《大易象數鉤深圖》

This passage explains the process by which Taiji (Supreme Ultimate, the cosmic origin) evolves and generates all things. The Taiji Diagram transmitted by Zhou Dunyi (courtesy name Maoshu) to the Cheng brothers (Cheng Hao and Cheng Yi) reveals the mystery of cosmic generation.

Initially, there was Wuji (the formless, imageless primordial state), from which Taiji emerged. The movement of Taiji generates Yang Qi (vital energy). When movement reaches its extreme, it transforms into stillness; when stillness reaches its extreme, it reverts to movement—movement and stillness depend on each other. In this way, the two modes of Yin and Yang (heaven and earth) are differentiated. The interaction and fusion of Yin and Yang give rise to the Five Phases (Wood, Fire, Earth, Metal, Water), which distribute in sequence to form the cycle of the four seasons. The essence of the Five Phases is Yin-Yang, the essence of Yin-Yang is Taiji, and the origin of Taiji is Wuji.

When the Five Phases are generated, each possesses its own characteristics. The true meaning of Wuji combines wondrously with the essence of Yin-Yang and the Five Phases. The Dao of Qian (Yang energy) forms the male, while the Dao of Kun (Yin energy) forms the female. The interaction of these two Qi (energies) transforms and generates all things, which then multiply endlessly in infinite variations.

Initially, Taiji has no concrete form—it is simply a mass of chaotic Qi. When this Qi divides, the light and clear part ascends to become heaven, while the heavy and turbid part descends to become earth. This is how Taiji gives rise to the two modes (Liangyi). After the two modes are formed, Metal, Wood, Water, and Fire are distributed in the four directions—this is how the two modes give rise to the four phenomena (Sixiang). The number six of Water in the northern Kan position generates the Qian trigram; the number nine of Metal in the western Dui position generates the Kun trigram; the number seven of Fire in the southern Li position generates the Xun trigram; the number eight of Wood in the eastern Zhen position generates the Gen trigram—this is how the four phenomena give rise to the eight trigrams (Bagua).

The three lines of the Qian trigram represent heaven because "one" contains "three." The six lines of the Kun trigram represent earth because the even number "three" is "six." The heavenly number is the odd one, while the earthly number is the even two—the fundamental numerical principle is self-evident without comparison. The mystery lies in "one containing three, two containing six": the one of Qian contains three, thus giving rise to the three Yang trigrams (Zhen, Kan, Gen); the two of Kun contains six, thus giving rise to the three Yin trigrams (Xun, Li, Dui). This is the profound principle of the generation of heaven and earth.

The Zhen trigram symbolizes thunder—thunder emerges from beneath the earth, so the Yang line is at the bottom. The Kan trigram symbolizes water—water accumulates within the earth, so the Yang line is in the middle. The Gen trigram symbolizes mountains—mountains manifest on the earth's surface, so the Yang line is at the top. Yang governs movement, while Yin governs stillness: Zhen is based on movement, while Gen is based on stillness. Kan, being in the intermediate state, is neither entirely internal nor external, thus manifesting in different states of flow or stillness. The Xun trigram symbolizes wood—trees grow upward from the earth, so the Yin line is at the very bottom.

This passage explains the relationship between the Eight Trigrams (Bagua) from the Book of Changes (Yijing) and natural phenomena using Yin-Yang and Five Phases (Wuxing) theory.

The Li trigram (symbolizing Fire) occupies the lower position. Since fire arises from wood, it contains a single broken (Yin) line at its center. The Dui trigram (symbolizing Marsh) resembles water gathering upon the earth, hence it bears a broken line above. Yin represents softness while Yang represents strength—just as a tree begins tender but ends strong because Yang energy concentrates at its extremities.

Fire's nature appears bright externally but dark internally, with Yang outside. Marsh appears moist externally but dry internally, with Yang within. Someone might ask why marshes are dry inside? Precisely because internal dryness generates Metal (one of the Five Phases), while external moisture gathers Water. Metal begets Water, Earth begets Metal—these principles become clear through observing marshes. The sage's wisdom wasn't attained arbitrarily.

Yang energy begins growing at the Zi hour (midnight), reaching full six-Yang at Si hour (mid-morning). The Qian trigram (symbolizing Heaven) resides in the northwest, positioned before the Hai hour (late night), thus it knows all things' beginnings, representing creation's origin. Yin energy starts growing at Wu hour (noon), completing six-Yin by Hai hour. The Kun trigram (symbolizing Earth) in the southwest corresponds to Shen hour (mid-afternoon). All things mature at You hour (evening)—Kun's influence begins at Shen and completes at You, hence it perfects all things.

