwest corner faces Tai in the northeast, which is precisely “Pi and Tai are of opposite kinds.” Zhu Xi marveled that this arrangement was so ingenious as to be hard to comprehend.

Cheng Zhifang of Xin’an said that Shao Yong’s teaching of the Earlier Heaven is a method of the mind. The diagrams all unfold from the center, from which the ten thousand changes and things arise. “All” here refers to both the circular and square diagrams. “Heaven and earth take their places” describes the circular diagram unfolding from the center; “Thunder stirs and wind disperses” describes the square diagram unfolding from the center. The circular diagram is dynamic, with the determination of positions as its foundation; the square diagram is still, with the changes of stirring and dispersal as its function. In movement there is no fixed, unchanging movement; in stillness there is no absolute standstill. This is the method of the mind in the teaching of the Earlier Heaven.

The Commentary on the Changes says: “When the Eight Trigrams are arranged in rows, the images of the myriad things are contained in them; when the trigrams are further doubled, the hexagram lines are contained in them.” Firm and yielding lines push one another back and forth, giving rise to change. The passage also says that the circular diagram is dynamic, with the determination of positions as its foundation, while the square diagram is still, with the changes of stirring and dispersal as its function. In movement there is no fixed, unchanging movement; in stillness there is no absolute standstill. This is the method of the mind in the teaching of the Earlier Heaven.

The “Great Commentary” of the Book of Changes says: “When the Eight Trigrams are arranged, the images of the myriad things are contained within them. When the Eight Trigrams are doubled in pairs, the six lines are contained within them. As firm and yielding lines push and shift against one another, change is contained within them. When words explaining good and ill fortune are attached to the hexagrams and lines, the actions and changes of things under Heaven are contained within them. Good fortune, bad fortune, regret, and distress all arise from action.”

This is the opening section of the “Lower Commentary” of the Great Commentary. It explains the meaning of the square diagram of the sixty-four hexagrams arranged according to the Earlier Heaven sequence. “The Eight Trigrams are arranged” means that the trigrams Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun are set out in a row. Counted from top to bottom and from left to right, they form a row; counted outward from the center, Zhen, Li, Dui, Qian, Xun, Kan, Gen, and Kun also form a row. They can be arranged horizontally, diagonally, in winding lines, or straight, and in any direction—left or right, forward or back. Within them are the images of Heaven, Earth, Water, Fire, Thunder, Wind, Mountain, and Lake.

“To double the Eight Trigrams in pairs” means that each trigram is combined in turn with all eight trigrams, thereby forming the sixty-four hexagrams. Yin and Yang lines are interwoven, firm and yielding lines are used in succession, and the six line positions—first, second, third, fourth, fifth, and top—are formed.

“Firm and yielding lines push and shift against one another” means that the firm line begins with the first nine in the hexagram Fu, then shifts in order from the first line to the second, third, fourth, and fifth, until it reaches the six lines of the hexagram Qian. The yielding line begins with the first six in the hexagram Gou and likewise shifts gradually from the first line, until it reaches the six lines of the hexagram Kun. The changes of the hexagrams and lines are revealed in this way. The sages based their words explaining good fortune, bad fortune, regret, and distress on these changes. Thus, all the actions of things under Heaven, and their transformations, are contained within them.

This concludes the middle volume of the Inner Chapters of Illustrations and Explanations of the Images in the Book of Changes.

Illustrations and Explanations of the Images in the Book of Changes, Inner Chapters, Lower Volume.

The diagram above shows how the sixty-four hexagrams transform into one another and flow in their operation.

The Commentary on the Book of Changes says: “Firmness and yielding provide the basis for establishing what is fundamental; change and free passage are the means of responding to the times. Judgments of good and ill fortune depend on upholding what is right and seeking success. The movements of Heaven and Earth follow constant patterns, and by upholding what is right they give rise to things worth observing. The movements of the sun and moon follow constant patterns, and by upholding what is right they remain luminous. The movements and transformations of all things under Heaven take a single fundamental principle as their guide.”

