《易數鉤隱圖》

The first volume of Yishu Gouyin Tu explains the process by which the Supreme Ultimate (Taiji, the cosmic origin) gives rise to all phenomena in heaven and earth. Initially, the Supreme Ultimate is an undifferentiated mass of primordial Qi (vital energy), without form or numerical distinction. This Qi then divides into the two modalities (Liangyi) of Yin and Yang: the light, pure Yang Qi ascends to form heaven, while the heavy, turbid Yin Qi descends to form earth. At this stage, though heaven and earth are separate, they have not yet fully intermingled.

When the two Qi of Yin and Yang begin to interact, the heavenly Yang Qi descends to produce water (represented by the number one), while the earthly Yin Qi ascends to produce fire (represented by the number two). This marks the beginning of physical forms in the myriad things. Subsequently, through the numerical correspondences of "heaven three, earth four," and the completion of the Five Phases (Wuxing)—Wood, Fire, Earth, Metal, and Water—the concrete manifestations of living beings and objects emerge. Here, it is emphasized that the "two modalities" refer to the fundamental principles of heaven and earth, while "heaven and earth" themselves are the tangible expressions of these two modalities.

The number five holds a special place in this system. It does not belong to the foundational four images (heaven one, earth two, heaven three, earth four) that generate the myriad things but instead represents the harmonizing Qi at the center, which governs transformation. This Qi is indefinable yet capable of balancing the energies of heaven and earth, facilitating the characteristics of the Five Phases, and permeating all phenomena. When the three fundamental forces of heaven, earth, and humanity are complete, this mysterious power withdraws into concealment, manifesting as the unfathomable subtlety of Yin and Yang.

Finally, the text explains why the numbers of heaven and earth total fifteen: the sum of the foundational numbers one through five is fifteen, encompassing all possible transformations needed to generate the Eight Trigrams (Bagua). Only through the dynamic interplay of three and five, combined with the mature numbers seven, eight, nine, and six, can the complete system of the Eight Trigrams ultimately unfold.

This passage explains the generative numbers of heaven and earth in ancient numerology and their patterns of transformation. The total generative number of heaven and earth is fifteen, comprising the celestial numbers from one (Heavenly One) to five (Heavenly Five). The sum of the odd celestial numbers one, three, and five is nine, representing the Yang number, hence the Qian (Heaven) trigram uses nine. The sum of the even terrestrial numbers two and four is six, representing the Yin number, thus the Kun (Earth) trigram uses six. When combined with the completed number of the Five Phases (Metal, Wood, Water, Fire, Earth), which is forty, the total becomes fifty-five—the supreme numerical combination between heaven and earth that can deduce transformations and comprehend spiritual mysteries.

The specific pattern of numerical generation operates as follows: the Heavenly One generates below to produce the Terrestrial Six in the fifth position; the Terrestrial Two generates above to produce the Heavenly Seven in the sixth position; the Heavenly Three generates leftward to produce the Terrestrial Eight in the seventh position; and the Terrestrial Four generates rightward to produce the Heavenly Nine in the eighth position. Through the coordinated transformations of three (odd) and five (even), intricate numerical combinations form the patterned veins of heaven and earth. Exhaustive study of these numbers determines all phenomena under heaven. Here, "can" (参) refers to the union of odd numbers, while "wu" (伍) denotes the pairing of even numbers. For instance, the Heavenly Five paired with the Heavenly One generates the Terrestrial Six—through such alternating transformations emerge the numerical foundations of the Four Symbols (Lesser Yang, Greater Yang, Lesser Yin, Greater Yin) and the Eight Trigrams.

Regarding the interpretation of "the Two Forms (Yin-Yang) generate the Four Symbols," traditional commentaries suggest that Metal, Wood, Water, and Fire emerge from heaven and earth, hence the expression, while Earth disperses throughout the four seasons. However, the author critiques this view, arguing that Metal, Wood, Water, and Fire are concrete substances that cannot properly be called "symbols." Alternative interpretations identify the Four Symbols as the substantial, provisional, conceptual, and functional symbols within the sixty-four hexagrams. The author maintains that these four aspects (heaven-born spiritual things, cosmic transformations, celestial manifestations, and the Hetu-Luoshu diagrams) represent functions beyond the Yijing system itself—they do not belong to the internal content of the Classic of Changes.

This passage primarily elucidates ancient methods of deducing cosmic patterns through numerical calculations, emphasizing the mathematical relationships of odd-even pairing and Yin-Yang transformations, while also offering critical corrections to traditional annotations.

This passage examines two distinct interpretations of the "Four Images" (四象) concept in the Book of Changes (易经). It first clarifies that "Four Images" carries dual meanings: The first refers to the four states of Yin-Yang transformation derived from the Two Modes (两仪) - Old Yang (represented by 9), Young Yin (8), Young Yang (7), and Old Yin (6). These numerical representations of shifting cosmic forces form the foundation for generating the Eight Trigrams (八卦). The second meaning denotes four symbolic categories used in the Book of Changes to demonstrate universal transformations: fortune/misfortune (symbolizing gain/loss), regret/hesitation (symbolizing anxiety), change/transformation (symbolizing advance/retreat), and firm/yielding (symbolizing day/night).

The text criticizes scholars who conflate these two interpretations, particularly targeting Kong Yingda and others whose commentaries mistakenly equated the numerical Four Images (7-8-9-6) with the symbolic categories. This confusion represents a significant misunderstanding. The passage also discusses the mystical numerical arrangement in the River Chart (河图), where the number 45 follows a specific pattern: five occupies the central position, harmonizing with the four directional numbers to create the pattern of "Heaven and Earth in harmonious interaction" (天地交泰).

Regarding the formation of the Eight Trigrams, the text explains that the hexagrams Kan (坎), Li (离), Zhen (震), and Dui (兑) occupy the proper positions of the Four Images, while the number five remains positionless yet knowable through these four configurations. The commentary ultimately emphasizes that the four symbolic categories mentioned in the Great Treatise (系辞传) - gain/loss, anxiety, advance/retreat, and day/night - constitute the authentic "Four Images" corresponding to hexagram statements, not the numerical representations of Yin-Yang states.

