《易数钩隐图(刘牧)》

This book was originally titled Yishu Gouyin Tu and is attributed to Liu Mu of Sanqu. It comprises three volumes and is included in the Zhonghua Daozang under the category of “Daoist Yi studies.” The extant edition takes as its base text the Zhengtong Daozang, Dongzhen section of the Three Caverns (Dongzhen/Dongxuan/Dongshen), Lingtu category, and collates it with the Wenyuan Pavilion Siku Quanshu, Jing (scripture/classic) section, Yi category edition.

The table of contents of the entire work begins with the “Preface” and is divided into an Upper Volume, a Middle Volume, and so on. The Upper Volume sequentially explains the generative relationships of Taiji (Supreme Ultimate), the Two Modes, the Four Images, and the Bagua (Eight Trigrams), together with the numbers of Heaven and Earth, the Great Expansion number, and “its use of forty-nine,” among other mathematical principles of Yi studies. It then discusses Lesser Yang, Lesser Yin, Old Yang, and Old Yin, as well as the line numbers seven, eight, nine, and six, and also treats the hexagram drawings of Qian and Kun, the relations of Yin-Yang, and the endowment of the Five Phases (Wood, Fire, Earth, Metal, Water) to human beings. The contents further list Li as Fire, Kan as Water, Zhen as Wood, Dui as Metal, and the combination of Heaven Five with Earth Ten as Earth, among other topics.

Here “Taiji” refers to the fundamental state in which Yin and Yang remain undivided and from which the myriad things are generated; the “Two Modes” refer to Yin-Yang, the “Four Images” are the four states formed by further combinations of Yin and Yang, and the “Bagua” are the eight trigram images used in the Yi to symbolize the transformations of Heaven, Earth, and all things. The “Great Expansion number” is the mathematical principle employed in Yi divination calculations; “using forty-nine” refers to performing the operations with forty-nine yarrow stalks during divination. The Lesser Yang, Lesser Yin, Old Yang, Old Yin, and the numbers six, seven, eight, and nine listed in the contents are terms used in yarrow-stalk divination to determine the line images and the changes of Yin-Yang.

"Qian Kun Sheng Liu Zi" is the thirty-fourth chapter. The chapters that follow discuss in succession the intermingling of the Qian and Kun hexagrams, Zhen as the eldest son, Xun as the eldest daughter, Kan as the middle son, Li as the middle daughter, Gen as the youngest son, and Dui as the youngest daughter, together with Kan giving rise to the Fu hexagram, Li giving rise to the Shen hexagram, the Three Powers, and the notion of “return in seven days.” These titles center on the Yin-Yang transformations of the Bagua (Eight Trigrams) in the Yijing and on their symbolic meanings.

The table of contents also includes “Discussion, Upper,” “Discussion, Middle,” and “Discussion, Lower,” along with an account of the Lin hexagram and the “eighth month.” The lower volume gathers chapters on the Hetu, the Heaven-and-Earth numbers of the Hetu, the Four Images of the Hetu, the Bagua of the Hetu, the generating and completing numbers of the Five Phases (Wood, Fire, Earth, Metal, Water) in the Luoshu, the ten days and the mutual generation of the Five Phases, as well as “Discussion of the Dragon Chart and Turtle Writings, Upper” and “Discussion of the Dragon Chart and Turtle Writings, Lower.” These pieces mainly examine the relations among the numbers of the Changes, the Five Phases, and the Hetu and Luoshu.

The preface to the Yi Shu Gou Yin Tu is signed as composed by Liu Mu of Sanqu.

The Yi discusses the principles of the interaction and transformation of the two Qi of Yin-Yang. When Yin and Yang have not yet interacted, there are no Four Images (the four basic forms produced by Yin-Yang transformation); when the Bagua (Eight Trigrams) have not yet differentiated, from where would the myriad things arise? Therefore the Two Modes (Yin and Yang) transform to produce the Four Images, the Four Images transform to produce the Bagua, and the Bagua overlap and combine to form the sixty-four hexagrams. At this point the principles of change governing all things under heaven are fully contained therein.

The hexagrams were established by the sages in order to observe the images of things. Images are the portents that appear before physical forms become manifest. Tracing back to the root, physical forms arise from images, and images are established according to numbers. Apart from numbers one cannot discern whence the Four Images come. Therefore when Confucius praised and elucidated the Yi he invariably listed the extreme numbers of heaven and earth (the ultimate numbers upon which the transformations of heaven and earth depend), thereby explaining how change takes form and how the way of ghosts and spirits operates. From this we know that the book of the Yi must exhaustively investigate numerical principles in order to recognize its foundation.

Examining the scholars who annotated the Yi, we find that they analyze the Jing (scripture/classic) and elucidate its meanings, often with great precision and depth; yet when they come to the numerical principles of the interweaving transformations of heaven and earth their explanations are quite brief and cannot corroborate the relevant passages of the Xici, so that students find it difficult to grasp the meaning. I have therefore collected the numerical principles of the odd and even numbers of heaven and earth, beginning from Taiji (Supreme Ultimate) generating the Two Modes and continuing all the way to the Fu hexagram, listing a total of fifty-five positions and drawing them as diagrams. Beneath each diagram I explain its meaning separately, hoping that readers will find it easier to understand.

The principles of the Yi are profound and subtle; even the ancient sages and worthies found them difficult to fathom completely. I, Liu Mu, of limited talent and learning, inheriting the teachings of my predecessors, indeed cannot avoid appearing presumptuous and careless. Yet images occupy fixed positions and transformations follow definite numerical principles; I will not arbitrarily force associations. Learned and penetrating gentlemen, please examine this carefully.

Yishu Gouyin Tu, Volume One

Taiji, the First

Taiji (Supreme Ultimate) originally possesses neither specific number nor form. Now, by taking the images of the two kinds of Qi (vital energy) and combining them into a single depiction, this is done in order to illustrate the process by which the two kinds of Qi belonging to heaven and earth arise from Taiji.

Taiji Generates the Two Modes, Second

The Yijing states: “The Yi has Taiji, and from Taiji the Two Modes (Liangyi) are produced.” Taiji is the primordial Qi. Before heaven and earth had yet separated, this primordial Qi was chaotically fused as one; once this mass of primordial Qi differentiated, it came to be called the “Two Modes.”

Why does the Yijing refrain from speaking directly of “heaven and earth,” employing instead the term “Two Modes”? The reason is that “Two Modes” designates the condition in which the two kinds of Qi have only just begun to differentiate, whereas to speak of “heaven and earth” implies that the bodily forms of heaven and earth have already become manifest. Inasmuch as the discussion treats of the initial configuration in which heaven and earth first divide into two parts, the expression “Two Modes” is used.

How is this to be understood? The light and clear portion of the Qi occupies the upper position, while the heavy and turbid portion occupies the lower. That which is light, clear, and circular is the image of heaven; that which is heavy, turbid, and square is the image of earth. At this juncture, heaven above and earth below have not yet interacted; they simply display their respective forms. Only when the two kinds of Qi commence their interaction does the single Qi of heaven descend to generate Water, and the dual Qi of earth ascend to generate Fire; this constitutes the inception of the formation of bodily shapes. Once the Five Phases (Wood, Fire, Earth, Metal, Water) are fully present, animals and plants then come into existence. The statement “images are completed in heaven, forms are completed on earth” refers precisely to this sequence of events.

It may thus be known that the Two Modes constitute the images of heaven and earth, while heaven and earth constitute the actual substances of the Two Modes. In the accompanying diagram, heaven is shown revolving toward the left, corresponding to the positions of Heaven-One and Heaven-Three; earth is shown revolving toward the right, corresponding to the positions of Earth-Two and Earth-Four. Depicting heaven and earth separately, each in its own position, serves to indicate the state in which they have not yet interacted above and below.

Heaven Five, Third

Heaven One, Earth Two, Heaven Three, and Earth Four are the four basic generating numbers of Heaven and Earth. When Heaven Five is reached, it occupies the center and governs transformation. People do not know what it truly is and can only provisionally call it the Qi (vital energy) of central harmony. It causes the Qi of Heaven and Earth to intermingle, forming the concrete configurations of the Five Phases (Wood, Fire, Earth, Metal, Water), so that the transformations of the myriad things interweave, operate, and extend everywhere. After the Dao (the Way) of the Three Powers of Heaven, Earth, and Humanity is complete, it conceals itself once more, becoming unmanifest and returning to stillness and Wuwei (non-action). This is what is meant by the statement that the transformations of Yin-Yang are difficult to fathom and therefore called Shen (spirit).

Although the Yijing states that the Four Images generate the Bagua (Eight Trigrams), it is still necessary to pass through the transformations of three and five and to possess the completing numbers of seven, eight, nine, and six before the Bagua can be generated and the positions of the hexagrams determined.

The number of Heaven and Earth totals fifteen. Someone asked why the numbers of Heaven and Earth undergo transformation initiated by Heaven Five. It was answered that the generating numbers of Heaven and Earth are already complete and thus able to produce transformation. The generating numbers of Heaven and Earth from Heaven One to Heaven Five total fifteen. Heaven One, Heaven Three, and Heaven Five added together make nine, which is a Yang number, so the Qian hexagram takes nine as its use. Earth Two and Earth Four added together make six, which is a Yin number, so the Kun hexagram takes six as its use. Adding the completing numbers of the Five Phases, which amount to forty, the total is fifty-five, fully providing the ultimate numbers of Heaven and Earth. Therefore they are able to accomplish transformation and to set ghosts and spirits in motion.