This passage from the Commentary mainly explains how the sixty-four later-heaven hexagrams are derived from one another through changes in Yin and Yang lines. Firmness and yielding are the basis of change; adaptation is how firmness and yielding are applied in response to the times.

In the hexagram diagrams, Qian is firm and Kun is yielding, occupying the upper and lower positions respectively. This is the relatively stable underlying arrangement, which is why the text says, “Firmness and yielding are what establish the foundation.” Beginning with its first line, the Kun hexagram changes from Yin to Yang, developing step by step into Fu, Lin, Tai, Dazhuang, and Guai, and finally becoming Qian. This symbolizes the passage from winter to summer, as Yang energy gradually increases. Beginning with its first line, the Qian hexagram changes from Yang to Yin, developing step by step into Gou, Dun, Pi, Guan, and Bo, and finally becoming Kun. This symbolizes the passage from summer to winter, as Yin energy gradually increases. Thus adaptation means responding to the conditions of the time.

As Qian and Kun change beginning with their first lines, each gives rise to six hexagrams with one Yin or one Yang line, derived respectively from Fu and Gou. Changing two lines yields fifteen hexagrams each with two Yin or two Yang lines, derived from Lin and Dun. Changing three lines yields twenty hexagrams each with three Yin or three Yang lines, derived from Tai and Pi. Changing four lines yields fifteen hexagrams each with four Yin or four Yang lines, derived from Dazhuang and Guan. Changing five lines yields six hexagrams each with five Yin or five Yang lines, derived from Guai and Bo. These hexagrams can be derived from one another vertically or horizontally, and in forward or reverse order. Understanding the principles of change keeps one from being confined by fixed rules and allows one to deal with things fluently. The Commentary on the Changes expresses this idea when it says, “Change does not remain in one place, but circulates through the six positions; above and below have no fixed order, and firmness and yielding exchange places. They cannot be reduced to fixed rules; one must follow whatever change calls for.” Yin and Yang lines are continually changing, so no single fixed standard can encompass them; one can only respond in accordance with change.

Yang energy advances, rising toward the upper left from the Fu hexagram; Yin energy retreats, descending toward the lower right from the Gou hexagram. The Tai and Pi hexagrams show a configuration in which Yin and Yang are evenly divided: from the hour of Yin to the hour of Shen is daytime, when the Yang energy represented by Qian prevails; from the hour of You to the hour of Chou is nighttime, when the Yin energy represented by Kun takes over. Thus the Great Treatise, Part One says that change symbolizes advance and retreat, while firmness and yielding symbolize day and night. As firmness and yielding alternate, gain and loss follow, and the principles of good fortune and misfortune wax and wane in turn.

Qian above and Kun below is the stable configuration of Heaven and Earth, expressing the enduring and observable nature of their Way. Li in the south and Kan in the north, with the sun illuminating the day and the moon appearing at night, express the enduring and clear nature of the Way of the sun and moon. The transformations of all things under Heaven are endless, yet following the principles of things brings good fortune, while going against them brings misfortune. To grasp these transformations through enduring principles is, in the end, to follow a single Way.

Zhu Xi said that the Cantong qi (a Daoist alchemical classic) compares the Qian and Kun hexagrams to the vessel, and the Kan and Li hexagrams to the medicines. The other sixty hexagrams represent the timing and intensity of the alchemical fire. Following this diagram, one may infer that the hexagrams correspond to the human body and to Yin-Yang in Heaven and Earth.

The Qian hexagram symbolizes the head and is positioned above; the Kun hexagram symbolizes the abdomen and is positioned below. The Li hexagram symbolizes the heart, and the Kan hexagram the kidneys. The heart belongs to Fire and the kidneys to Water, so Li is above and Kan below.