This passage primarily discusses the relationship between the Eight Trigrams (Bagua) and the generative numbers of the Five Phases (Wuxing), as well as the distinction between the numbers of Heaven-Earth and the Great Expansion (Dayan) number.

Regarding the generation of the Eight Trigrams: Water corresponds to the Kan trigram (north) with the number six, generating the Qian trigram; Metal corresponds to the Dui trigram (west) with the number nine, generating the Kun trigram; Fire corresponds to the Li trigram (south) with the number seven, generating the Xun trigram; Wood corresponds to the Zhen trigram (east) with the number eight, generating the Gen trigram. Thus, the Four Symbols (sixiang, four cardinal directions) generate the Eight Trigrams.

Concerning the numbers of Heaven-Earth: The sum of celestial and terrestrial numbers totals fifty-five, derived from the generative numbers of the Five Phases in the Luo River Chart (Luoshu, ancient mystical diagram). Among these, fifteen represents the fundamental operational number of cosmic movement, nine and six represent the transformations of Yin-Yang, combined with the forty numbers of the Five Phases, totaling fifty-five—the complete numerical system governing cosmic operation.

The Great Expansion number is fifty, five less than the Heaven-Earth number. This is because the "celestial five" (central Earth number), while existing, is not directly employed—it governs and coordinates the other four symbols (Water, Fire, Wood, Metal). Just as one, two, three, and four are generative numbers, the celestial five operates through these to form the completed numbers seven, nine, six, and eight. Thus, the Great Expansion's fifty represents practical application, while the Heaven-Earth's fifty-five represents theoretical completeness.

This content reflects Daoist understanding of cosmic numerology, where numbers signify not merely quantity but embody the principles of cosmic operation. The concept of "the celestial five being unused" exemplifies the Daoist principle of "governing through non-action" (wuwei)—what appears unused actually plays a pivotal role.

This passage discusses the symbolic significance of using 49 yarrow stalks (a divination tool) in Zhouyi (Book of Changes) divination, rather than the full set of 50.

Ancient sages believed the total number representing cosmic operation was 50 (the "Great Expansion Number Fifty"), yet only 49 stalks were actually used in practice. Various schools offered different interpretations: Han Kangbo considered the unused one as representing "Taiji" (Supreme Ultimate), the origin of all things; Jing Fang associated the 50 with the combined tally of the Ten Heavenly Stems, Twelve Earthly Branches, and Twenty-Eight Lunar Mansions, with the unused stalk symbolizing "generative Qi" (life energy); Ma Rong identified the motionless "one" as the North Star, while the remaining 49 represented the movements of the sun and moon; Xun Shuang derived the 50 from calculations based on the six lines and eight trigrams, with the unused stalk corresponding to the "hidden dragon" line in the first nine of the Qian hexagram; Zheng Xuan proposed subtracting the Five Phases (Wood, Fire, Earth, Metal, Water) from the total heaven-earth number 55, then deducting one more to arrive at 49.

The core idea is that deliberately leaving one stalk unused embodies "substantial reality" through "emptiness"—using the visible 49 stalks to deduce the invisible patterns of heaven and earth. This unused "one" symbolizes either the cosmic origin (Taiji) or the governing principle (North Star). Though not directly involved in calculations, it forms the philosophical foundation of the entire divination system. While interpretations vary, all traditions agree this "unused one" carries profound metaphysical significance.

This passage discusses the relationship between the Taiji (Supreme Ultimate) concept in the Zhouyi (Book of Changes) and numerical calculations. It first points out that while Taiji is recognized as the cosmic origin, its precise derivation remains unclear. From Taiji emerges the Two Modes (Yin-Yang), whose differentiation produces the heavenly number one, followed by the Four Symbols and the Five Phases (Wood, Fire, Earth, Metal, Water). The sum of these numbers equals fifty-five, considered the ultimate number of heaven and earth.

If one regards Taiji as an abstract "one" representing nothingness, then the Dayan number (used for divination) should be fifty-four. However, this leaves the remaining five unaccounted for. Moreover, since the Dayan number derives from calculations of heaven and earth's numerical patterns, it clearly belongs to the post-creation phase of the cosmos. Therefore, Taiji cannot be simplistically equated with a void "one."

In truth, Taiji represents the primordial Qi (vital energy) in its undifferentiated unity—already manifesting signs of existence rather than pure nothingness. The text critiques Han Kangbo's (a Jin dynasty Yijing scholar) commentary as overly pedantic, suggesting he may have misunderstood Wang Bi's (a Three Kingdoms period metaphysician) original intent. The Yijing explicitly states "In Change there is Taiji," where the word "has" (you) confirms Taiji's substantial nature rather than nothingness.

The subsequent discussion examines the relationship between heaven-earth numbers and Five Phases numerology: while fifteen numbers pertain to internal heaven-earth patterns, forty belong to external Five Phases operations, yet only forty-nine are practically used. This is because the heavenly five (the numeral five among the Five Phases) represents the inception of transformation—dispersed throughout the phases without fixed form. The heavenly one (numeral one) symbolizes all things' origin, serving as the unchanging sovereign of creation that resides in the honored position without movement, embodying the function of heavenly De (Virtue/Power) through the number nine.

This passage explains the principle of numerical interactions between Yin and Yang in the Book of Changes (Yijing). The number of Heaven (Qian) is three, representing Yang, while Earth (Kun) combines the numbers two and four to make six, representing Yin. Although Earth’s principle does not initiate creation on its own, it complements Heaven to complete transformation. The Yang number three can encompass the Yin number six, and together they form nine, the ultimate Yang number, achieving numerical transformation through the cyclical movement of the Five Phases (Wuxing).