Heaven One generates Earth Six downward. Earth Two generates Heaven Seven upward. Heaven Three generates Earth Eight to the left. Earth Four generates Heaven Nine to the right.

The Yijing (Book of Changes) says: “Combine the numbers together, then match them according to the transformations of Yin-Yang, and interweave these numbers comprehensively. When one thoroughly understands their transformations, the patterns of Heaven and Earth take form; when one exhausts these numbers, the images of all things under Heaven can be determined.”

Here, “can” (参) means to combine together; “wu” (伍) means to pair in matching couples. For example, the heavenly number five combines with one and, moving downward, generates the earthly number six, and so forth. Through these pairings one accounts for change, and then by interweaving and combining the numbers, the numerical principles of the Four Images and the Bagua (Eight Trigrams) are formed. “The patterns of Heaven and Earth” refers to the textures and orderly structure that appear after Yin and Yang mutually interpenetrate. “Exhausting the numbers” means thoroughly investigating the numbers of Heaven and Earth; the total of the Heaven and Earth numbers is fifty-five. Once the numbers of Heaven and Earth are established, the images of all things between Heaven and Earth are thereby determined.

The Two Modes Generate the Four Images, Section Nine: this section discusses how the Two Modes of Yin-Yang generate the Four Images, and is the ninth section of this chapter.

The Yijing (Book of Changes) says: “The two modes generate the four images.” In his subcommentary in the Zhouyi Zhengyi, Kong Yingda held that metal, wood, water, and fire take shape by receiving the Qi (vital energy) of heaven and earth and are therefore called the “four images”; earth is apportioned among the four seasons, and apart from this, earthly things are said to have only four images. Liu Mu objected that metal, wood, water, and fire are all physical objects, so how can they be called “images”? Kong Yingda’s interpretation strays far from the original intent.

Another explanation holds that the Yijing possesses four images used to display principles. Master Zhuang regarded these four images as the actual images, hypothetical images, meaning images, and functional images within the sixty-four hexagrams. Liu Mu stated that he had already refuted this view while explaining hexagram meanings. Master He interpreted the four images as four matters: Heaven produces marvelous things, which the sage takes as models; heaven and earth undergo transformation, which the sage imitates; Heaven reveals signs to indicate fortune and misfortune; the Hetu (River Chart) appears in the Yellow River and the Luoshu (Luo Writing) appears in the Luo River, which the sage takes as models. Liu Mu maintained that these are all actions performed by the sage outside the Yijing and cannot be used specifically to explain the images of fortune and misfortune within the Yijing.

The Yijing states “there are four images, used to display,” and also “append statements, used to inform.” Since “images” and “statements” stand in correspondence, the “statements” are the written remarks beneath the hexagrams and lines, so the “images” ought to be the images presented by the hexagrams and lines. The earlier phrase “the two modes generate the four images” refers to the four numbers seven, eight, nine, and six. Many Confucian scholars also call seven, eight, nine, and six the four images, and Liu Mu provisionally adopts this usage here. Yet if these four numbers are taken directly as the four images that the Yijing uses to display, the meaning becomes confused. Seven, eight, nine, and six stand respectively for lesser yin, lesser yang, old yin, and old yang; they are the four numbers employed in generating the Bagua (Eight Trigrams) and are not the four images that the Yijing uses to display.

The four images have two senses: one is the four images generated by the two modes; the other is the four images that the Yijing uses to display principles. Liu Mu illustrated the former through the numerical relationships of the Hetu: Heaven-one, Earth-two, Heaven-three, Earth-four, together with the transformations and interactions of Heaven-five, make up the total of forty-five needed to generate the Bagua. Thus Kan, Li, Zhen, and Dui occupy the proper positions of the four images. The reason “five images” is not mentioned is that five has no fixed position; referring to the four images already indicates that five participates as well.

Specifically, five situated above pairs with Heaven-one and generates Earth-six downward; situated below it pairs with Earth-two and generates Heaven-seven upward; situated on the right it pairs with Heaven-three and generates Earth-eight leftward; situated on the left it pairs with Earth-four and generates Heaven-nine rightward. This is the arrangement of the forty-five numbers of the Hetu. Liu Mu declared that this constitutes “the four images generated by the two modes” and is also the four images that the Yijing uses to display.

The four kinds of images mentioned in the Xici (Appended Statements) belong to another level of meaning: fortune and misfortune are images of gain and loss; regret and stinginess are images of worry and difficulty; change is the image of advance and retreat; firmness and softness are images of day and night. These appear in the Xici and also correspond to the meanings of the hexagrams and lines. Kong Yingda had said that images correspond to statements: statements are the written remarks beneath the hexagrams and lines, while images are those presented by the hexagrams and lines; he likewise cited seven, eight, nine, and six to explain “the two modes generate the four images.” Liu Mu considered the former view reasonable, yet taking seven, eight, nine, and six as the four images that the Yijing uses to display is greatly mistaken.

Among the completed numbers of the Five Phases (Wuxing), Water is six, Metal is nine, Fire is seven, and Wood is eight. Water corresponds to the Kan trigram, from which the Qian trigram is generated; Metal corresponds to the Dui trigram, from which the Kun trigram is generated; Fire corresponds to the Li trigram, from which the Xun trigram is generated; Wood corresponds to the Zhen trigram, from which the Gen trigram is generated. Si occupies the four cardinal positions, and from it Qian, Kun, Gen, and Xun are generated, combining to form the Eight Trigrams (Bagua).

The generating and completing numbers of the Five Phases originally belong to the Luo Shu. These numbers are drawn here in order to complete the fifty-five numbers of Heaven and Earth. Wood corresponds to the Zhen trigram and generates the Gen trigram; Si occupies the four cardinal positions, and from it Qian, Kun, Gen, and Xun are generated, combining to form the Eight Trigrams.

Among the numbers of Heaven and Earth, fifteen is taken as the root of the functioning of Heaven and Earth, which includes the numbers nine and six; adding the forty of the Five Phases numbers yields a total of fifty-five, thereby completing the numbers of Heaven and Earth.

The Yijing says: “The numbers of Heaven and Earth together total fifty-five; these are used to form changes and to set in motion the Dao (the Way) of ghosts and spirits.” It also says: “The number of the Great Expansion is fifty.” This means that the number of the Great Expansion subtracts five from the total numbers of Heaven and Earth. Han Kangbo said: “In extrapolating the numbers of Heaven and Earth, what is relied upon is fifty.” He did not explain why five is subtracted. In his subcommentary in the Zhouyi Zhengyi, Kong Yingda held that fifty-five is the total of the odd and even Yin-Yang numbers of Heaven and Earth, and is not the number used for extrapolating the yarrow stalks of Heaven and Earth.

However, when various Confucian scholars explain the number of the Great Expansion, they discuss both the meaning of “dividing into two” and how the fifty-five numbers of Heaven and Earth are employed, and they finally also set forth the principle that “four operations complete the Yi and eighteen changes form a hexagram.” Since both the beginning and the end involve the numbers of Heaven and Earth, how can it be said that the number used in the intervening process of extrapolation differs from them? Since the number of the yarrow stalks is used to symbolize Heaven and Earth, how can one discard the number itself and speak only of the meaning it symbolizes? This, too, is a shortcoming of the commentators: they have not investigated the meaning of “Heaven’s five withdraws and is stored in secrecy.”

Fifty-five is the total of the numbers of Heaven and Earth; the number of the Great Expansion is the number used when Heaven and Earth are in operation. Heaven’s five is not directly included in the number of the Great Expansion, so the number of the Great Expansion is five less than the total of Heaven and Earth. Someone asks: “Why does Heaven’s five not participate in the extrapolation of the Great Expansion?” The answer is that Heaven’s five is not entirely unused, but is used to unify and govern the Four Images. Heaven-one, Earth-two, Heaven-three, and Earth-four are the generating numbers of the Four Images; Heaven’s five commands these four generating numbers, causing them to form the four completing numbers of seven, nine, six, and eight. Therefore five actually participates in the functioning of the Four Images and is by no means unused. Five is contained within each of the Four Images; five is able to encompass the Four Images, and the Four Images are all the functioning of five. By simply enumerating the Four Images, five is already present among them, so the Yijing speaks only of the “Four Images,” thereby indicating that five is not listed separately as an additional image.

The number of the yarrow stalks is the number used in divination to take as image the operation of Heaven and Earth. Therefore the number of the Great Expansion is five less than the total numbers of Heaven and Earth.

The number of the Great Expansion is fifty, but the number actually used in yarrow-stalk divination is forty-nine. Han’s commentary explains that the derivation of the numbers of Heaven and Earth rests upon fifty; employing forty-nine means that one number among them takes no part in the operations. Though this number is never used directly, it allows the remaining numbers to circulate and function; it itself is not counted among the numbers, yet the numerical principles are thereby established. This unused number is the Taiji (Supreme Ultimate) of the Book of Changes—the fundamental, still-undifferentiated state of the myriad things. Forty-nine marks the utmost limit of number. The fundamental principle cannot be made evident merely by the words “fundamental”; it must be displayed through concrete existence. Therefore one must seek the origin of the myriad things from the extreme limit of their numbers.