Among numbers one through ten, Heaven above is honored while Earth below is humble. The noble Qian represents ruler, father and husband; the humble Kun represents minister, mother and wife—all stemming from Heaven's supremacy over Earth's lowliness. Thus it's said: "Heaven supreme, Earth humble—Qian and Kun's positions are fixed."

Qian employs nine (Yang's ultimate number) to symbolize triple Heaven; Kun uses six (Yin's central number) to signify double Earth—hence "triple Heaven and double Earth establish the numbers." Nine and six are fundamental generative numbers. Combining the characters for "sun" (日) and "moon" (月) resembles Daoist talismanic script (Fulu) where sun below meets moon above, representing their alternating movements—thus Yin-Yang principles find embodiment in sun and moon.

In numerical arrangement: nine above, one below; three left, seven right; two and four like shoulders; six and eight like feet; five at the center—totaling forty-five, with all lines summing to fifteen. Heaven's number five dwells centrally. Observing this pattern, sages established the Eight Trigrams' imagery. The River Chart's (Hetu) number is forty-five because sages excluded ten (Heaven-one, Earth-two, Heaven-three, Earth-four), retaining only Heaven-five governing Earth from the center.

The Dayi Xiangshu Goushen Tu explains how the Hetu (River Chart) and Luoshu (Luo Writing)—two ancient mystical diagrams—evolved into the Bagua (Eight Trigrams). The Hetu originally contained four fundamental numerical symbols: Heaven's One, Earth's Two, Heaven's Three, and Earth's Four. When Heaven's Five took the central position governing Earth, though capable of transformation, it had not yet taken form—this stage is called the "Four Images" (Sixiang). The Luoshu, however, possessed the complete number "Earth's Ten," enabling Water, Fire, Metal, and Wood to take shape through the pairing of odd and even numbers.

In detail: Heaven's One resides in the northern Kan position representing Water; Earth's Two in the southern Li position represents Fire; Heaven's Three in the eastern Zhen position represents Wood; and Earth's Four in the western Dui position represents Metal. These four, occupying the cardinal directions, are called the "Generative Numbers." Heaven's Five in the center belongs to Earth, which has no fixed direction but governs the four quarters. When Water's One combines with Earth's Five, it becomes Six; Fire's Two with Earth's Five becomes Seven; Wood's Three with Earth's Five becomes Eight; and Metal's Four with Earth's Five becomes Nine—thus completing the formation of the Four Images.

Fuxi (the legendary creator of the Bagua) first established the positions of the Eight Trigrams based on the Hetu's eight directions, then used the Luoshu's complete number "Earth's Ten" to define the forms of the trigrams. By observing Yin-Yang, he created the two lines—the solid (Yang) and broken (Yin) strokes—and by observing the Three Powers (Heaven, Earth, and Humanity), he established the upper, middle, and lower lines (Yao). For example, three solid Yang lines form the Qian (Heaven) trigram, while six broken Yin lines form the Kun (Earth) trigram. One Yang line beneath two Yin lines, capable of bending and stretching, forms the Zhen (Thunder) trigram; one Yin line beneath two Yang lines, yielding without opposing strength, forms the Xun (Wind) trigram. One Yang line between two Yin lines, weak above and below, creates the Kan (Water) trigram, while one Yin line between two Yang lines forms the Li (Fire) trigram.

The Hetu determines the eight directional positions, while the Luoshu completes the images of the Five Phases (Wood, Fire, Earth, Metal, Water). Only when the heavenly numbers reach completion through the Luoshu's "Earth's Ten" do the two diagrams combine to fully manifest the Eight Trigrams. All eight trigrams evolve from these four fundamental images.

This passage primarily explains the mathematical principles and symbolic meanings of the Yin and Yang lines in the Book of Changes (Yijing), using numerical patterns and trigram imagery to illustrate the fundamental laws governing the interaction between celestial and terrestrial forces.