Someone might ask: The Yijing states that the Kun hexagram uses the number six, but if Qian’s three incorporates Kun’s six, doesn’t that render the six redundant? The answer is no—the six is inherently included. The Yijing often uses the greater number to encompass the lesser. When nine is mentioned, six is naturally implied. It’s like using nine when Yang advances and six when Yang recedes. Similarly, when calculating dates, the focus is on the numbers of old Yin and old Yang, while the numbers of young Yin and young Yang are already contained within. This is the Yijing’s conventional mode of expression.

The numerical combinations are further explained: Old Yang is the sum of four nines (36), young Yang four sevens (28), old Yin four sixes (24), and young Yin four eights (32). The Qian hexagram uses three Yang lines (odd numbers for Yang), while the Kun hexagram uses three Yin lines (even numbers for Yin). By arranging these odd and even numbers, the sequence of Yin and Yang can be determined.

Finally, Han Kangbo’s commentary is cited to illustrate the nature of the Dao (the Way): The Dao itself is formless and without appearance (Wu, "non-being"), yet it permeates all things. Though Yin and Yang differ in nature, they are unified in this root of "non-being." By observing transformation, one can perceive the divine mystery (Shen), and through this mystery, grasp the essence of the Dao. Though Yin and Yang manifest differently, they both follow a single, unifying principle.

This passage explains how the interaction of Yin-Yang and the Five Phases generates all things in existence. Yin and Yang must cooperate to produce effects—neither can create the myriad things in isolation. What we call the "Dao" refers precisely to this principle of Yin-Yang union that gives birth to all phenomena.

Heaven and Earth themselves represent pure Yang and pure Yin respectively: Heaven is pure Yang (solitary Yang), while Earth is pure Yin (solitary Yin). However, when examining the Five Phases (Water, Fire, Wood, Metal, Earth), each element embodies the fusion of both Yin and Yang Qi. For example:

• Heaven's One (Yang) combines with Earth's Six (Yin) to generate Water
• Earth's Two (Yin) combines with Heaven's Seven (Yang) to generate Fire
• Heaven's Three (Yang) combines with Earth's Eight (Yin) to generate Wood
• Earth's Four (Yin) combines with Heaven's Nine (Yang) to generate Metal
• Heaven's Five (Yang) combines with Earth's Ten (Yin) to generate Earth

Earth holds a unique position—it has no fixed form and disperses across the four seasons. The Earth itself consists of pure Yin Qi and cannot generate things alone; it must unite with Heaven's number Five (Yang Qi) to form Earth as one of the Five Phases. Thus, while the Earth represents pure Yin, the Phase of Earth contains both Yin and Yang energies.

Finally, humans too are born by receiving the Qi of the Five Phases. The Yijing (Book of Changes) encompasses all phenomena precisely because it contains both the laws of Heaven's Dao and the principles of human affairs. From the Yin-Yang of Heaven and Earth to the generation of the Five Phases, and further to human endowment, this reveals a complete cosmological system of creation.

This scripture elucidates the relationship between the Three Powers (Heaven, Earth, and Humanity) and the Five Phases (Wood, Fire, Earth, Metal, Water). The Dao of Earth encompasses the Three Powers, with each power possessing both Yin and Yang aspects, resulting in six transformative states. These six transformations fundamentally represent the operational principles of the Three Powers.

The Dao of the Three Powers manifests in upper, middle, and lower positions, yet its functioning relies entirely on the Five Phases. Human life follows the same pattern: externally dependent on the material conditions provided by the Five Phases, while internally embodying their inherent qualities. Each phase corresponds to a specific virtue: Wood governs benevolence, Fire governs propriety, Earth governs sincerity, Metal governs righteousness, and Water governs wisdom.

Humans, with their round heads and square feet (symbolizing the round Heaven and square Earth), stand as the most spiritually endowed beings between Heaven and Earth precisely because they embody these Five Phase virtues. Even the most dull-witted individuals unconsciously employ the functions of the Five Phases in daily life. Yet when one's inner clarity becomes obscured and fails to follow the teachings of the Five Constants (benevolence, righteousness, propriety, wisdom, and sincerity), it becomes truly lamentable.

(Note: The "Three Powers" refer to the three fundamental elements of Heaven, Earth, and Humanity; the "Five Phases" represent the five basic elements in ancient Chinese philosophy that constitute all phenomena, each corresponding to specific attributes and virtues; the "Five Constants" denote the Confucian five cardinal moral principles.)

This passage explains the fundamental principles of the Bagua (Eight Trigrams) generation and transformation in the Yijing (Book of Changes). It first employs familial relationships as metaphors for the trigrams: Qian (Heaven) resembles the father, Kun (Earth) the mother, whose interaction gives birth to six offspring trigrams. Zhen (Thunder) is the eldest son (first acquired Yang line), Xun (Wind) the eldest daughter (first acquired Yin line); Kan (Water) is the middle son (second acquired Yang line), Li (Fire) the middle daughter (second acquired Yin line); Gen (Mountain) is the youngest son (third acquired Yang line), and Dui (Lake) the youngest daughter (third acquired Yin line). This arrangement illustrates the natural interaction of Heaven and Earth and the generative principle of all things.

The text then explains how the eight trigrams evolve into sixty-four hexagrams. The Taiji (Supreme Ultimate) generates the two polarities of Yin and Yang, which in turn produce the four images (lesser Yang, greater Yang, lesser Yin, greater Yin), and these four images give rise to the eight trigrams. The overlapping of trigrams forms the sixty-four hexagrams, encompassing all possible transformations of the lines. The Fu hexagram (Earth over Thunder) marks the beginning of the sixty-four hexagrams, symbolizing the nascent Yang energy. It emerges from Kan (Water), activates through Zhen (Thunder), and interacts with Kun (Earth). Through two cycles of Zhen, two of Dui, and two of Qian, the progression from Fu to Qian spans six months, demonstrating the ascent of Yang energy. Conversely, the Gou hexagram (Heaven over Wind) originates from Li (Fire), dissipates beneath Xun (Wind), and interacts with Qian (Heaven). Through two cycles of Xun, two of Gen, and two of Kun, the transition from Gou to Kun also takes six months, illustrating the growth of Yin energy.