Kong Yingda’s subcommentary cites Jing Fang: fifty comprises the ten days, the twelve earthly branches and the twenty-eight lunar mansions, totaling fifty; one of them is left unused so that the real principle may be sought from emptiness, and thus forty-nine are employed. Ma Jichang held that the Taiji of the Changes is the North Star (Beichen, the Pole Star). The North Star generates the Two Modes, the Two Modes generate the sun and moon, the sun and moon generate the four seasons, the four seasons generate the Five Phases (Wood, Fire, Earth, Metal, Water), the Five Phases generate the twelve months, and the twelve months generate the twenty-four solar terms. The North Star remains motionless in its original place while the other forty-nine numbers move and take effect. Xun Shuang noted that each hexagram has six lines, so the eight trigrams yield forty-eight lines; adding the “use” of the Qian and Kun hexagrams produces fifty. Because the first yang line of Qian states “the hidden dragon should not be used,” only forty-nine are actually employed. Zheng Xuan said the numbers of Heaven and Earth total fifty-five; because the Qi (vital energy) of the Five Phases pervades all things, five are subtracted, and the Great Expansion number subtracts one more, leaving forty-nine. Yao Xin and Dong Yu stated that from the fifty-five numbers of Heaven and Earth one subtracts six, symbolizing the six-line hexagrams, so forty-nine remain. Gu Ju observed that the number fifty is set up in order to seek the mysterious principle; the mysterious principle itself is not a number, yet it becomes manifest through numbers, therefore one number is left vacant to show that something ineffable is present.

The author finds that earlier interpretations differ widely. Although each scholar advances a claim, none of the explanations is entirely satisfactory. He therefore examines them in turn. Han identifies the unused number with Taiji, yet never accounts for the basis of this identification. Taiji generates the Two Modes; after the Two Modes have separated, Heaven begins to produce the number one and numerical principles thereby arise. Only then appear the Four Images, the Five Phases and the remaining numbers, which together amount to fifty-five—the true limit of the numbers of Heaven and Earth. If Taiji were counted as the unused number, the Great Expansion ought to employ fifty-four; otherwise the leftover five numbers would be an arbitrary and unfounded addition.

Moreover, what the Great Expansion derives are the numbers of Heaven and Earth—that is, the numerical principles that obtain after Heaven and Earth have already taken form. Consequently Taiji cannot be assigned the role of the unused number. Taiji is the state in which primordial Qi is still fused into a single whole; once the first sprout of Qi has appeared, it can no longer be described as entirely formless and traceless. Han’s interpretation therefore appears forced.

Some may object that Han’s commentary merely continues Wang Bi’s intention, and that Wang Bi’s annotations on the Changes have long been held in high esteem, so one ought not criticize them lightly. The author replies that this may be only Han’s own elaboration and not Wang Bi’s original meaning. The Changes itself states, “There is Taiji, and thereby are generated the Two Modes.” The very word “there is” shows that it does not refer to absolute nothingness. In the author’s view, Jing Fang, Xun Shuang, Ma Rong, Zheng Xuan and the rest likewise drew upon ready-made names and numbers already present in Heaven and Earth and forced them into correspondence with the Great Expansion number. If one insists on pairing every sort of celestial and terrestrial number, almost any explanation can be made to work. Yet the numbers of Heaven and Earth generate one another in successive order and form a coherent sequence; one should not arbitrarily introduce further forced associations. Even if one reluctantly constructs arguments in support of these views, further inquiry still fails to uncover the genuine origin of the numerical principles. The author notes that the matter will be discussed more fully in later sections.

The numbers of Heaven and Earth total fifteen, situated within the principles of number and circulating outward. The numbers of the Five Phases (Wuxing) total forty. Why, then, is only forty-nine used here? It is because Heaven-five is the starting point of change, distributed among the respective positions of the Five Phases, and so the central position (zhongyuan, the occupying middle numerical place) is employed to determine the hexagram images.

Heaven-one occupies the honored position without moving, thereby manifesting Heavenly De (Virtue). The number of Heavenly De is nine. Heaven-one is the origin of the myriad images, the root from which the ten thousand things grow, and the governor of creation and transformation; therefore it occupies the honored position and remains unmoving. Heaven-three, Earth-two, and Earth-four together form the Yang number nine. Heaven-three symbolizes the three lines of the Qian hexagram, while Earth-two and Earth-four symbolize the six lines of the Kun hexagram. The Dao of Earth initially generates the ten thousand things and also stands in for them in bringing them to completion; therefore Yang is able to encompass Yin. The three lines of Qian combined with the six lines of Kun constitute the Yang number nine, which sets in motion the completed numbers of the Five Phases and allows change to circulate. This is the principle of counting the yarrow stalks to obtain images.

Someone asked: “The Yijing says that the Kun hexagram employs six, yet now it is said that the three lines of Qian combine with the six lines of Kun. Does this mean that Kun’s six is unused?”

The reply was: “No, Kun’s six is already contained therein. This is because when the Yijing discusses numbers it cites the greater ones. Six is the lesser number; by citing the greater, the lesser is included. From this it may be known that when Yang qi (vital energy) advances and flourishes, Qian employs nine; when Yang qi recedes and conceals itself, Kun employs six. It is likewise with the numbers obtained in milfoil divination, which accord only with those of old Yin and old Yang, while the numbers of young Yin and young Yang are contained within them. Citing the greater number while encompassing the lesser is how the principles of the Yijing generally proceed.”

Lesser Yang, the seventeenth. Lesser Yin, the eighteenth. Old Yang, the nineteenth. Old Yin, the twentieth.

The twenty-first section concerns the combined numbers of seven, eight, nine, and six. These four numbers are each formed by adding four numerical positions. Old yang consists of four nines added together, totaling thirty-six; young yang consists of four sevens, totaling twenty-eight; old yin consists of four sixes, totaling twenty-four; and young yin consists of four eights, totaling thirty-two.

The twenty-second section treats the three lines of the Qian trigram, and the twenty-third the three lines of the Kun trigram. The line strokes of the Qian trigram are odd numbers, while those of the Kun trigram are even numbers. Once the respective positions of Qian and Kun are distinguished from each other, the odd and even positions arrange themselves into six places, and the sequential order of Yin-Yang positions is thereby determined.

The twenty-fourth section discusses yin within yang, the twenty-fifth yang within yin, the twenty-sixth the purely yang Qian trigram, and the twenty-seventh the purely yin Kun trigram.

The Yijing states: “The movement and transformation of one yin and one yang constitute the Dao (the Way).” Han Kangbo comments that “Dao” is a designation for yuan; yuan penetrates everywhere without obstruction and follows no fixed path. Spoken of under the name Dao, it is silent and formless, possessing no visible image; yet when its function is fully displayed and its formless efficacy becomes manifest, transformation leads into the marvelous. The Yijing itself has no fixed form, and from this one can perceive the Dao. By exhausting transformation one comes to know the marvelous; through marvelous transformation one makes the Dao evident. Although yin and yang differ, they are both governed by the same root: on the yin side it is called primordial yin, and yin is generated thereby; on the yang side it is called primordial yang, and yang is accomplished thereby, hence the phrase “one yin and one yang.” Kong Yingda likewise says that “one” refers to primordial yin and primordial yang, whose movement is called the Dao. Many commentators have followed the practice of explaining the Dao in terms of yuan, yet they have not clarified how the Dao exerts its marvelous function.

The Dao has no physical form, yet its fundamental purport still requires explanation. The Yijing’s statement that “one yin and one yang constitute the Dao” is intended precisely to express the principle of the union of yin and yang. Let us attempt a brief account: the expression “one yin and one yang” indicates yin and yang each existing independently. Isolated yin or isolated yang cannot generate anything; only when yin and yang unite can they exert their subtle function and produce transformation. The Four Images (the four states formed by the transformations of yin and yang) arise from this, and the myriad things are likewise generated from this. Thus the union of yin and yang and their transformative movement constitute the function of the Dao.

Isolated yin and yang are the attributes with which Heaven and Earth are respectively endowed: Heaven belongs to yang, Earth to yin. As for the Five Phases (Wood, Fire, Earth, Metal, Water), each contains yin-yang qi (vital energy) and is thereby generated. According to the pairing of Heavenly Stem numbers with the Five Phases, Heaven-one and Earth-six combine to generate Water, Earth-two and Heaven-seven combine to generate Fire, Heaven-three and Earth-eight combine to generate Wood, Earth-four and Heaven-nine combine to generate Metal, and Heaven-five and Earth-ten combine to generate Earth. This shows that each of the Five Phases is formed by receiving yin and yang qi. Animals and plants are generated by the confluence of the qi of the Five Phases. To elucidate this principle, the author first sets forth the situation in which Heaven and Earth each possess either yin or yang, then explains the condition in which the Five Phases contain both yin and yang, and finally shows that human beings are formed by receiving the substance of the Five Phases.

Li symbolizes Fire and is ranked twenty-eighth. Kan symbolizes Water and is ranked twenty-ninth. Zhen symbolizes Wood and is ranked thirtieth.

Yishu Gouyintu, upper volume.