The text begins by analyzing the line strokes in the Qian (pure Yang) and Kun (pure Yin) hexagrams. The Qian hexagram contains twelve strokes (three Yang lines with four strokes each), while the Kun hexagram contains twenty-four strokes (six Yin lines with four strokes each). The Yang lines represent the sovereign principle that embraces all things, totaling thirty-six strokes (12+24), hence Yang lines are designated by the number "nine." Yin lines embody the ministerial principle that must not overstep its bounds, totaling twenty-four strokes, thus being denoted by "six." The combination of Qian's three lines and Kun's six lines forms the conceptual basis for Yang's numerical representation as "nine."

The passage then discusses the numbers of Heaven and Earth: Heaven's number is twenty-five, Earth's thirty. The calculation units (ce) for Qian total thirty-six, while Kun's sum to twenty-four—all manifestations of these natural numerical relationships. Six interpretive approaches are presented:

1) The He River Chart's (Hetu)纵横 sums all equal fifteen;

2) The sequence Heaven-one, Earth-two, Heaven-three, Earth-four, Heaven-five also totals fifteen;

3) The numerical transformations during Taiji's differentiation into Two Forms (Liangyi), Four Images (Sixiang), and Eight Trigrams (Bagua) similarly manifest fifteen;

4) The generative numbers of the Five Phases (Water-one, Fire-two, Wood-three, Metal-four, Earth-five) sum to fifteen;

5) When dividing the Five Phase numbers into Yin-Yang, seven represents lesser Yang (shaoyang) and eight lesser Yin (shaoyin), again reflecting fifteen;

6) The dynamic transformations between lesser Yin and Yang—where Yin recedes to six and Yang advances to seven—all demonstrate the operational laws of cosmic Yin-Yang interactions.

These numerical patterns and trigram transformations ultimately describe the fundamental principles governing the dynamic interplay of Yin and Yang Qi throughout the cosmos.

This passage explains the ancient Chinese theory of Yin-Yang and the Five Phases (Wood, Fire, Earth, Metal, Water), where numbers correspond to cosmic patterns. The numbers one through ten represent the interactions between heaven, earth, and the Five Phases.

Odd numbers symbolize heaven (Yang), while even numbers represent earth (Yin). The union of heavenly one (1) and earthly six (6) generates Water in the north; earthly two (2) and heavenly seven (7) produce Fire in the south; heavenly three (3) and earthly eight (8) form Wood in the east; earthly four (4) and heavenly nine (9) create Metal in the west; heavenly five (5) and earthly ten (10) combine to form Earth at the center. This reveals the fundamental principle of creation: Yang (odd) manifests through Yin (even), and Yin (even) manifests through Yang (odd).

The total sum of these numbers (55) minus five (representing the cyclical operation of the Five Phases) leaves fifty—the number of the Great Expansion (Dayan). One is set aside unused, symbolizing the supreme nature of primordial Qi (the cosmic origin). The five heavenly numbers initiate transformation, distributed among the Five Phases' directions, which is why the center has no fixed form. First, heavenly one (1) initiates creation, then generates the Four Symbols (lesser Yang, greater Yang, lesser Yin, greater Yin) and the Five Phases, yet one remains unused—demonstrating that primordial Qi is the foundation of all transformation.

In celestial observation, numbers two through five correspond to longitude, while seven through six (7,8,9,6) represent latitude. The heavens use the Four Symbols (Azure Dragon, White Tiger, Vermilion Bird, Black Tortoise) as longitude and planets (Jupiter, Mars, Venus, etc.) as latitude. Only the Northern Dipper and Polaris are visible in the north—though called "north," they actually occupy the celestial center, implying the hidden numerical pairing of one and six (Taiji) within five. In the ancient River Chart (Hetu), six and one reside in the northern positions (Hai and Zi), while five occupies the center, showing that both center and north embody Taiji principles.

Saturn is omitted from the planetary count because it completes its celestial circuit every 28 years, while other planets pass through its constellations—just as the Yin-Yang school states: "Earth governs the center, commanding the four seasons." The 384 lines of the Yi Jing (Book of Changes) correspond to celestial patterns, with auspicious or ominous signs divined through the numbers seven, eight, nine, and six—much like predicting fortune by observing planetary movements.

This passage discusses the transmission of Fu Xi's Bagua (Eight Trigrams) diagram and the characteristics of various schools of thought. Fu Xi initially drew the eight basic trigrams (Qian, Kun, Gen, Dui, Kan, Li, Zhen, and Xun), which were later paired to form sixty-four hexagrams. The Zheng school mentions that ancient studies on the "Prior Heaven Diagram" (Fu Xi's Bagua arrangement) included Yang Xiong's Canon of Supreme Mystery (Taixuan Jing), Guan Ziming's Scripture of the Ultimate Cavern (Dongji Jing), Wei Boyang's Triple Unity (Cantong Qi), and Shao Yong's (styled Yaofu) Supreme Principles Governing the World (Huangji Jingshi).