Yang Qi begins at the position symbolized by the Fu hexagram and moves upward along the left. This corresponds to the Yang Qi in the body’s Governing Vessel, which runs up the back: it rises from the coccyx along the spine and reaches the head. Yin Qi begins at the position symbolized by the Gou hexagram and moves downward along the right. This corresponds to the Yin Qi in the body’s Conception Vessel, which runs down the front of the body: it passes through the throat and chest and descends to the abdomen.

The twenty hexagrams above take Heaven as their model. Heaven belongs to Yang, and its Qi is clear and light, so these hexagrams each have four or five Yang lines. The twenty hexagrams below take Earth as their model. Earth belongs to Yin, and its Qi is heavy and turbid, so these hexagrams each have four or five Yin lines. The twenty hexagrams in the middle symbolize humanity. People receive the virtues of Heaven and Earth and are born from the union of Yin and Yang, so these hexagrams each have three Yin and three Yang lines. This also reflects the body’s meridians and the three Yin and three Yang divisions in the hands and feet. Since the upper part of the body can also be modeled on Heaven, the middle on humanity, and the lower on Earth, the diagram may be understood in this way as well.

From this, it seems that the Cantong qi’s claims are not baseless. As for the Heng hexagram’s position at the center, it may be connected with the “constant nature” mentioned in the Book of Documents, “remaining constant in one virtue” in the Zuo Commentary, and the “constant heart” in the Mencius. The Tuan Commentary says: “The sun and moon follow the course of Heaven and can therefore shine for a long time; the four seasons change without interruption and can therefore bring all things to completion for a long time; the sage remains on the right path and can therefore bring the world to successful transformation. Observe what is constant in things, and you will see the true condition of Heaven, Earth, and all things.”

Hexagram Diagram Ten

The diagram above shows how the sixty-four hexagrams function.

The “Discussion of the Trigrams” says: The vitality of all things begins with the Zhen trigram, which symbolizes the east, spring, and sprouting. It develops in orderly fashion through the Xun trigram, which symbolizes the southeast, wind, and growth, and becomes visible in the Li trigram, which symbolizes the south and brightness. In the Kun trigram, which symbolizes the earth, each thing finds its proper use. All things follow their own constant ways over time, and through this the world is brought to order by education. By observing the enduring patterns of all things, we can discern the condition of everything between heaven and earth.

Diagram Ten: A diagram showing how the sixty-four trigrams function.

The “Discussion of the Trigrams” also says: The vitality of all things begins with the Zhen trigram, develops in orderly fashion through the Xun trigram, becomes visible in the Li trigram, and finds its proper use in the Kun trigram. In the Dui trigram, which symbolizes joy and speech, it expresses itself with delight; in the Qian trigram, which symbolizes strength and heaven, it engages in contention and transformation; in the Kan trigram, which symbolizes danger and water, it undergoes toil; and finally, in the Gen trigram, which symbolizes stillness and mountains, it reaches completion.

The preceding explanation described the hexagram configurations shown in the diagram of the sixty-four later-heaven hexagrams. Zhu Xi once questioned how the positions of the hexagrams had been determined, suggesting that the matter be left open for the time being rather than forced into an explanation. Later, some Confucian scholars used changes in the hexagram lines and arrangements of the Five Phases (Wood, Fire, Earth, Metal, Water) to account for the positions. But these were conjectures attached to the established directions through imagination, with no reliable basis. Here, the diagram is redrawn and explained by drawing on the relations between images and numbers in the Hetu (a traditional diagram that represents the patterns and numbers of celestial phenomena), and by consulting the positions of the earlier-heaven hexagrams and divination books passed down among the people.

The Qian hexagram, which symbolizes Heaven, begins in the northwest, following the saying that “Heaven inclines toward the northwest.” If Qian is in the northwest, then the Kun hexagram, which symbolizes Earth, should be in the southeast. But because Heaven and Earth are incomplete in the southeast, the Xun hexagram, which symbolizes wind and also represents the eldest daughter, takes its place there. In the earlier-heaven arrangement, Xun is opposite Dui. Kun therefore withdraws to the southwest, and all three of its lines change to form Qian; all three lines of Qian likewise change to form Kun. The two hexagrams oppose each other, so their positions are arranged one above the other.