Here the base text is missing one character, which is likewise absent from the Siku edition; it is suspected that the base text omitted the character “xi” (羲). The character “xin” (信) was originally omitted and has been supplied from the Siku edition; the base text leaves a blank space at this point. The character “hua” (画) was originally omitted and supplied from the Siku edition; a blank space remains in the base text. After “qi yi” (其义), both the base text and the Siku edition have missing text, and the Siku edition additionally marks it with “que” (阙, lacuna). After “bu ke” (不可), the base text has missing text, which the Siku edition marks with “que.” The character “wei” (位) was originally missing and is also absent from the Siku edition; it has been restored here on the basis of context. The character “ze” (则) is lacking in the Siku edition, which marks “que” at this point to indicate a lacuna in the original text.

Dui symbolizes Metal and is ranked thirty-first.

The heavenly number five combining with the earthly number ten generates Earth and is ranked thirty-second.

Earth is the original substance that possesses form and separately governs the four seasons. The earth is a dark place formed by the accumulation of yin Qi (vital energy); pure yin Qi cannot give birth to and nourish the myriad things. Only when the heavenly number five combines with the earthly number ten is Earth generated, enabling the myriad things to take on concrete physical forms. Earth adheres to the ground and supports the myriad things, and is therefore also one of the Five Phases (Wood, Fire, Earth, Metal, Water). Thus the Shu commentary states: “Earth is merely another existence within the earth.” Therefore the earth is called pure yin, while Earth is endowed with both yin and yang Qi.

Human beings receive the Qi of the Five Phases and are ranked thirty-third.

The Yi is vast and complete in content, encompassing the Way of Heaven, the Way of Humanity, and the Way of Earth. It comprises the three powers of Heaven, Earth, and Humanity, and divides each power into yin and yang aspects, thereby totaling six lines.

The Book of Changes is vast and complete in its content, treating of the Dao (the Way) of Heaven as well as the Dao of Humanity and the Dao of Earth. It divides each of Heaven, Earth, and Humanity—the Three Powers—into Yin and Yang aspects, thereby constituting the six lines; what the six lines embody is precisely the Dao of the Three Powers. Each of the Three Powers occupies upper, middle, and lower positions; giving play to the functions of the Three Powers cannot be separated from the coordination of the Five Phases. A person living in the world benefits in body and livelihood from the workings of the Five Phases and is inwardly endowed with the nature of the Five Phases. The Five Phases are Wood, Fire, Earth, Metal, and Water: Wood governs benevolence, Fire governs propriety, Earth governs trustworthiness, Metal governs righteousness, and Water governs wisdom. Thus, although humans are born with physical form, they can become the most spiritually endowed beings between Heaven and Earth because they are endowed within with these De (virtues). Even a dull-witted person cannot do without the operations of the Five Phases in daily life; if one obscures one’s own virtues and fails to follow the teachings of benevolence, righteousness, propriety, wisdom, and trustworthiness, it is truly a matter for regret.

Qian and Kun generate the six children. The hexagrams Qian and Kun interact to produce six child hexagrams. Qian symbolizes Heaven and is therefore called the Father. The yang Qi (vital energy) of Qian descends to interact with Kun, allowing all things to receive nourishment and to manifest brightness. Kun symbolizes Earth and is therefore called the Mother. The yin Qi of Kun, residing below, interacts upward with Qian. Zhen, obtained after Qian and Kun have united once, is the eldest son and is therefore called the eldest male. Xun, obtained after one union, is the eldest daughter and is therefore called the eldest female. Kan, obtained after two unions, is the middle son and is therefore called the middle male. Li, obtained after two unions, is the middle daughter and is therefore called the middle female. Gen, obtained after three unions, is the youngest son and is therefore called the youngest male. Dui, obtained after three unions, is the youngest daughter and is therefore called the youngest female. These natural images are arranged in this sequence in order to illustrate the principle of Yin and Yang interacting above and below and naturally generating one another, as well as the significance of the transformations that form the Bagua (Eight Trigrams).

The Yijing contains Taiji (Supreme Ultimate), the root from which all things are generated. Taiji produces the Two Modes (Yin and Yang), the Two Modes produce the Four Images, and the Four Images produce the Bagua (Eight Trigrams). Once the Bagua are arranged, the images of all things are contained within them. Pairing the Bagua two by two then manifests the transformations of the six yao. Thus Taiji is the origin of the Two Modes, while the pairing of the Bagua is the origin of the double hexagrams. The double hexagrams begin with the Fu hexagram. Why? Because Fu symbolizes the first sprouting of Yang Qi (vital energy).

A brief explanation follows. The four Zheng gua serve to demarcate the positions of the four seasons and the twelve months. They are further combined with the Qian, Kun, Gen, Zhen and other gua in order to interpenetrate the processes of change. Overlapping the gua then serves to express the functioning of transformation. By observing the changes in the gua images, one can discern that each has its proper foundation.

The Yang Qi of the Fu hexagram germinates from the Kan gua, is set in motion upon the Zhen gua, and unites with the Kun gua. It thereafter transforms into two Zhen gua, two Dui gua and two Qian gua, finally attaining Qian. The passage from Fu to Qian occupies six months and illustrates the principle of Yang yao progressively advancing upward. The Yin Qi of the Gou hexagram germinates from the Li gua, waxes and wanes beneath the Xun gua, and unites with the Qian gua. It thereafter transforms into two Xun gua, two Gen gua and two Kun gua, finally attaining Kun. The passage from Gou to Kun occupies six months and illustrates the principle of Yin yao progressively advancing downward.

From Fu to Gou there are twelve hexagrams in all, corresponding to the twelve months. These twelve hexagrams are further divided into the twenty-four qi, while the yao correspond to the seventy-two hou, circulating in coordination with the calendrical numbers of sun and moon. Therefore Li and Kan separately govern Heaven and Earth, taking Zi and Wu as the boundary: that which lies east of the Zi-Wu axis belongs to Yang, that which lies west belongs to Yin. If the remaining gua images are further interwoven and combined, the total of three hundred and eighty-four yao amply manifests the principles of the Three Powers of Heaven, Earth and Humanity.

Someone asked: “When these numbers are incorporated into a diagram and calibrated, with the gua and yao corresponding respectively to the positions of the four seasons and twelve months, and also drawing upon Qian and Kun...”

The transformations of the two hexagrams Gen and Xun must both be explained through the interaction of one hexagram with another. For example, the hexagram Fu is generated within Kan, set in motion in Zhen, and further interacts with Kun. The Yijing says, “Thunder within the earth: Fu,” which accords precisely with this meaning.

As for the hexagram Gou, it is generated within Li, recedes in Xun, and interacts with Qian. The Yijing says, “Wind under heaven: Gou.” Xun is not one of the four cardinal hexagrams, and therefore its meaning differs from that of Fu. Now the hexagram image shows Xun receiving Qian, yet also changing position so as to come from Dui. Why is this?

The answer is that this takes the image of the hexagram Guimei. The Yijing says, “Guimei is the great meaning of heaven and earth.” If heaven and earth do not interact, the myriad things cannot grow. Guimei concerns the beginning and end of human affairs. It employs the image of the eldest son interacting with the youngest daughter to show that when the youngest daughter marries, the eldest daughter presides over the hexagram image. This is because the younger sister follows the elder sister in marriage and is not the principal wife, just as in the ancient nuptial custom in which nieces and younger sisters accompanied the bride as secondary consorts.

If the eldest son were paired with the eldest daughter, this would indeed embody the constant way of husband and wife remaining together for a long time, yet it would not fully express the principle of proliferation and expansion. From this it may be known that what is able to cause an ending to open anew must be the hexagram Guimei; hence the Yijing calls it the great meaning of heaven and earth. Therefore the transformation of hexagram images must take its model from Guimei: since the younger sister is not the principal consort, the elder sister presides over her hexagram image. The hexagram body is taken from the combination of Dui and Zhen, while the hexagram name is taken from the sense of Xun receiving Qian. The principle of hexagram transformation, in all likelihood, lies herein.

The Three Powers, Forty-Five.

When earlier scholars explained the “Three Powers” (sancai: Heaven, Earth, and Humanity), most believed that the sages arbitrarily drew two kinds of lines—the firm (yang) and the yielding (yin)—and then arranged these two types of lines into three layers to symbolize Heaven, Earth, and Humanity. This view does not carefully examine the meaning of the Xici (Appended Phrases).

The images of the gua are natural forms presented by Heaven. The sages first received inspiration from the Hetu (Yellow River Chart) and Luoshu (Luo River Writing), observed the patterns of odd and even numbers between Heaven and Earth, and on this basis drew the lines, arranging them into three layers to form the Bagua (Eight Trigrams). Therefore drawing the gua was not done arbitrarily. In brief, forming a gua with three lines takes as its model the odd and even numbers of Heaven and Earth in nature. The Qian gua has three lines divided into three layers because Heaven’s odd number is three; Kun’s even number is also three, so it likewise is drawn in three layers. The remaining six gua are all transformations of Qian and Kun; their fundamental forms are the same, and thus they too are divided into three layers.

Heaven belongs to pure Yang, Earth to pure Yin. Pure Yang or pure Yin alone cannot generate the myriad things. Only when the Qi (vital energy) of Heaven and Earth intermingles and the numbers of the Five Phases (Wood, Fire, Earth, Metal, Water) are established can plants and animals come into being. Thus the Yijing says: “There being Heaven and Earth, thereafter the myriad things are generated.” Does this mean that a single line already contains the Dao (the Way) of the Three Powers? The phrase “combining the Three Powers and doubling them” refers to the principle by which the sages stacked the gua drawings; it does not refer to the eight three-line gua.