The author criticizes Yang Xiong and Guan Ziming for overly imitating the Book of Changes (Yijing), rigidly adhering to its textual form like adding a roof on top of another—superfluous. Wei Boyang's Triple Unity, though discussing cultivation methods, deviates from the Dao of the sages. Only Shao Yong transcended textual constraints, yet regrettably, later generations merely applied his work to calendrical calculations. These four schools all originate from the ancient Prior Heaven Diagram, which is the fundamental source of the Book of Changes. Sadly, lacking textual annotations, it has been overlooked by the world.

Fu Xi established the Bagua by observing celestial and terrestrial patterns: upward, he studied astronomical phenomena like the movements of the sun, moon, and stars, and the changes of the four seasons; downward, he examined geographical features such as the nine regions, birds, beasts, plants, and the twelve Earthly Branches (Zi, Chou, Yin, Mao, etc.). The Bagua system encompasses the principles of all things in heaven and earth. The Qian trigram (Yang) is positioned above, and the Kun trigram (Yin) below. Qian moves leftward from the Zhen trigram, while Kun moves rightward from the Xun trigram, forming a dynamic state where heaven and earth interact, and hardness and softness complement each other.

The trigrams stimulate and shift one another: Zhen stirs Gen and Dui; Kun stirs Li and Xun; Kan stirs Qian. The Han dynasty Yijing scholar Jing Fang described this movement as "Yin entering Yang, Yang entering Yin." The number seven holds great significance—seven times seven equals forty-nine, representing perfect virtue (De). The number of the trigrams is eight, and eight times eight yields sixty-four, forming all sixty-four hexagrams.

The Dayi Xiangshu Goushen Tu (Great Changes Symbol and Number Profundity Diagrams) primarily explains the patterns of hexagram transformations in the Yijing (Book of Changes), using the waxing and waning of Yin-Yang to interpret the operational laws of heaven, earth, and all things.

Square and circle represent two fundamental characteristics: the square symbolizes stability and regularity, suitable for deducing the past, while the circle embodies infinite variability, capable of foreseeing the future. This concept originates from the line-changing patterns of the Qian hexagram (representing heaven) and the Kun hexagram (representing earth).

Starting from the Nine in the Second Line of the Qian hexagram, transformations proceed first to the Tongren hexagram, then to the Wuwang hexagram, the Yi hexagram, the Yi hexagram, and finally culminate in the Li hexagram. Similarly, the Six in the Second Line of the Kun hexagram transforms first into the Shi hexagram, followed by the Sheng hexagram, the Heng hexagram, the Daguo hexagram, and ultimately concludes with the Kan hexagram. Thus, the upper section of the Yijing begins with the Qian and Kun hexagrams and ends with the Kan and Li hexagrams.

The waxing and waning of Yin-Yang follow a cyclical pattern: at the winter solstice in the eleventh month, Yang energy begins to emerge (corresponding to the Fu hexagram), reaching its peak in the fourth month with the pure Yang of the Qian hexagram, known as "opening the gate" (pihu). At the summer solstice in the fifth month, Yin energy first arises (Gou hexagram), culminating in the tenth month with the pure Yin of the Kun hexagram, referred to as "closing the gate" (hehu). This illustrates the natural rhythm of Yin and Yang alternating in dominance.

Hexagram transformations proceed in a fixed sequence: starting from the Fu hexagram, progressing through the Lin, Tai, Dazhuang, and Guai hexagrams, and culminating in the Qian hexagram at the zenith of Yang energy. Then, beginning with the Gou hexagram, the sequence moves through the Dun, Pi, Guan, and Bo hexagrams, ending with the Kun hexagram at the height of Yin energy. Each transformation follows a strict order—for example, the Qian hexagram undergoes five changes before halting at the Bo hexagram, while the Kun hexagram transforms five times before stopping at the Guai hexagram.

The transformations of Yin and Yang exhibit symmetry: Yang energy grows from one Yang line (Fu hexagram) to sixteen Yang lines, while Yin energy expands from one Yin line (Gou hexagram) to sixteen Yin lines. Numerologically, this is expressed as "one combining with nine makes ten, returning to five (the center); ten combining with six makes sixteen, returning to two (the Yin position)." This constitutes a significant numerical principle in ancient symbolic numerology.