The Li hexagram, which symbolizes fire, rises upward, so it is placed in the south. The Kan hexagram, which symbolizes water, flows downward, so it is placed in the north. All three lines of Kan change to form Li, and all three lines of Li change to form Kan. The two hexagrams correspond to each other, so Kan and Li are also arranged one above the other.

The Gen hexagram, which symbolizes a mountain, is opposite Zhen in the earlier-heaven arrangement, so it is placed in the northeast. Xun is opposite Dui in the earlier-heaven arrangement, so it is placed in the southeast. All three lines of Gen change to form Dui, which, when viewed from the opposite direction, becomes Xun. All three lines of Xun change to form Zhen, which, when viewed from the opposite direction, becomes Gen. The two hexagrams correspond to each other, so Gen and Xun are also arranged one above the other.

Thunder is stirred by lightning, so the Zhen hexagram, which symbolizes thunder, is placed due east, where Li stands in the earlier-heaven arrangement. Since fire burns upward, changing the top line of Zhen forms Gen. Changing all three lines of Zhen forms Xun, which, when viewed from the opposite direction, becomes Dui. Water gathers into a marsh, so the Dui hexagram, which symbolizes a marsh, is placed due west, where Kan stands in the earlier-heaven arrangement. Since water flows downward, changing the bottom line of Dui forms Zhen. Changing all three lines of Dui forms Gen, which, when viewed from the opposite direction, becomes Zhen. Zhen and Dui face each other from left and right, so their positions are arranged side by side.

Shao Yong said, “Zhen and Dui are arranged side by side, while the other six hexagrams are arranged one above the other. This is how the Changes are put to use.” These are profound words. For this reason, the Eight Palaces hexagrams (a sequence that classifies hexagrams into eight home palaces) found in divination books today also show Qian and Kun, Kan and Li, Zhen and Dui, and Gen and Xun in opposing pairs.

The Gou hexagram in the Qian Palace derives from Kun; viewed from the opposite direction, it is Guai. Dun in the Qian Palace is opposite Dazhuang in the Kun Palace; Pi is opposite Tai, Guan is opposite Lin, and Bo is opposite Fu.

The Jie hexagram in the Kan Palace derives from Li; viewed from the opposite direction, it is Huan. Tun is opposite Meng, Jiji is opposite Weiji, Ge is opposite Ding, and Feng is opposite Lü.

The Bi hexagram in the Gen Palace derives from Xun; viewed from the opposite direction, it is Shike. Daxu is opposite Wuwang, Sun is opposite Yi, Kui is opposite Jiaren, and Lü is opposite Xiaoxu.

The Yu hexagram in the Zhen Palace derives from Dui; viewed from the opposite direction, it is Qian. Jie is opposite Jian, Heng is opposite Xian, Sheng is opposite Cui, and Jing is opposite Kun.

The Wandering Soul and Returning Soul hexagrams do not belong to the regular sequence of changes in the Eight Palaces. Changing the fifth line of the home-palace hexagram produces an outer trigram; then changing all three lines of the inner trigram produces a Wandering Soul hexagram. “Wandering” means moving from the inside to the outside. If only the fifth line is changed while the three lines of the inner trigram remain unchanged, the result is a Returning Soul hexagram. “Returning” means coming back from the outside to the inside. In this way, the hexagram configurations shift back and forth between inside and outside, above and below, expressing an ordered cycle of advance and retreat.

The Commentary on the Changes says, “The number of the Great Expansion is fifty; in actual divination, forty-nine are used.” Zhu Xi explained that the number of the Great Expansion comes from the Yellow River Chart, an ancient legendary numerical diagram: multiplying the heavenly number five by the earthly number ten, or the earthly number ten by the heavenly number five, gives fifty. Divination uses only forty-nine yarrow stalks, the stems used in ancient divination. This follows naturally from principle and circumstance; it is not something human effort can increase or decrease.