These transformational patterns follow inherent principles. The four cardinal trigrams (Kan, Li, Zhen, Dui) demarcate the positions of the four seasons and twelve months, while the addition of Qian, Kun, Gen, and Xun fully manifests the transformations of Heaven, Earth, and all phenomena. The application of overlapping hexagrams (sixty-four) precisely emulates these laws of natural transformation.

This scripture primarily discusses the correspondence between the hexagrams of the Book of Changes (Yijing) with time and space, as well as the special significance of the "Returning Maiden" hexagram (Guimei).

First, it explains how the twelve hexagrams correspond to the twelve months, with each hexagram's six lines totaling seventy-two lines that match the seventy-two pentads (ancient five-day periods used in calendrical calculations). The Li hexagram (Fire) and Kan hexagram (Water) represent the Yin-Yang of heaven and earth respectively, with the area east of the meridian line being Yang and west being Yin. All sixty-four hexagrams with their three hundred and eighty-four lines exhaustively encompass the Dao of the Three Powers (heaven, earth, and humanity).

A question is raised: The Fu hexagram (Earth over Thunder) emerges from the center of the Kan hexagram, with thunder stirring within the Kun hexagram, aligning with the Yijing's statement "thunder within the earth." However, the Gou hexagram (Heaven over Wind) originates from the Li hexagram, dissipates in the Xun hexagram, and intersects with the Qian hexagram. Though the Yijing states "wind beneath heaven," the Xun hexagram is not one of the four cardinal hexagrams (Kan, Li, Zhen, Dui), making it different from the Fu hexagram. Why does the Gou hexagram's imagery show Xun supporting Qian, yet in transformations it takes its symbolism from the Dui hexagram?

The answer lies in the symbolic meaning of the "Returning Maiden" hexagram (Guimei). The Yijing states that this hexagram embodies the great meaning of heaven and earth, for without their interaction, all things would not be born. The Returning Maiden hexagram depicts a young maiden (Dui) marrying an elder brother (Zhen), but with the elder sister (the eldest daughter, Xun) presiding over the marriage. This shows the younger sister's marriage is not as the primary wife but follows the ancient "niece and younger sister" accompanying marriage custom. While a union between an elder brother and eldest sister represents the proper way of husband and wife, it cannot widely extend progeny. Thus, what can endure must be the Returning Maiden hexagram—this is the principle behind hexagram transformations.

Finally, it discusses the "Three Powers" (Sancai, heaven-earth-humanity), criticizing earlier interpretations that arbitrarily used solid and broken lines to represent Yin-Yang energies and three positions to symbolize the Three Powers, neglecting careful study of the Great Treatise's (Xici) original intent. In truth, the eight trigrams manifest natural phenomena revealed by heaven. The sages derived inspiration from the River Chart (Hetu) and Luo Writings (Luoshu), observing heaven and earth's odd and even numbers to delineate the trigrams—they were not created arbitrarily.

The Book of Changes uses three lines to form a trigram, adopting the natural odd and even numbers formed by heaven and earth. The three lines of the Qian hexagram (representing heaven) symbolize heaven's odd number "three," hence depicted as three solid lines; the three lines of the Kun hexagram (representing earth) symbolize earth's even number "three," also drawn as three broken lines. The remaining six trigrams are all derived from Qian and Kun, sharing the same structure, so they too are composed of three lines.

Heaven is pure Yang, earth is pure Yin, yet pure Yang or Yin alone cannot generate the myriad things. Only when the qi of heaven and earth combines with the numerical principles of the Five Phases (Wood, Fire, Earth, Metal, Water) can living creatures and plants come into being. Thus the classic states, "Only after heaven and earth exist can the myriad things be born." Could it be that within this primordial qi already lies the principle of the Three Powers (heaven, earth, and humanity)? The phrase "combining the Three Powers and doubling them" refers to the sage's profound intention in stacking the trigrams, not merely speaking of the eight basic trigrams. The Three Powers are heaven, earth, and humanity, while "doubling" means to stack or overlap.

In the six-line hexagram: the top two lines represent heaven, the middle two represent humanity, and the bottom two represent earth. Because humans are born from the fusion of heaven and earth's qi, they dwell between them. This explains why the second yang line (九二) states "seeing a dragon in the field" to elucidate earth's way, while the fifth yang line (九五) says "a flying dragon in heaven" to clarify heaven's way. This principle is perfectly clear.

For verification, consult the Commentary on the Appended Judgments: "The changes of the six lines embody the principles of the Three Ultimates (heaven, earth, humanity)." It further states, "There is heaven's way, humanity's way, and earth's way. Combining the Three Powers and doubling them, thus six lines are used. The six lines are nothing other than the way of the Three Powers." It also says, "The ancient sages created the Book of Changes to accord with the principles of nature and life: establishing heaven's way through Yin and Yang, earth's way through softness and hardness, and humanity's way through benevolence and righteousness. Combining the Three Powers and doubling them, therefore the Book of Changes forms hexagrams with six lines." These all demonstrate that the six lines contain the meaning of the Three Powers, not that the three lines embody the Three Powers.

As for all six lines involving human affairs, this symbolizes the imitation of heaven, earth, and human relationships. Thus both the initial and top lines also contain meanings pertaining to human affairs.

(Regarding the "return in seven days" in Chapter 46, the discussion is divided into three parts.)

The first part explains: When Yang qi begins to peel away completely, it refers to Yang qi starting anew after being completely exhausted.

This passage explores the profound meaning behind the phrase "return comes in seven days" from the Book of Changes (Zhouyi). It primarily discusses the cyclical principle of Yang Qi (vital energy): from the initial emergence of Yin Qi in the fifth month to the rebirth of Yang Qi in the eleventh month, the process spans seven months by lunar reckoning. However, the scripture deliberately states "seven days" rather than "seven months" to emphasize the rapid resurgence of Yang Qi.