This passage explains the generative principles of the Eight Trigrams (Bagua) in the Book of Changes (Yijing). Yang trigrams (symbolizing masculine energy) follow a descending sequence—from the number one decreasing to nine, ultimately settling at five as the sovereign position. Yin trigrams (symbolizing feminine energy) ascend inversely—from ten rising to six, culminating at two as the ministerial position.

The transformations of trigrams follow fixed patterns: A single yin line interacting with five yang lines yields six variations, and vice versa. Two yin lines with four yang lines produce twelve variations, and the same applies inversely. When trigrams achieve perfect symmetry (remaining unchanged), there are eight possible configurations. Three yin and three yang lines generate twenty-four variations.

The Qian (Heaven) and Kun (Earth) trigrams form the foundation of the Bagua. Qian corresponds to the number one, the square, clear Qi (vital energy), and movement; Kun aligns with the number two, the circle, turbid Qi, and stillness. Qian embodies the dual nature of Yin-Yang (two polarities), divided into upper and lower aspects, while Kun encompasses the Four Symbols (lesser yang, greater yang, lesser yin, greater yin), oriented to the four cardinal directions. Together with Qian and Kun themselves, these elements complete the Eight Trigrams system.

Beginning from the Supreme Ultimate (Taiji, the cosmic origin), the process unfolds through successive divisions: one becomes two, two becomes four, four becomes eight, and so on until the sixty-four hexagrams fully manifest the Dao’s operation, seasonal cycles, and human affairs. Thus, the Yijing opens with the Qian and Kun hexagrams. Practitioners who reverse this process—tracing the sixty-four hexagrams back to Taiji—may grasp the true wisdom transmitted by Fuxi, King Wen, and Confucius, even comprehending the subtle principles of spiritual transformation.

Regarding the Zhun hexagram (symbolizing initial hardship), two cultivation approaches are noted: External learning relies on sensory perception, but excessive dependence on external phenomena harms one’s innate nature. Internal learning emphasizes intuitive insight and seizing opportunities, yet overreliance on cunning becomes a constraint. Just as the yang line in the Kan (Water) hexagram awaits the strengthening influence of Qian’s masculine energy, the interplay of yin lines—advancing or retreating—shapes the auspicious or inauspicious changes of the Xu (Waiting) hexagram. These are the profound meanings concealed by sages within the trigrams.

This passage explains the principles of Yin-Yang transformations and hexagram correspondences in the Book of Changes (Yijing). It states that while the two Yin lines (referring to the Kun hexagram) are not emphasized, the three Yang lines (Qian hexagram) are valued more. Yet greatest importance is placed on the single Yang line at the center of the Kan hexagram (water trigram ☵), as this represents the locus of benefit. Hence the analogy of wine and food—while nourishment is sought by all, overindulgence brings harm. The petty man's tendency to pursue small gains only to suffer consequences must be countered with proper virtue (De); the key lies in steadfast adherence to the Dao to attain auspiciousness. "Zhen" (steadfastness) signifies central rectitude—when inner integrity is firm, outward stability follows, preventing entrapment in difficulties.

The Qian trigram corresponds to the Hai position (northwest), while Kan originates from Zi (due north). Both Hai and Zi belong to the northern water element, initially conflict-free. But once water separates from its form—when heaven tilts westward and waters flow eastward, with heaven circling above and water nourishing below—contention arises.

The Kun hexagram represents the populace, as does the Shi (Army) hexagram, which embodies leadership of multitudes. To lead people without virtue is impossible, hence the Qian hexagram's second Yang line enters Kun to form Shi, manifesting Qian's virtue in the second position. Musical tones arise from numbers, and numbers begin from the center—the Huangzhong pitch (foundation of the twelve tones) cannot tolerate the slightest deviation. The northern Kan trigram is Huangzhong's root, hence the hexagram statement mentions "elder" (virtuous leader) and the line statement "pitch-pipes"—both measurement and law stem from virtue.

North symbolizes darkness and execution, while south represents brightness and assembly. In hexagrams, the second line occupies the southern Li (fire ☲) position of illumination, hence the Bi (Closeness) hexagram faces south. The fifth line resides at the center rather than the north, for looking skyward from the north one sees only the Big Dipper and Polaris (the celestial pivot). Though called "north," it's actually heaven's center. Shi faces north, embodying military formations of five-man squads; Bi faces south, symbolizing five ranks of nobility. When the top line occupies the fifth position yet lags behind the ruler, we see the warning "latecomer meets misfortune."