Tie the forty-nine yarrow stalks into a bundle with a ribbon to symbolize Taiji (the Supreme Ultimate), the undivided whole of the universe. The number forty-nine is obtained by adding together the numbers of the line patterns that form the Eight Trigrams. The yang mode has seven lines: one for the mode itself, two for its image, and four for its trigrams. The yin mode also has seven lines, likewise made up of one for the mode, two for its image, and four for its trigrams. Taking seven as the base, seven times seven gives forty-nine.

The Commentary on the Changes says, “The virtue of the yarrow stalks is round and mysterious; the virtue of the trigrams is square and wise.” “Round” refers to odd numbers; when seven groups of yarrow stalks are gathered together, they naturally form a circle. “Square” refers to even numbers; when the eight directions are arranged and combined, they naturally form a square. “Mysterious” means that their workings are subtle and hard to fathom; “wise” means that their changes are far-reaching and unobstructed. The yarrow stalks belong to yang, while the trigrams belong to yin; the stalks are active, while the trigrams are still. This shows that both the substance and function of the Changes are fully complete.

The Commentary on the Changes says, “Divide the yarrow stalks to symbolize the Two Modes, then take one stalk and set it aside to symbolize the Three Powers.” The Two Modes are Heaven and Earth; the Three Powers are Heaven, Earth, and humanity. “Set aside” means to place apart. Here the explanation draws on the Yunhui dictionary, which says that “set aside” means putting something to one side so that it does not take part in the calculation. Older explanations say that this stalk is placed between the little finger and ring finger, and therefore interpret “after the second counting, set one aside” to mean that another stalk must be set aside during the second change. This interpretation is awkward. If the meaning of “set aside” is not understood, it can lead to many strained and convoluted explanations.

When divining with forty-nine yarrow stalks, first divide them into a left and a right group to symbolize the Two Modes. Then take out one stalk and place it in the middle to symbolize humanity. This leaves a total of forty-eight stalks in the two groups.

Forty-nine yarrow stalks are taken and divided into two bundles, symbolizing the Two Principles of Yin and Yang. One stalk is then taken from among them and set aside in the middle, symbolizing the human being situated between Heaven and Earth. The two bundles on either side contain forty-eight stalks altogether. This number encompasses the total number of lines in the hexagram figures: the eight trigrams each have three lines, making twenty-four lines in all; when two trigrams are combined, they make forty-eight lines. Each of the eight trigrams also has eight possible changes, giving forty-eight lines altogether.

To perform the calculation, first hold the left-hand bundle in the left hand. With the right hand, take one stalk from the right-hand bundle and set it aside in the middle, where it remains untouched. This stalk symbolizes the human being dwelling between Heaven and Earth. Yin and Yang, cold and heat, day and night, and the transformations of all things are left to the workings of the Dao of Heaven; humans do not interfere. Although this stalk does not take part in the calculation, it is always used together with the other forty-eight, and together they symbolize the Three Powers of Heaven, Earth, and humanity.

Next, use the right hand to count the stalks held in the left hand in groups of four. Place the one to four stalks left over between the little finger and ring finger. This is called le, symbolizing an intercalary month once every three years. Then take the stalks on the right and count them in groups of four in the same way, placing the remainder according to a specific rule: if one remains, take three; if three remain, take one; if two remain, take six; if four remain, take four. Hold these between the ring finger and middle finger. This is called “the second le,” symbolizing another intercalary month after five years. Then combine the remainders from the two counts and place them beside the stalk set aside earlier. This step is called “the final placing.” The Yunhui explains that this means combining them and placing them together.