The Three Powers are Heaven, Earth, and Humanity; “doubling them” means stacking the gua. After the gua are stacked, the upper two lines belong to Heaven, the middle two lines belong to Humanity, and the lower two lines belong to Earth. Humanity is born by receiving the Qi of Heaven and Earth, so the Qi of Heaven and Earth is divided, allowing the lines that represent Humanity to occupy the middle. Therefore the line statement of Nine Two says “in the field,” showing that it embodies the Dao of Earth; the line statement of Nine Five says “the flying dragon in Heaven,” showing that it embodies the Dao of Heaven. This principle is clear and evident.

If this were not so, it can be verified from the Xici. The Xici states: “The transformations of the six lines embody the Dao of the Three Extremes.” It also states: “There is the Dao of Heaven, the Dao of Humanity, and the Dao of Earth; combining the Three Powers and stacking them, therefore they become six lines.” What the six lines embody is precisely the Dao of the Three Powers. The Xici further says: “The ancient sages created the Yi in order to accord with the principle of nature and life. Therefore they established the Dao of Heaven as Yin and Yang, established the Dao of Earth as yielding and firm, and established the Dao of Humanity as humaneness and righteousness; combining the Three Powers and stacking them, therefore the Yi constitutes a gua with six drawings.” All these statements show that the six-line gua contain the meaning of the Three Powers; they do not say that the three-line gua represent the Three Powers.

As for the fact that all six lines can be used to illustrate human affairs, this is because human ethics take as their model the images of Heaven and Earth; therefore the initial line and the upper line also contain meanings related to human affairs.

The phrase “return in seven days” in the Yijing means that yin qi begins to increase from the Bo hexagram until yang qi is completely exhausted; thereafter yang qi is reborn, and by the time the Fu hexagram appears, seven days have elapsed. The Zhengyi commentary holds that the annotations have already made this perfectly clear. Both Master Chu and Master Zhuang state that the first yin appears in the fifth month and the first yang in the eleventh month, spanning a total of seven months. The classic does not say “seven months” but “seven days” in order to show that the return and growth of yang qi is rapid, and therefore substitutes “day” for “month.”

A commentator named Han Si maintains that from the Bo hexagram, when yin qi reaches its fullest, to the Fu hexagram, when yang qi arrives, seven months actually elapse. As for counting from the fifth month yet saying “seven days” rather than “seven months,” this is in order to express…

The growth of yang Qi (vital energy) ought to be rapid, so here “days” are used to illustrate it rather than “months.” Some people nowadays believe that from the Bo hexagram (where yin Qi is at its peak and yang Qi is about to be exhausted) to the Fu hexagram (where yang Qi begins to return) seven months must elapse. If one counts from the fifth month, how can it be said that yang Qi has only just been exhausted? Moreover the Lin hexagram also indicates the growth of yang Qi and speaks of “the eighth month”; the Fu hexagram likewise indicates the growth of yang Qi, so why specifically change to speaking of “days”? Judging from the sense of the Commentary (Wang Bi’s annotations), it is certainly not explained in that way. This perhaps follows the “six days and seven fen” theory of the Yiwei and agrees with the interpretation of Zheng Kangcheng (Zheng Xuan), only the wording is concise and does not fully state the reasons.

The Yiwei: Jilantu states that hexagram Qi (the matching of hexagram images with solar terms and days) originates from Gen, Xun, Li, Kan, Zhen and Dui, each governing a direction. The sixty hexagrams have altogether three hundred sixty lines, corresponding to three hundred sixty days; in addition there are five and a quarter days. If one day is divided into eighty fen, five days amount to four hundred fen and a quarter day is twenty fen, totaling four hundred twenty fen. These are distributed among the sixty hexagrams at seven fen each; therefore each hexagram governs six days and seven fen.

The yang Qi of the Bo hexagram is exhausted by the end of the ninth month, and the tenth month is governed by the purely yin Kun hexagram (all six lines yin). The Kun hexagram is placed in the sequence of six days and seven fen per hexagram. After the yang Qi of Bo is exhausted, until the yang Qi of Fu returns, there intervenes the six days and seven fen governed by Kun. Summarizing this, Wang Fusi (Wang Bi) therefore calls it “seven days.”

Regarding the explanation of “return in seven days,” Kong Yingda’s Subcommentary (the notes that explicate the classic) is reasonable in its earlier part but has some inadequacies later. The classic text says “return in seven days,” and Wang Bi’s commentary also says “seven days”; he quotes the classic and the commentary to correct the errors of Messrs. Chu and Zhuang, which is correct. Yet he then cites the “six days and seven fen” of the Yiwei and Zheng Xuan, which in reasoning contradicts the classic and the commentary. Moreover, although the Yiwei and Zheng Xuan propose that each hexagram governs six days and seven fen, they do not explain how these six days and seven fen constitute the cycle of one hexagram.

Here an attempt is made to explain: Kan, Li, Zhen and Dui are the four cardinal hexagrams (occupying the four directions and representing the four seasons), occupying four positions, and from them are generated Qian, Kun, Gen and Xun. Each position governs a period of time and each line governs one month; this is the arrangement of the four pure hexagrams. Looking further at the six-line compound hexagrams: from Fu to Qian there are six lines spanning six months; from Gou to Kun there are likewise six lines spanning six months. Thus the principle that one line governs one month is quite clear. If “six days and seven fen” is taken as the explanation, the author of the Subcommentary has not thought the matter through carefully.

The so-called “return in seven days” means that when the tenth month is drawing to a close the yin Qi of the Kun hexagram has completed its course, yin Qi recedes and yang Qi is regenerated. Heaven has ten days and yang Qi grows upward; at the stage of “seven” it belongs to lesser yang. Yin and yang generate each other in alternation, and at the moment when yang Qi returns it corresponds to old yin.

When the numbers of yin have run their course, on the seventh day the lesser yang (the newly arising yang Qi (vital energy)) appears.

“Return after seven days” (yang Qi returning after seven days) thus accords with the meaning of the Jing (scripture) and the Zhu (commentary).

On the Center

The Xici says: “Heaven one, Earth two, Heaven three, Earth four, Heaven five, Earth six, Heaven seven, Earth eight, Heaven nine, Earth ten.” These are the generating numbers of the Five Phases (Wuxing). Heaven one generates Water, Earth two generates Fire, Heaven three generates Wood, Earth four generates Metal, Heaven five generates Earth; these are the generating numbers of the Five Phases.

In this way the yang numbers have no pairs and the yin numbers have no pairs, so Earth six is used to complete Water, Heaven seven to complete Fire, Earth eight to complete Wood, Heaven nine to complete Metal, and Earth ten to complete Earth. Thus Yin-Yang each have their mates and the myriad things can take form; they are therefore called the “completing numbers.”

The yang numbers have no pairs and the yin numbers have no pairs, so Earth six is used to complete Water, Heaven seven to complete Fire, Earth eight to complete Wood, Heaven nine to complete Metal, and Earth ten to complete Earth. Thus Yin-Yang each have their mates and the myriad things can take form; they are therefore called the “completing numbers.”

The Xici further says: “The heavenly numbers are five, the earthly numbers are five; the five positions obtain one another, each having its complementary match.” This refers to how the myriad things thereby undergo transformation and change, and the way of ghosts and spirits also operates thereby.

The origin of numbers lies in Yin-Yang; the coming and going transformations of Yin-Yang are manifested in the trajectory of the sun’s movement. From the winter solstice in the eleventh month to the summer solstice ought to be the time of yang Qi growth. The first month belongs to spring, which is the direction of Wood; at this time the sun is at the southern extreme, yang Qi arrives and yin Qi recedes. Winter belongs to Water, and the initial arising of one yang should be taken as the number of Water.

In the fifth month at the summer solstice the sun reaches the northern extreme, yin Qi increases and yang Qi recedes. Summer belongs to Fire, and the initial arising of one yin should be taken as the number of Fire. But yin numbers are not named with odd numbers, so only in the sixth month, when two yins arise, is this taken as the number of Fire. Therefore the Yi says that the Qian hexagram takes the eleventh month as its principal and the Kun hexagram takes the sixth month as its principal; the transformations of Yin-Yang both move to the left. From this it can be known that from winter solstice to summer solstice is the process of yang Qi arriving.

The first month belongs to spring, the direction of Wood; at this time three yangs have already arisen, so three is the number of Wood. After the summer solstice until the winter solstice is the process of yin Qi increasing. The eighth month belongs to autumn, the direction of Metal; at this time four yins have already arisen, so four is the number of Metal. The third month is the end of spring and belongs to Earth; at this time five yins arise, so five is the number of Earth. This is….

Furthermore, the root of the myriad things is generated from primordial Qi, and their manifestation begins from the subtle. When the myriad things form their physical bodies, they must….

The subtle and the manifest form a process of gradual change; the sequential arrangement of the Five Phases (Wuxing: Wood, Fire, Earth, Metal, Water) is likewise regarded as following an order from the subtle to the manifest. Among the natures of the Five Phases, Water is the most subtle and is numbered one; Fire grows gradually more apparent and is numbered two; Wood has acquired a concrete physical form and is numbered three; Metal possesses a solid texture and is numbered four; Earth possesses a vast texture and is numbered five. Such an arrangement may also be considered appropriate. Liu Mu and Gu Jiegang both held that Water, Fire, Wood, and Metal each receive Earth’s number in order to take form, so that Water’s completed number is six, Fire’s seven, Wood’s eight, Metal’s nine, and Earth’s ten. This interpretation likewise has its reasons.