The Xun (wind ☴) trigram occupies the southeast. Qi from Qian enters Xun's position between Zi (north) and Si (southeast), where it's gathered—this forms the Xiao Xu (Small Accumulation) hexagram, as Yin first emerges in Xun, representing Yin's subtle state. Gen (mountain ☶) resides northeast, where Qian's Qi from Zi to Yin (northeast) is gathered as Da Xu (Great Accumulation), since Yang culminates in Gen, the terminus of Yang. The three-hour period from Zi to Yin corresponds to the three-line trigram structure.

This scripture primarily explains the interrelationships and symbolic meanings of several hexagrams from the Book of Changes (Yijing).

The Qian (Heaven) hexagram, with its six unbroken yang lines from midnight (子时) to mid-morning (巳时), represents the complete Qian hexagram. The Gen (Mountain) hexagram can accumulate and nourish the energy of Qian (Heaven). Maintaining integrity (zhen) and humility (xun) enables one to attain power, just as the Great Accumulation (Daxu) hexagram gains power through humble conduct. Conversely, arrogance leads to loss of power, as seen in the Small Accumulation (Xiaoxu) hexagram.

When Qian occupies the position of Hai (亥位), its first line corresponds to the constellations Shi and Bi, while the second line aligns with Kui. When Kun (Earth) occupies the position of Shen (申位), it corresponds to the constellation Shen. These celestial arrangements symbolize the dangers one might encounter while walking (as in "treading on a tiger's tail" in the Lu hexagram). However, if Qian is positioned beneath Dui (Lake), the danger of being bitten by the tiger is averted.

Observing the Tai (Peace) hexagram reveals the origins of the Pi (Stagnation) hexagram, and examining Pi uncovers the seeds of Tai. This phenomenon arises from the ascending and descending movements of yin and yang qi. Thus, both Tai and Pi illustrate the principle of cyclical transformation.

The upper Qian hexagram consists of thirty-six yarrow stalks (used in divination). Changing its central line transforms it into the Li (Fire) hexagram. The lower Li hexagram consists of twenty-four stalks, and altering its central line reverts it to Qian. This demonstrates that while two individuals may appear different externally, their inner intentions can align.

In the Dayou (Great Possession) hexagram, multiple yang lines flourish, yet the fifth line remains yin, symbolizing that a ruler should maintain their position through benevolence (ren) and virtue (de). Each line position carries distinct symbolism: the fourth line represents attendants, the third line signifies high ministers (三公), the second line denotes feudal lords, and the first line symbolizes remote regions. Implementing benevolent governance brings blessings to ancestral temples and ensures enduring foundations.

The Gen hexagram in the position of Yin (寅位) belongs to the Wood phase, symbolizing benevolence (ren), while Kun in Shen (申位) belongs to Metal, representing righteousness (yi). The Qian (Modesty) hexagram is rooted in sincerity—words spoken from the heart are genuine, whereas hypocritical speech does not reflect true intent. Authentic humility arises from within; outward modesty masking inner competitiveness is mere pretense.

This scripture primarily explains the symbolic meanings and interrelationships of several hexagrams from the Book of Changes (Yijing):

The Zhen hexagram (representing thunder) positioned beneath the Kun hexagram (representing earth) symbolizes the initial emergence of yang qi (vital energy), reflecting the fundamental principle of heaven and earth's cyclical movement. When yang qi ascends above Kun, it forms the Yu hexagram, which similarly embodies the Dao of heaven and earth. The middle line of Kun represents the ultimate state of stillness, hence described as "firm as a rock"; whereas the middle line of Zhen signifies stillness within movement, thus stating "persistent illness but never death."

The transition from Zhen to Dui (representing marsh) mirrors the journey from east to west, symbolizing the natural rhythm of spring planting and autumn harvest. This illustrates how yang qi arises from yin qi, while yin qi follows yang qi's movement. The top line of Dui carries connotations of restraint and regulation.

The Xun hexagram (representing wind) occupies the southeastern position (Si direction), where metal qi grows. By the due west (You direction), when metal qi reaches its peak, Xun's function is fulfilled. The fifth line of Xun mentions "Geng" (associated with metal), while positioned beneath Gen (representing mountain) in the Yin direction (associated with wood), it references "Jia" (associated with wood). Jia and Geng correspond to north and south respectively, cycling endlessly to manifest the principle of strategic adaptation.