After the remainders have been gathered, their total is either four or eight, never “five or nine.” Four represents one group of four; eight represents two groups of four. Then gather the remaining stalks together. There may be forty-four or forty. Divide, count, set aside the remainders, and place them as before to complete the second change. Gather the stalks remaining after the second change; there may be forty, thirty-six, or thirty-two. Perform the same procedure to complete the third change.

After three changes, determine whether the resulting line is old or young, Yin or Yang, from the results of the three calculations. If all three results are odd, it is old Yang; if all three are even, it is old Yin. If two are even and one is odd, the odd result prevails, making it young Yang. If two are odd and one is even, the even result prevails, making it young Yin. Each set of three changes forms one line, and eighteen changes form one hexagram. A hexagram can transform into any of the sixty-four hexagrams, encompassing all 4,096 possible hexagram configurations.

The Commentary on the Changes says: To derive one line by means of yarrow stalks—the stems used in divination—requires eighteen transformations to form a hexagram. A hexagram can then continue to change, producing the sixty-four hexagrams and encompassing all 4,096 possible changes.

The Commentary on the Changes also says: Each time, the yarrow stalks are counted in groups of four, symbolizing the four seasons. Any stalks left over are set aside to symbolize an intercalary month. There are two intercalary months in five years, so the leftovers are placed aside in two stages before the stalks are suspended. According to the method shown in this diagram, after the stalks are divided into four bundles, if one stalk remains on the left, three remain on the right; if three remain on the left, one remains on the right. Together, these two cases give the number of stalks assigned to the Yang in the Two Forms. If two remain on one side, six are taken as the remainder on the other; if four remain on the left, four also remain on the right. Together, these two cases give the number of stalks assigned to the Yin in the Two Forms.

Zhu Xi says: An odd number symbolizes the circle, whose diameter is one and circumference is three; Yang takes the complete number. Old Yang is made up of three odd numbers, and three times three is nine. The number remaining after the yarrow stalks are counted is also four times nine, or thirty-six. An even number symbolizes the square, whose side is one and perimeter is four; Yin takes half the number. Old Yin is made up of three even numbers, and three times two is six. The number remaining after the stalks are counted is also four times six, or twenty-four. Young Yang is made up of one odd number and two even numbers: the odd number counts as three, and each even number as two, giving a total of seven. The number remaining after the stalks are counted is four times seven, or twenty-eight. Young Yin is made up of one even number and two odd numbers: the even number counts as two, and each odd number as three, giving a total of eight. The number remaining after the stalks are counted is four times eight, or thirty-two. This is the subtle relationship that naturally arises between the numbers of the yarrow stalks and the lines of the hexagrams.

After each set of three changes, one line is formed. If all three results are odd, the pattern resembles the Qian trigram, and a yang line changes into a yin line. If all three results are even, the pattern resembles the Kun trigram, and a yin line changes into a yang line.

If two of the three results are odd and one is even, the even result takes precedence. When the even result occurs on the first, second, or third change, the patterns respectively resemble the Xun, Li, and Dui trigrams. The resulting line is yang and does not change. If two results are even and one is odd, the odd result takes precedence. When the odd result occurs on the first, second, or third change, the patterns respectively resemble the Zhen, Kan, and Gen trigrams. The resulting line is yin and does not change.

These make eight patterns in all, corresponding to the images of the Eight Trigrams (Bagua). There are sixty-four related patterns in total, as explained below.

When two results are even and one is odd, the odd result takes precedence. This is young yang, the lesser category among yang lines, and corresponds to the stalk counts of the Gen, Kan, and Zhen trigrams, totaling twenty-four stalks. If the odd result appears only on the third change, this is the stalk count of the Gen trigram: eight stalks. If it appears on the second change, this is the stalk count of the Kan trigram: eight stalks. If it appears on the first change, this is the stalk count of the Zhen trigram: eight stalks. Returning the remainder yields five; returning the remainder of five groups of five yields seven. Seven groups of four stalks give the fixed number for a yang line, which no longer changes.