After examining the views of various schools, I hold that designating Heaven-one through Heaven-five as the generating numbers of the Five Phases does not explain by what means they enable the Five Phases to arise; designating Earth-six through Earth-ten as the completing numbers of the Five Phases likewise does not explain by what means they enable the Five Phases to take shape. Scholars therefore often fail to grasp the essential purport. This is because they have not distinguished “image” from “form,” nor clarified the upper and lower levels of the Dao (the Way) and the implement. I shall attempt a brief explanation. The Book of Changes (Yijing) states: “That which is above form is called the Dao; that which is below form is called the implement.” Therefore that which lies above Earth-six belongs to the Dao, and that which lies below Earth-six belongs to the implement.

The four numbers Heaven-one, Earth-two, Heaven-three, and Earth-four merely present the Four Images and have not yet manifested concrete physical forms, and thus belong to the “above-form” Dao. Heaven-five circulates and transforms: matching upward with Heaven-one and generating Earth-six downward, it forms the number of Water; matching downward with Earth-two and generating Heaven-seven upward, it forms the number of Fire; matching rightward with Heaven-three and generating Earth-eight leftward, it forms the number of Wood; matching leftward with Earth-four and generating Heaven-nine rightward, it forms the number of Metal. Earth-ten corresponds with Heaven-five, occupies the center, and is the number of Earth. These numbers have already manifested concrete forms, and thus belong to the “below-form” implement.

As for what is called “image” and “form,” the Book of Changes states: “That which becomes apparent is called the image.” The Hetu (the legendary diagram displaying the numerical principles of Heaven and Earth) is used to present the image; “form” is the implement, and the Luoshu (the legendary diagram presenting the numerical principles of Heaven and Earth) is used to display form. Things rooted in Heaven draw close to the above; things rooted in Earth draw close to the below. Hence it is said: “The Hetu communicates the Qian Dao and issues forth from Heaven; the Luoshu flows with the Kun Dao and is emitted from Earth.” The Book of Changes treats of the Dao and the implement, and therefore the sages took both into account in composing the Changes. The scripture says, “The Yellow River produced the Hetu, the Luo River produced the Luoshu, and the sages modeled themselves upon them,” referring precisely to this matter.

The numbers of the Hetu total only forty-five and do not explicitly indicate Earth’s number. This is because the Hetu is used to present the images of the Eight Trigrams (Bagua); if Earth’s number were also included, it would enter the realm of form-numbers. Thus the Hetu possesses the functions of the Five Phases yet does not display their completing numbers. The Luoshu has fifty-five numbers, used to present the process whereby transformation is completed and form-implements become manifest. Therefore the Hetu arrays the Four Images without discussing the Five Phases, while the Luoshu elaborates the Five Phases without discussing the Four Images.

The Four Images may also be regarded as the completing numbers of Metal, Wood, Water, and Fire: in the Hetu they correspond to the numbers of old yang, old yin, young yang, and young yin; in the Luoshu they correspond to the numbers of Metal, Wood, Water, and Fire. The two differ because the Four Images, combining with Earth’s number, form concrete substantial bodies and thereby become distinguished from the Five Phases; yet both derive from the transformations of Heaven-five.

“The numbers of Heaven are five, the numbers of Earth are five; the five positions obtain one another and each has its combination” refers to the numbers employed in the mutual generation of the Five Phases. Although the Five Phases each have completing numbers, if they have not yet combined with one another there is no basis for mutual generation. Therefore Heaven-one combines with Earth-six to generate Water, Earth-two with Heaven-seven to generate Fire, Heaven-three with Earth-eight to generate Wood, Earth-four with Heaven-nine to generate Metal, and Heaven-five with Earth-ten to generate Earth. Since the time of Fuxi people have merely followed these numbers; only in the era of the Yellow Emperor did they begin to receive names. The original text here contains missing characters.

Some scholars assign the first arising of one yang as the number of Water, the first arising of two yin as the number of Fire, the first arising of three yang as the number of Wood, the first arising of four yin as the number of Metal, and the first arising of five yang as the number of Earth. This account is a strained analogy and is not the natural numerical principle of Heaven and Earth. As for arranging the Five Phases according to the subtle and the manifest, this too is not a comprehensive explanation. Why? If one considers degree of solidity, Earth ought not to be placed after Metal; if one considers degree of vastness, Fire ought not to be placed after Water. The Five Phases each possess their innate natures, arising through incidental pairing and succeeding according to numerical principles; to explain their sequence by means of the subtle and the manifest indeed does not accord with the original intent of the classics.

Furthermore, the first arising of one yang in the eleventh month being termed an odd number means that Heaven-one is set in motion within the Kan trigram; the first arising of one yin in the fifth month being termed an even number means that Earth-two is set in motion within the Li trigram. As for also regarding the first arising of two yin in the sixth month as an even number, one cannot discern the basis for this claim.

Upon a more detailed examination of the accounts in the Yiwei Jilantu and those of Zheng Xuan concerning the “six days and seven parts,” these generally consist in combining the yarrow-stalk numbers of old yang and old yin from the Qian and Kun hexagrams in order to perform the calculation. The Yijing (Book of Changes) states: “The yarrow-stalk number of the Qian hexagram is two hundred and sixteen, that of the Kun hexagram is one hundred and forty-four, totaling three hundred and sixty, which corresponds exactly to the number of days in a year.” The commentaries explain that this refers to an approximate figure that does not take the extra five and one-quarter days into account. There is also a commentary that says: …

Some say that the Zhouyi comprises two parts, upper and lower, with a total of three hundred and eighty-four lines, yin lines and yang lines each constituting half. There are one hundred and ninety-two yang lines, each counted as thirty-six, totaling six thousand nine hundred and twelve; there are likewise one hundred and ninety-two yin lines, each counted as twenty-four, totaling four thousand six hundred and eight. Yin and Yang together amount to eleven thousand five hundred and twenty, symbolizing the number of the myriad things.

The Zhouyi employs the combined number of three hundred and sixty from the old yang and old yin within the Qian and Kun hexagrams to correspond with the days of a year, so there is no need to generate any additional number. As for the numbers of the hexagrams and lines, I do not consider that they ought to be calculated according to the “six days and seven parts” interpretation set forth in the Yiwei (apocryphal texts that explain the Yijing) and by Zheng Xuan. The yin and yang lines total three hundred and eighty-four in all. Although the Yiwei and Zheng Xuan conceal the line numbers of the four cardinal hexagrams Kan, Li, Zhen, and Dui within the number twenty-four in order to make them accord with the days of a year, this nevertheless stands at variance with the scripture of the sages.

Why is this so? A year runs from the zi month to the hai month, comprising twelve months, and therefore the twelve months correspond to the line positions of the twelve hexagrams. These twelve hexagrams are the sequence from the Fu hexagram to the Kun hexagram. How can one take the statements of miscellaneous books and later worthies and thereby violate the original meaning of the twelve hexagrams’ line positions as given in the sages’ scripture? Some say that this is not the case; then how is the Xici (one of the attached commentaries on the Yijing) to be explained?

The Lin hexagram, the eighth month, the forty-seventh.

The Huan hexagram, the forty-eighth.

The Lin hexagram states: “When the eighth month arrives, there will be misfortune.” The Xiang Zhuan (Commentary on the Images) explains that the Lin hexagram symbolizes the gradual increase of yang-firm Qi (vital energy), being harmonious and compliant. A yang line occupies the central position and corresponds with the matching yin line, and therefore it is greatly prosperous and penetrating, which accords with the correct principle of Heaven’s Dao (the Way). The phrase “there is misfortune in the eighth month” means that the tendency of yang Qi to recede will soon become apparent.

Regarding how the “eighth month” is to be calculated, the original text notes that the various commentaries differ, and then proceeds to examine them one by one. Mr. He begins the count from the Jianzi month (the calendrical month that takes the zi month as the start of the year), when yang Qi first arises, and considers it eight months until the Jianwei month. Mr. Chu begins from the Jianyin month and regards it as eight months until the Jianyou month. Kong Yingda’s subcommentary holds that one should count from the Jianchou month, which corresponds to the Lin hexagram, to the Jianshen month, which corresponds to the Pi hexagram, and call this period eight months. The author considers that none of these views fully accords with the meaning of the Lin hexagram: if one counts from the Jianzi month, the wording ought to belong to the Fu hexagram; if from the Jianyin month, it ought to belong to the Tai hexagram; and if one takes the Pi hexagram of the Jianshen month as the eighth month, the receding associated with the six-three line of Pi cannot be made to correspond with the nine-three line of Lin.

The author regards it as more appropriate to take the Jianwei month as the eighth month. At that time the yin line of six-two in the Dun hexagram recedes the yang line of nine-two in the Lin hexagram, so that the relationship of the line positions accords with the hexagram meanings. The Xiang Zhuan of Lin speaks of yang Qi gradually increasing, which commentators explain as the yang Dao progressively advancing while the yin Dao recedes day by day. The Xiang Zhuan of Dun likewise speaks of yin Qi gradually increasing, and commentators say that the yin Dao is about to advance, yet the correct Dao has not yet completely vanished. The two hexagrams have corresponding line positions, and both discuss the gradual growth and decline of Yin-Yang; on this basis the author therefore calls Jianwei the eighth month.