Several scholarly interpretations are mentioned: Scholars Chu and Zhuang argue that it refers to the seven-month period from the fifth to the eleventh month, while Wang Bi (Fusi) interprets it as the seven-day transition from the Bo hexagram (symbolizing the exhaustion of Yang Qi) to the Fu hexagram (symbolizing its revival). The author points out that if calculated from the fifth month, it would be inaccurate to describe this as "the exhaustion of Yang Qi."

The passage then cites the Yiwei (Apocryphal Texts on the Changes) theory of "six days and seven parts": a 360-day year corresponds to sixty hexagrams, with each hexagram governing six days and seven parts (an ancient division where one day equals 80 parts). The Bo hexagram marks the complete exhaustion of Yang Qi at the end of the ninth month, followed by the pure Kun hexagram governing the tenth month. The interval from the exhaustion of Yang Qi to its revival precisely spans Kun's six days and seven parts, rounded to seven days.

The author critiques Kong Yingda's commentary, noting that while his initial explanation is correct, his subsequent citation of Zheng Xuan's (Kangcheng) "six days and seven parts" theory ultimately contradicts the original intent of the scripture. Finally, the passage highlights the special status of the four cardinal hexagrams—Kan (Water), Li (Fire), Zhen (Thunder), and Dui (Lake)—which govern the four directions and seasons, while the remaining hexagrams each oversee specific time periods. This reflects the unique hexagram-Qi theory of Han Dynasty image-numerology (Xiangshu) in the study of the Changes.

This scripture primarily discusses two key aspects: the correspondence between hexagram lines and temporal cycles, and the foundational principles of Yin-Yang and the Five Phases (Wuxing) generative numbers.

The first section explains the relationship between hexagram lines and months. Each line of a pure hexagram (composed of identical trigrams) represents one month. For instance, the six lines from the Fu hexagram to the Qian hexagram correspond precisely to six months, just as the six lines from the Gou hexagram to the Kun hexagram also match six months. Here, the text refutes the "six days and seven parts" theory, dismissing it as a superficial misinterpretation by commentators. The phrase "return comes in seven days" refers to the resurgence of Yang Qi (vital energy) at the end of the tenth month when Kun hexagram concludes and Yin Qi recedes. Since the celestial stems cycle through ten positions, when Yang Qi ascends to the seventh position—associated with Lesser Yang—it takes seven days for this energy to fully return.

The second section elaborates on the generative numbers of the Five Phases. Heavenly numbers (odd) and earthly numbers (even) combine to generate the Five Phases: Heaven's one generates Water, Earth's two generates Fire, Heaven's three generates Wood, Earth's four generates Metal, and Heaven's five generates Earth—these are the "generative numbers." To ensure balanced Yin-Yang pairing, "completion numbers" are introduced: Earth's six completes Water, Heaven's seven completes Fire, Earth's eight completes Wood, Heaven's nine completes Metal, and Earth's ten completes Earth. This pairing allows for the harmonious creation of all things. These numerical relationships originate from transformations of Yin-Yang, particularly the sun's annual motion. From the winter solstice (November) to summer solstice, Yang Qi expands, with the first month corresponding to spring's Wood phase. From summer solstice to winter solstice, Yin Qi grows, with the eighth month aligning with autumn's Metal phase. Thus, the single Yang born at winter solstice corresponds to Water's number one, while the dual Yin born at summer solstice matches Fire's number two (since Yin numbers must be even). This explains why the Yijing associates Qian hexagram with November and Kun hexagram with June.

This scripture primarily explains the generative principles and philosophical implications behind the numerical associations of the Five Phases (Wood, Fire, Earth, Metal, Water). It notes that the third month of spring corresponds to Earth, represented by the number five, as five occupies the transitional position between Yin and Yang. All phenomena emerge from nothingness and gradually manifest from subtle beginnings—a pattern reflected in the Five Phases sequence: Water, being most subtle, is one; Fire, slightly more manifest, is two; Wood, taking form, is three; Metal, solidifying, is four; and Earth, most substantial, is five.

Scholars Liu and Gu propose that Water, Fire, Wood, and Metal require combination with Earth's number to achieve completion: Water becomes six, Fire seven, Wood eight, Metal nine, and Earth ten. This interpretation also holds merit. However, many discussions focus solely on the "Heavenly Numbers" (Water one to Earth five) as the generative numbers of the Five Phases and the "Earthly Numbers" (six to ten) as their completed forms, without explaining how these numbers arise. This oversight stems from failing to distinguish between "image" (abstract principle) and "form" (concrete manifestation), as well as overlooking the relationship between "Dao" (the metaphysical) and "vessel" (the physical).

The Yijing (Book of Changes) states that what transcends form belongs to the "Dao," while what is visibly concrete belongs to "vessel." Numbers above Earth six represent the "Dao," while those below pertain to "vessel." The four symbols—Heaven one, Earth two, Heaven three, and Earth four—lack concrete form and belong to the "Dao." From Heaven five onward, movement and transformation generate Earth six (Water), Heaven seven (Fire), Earth eight (Wood), Heaven nine (Metal), and Earth ten (Earth)—these specific numbers fall within the realm of "vessel."

The Hetu (River Chart) reveals abstract "images," while the Luoshu (Luo Writing) presents concrete "forms." Heavenly images align with what is above, and earthly forms with what is below; thus, the Hetu symbolizes the Qian (Heaven) hexagram of the celestial Dao, and the Luoshu embodies the Kun (Earth) hexagram of the earthly Dao. The Yijing encompasses both "Dao" and "vessel," which is why the sages integrated the two in its creation—a revelation echoed in the legend of "the River bringing forth the Chart."

This passage explains the correspondence between numbers in the Hetu (River Chart) and Luoshu (Luo Writing)—ancient mystical diagrams—and the Five Phases (Wuxing). The Hetu contains a total of 45 numbers arranged in a pattern that subtly conceals the symbolism of the Eight Trigrams (Bagua), deliberately omitting the number for Earth as it is already integrated into concrete forms. The Luoshu, with its 55 numbers, specifically illustrates the laws governing transformation and material manifestation.