When two results are odd and one is even, the even result takes precedence. This is young yin, the lesser category among yin lines, and corresponds to the stalk counts of the Xun, Li, and Dui trigrams, totaling twenty-four stalks. If the even result appears on the first change, this is the stalk count of the Xun trigram: eight stalks. If it appears on the second change, this is the stalk count of the Li trigram: eight stalks. If it appears on the third change, this is the stalk count of the Dui trigram: eight stalks. Returning the remainder yields sixteen stalks, while counting the stalks in groups yields thirty-two. Dividing by four gives four for the remainder; counting the stalks in groups of four gives eight. Eight groups of four stalks give the fixed number for a yin line, which no longer changes.

In the three changes described above, the total obtained by gathering the stalks is sixteen, and the total obtained by counting out the stalks is thirty-two. Divide each total by four: the gathered total gives four, while the counted-out total gives eight groups of four, yielding eight. Eight is the proper number of the Yin line and represents an unchanging Yin line.

If all three of the changes described above produce odd numbers, the result is old Yang, and the stalk count for the Qian hexagram is eight. The gathered total is twelve, and the counted-out total is thirty-six. Divide each total by four: the gathered total gives three, while the counted-out total gives nine groups of four, yielding nine. Nine is the extreme of Yang and changes from Yang to Yin. Since divination with the Yi is based on change, any Yang line that changes is called “nine.”

If all three of the changes described above produce even numbers, the result is old Yin, and the stalk count for the Kun hexagram is eight. The gathered total is twenty-four, and the counted-out total is also twenty-four. Divide each total by four: the gathered total gives six, and the counted-out total gives six groups of four, yielding six. Six is the extreme of Yin and changes from Yin to Yang. Since divination with the Yi is based on change, any Yin line that changes is called “six.”

Here, “stalk count” refers to the number of yarrow stalks used in divination with the Yi; “gathering the stalks” and “counting out the stalks” are steps in dividing and tallying the stalks to cast a hexagram.

The eight forms of the Bagua listed on the right each have eight variations; together they produce the images of the sixty-four hexagrams. The yarrow-stalk divination method used here follows Cheng Yi’s account. Zhang Zai said, “In the second and third changes, one stalk is no longer set aside.” That is, in the first change, one yarrow stalk is set aside to symbolize the human being. The next two changes follow the same procedure but do not set aside another stalk. This is the correct method.

The practice of counting only the stalks on the left, and not those on the right, follows the accounts of Zhang Yuan and Zhuang Chuo of the Tang dynasty. Heaven is active and Earth is still. The number one belongs to Yang; it symbolizes the human being and is set aside. The next two changes follow the same procedure but do not set aside another stalk. The remainder on the left is matched by the remainder on the right: if one remains on the left, three are matched on the right; if three remain on the left, one is matched on the right. Together these make an odd number, symbolizing Yang. If two remain on the left, six are matched on the right; if four remain on the left, four are matched on the right. Together these make an even number, symbolizing Yin. The counts of Yin, Yang, Greater, and Lesser are thereby balanced and orderly.

If one uses the more recent method of setting aside one stalk in every change and counting stalks on both the left and right, the results are twelve Old Yang, twenty-eight Lesser Yin, twenty Lesser Yang, and four Old Yin—a distribution that is uneven. If one sets aside a stalk in the first change but not in the next two, while still counting stalks on both sides, the results are twenty-seven Greater Yang, twenty-seven Lesser Yin, nine Lesser Yang, and one Greater Yin. Although the total is still sixty-four, Greater Yin is exceedingly rare. Some people have even repeated the divination all year without encountering the hexagram in which pure Kun changes into Qian. Those who understand the transformations of the yarrow-stalk method should examine its subtle principles carefully.

On examining changing hexagrams and divination.