Someone further asks: when King Wen elaborated the hexagram images it was the last years of the Shang dynasty, so how can one employ the first month of the Zhou calendar to interpret the text? The author replies that the Duke of Zhou composed the line statements, completing the work by continuing King Wen’s enterprise, and therefore the line statements frequently involve matters subsequent to King Wen. This shows that King Wen’s thought was narrated and completed by the Duke of Zhou, so that the Zhou calendar is used to determine the months. Moreover, the Yi (Changes) once had different names: in the Xia dynasty it was called the Lianshan, in the Shang dynasty the Guicang, and in the Zhou dynasty the Zhouyi. Naming it “Zhouyi” served to distinguish it from the Yi learning of other ages, and it is the same as the nomenclature used for Zhou ritual institutions. Since it is named Zhouyi, the Duke of Zhou ought to determine the months according to the calendrical system of the Zhou calendar.

The author also notes that Kong Yingda cites Wang Bi’s commentary, which explains the omen of misfortune by “the Dao of the noble person recedes and the Dao of the petty person grows,” and that this need not be restricted to the Pi hexagram alone. When yin Qi increases one may speak of the Dao of the petty person growing; when yang Qi increases one may speak of the Dao of the noble person growing.

Wang’s Gualue (Outline of the Hexagrams) states that the Dun hexagram symbolizes the gradual growth of the Dao of the petty person, with danger within and prosperity without, standing opposite to Lin: when yang-firmness grows in Lin, yin-softness is in danger; when yin-softness grows in Dun, yang-firmness is in danger. Lin has two yang lines occupying the interior, symbolizing the Dao of the noble person growing day by day; Dun has two yin lines occupying the interior, symbolizing the Dao of the petty person developing step by step. Therefore “there is misfortune in the eighth month” serves, at the time when yang Qi occupies its proper and central position, as a prior reminder to remain vigilant against the receding of yang Qi.

According to this account, yang Qi begins to increase from the eleventh month, corresponding to the Fu hexagram, and by the twelfth month corresponds to the Lin hexagram. Yang Qi begins to recede from the fifth month, corresponding to the Gou hexagram, and by the sixth month corresponds to the Dun hexagram. Counting from the zi month to the wei month yields a total of eight months.

Here ends the middle volume of the Yishu Gouyin Tu (Hidden Diagrams of the Numbers of the Changes).

Collation notes: At the first point, the phrase “sun and moon” appears in the original as “moon and sun” and has been corrected on the basis of the Siku Quanshu edition. At the second point a character is missing in the original; the character “east” has been supplied from the Siku Quanshu. At the third point the original reads “must be otherwise”; the Siku Quanshu edition omits the word “must,” leaving “is otherwise.” From the fourth through the eighth points the original has lacunae, and the Siku Quanshu edition has the same gaps. At the seventh point the original has “five yin,” while the Siku Quanshu has “five yang.” At the ninth point the original reads “does not speak,” which has been changed to “does not manifest” following the Siku Quanshu. At the tenth point “Master Zheng” refers to Zheng Kangcheng (the Eastern Han classicist Zheng Xuan); the original writes only “Zheng,” and the honorific shi has been added according to the sense of the passage. At the eleventh point the character “yang” was missing in the original and has been inserted from the Siku Quanshu. At the twelfth and thirteenth points the original has missing text which the Siku Quanshu edition likewise does not restore.

Lower volume of the Yishu Gouyin Tu. The forty-ninth diagram is the Hetu (Yellow River Chart). The fiftieth treats the numbers of Heaven and Earth in the Hetu. The fifty-first treats the numbers of the Four Images in the Hetu. The fifty-second treats the Bagua (Eight Trigrams) of the Hetu. The fifty-third treats the generating numbers of the Five Phases in the Luoshu (Luo River Writing).

Someone asked: “The Luoshu (Luo Writing) says that one is Water, two is Fire, three is Wood, four is Metal, and five is Earth. This differs from the pairing of the numbers of the Five Phases (Wuxing) with the directions in the Longtu (Dragon Chart). Why is that?”

The reply was: “What is listed here are the generating numbers of the Five Phases. Although they are spoken of as generating numbers, they are already the numbers after combination. The following section will discuss Earth ruling the four seasons (that is, Earth having periods of governance in each of the four seasons), at which time the complete completing numbers will be set forth. Both the Luoshu and the Nine Categories (the legendary nine great methods of governing the state) are deduced from the numbers of the Five Phases, so the generating numbers after combination are first listed and then supplemented with the Earth numbers, in order that the completing numbers of the Five Phases may be seen.”

The numbers of the Five Phases paired with the ten Heavenly Stems days and their relationships of generation are as follows: Heavenly One is paired with Earthly Six, Earthly Two with Heavenly Seven, Heavenly Three with Earthly Eight, Earthly Four with Heavenly Nine, and Heavenly Five with Earthly Ten; these numbers combining form Water, Fire, Wood, Metal, and Earth. The “ten days” spoken of here refer to the yang days. “Generation” means Metal generates Water, Water generates Wood, Wood generates Fire, Fire generates Earth, and Earth generates Metal; “conquest” means Metal conquers Wood, Wood conquers Earth, Earth conquers Water, Water conquers Fire, and Fire conquers Metal.

The Book of Changes says: “A dragon-horse appeared in the Yellow River bearing the Chart, a divine turtle appeared in the Luo River bearing the Writing, and the sages modeled themselves upon this.” The Chunqiu wei (apocryphal texts on the Spring and Autumn Annals) says: “The Yellow River communicates with the way of Qian, revealing the omens of Heaven; the Luo River flows with the way of Kun, emitting the auspicious signs of Earth.” When the dragon-horse appeared, the Hetu (River Chart) was thereby manifested; when the divine turtle responded, the Luoshu thereby emerged.

The Yijing says: “A chart appeared in the Yellow River and a writing appeared in the Luo River; the sages acted in accordance with them.” The Chunqiu Wei states that the Yellow River communicates with the Heavenly Dao and thus manifests heavenly omens, while the Luo River bears the Earthly Dao and presents earthly auspicious signs; the dragon chart appeared in the Yellow River, and the turtle writing emerged from the Luo River. The Hetu comprises nine chapters, and the Luoshu six chapters.

The Shangshu Zhengyi explains that the Luoshu is divided into nine categories, each possessing writing, and these writings constitute the book; the Shangshu further says “Heaven bestowed it upon Yu,” referring to the Luoshu. In the Han dynasty’s Wuxingzhi, Liu Xin held that Fuxi inherited the Heavenly Mandate to become king, a chart appeared in the Yellow River, and Fuxi drew the Bagua (Eight Trigrams) according to it; when Yu regulated the floods, Heaven bestowed the Luoshu, and Yu arranged the Hongfan according to it. Kong Yingda shared this view.

However, the original text of the Shangshu does not mention a divine turtle bearing the Luoshu. The Zhonghou and various weishu frequently recount how the Yellow Emperor, Yao, Shun, Yu, Tang, King Wen, and King Wu obtained the charts and writings, speaking of a dragon carrying the chart and a turtle carrying the writing. The authors of the weishu are unknown, and scholarly research suggests these texts arose around the reigns of Emperor Ai and Emperor Ping. Even so, earlier scholars must have transmitted related traditions, which is why Kong Anguo interpreted the nine categories of the Hongfan as a divine turtle appearing with writings arranged on its back, numbered from one to nine; Yu, seeing these, sequentially organized them into nine categories. Once arranged and implemented, the constant Dao acquired its order. It is attributed to Yu’s arrangement because the words of heavenly spirits ought to be concise and should not enumerate sequences in such detail with repeated exhortations; thus the order was compiled by Yu.

After Yu received the nine categories, the constant Dao obtained a definite sequence. Yet prior to the appearance of the Luoshu, the constant Dao was not in disarray: ages differ in simplicity and sophistication, teachings vary in brevity and thoroughness; even before the Three Sovereigns, when there was no writing, society could still be ordered. Hence one cannot claim that the constant Dao existed only after the Luoshu appeared. Rather, once the nine categories were obtained, following them brought order and violating them brought chaos.

The original form of the Luoshu can no longer be known with certainty. Words conveying Heaven’s will must be succinct and need not originally have possessed itemized sequences. The Shangshu Zhengyi states that Yu arranged them accordingly, so the twenty-eight characters beginning “the first is... the next is...” were likely added by Yu. As for the eighteen characters such as “reverently employ” and “industriously employ,” Elder Liu and Master Gu regarded them as the writings on the turtle’s back, while Younger Liu considered them also arranged by Yu. Whether the turtle’s back bore only twenty characters or additional writing lacks clear evidence, so both views may stand.