The Hetu displays the Four Symbols (Sixiang: Greater Yang, Greater Yin, Lesser Yang, Lesser Yin) without mentioning the Five Phases, while the Luoshu demonstrates the Five Phases (Metal, Wood, Water, Fire, Earth) without referencing the Four Symbols. In essence, the Four Symbols represent the final numerical states formed by Metal, Wood, Water, and Fire. Their distinction lies in how the Four Symbols require combination with Earth's number to manifest materially—hence their difference from the Five Phases—though both originate from the transformative operations of the celestial number Five (Tianwu).

Heaven and Earth each possess five fundamental numbers. Their mutual interaction generates the cyclical production sequence of the Five Phases: Heavenly One (Yang) combining with Earthly Six (Yin) produces Water; Earthly Two (Yin) combining with Heavenly Seven (Yang) generates Fire, and so forth until Heavenly Five joins with Earthly Ten to form Earth. These numerical patterns were applied since Fuxi's era but only received formal nomenclature during the Yellow Emperor's reign.

Some modern scholars forcibly pair numbers with the Five Phases—assigning One-Yang to Water, Two-Yin to Fire, etc.—contrary to natural cosmological principles. For instance, Earth shouldn't follow Metal in terms of solidity, nor should Fire follow Water in terms of expansive capacity. The Five Phases emerge spontaneously from nature, as do their numerical correspondences.

Special note: The initial emergence of Yang energy in the eleventh month is called "odd-numbered birth," referring to Heavenly One (Yang) activating within the Water trigram (Kan). The first appearance of Yin energy in the fifth month is termed "even-numbered birth," indicating Earthly Two (Yin) stirring within the Fire trigram (Li). These transformations follow natural laws and shouldn't be simplistically forced into "from subtle to manifest" theoretical frameworks.

This passage primarily examines the correspondence between the numerical values of Yin and Yang lines in the Book of Changes (Yijing) and calendrical systems, along with various interpretations from different schools.

Regarding the theory that "two Yin lines emerge in the sixth month as even numbers," the author questions its theoretical foundation. Investigating the Yiwei Jilan Tu (Apocryphal Treatise on the Changes: Chart of the Comprehensive Survey) and Zheng Xuan's "six days and seven parts" doctrine, it becomes clear that these employ the 216 calculations of the Qian hexagram (Old Yang) and the 144 calculations of the Kun hexagram (Old Yin) to form a ratio, totaling 360 calculations that correspond to the number of days in a year (note: ancient calendars approximated a year as 360 days, excluding the fractional five and a quarter days).

Detailed line statistics: The Book of Changes contains 384 lines across its upper and lower sections, equally divided between Yin and Yang. There are 192 Yang lines, each valued at 36 calculations, totaling 6,912 calculations; and 192 Yin lines, each valued at 24 calculations, totaling 4,608 calculations. Combined, these yield 11,520 calculations, symbolizing the number of all things. However, the scripture itself only uses the 360 calculations of the Qian and Kun hexagrams to correspond to the annual cycle, without introducing new numerical values.

The author points out that while the Yiwei and Zheng Xuan's methods—subtracting 24 from the line counts of the four cardinal hexagrams Kan (Water), Li (Fire), Zhen (Thunder), and Dui (Lake)—can align with the annual day count, this approach deviates from the original intent of the sages' scriptures. The twelve months correspond to twelve hexagrams (from Fu to Kun), and the theories of later scholars from miscellaneous texts should not override the canonical meaning established by the sages.

Finally, the passage discusses divergent interpretations of the phrase "the eighth month brings misfortune" in the Lin hexagram. He Yan argues that counting from the eleventh month (Zi) to the sixth month (Wei) constitutes eight months; Chu Shi contends that counting from the first month (Yin) to the eighth month (You) equals eight months; Kong Yingda's commentary offers yet another perspective. These annotations reveal significant discrepancies among the various schools of thought.

This passage discusses the relationship between the Lin hexagram (one of the twelve seasonal hexagrams representing the twelfth lunar month, Chou) in the Book of Changes (Yijing) and its correspondence with the eighth month. Scholars hold differing views on this matter:

He Yan advocates calculating from the eleventh month (Zi) when the Fu hexagram marks the initial emergence of Yang qi, arguing that the hexagram statement should belong to Fu rather than Lin. Chu Zhongdu, however, begins calculations from the first month (Yin), maintaining the statement should fall under the Tai hexagram. Kong Yingda proposes correlating the eighth month with the seventh month's (Shen) Pi hexagram, though this doesn't correspond with the third Yang line of Lin.

The author posits the most reasonable interpretation aligns the eighth month with the sixth month's (Wei) Dun hexagram, using Dun's second Yin line to resolve Lin's second Yang line. This view finds support in two key evidences: first, both Lin and Dun's judgments mention "gradual growth" (describing the waxing and waning process of Yin and Yang qi), and second, their line images correspond systematically.

Regarding calendrical systems, the author notes that while King Wen developed the hexagrams using the Shang calendar (which began the year with the twelfth month), the Zhouyi was ultimately completed by the Duke of Zhou employing the Zhou calendar (starting the year with the eleventh month). Just as the Classic was called Lianshan in the Xia era (Age of Shennong), Guizang in the Shang (Age of Xuanyuan), and finally Zhouyi in the Zhou dynasty, the monthly calculations should follow Zhou standards. Thus, He Yan's method of calculating the eighth month from Zi to Wei fundamentally misapplies the proper calendrical framework.

This passage discusses the principles of Yin-Yang waxing and waning, and the shifting dynamics between noble individuals (junzi) and petty persons (xiaoren) as described in the Yijing (Book of Changes). Confucius cites Wang Bi's (style name Fusi) commentary, explaining that when the Dao of noble individuals declines while the Dao of petty persons flourishes, this often corresponds to the hexagram of Pi (Heaven and Earth Not in Communion). However, the author points out that the principle where flourishing Yin Qi signifies petty persons gaining power while flourishing Yang Qi indicates noble individuals rising to prominence isn't exclusive to the Pi hexagram.