The total number of stalks represented by the lines of the Qian hexagram is 216, while the total for the lines of the Kun hexagram is 144. Together they make 360, approximately the number of days in a year. The total number of stalks represented by all the lines in the upper and lower sections is 11,520, symbolizing the number of all things. Thus, the Yi hexagrams can be formed through four steps of calculation, and a single hexagram can be completed through eighteen transformations. Once the Eight Trigrams have taken shape, the basic images of the hexagrams are established. By extending and applying these images through analogy, one can investigate all the principles and affairs of the world.

The number of stalks represented by the Qian hexagram is obtained by multiplying the number for old Yang, 36, by its six lines, giving 216. In this way, a complete hexagram image is formed. By extending and applying it through analogy, one can investigate all the principles and affairs of the world.

The number of counting rods assigned to each line of the Qian hexagram, used to calculate the numerical value of a hexagram line, is the number of the old Yang: thirty-six. Across all six lines, this gives a total of 216. Each line of the Kun hexagram is assigned the number of the old Yin: twenty-four, giving 144 across its six lines. Added together, these totals make 360, corresponding to the number of days in a year. A year has about 354 days when counted by lunar months, and about 365¼ days when counted by the solar terms. Here, 360 is used as an approximate figure between the two.

The number of counting rods for the young Yang is twenty-eight; multiplied by the six lines of the Qian hexagram, this gives 168. The young Yin has a value of thirty-two; multiplied by the six lines of the Kun hexagram, this gives 192. Their sum is also 360. The Commentary on the Changes does not mention this calculation because the Changes uses nine and six to represent Yang and Yin lines, not seven and eight.

The upper and lower sections of the classic together contain sixty-four hexagrams, with 192 Yang lines and 192 Yin lines. Counting each Yang line as the number of the old Yang, thirty-six, gives a total of 6,912; counting each Yin line as the number of the old Yin, twenty-four, gives 4,608. Together they total 11,520, corresponding to the number of the myriad things.

If instead each Yang line is counted as the young Yang’s value of twenty-eight, the total is 5,376; counting each Yin line as the young Yin’s value of thirty-two gives 6,144. Their sum is still 11,520. This shows that the numbers of the young Yin and young Yang are contained within the numerical principles of the old Yin and old Yang: seven and nine are both Yang and odd, while six and eight are both Yin and even. This is why Qian and Kun use nine and six.

The statement for the use of nine in the Qian hexagram says, “A host of dragons appears, but none takes the lead. Auspicious.” The statement for the use of six in the Kun hexagram says, “It is beneficial to remain correct over the long term.” These explain the general rules for divining the sixty-four hexagrams when the nine and six lines change.

Zhu Xi said: If none of the six lines in a hexagram changes, consult the image and statement of the original hexagram. Treat the inner trigram as “zhen” (the host, or the inner party) and the outer trigram as “hui” (the guest, or the outer party).

The Zuo Commentary records that Kong Chengzi performed a divination to support the accession of Prince Yuan of Wei and obtained the Zhun hexagram (Zhen below, Kan above), whose statement says, “It is beneficial to establish a feudal lord.” When the Earl of Qin attacked Jin, he performed a divination and obtained the Gu hexagram (Xun below, Gen above). The diviner said, “In the Gu hexagram, zhen is wind and hui is mountain.” These are examples of consulting the statement and image of the original hexagram when none of its six lines changes.

If only one line changes, the divination is based on the statement for that changing line in the original hexagram. The text cites several divinations from the Zuo Commentary: some change from Zhun to Bi, others from Qian to Tongren, and still others from Dayou to Kui or from Guan to Pi, among others. The changing lines occur at the first, second, third, fourth, fifth, and top positions. These are all examples of divining according to the statement for the changing line in the original hexagram.

If two lines change, the divination is based on the statements for those two changing lines in the original hexagram, with the upper line’s statement taking precedence. The Zuo Commentary contains no examples of this kind of divination.

When two lines change, one may also consult the images and statements of both the original hexagram and the resulting hexagram, giving precedence to the original hexagram.