Examining the discussions of the various schools, many fail to accord with the original intent of the classics. Following the overall thread, the nine categories of the Hongfan ought to be Yu’s arrangement of the Luoshu into sequential order and formulation as a standard, not a divine turtle bearing a book in the age of Yu. Why so? In the Hongfan chapter of the Shangshu, Jizi states: formerly, when Gun regulated the waters, the Five Phases (Wood, Fire, Earth, Metal, Water) fell into disorder, the Lord on High was angered and did not bestow the nine domains of the Hongfan, so the constant Dao lost its order; after Gun was put to death, Yu succeeded him, and Heaven then bestowed the nine domains of the Hongfan upon Yu, establishing the constant Dao. This classic text records no divine turtle bearing charts and writings. Only Kong Anguo’s commentary claims that Heaven granted Yu the Luoshu, a divine turtle appearing with writings arranged on its back numbered to nine. Later Confucians elaborated the wording and character counts of this heavenly book, transmitting the notion that Yu personally received the Luoshu and listed the nine categories from it.

Among the classics, only the Xici of the Yijing mentions the charts and writings: “A chart appeared in the Yellow River, a writing in the Luo River; the sages acted in accordance with them.” This is Confucius speaking of the composition of the Yi. Thus the Hetu and Luoshu must have appeared in the time of Fuxi. In antiquity a dragon chart emerged from the Yellow River and a turtle writing from the Luo River; Fuxi drew the Bagua from them and then doubled the trigrams to form the sixty-four hexagrams. Subsequently King Wen composed the hexagram statements, the Duke of Zhou the line statements, and Confucius added the Ten Wings, whereupon the Dao of the Yi became clear.

The dragon chart circulating today contains nine positions embracing the Four Images and the Bagua; its horizontal and vertical arrangements also correspond to the natural numerical principles of Heaven and Earth, unlike something fabricated by later generations. The dragon chart reveals hexagram images that only a sage could draw; the hexagrams contain the principles of all things, which only a sage could elucidate. From this it follows that the Luoshu did not appear only in Yu’s era.

When the Shangshu says “Heaven bestowed the nine domains upon Yu,” it means Heaven endowed Yu with sagely De (Virtue/Power), enabling him truly to comprehend the principles of the Luoshu, which he then arranged in sequence and transmitted as a norm for later generations. Tradition holds that the Hetu’s numbers from one to nine encompass the meanings of the Four Images and Bagua as well as the numbers of the Five Phases; the Luoshu embodies solely the generative numerical principles of the Five Phases. In Fuxi’s time he merely drew the trigrams to instruct the world, and the numerical principles of the Five Phases were not yet fully revealed, so Yu further set forth the Five Phases and made the nine categories manifest.

The current Confucian claim that Yu received the Luoshu inscribed with the speech of heavenly spirits and specific character counts is not well-founded. When did Heaven ever speak? A sage follows Heaven’s intent and would not act according to a heavenly book filled with verbiage.

Some argue the matter remains unsettled and should be verified against the classics. Yao appointed nine officials, each overseeing one function; the contents of the nine domains correspond precisely to those official duties. “Industriously employ the eight policies” concerns offices such as the Minister of Works and Minister of Education, already established in the times of Yao and Shun; “harmoniously employ the five regulators” refers to the calendar already determined by the Xi and He families. These institutions therefore did not wait upon Yu’s receipt of the Luoshu.

Heaven displays omens which the sage observes and models; when the Hetu and Luoshu appear, the sage likewise follows them. Although celestial images convey meaning, a great sage is still required to understand them; likewise only Fuxi could render the Hetu and Luoshu into hexagram images, only King Wen could expound their hexagram meanings, and only the Duke of Zhou could clarify the line images. Confucius said, “King Wen has passed away, yet is not the cultural heritage still here with me?” and “Heaven has endowed me with this De.” Thus Heaven grants sages intelligence and wisdom so that they may secretly fathom subtle principles—this is called a “Heavenly bestowal.” The Zhonghui zhi Gao states “Heaven bestowed courage and wisdom upon the ruler,” likewise meaning Heaven confers De upon the sage so that he may rectify and govern the myriad states.

Kong Anguo, taking Jizi’s words “Heaven bestowed the nine domains upon Yu,” concluded this referred to a turtle writing appearing in the Luo River, without considering that “a chart from the Yellow River and a writing from the Luo River, which the sages followed” concerns events prior to the making of the Yi. Moreover, the regulations of the nine domains were already in force before Yao and Shun, so to claim that the constant Dao was first established only after Yu received the Luoshu is likewise untenable.

Isn't Shu (here possibly a person's name or a form of address) about to be falsely accused before long?

Discussion, Part Two

The Chunqiu Wei, Han-dynasty apocryphal texts that interpret the Spring and Autumn Annals, states that the Luo Shu comprises six chapters. Kong Shi said that the Luo Shu appeared as writing borne on the back of a divine turtle, with patterns arrayed on its shell and numbers ranging from one to nine. The turtle writings circulating today merely collect the numbers of generation and completion of the Five Phases (wuxing); it is uncertain which account is correct. I shall attempt a brief discussion.

Although the Chunqiu Wei mentions six chapters of the Luo Shu, it does not explain how they correspond to the numbers of the Five Phases or the Nine Categories of governance, nor does it clarify their meanings. The one-through-nine that Kong Shi associated with the Luo Shu refers to the Nine Categories of the Hong Fan in the Book of Documents, running from the first item “Five Phases” through the five blessings and six extremities, totaling nine items. Of these, only the Five Phases belong to the numbers that encompass the natural order of heaven and earth; the remaining eight were classified and established by Yu the Great with reference to heavenly seasons and human affairs, and were not original writings on the divine turtle’s back.

A close examination of the Hong Fan Five Phases Tradition shows that discussions of disasters and anomalies invariably take the Five Phases as their foundation. The Book of Documents further records that Gun, acting contrary to sagely virtue, disordered the sequence of the Five Phases, so that the constant way fell into disarray. From this it is clear that the Five Phases are the natural numbers manifested by Heaven, their writing borne forth by the divine turtle, while the remaining eight items were Yu’s own extensions and elaborations. The case is analogous to the Dragon Chart, which displayed only the Four Images and the eight fundamental trigrams; Fuxi later observed the heavens above and the myriad things below and, following the natures of things, expanded them into the sixty-four hexagrams expressed through the images of the lines.

The Five Phases contain natural qualities, while the Bagua (Eight Trigrams) present natural forms. Sages extrapolated transformations from these, classified them separately, and thereby determined auspiciousness and inauspiciousness. Consequently the turtle writings now in circulation are not empty talk. Remaining doubts can be resolved through further analysis.

One may ask why, if both the He Tu and Luo Shu appeared in Fuxi’s time, the Nine Categories were not already set forth then, yet are said to have been arranged by Yu. The He Tu and the Bagua reveal forms and can therefore display their positions directly, whereas the Luo Shu and the Five Phases contain qualities that require writing in order to distinguish the various classes. In Fuxi’s age the people were simple and writing had not yet arisen, so the Nine Categories could be conveyed only as numbers, not as texts. Only with Yu were they elaborated into nine classes that served as a standard for later generations; thus the Nine Categories took shape beginning with Yu.

A further question is why the turtle writing is still needed if the Dragon Chart already contains the Five Phases. Although the Dragon Chart includes the Five Phases, it possesses only the central position and lacks the number for Earth; its total of forty-five presents forms without specifying the individual numbers of the Five Phases, merely illustrating the principles of the Four Images and the Bagua. The turtle writing, by contrast, supplies the complete numbers of generation and completion of the Five Phases, totaling fifty-five. Because the Yi encompasses both form and concrete particular, the sages composed it on the basis of the He Tu and Luo Shu.

It may also be objected that the Book of Documents states Heaven granted Yu the Hong Fan Nine Categories, which must therefore be the Luo Shu, so that the present interpretation is mere conjecture. Confucius, however, located the appearance of the Chart from the Yellow River and the Writing from the Luo before Fuxi delineated the Yi; they cannot be postponed until the time of Xia Yu. Were the Luo Shu to have emerged only then, the Nine Categories would have been absent before Yu, yet the Canon of Yao already records the nine classes of government with perfect clarity.

Finally, some may regard the Dragon Chart and turtle writings now current as unattested in the classics and unexplained in the weishu, hence probably fantastic. Yet although they are not written in the jing, they have been transmitted from generation to generation by former worthies. Their numbers, images, and directional placements correspond exactly, the hexagrams match without surplus or deficit, and they accord with natural law in a manner that human wisdom could not invent. Moreover, Yin-Yang (yinyang) learning throughout the ages has largely rested upon them; they enable one to fathom the potency of the spiritual and to penetrate the principles of heaven and earth, yielding verifications as immediate as echo answering sound or shadow following form. How then can they be dismissed as empty invention?

The lower volume of the Yishu Gouyintu comes to a close. In collating the text, the phrase “as the knee” is given in the Siku Quanshu edition as “as the foot.” The expression “tied to Heaven” stands as such in the original and has been emended according to the Siku edition. After the words “thereafter,” several characters are missing from the base text, and the Siku edition shows the same lacuna. The graph “ji” (to calculate) is, judging by the sense of the passage, suspected to be an error for “ji” (already). The compound “huan xiang” appears identically in the Siku edition. After “Xi Huang,” a number of characters are wanting in the base text, as they are in the Siku edition. After “the sixty-four hexagrams,” several sentences are lacking in both the base text and the Siku edition; the same omissions occur after “heavenly images then,” after “to make it clear,” and after “yuan nai.” The phrase “of the Canon of Yao” originally read “Yao’s Canon,” and the word order has been adjusted on the testimony of the Siku edition.