Wang Bi elaborates further in his Gua Lue (Hexagram Outlines): The Dun hexagram (Mountain beneath Heaven, Retreat) symbolizes the gradual strengthening of petty persons' influence, where internal difficulties abound yet external circumstances remain favorable. This forms a contrast with the Lin hexagram (Earth above Lake, Approach) - while Lin shows the danger faced by the yielding when Yang Qi grows, Dun demonstrates the peril confronting the firm when Yin Qi increases. The Lin hexagram contains two Yang lines in the inner trigram, indicating the gradual flourishing of the noble Dao; whereas the Dun hexagram features two Yin lines in the inner trigram, representing the progressive ascendancy of petty persons' ways.

The text mentions the celestial principle of the "ominous eighth month": just as nature cycles between cold and heat, Yang Qi inevitably recedes after reaching its zenith. When a Yang line occupies the second position (properly positioned and centered), it's precisely the moment requiring vigilance against decline. Yang Qi begins its growth from the Fu hexagram in the eleventh month, reaches its peak with the Lin hexagram in the twelfth month, starts receding with the Gou hexagram in the fifth month, and completes its decline with the Dun hexagram in the sixth month. From the eleventh month (Zi) to the sixth month (Wei) spans exactly eight months - this constitutes the celestial cycle of the "ominous eighth month."

The Hetu (River Chart) and Luoshu (Luo Writing) from the Yijing (Book of Changes) are ancient mystical diagrams of great significance. In the Hetu arrangement, the central number five serves as the core, with six and eight positioned below like knees, two and four above like shoulders, three on the left and seven on the right, while nine crowns the top and one supports the base.

Regarding the Five Phases (Wuxing) numbers in the Luoshu, some question why Water is assigned one, Fire two, Wood three, Metal four, and Earth five, differing from the Dragon Chart. This is because these numbers represent the "generative numbers" (basic numbers) of the Five Phases, which already embody the concept of Yin-Yang interaction. Later discussions will reveal the complete "mature numbers" when Earth governs the four seasons. The Luoshu's nine-palace grid originates from these Five Phases numbers, so the generative numbers—already harmonized—are presented first, with Earth's number supplementing them to form the complete mature numbers.

The ten Heavenly Stems generate the Five Phases through mutual production and conquest:

• Heaven's one and Earth's six combine to form Water,
• Earth's two and Heaven's seven produce Fire,
• Heaven's three and Earth's eight generate Wood,
• Earth's four and Heaven's nine create Metal,
• Heaven's five and Earth's ten complete Earth.

The Heavenly Stems represent Yang energy. The Five Phases' production sequence is: Metal produces Water, Water produces Wood, Wood produces Fire, Fire produces Earth, and Earth produces Metal. Their conquest sequence is: Metal conquers Wood, Wood conquers Earth, Earth conquers Water, Water conquers Fire, and Fire conquers Metal.

Historical records about the Dragon Chart and Turtle Writing: The Yijing states that the Yellow River produced the Chart and the Luo River yielded the Writing, which the sages emulated. The Chunqiuwei (Apocrypha of the Spring and Autumn Annals) records that the Yellow River connected with the Qian (Heaven) trigram to manifest celestial patterns, while the Luo River flowed through the Kun (Earth) trigram to reveal terrestrial forms. The Hetu consists of nine sections, and the Luoshu has six. Han scholar Liu Xin believed Fuxi created the Eight Trigrams inspired by the Hetu, while Yu the Great composed the Hongfan (Great Plan) after receiving the Luoshu during flood control. However, Kong Yingda pointed out that classical texts lack definitive evidence for the turtle-borne writing, though various apocryphal texts mention legendary rulers like the Yellow Emperor, Yao, and Shun receiving prophetic charts and texts.

Regarding the origins of the Luoshu (Luo River Writing), scholars throughout history have held various interpretations. Some claim it was the Hetu (River Chart) borne by a dragon-horse and the Luoshu carried by a divine turtle, yet the true authorship of these apocryphal texts (Han Dynasty prognostications attached to classical works) remains unverifiable. Textual research suggests these texts were likely forged during the reigns of Emperor Ai and Emperor Ping of the Western Han Dynasty.

Such writings only began appearing in the late Western Han period, their precise origins now lost. Earlier scholars, however, universally accepted these legends. The Confucian school thus maintained that the "Nine Categories" of the Hongfan (Great Plan)—nine principles of statecraft—were derived from the patterned markings on the divine turtle's shell. These markings, arranged numerically from one to nine, were said to have inspired Yu the Great to systematize the nine governing precepts. Yet this account invites skepticism—divine revelations ought to be concise, unlikely to feature such meticulous numerical sequences.

In truth, even before Yu received the Nine Categories, ancient rulers governed with remarkable order. The era of the Three Sovereigns flourished without writing systems, let alone the Luoshu. The crux lies not in the text itself but in adherence to its principles: compliance brings order; defiance, chaos.

Concerning the Luoshu's original content, heavenly edicts would logically be terse, unlikely to enumerate sequences. Later traditions attributed its compilation to Yu, leading Confucian scholars to identify the Hongfan's opening passage—"First is the Five Phases (Wuxing)" and the subsequent twenty-seven characters—as Yu's additions. As for phrases like "Reverently attend to the five affairs," eminent scholars like Liu Xiang and Gu Shi considered them original turtle-shell inscriptions, while lesser scholars like Liu Xin deemed them Yu's editorial work. Both views persist due to lack of conclusive evidence.

Upon scrutiny, many interpretations deviate from classical intent. The Nine Categories were likely statecraft principles codified by Yu after studying the Luoshu, not literally delivered by a turtle during his reign. The Book of Documents (Shangshu) corroborates this: Jizi recounts that Gun’s failed flood control disrupted the Five Phases, provoking heaven’s wrath and denial of the Nine Categories, leading to his execution. Only when Yu succeeded was he granted these governing principles—with no mention of a turtle-borne text. Only Kong Anguo’s commentary asserts that heaven bestowed the Luoshu upon Yu via a numerically patterned divine turtle.

This passage recounts the origins of the Hetu (River Chart) and Luoshu (Luo Writing) and their connection to the Yijing (Book of Changes). According to legend, in ancient times, a dragon diagram (Hetu) emerged from the Yellow River while a turtle inscription (Luoshu) appeared in the Luo River. Based on these patterns, Fuxi (the Ox-Tamer Sovereign) drew the Eight Trigrams (Bagua) and later expanded them into sixty-four hexagrams. Subsequently, King Wen of Zhou composed the hexagram statements, the Duke of Zhou created the line statements, and Confucius (Zhongni) supplemented them with the Ten Wings, thereby completing the Yijing system.

The text explains that the Hetu contains numbers one through nine, encompassing the principles of the Four Symbols (Lesser Yang, Greater Yang, Lesser Yin, Greater Yin), the Eight Trigrams, and the Five Phases (Metal, Wood, Water, Fire, Earth). The Luoshu primarily manifests the cyclical generation and mutual reinforcement among the Five Phases. The author refutes a popular belief of his time—that the Luoshu was a celestial gift bestowed upon Yu the Great containing nine categories of governance principles during his flood control efforts. In reality, official positions like the Minister of Education and Minister of Works had already been established during the Yao and Shun eras to manage various affairs, and the concept of Five Phases had been formulated by Xi and He clans, long before Yu's reign.

The author emphasizes that the profound principles embedded in the Hetu and Luoshu could only be comprehended by sages. These mystical diagrams were not later fabrications but natural manifestations of cosmic patterns. Fuxi established the Eight Trigrams by observing these designs, while Yu the Great further elucidated their Five Phases principles, establishing enduring paradigms for later generations.

This passage examines the relationship between ancient sages and the Luo Shu (洛书) and He Tu (河图) diagrams, as well as the origins of natural numerical systems like the Five Phases (五行) and Eight Trigrams (八卦).

The sages Fu Xi, King Wen, and the Duke of Zhou each made distinct contributions: Fu Xi created the trigram symbols, King Wen developed the hexagram transformations, while the Duke of Zhou perfected the system of line images. Confucius once remarked, "After King Wen passed away, was not the cultural heritage preserved here?" He also stated, "Heaven has endowed me with virtue (De)," indicating that sage wisdom is divinely bestowed. This echoes the words of Zhong Hui, minister of King Tang of Shang: "Heaven grants rulers both courage and wisdom to govern all states."

The text questions certain traditional accounts: Confucius believed Jizi's reference to "the nine categories of governance bestowed by Heaven to Yu the Great" corresponded to the markings borne by the sacred turtle in the Luo Shu. However, the author points out that both the He Tu and Luo Shu predate the formation of the Yijing (易经), and the "nine categories" of governance were already implemented during Yao and Shun's reigns—how could they be attributed solely to Yu?

Divergent accounts exist regarding the Luo Shu's contents: the Han dynasty Chunqiuwei records it comprising six sections, while Confucius described the turtle's markings displaying numbers one through nine. The currently transmitted turtle diagram only shows the generative and controlling sequences of the Five Phases, leaving the accurate version uncertain. The author analyzes that among the "nine categories" recorded in the Shangshu (尚书), only the Five Phases represent Heaven and Earth's natural numerical patterns—the remaining eight categories were Yu's systematizations based on celestial timing and human affairs, unlikely to be the turtle's original markings.

The Five Phases manifest natural laws: examining the Hongfan Wuxing Zhuan reveals that all interpretations of portents ultimately root in the Five Phases. Just as Gun (Yu's father) disrupted cosmic order by violating these patterns, causing moral collapse, this confirms the Five Phases as Heaven-revealed natural principles whose markings were conveyed by the sacred turtle. Similarly, the Eight Trigrams encode patterns of natural phenomena—through observation and deduction, sages classified their transformations to determine auspicious and inauspicious signs. This presents a perspective differing from commonly transmitted explanations.

This dialogue examines the origins and transmission of the Hetu (River Chart) and Luoshu (Luo Writing). One skeptic questions: If both diagrams appeared during Fuxi's era, shouldn't the "Nine Categories" of governance from the Hongfan have also existed then? Why then are they credited to Yu the Great's systematic arrangement? The response clarifies: The Hetu reveals celestial patterns through the Eight Trigrams (Bagua), fully displaying their spatial orientations, while the Luoshu embodies the Five Phases (Wuxing) requiring textual classification. During Fuxi's time, society's simplicity predated written language, so the Nine Categories could only be transmitted numerically until Yu's era, when they were textualized into governance principles.

Another question arises: If the Dragon Diagram (Hetu) already contains the Five Phases, why was the Turtle Script (Luoshu) necessary? The explanation notes: While the Hetu implies the Five Phases, it lacks Earth's specific numerical value—showing only the total forty-five in latent form. The Luoshu, however, fully records the fifty-five numbers demonstrating the Five Phases' mutual generation. As the Yijing (Book of Changes) encompasses both symbolic patterns and concrete applications, sages needed both diagrams for their creative work.

Addressing the Shangshu (Book of Documents) account of "Heaven gifting Yu the Nine Categories," Confucius is cited to affirm that the Hetu-Luoshu predated Fuxi's trigrams—they couldn't have first appeared in Yu's Xia dynasty. Denying this would imply no governance framework before Yu, contradicting the Yaodian's explicit records of ninefold administrative methods.

The discussion concludes: Though absent from canonical texts, these diagrams were orally transmitted by sages across generations. Their numerical patterns perfectly correspond with trigrams and natural laws, transcending human invention. All yin-yang theories throughout history honor them as foundational. Their mystical resonance with cosmic forces proves their sacred authenticity—how could they be deemed mere fabrication? This exchange reveals Daoism's mystical cosmology, affirming the Hetu-Luoshu as divine "celestial revelations."