The Lin hexagram symbolizes a ruler governing the people, emphasizing the importance of bestowing De (virtue/power) below while maintaining sincerity above. Granting De resembles yang qi below resonating with the earth; preserving sincerity requires practicing the Middle Way with wisdom while prioritizing simplicity. Mere sweet words like those in Dui would be akin to a ruler issuing decrees without implementing benevolent governance—fundamentally divorced from true statecraft.

The Guan hexagram depicts yin qi gradually increasing yet not encroaching upon yang qi. It is called "observation" rather than "minor strength" because the growing yin shows no intention to invade. So long as those above maintain centrality and uprightness, those below will be naturally transformed, preventing any yin infringement upon yang.

Though the Shihe hexagram uses the mouth as its primary symbol, it also connects to feet, nose, ears, and eyes, for the entire body relies on nourishment through the mouth. Nourishment aligned with the Dao brings Shihe's blessings, while deviation invites its misfortunes. Regrettably, petty minds often drown in greed, reaping more calamity than fortune.

This passage explains the symbolic principles of the Shihe (Biting Through) and Bi (Adornment) hexagrams from the Yijing (Book of Changes), along with the patterns of Yin-Yang transformation.

The Shihe hexagram (symbolizing biting and chewing) manifests as lightning seen before thunder is heard, mirroring how the tongue moves before teeth begin chewing. Both Shihe and Bi depict something held in the mouth, yet Shihe's lower trigram Zhen (Thunder) signifies action, while Bi's upper trigram Gen (Mountain) represents stillness. The Li trigram (Fire/Sun), formed by yielding lines enclosing firm ones, resembles the sun traversing the sky; the Gen trigram, with firm lines enclosing yielding ones, mirrors mountains standing still while generating clouds and rain.

Celestial observation primarily focuses on solar-lunar cycles: their conjunction creates lunar phases, and their alternating concealment forms the four seasons. When the fourth line of Li transforms, it reveals the mutual attraction between sun and moon—the key to celestial phenomena.

The bottom Yang line in the Fu (Return) hexagram actually represents the top Yang line of Bo (Peeling) descending back to earth, like unripe fruit containing the seed of Yang energy. The Hai hour (9-11 PM) corresponds to the Qian (Heaven) position, symbolizing trees nurturing vitality in winter, akin to dormant fruit yet to sprout.

Yao positions use the concrete number six, while Taiji (Supreme Ultimate) employs the abstract six. All numerals derive from this base: six progressing becomes seven, regressing becomes five. Seven represents Lesser Yang (Zhen trigram), eight Lesser Yin (Dui trigram). Fu's "return in seven days" occurs because Kun's Yin peaks during Hai hour; after six phases, Yang reemerges from Kan (Water) position, totaling seven with the initial one. This numerical principle permeates both the sexagenary cycle and the ancient Three Systems calendar.

The hexagram Fu (Return) symbolizes the restoration of primordial Qi. The phrase "return comes on the seventh day" speaks of the natural cycle of Yin and Yang's alternation. Both Zhongfu (Inner Truth) and Wuwang (Innocence) discuss sincerity, yet their essence differs fundamentally: Zhongfu's sincerity arises as natural genuineness from within, whereas Wuwang's sincerity resembles compulsion by external forces. Just as the yang line enters from the outer trigram to become the ruling line in the inner trigram, this kind of sincerity does not emerge spontaneously from within, thus fundamentally distinguishing it from Zhongfu.

The hollow central image of Yi (Nourishment) resembles a spirit turtle's shell. The cultivated person, observing this hexagram, becomes self-vigilant like the turtle, while the petty person gazes upon it with covetous eyes as if seeing a pregnant woman. The third line symbolizes the lower teeth's biting motion, making its peril exceed that of the second and fifth lines. This restlessness stems from the first line's influence from the Zhen trigram (symbolizing thunder's movement).

In Daguo (Great Excess), fortune and misfortune hinge on the first and top lines. A sagging ridgepole padded with straw demonstrates extreme caution, whereas a broken ridgepole resembles trees submerged by floodwaters—this constitutes true "great excess." The hexagram statement manifests in the third yang line: excessive yang creates "great excess." The second yang line pairs with young yin, thus resembling a withered willow sprouting new shoots, while the fifth yang line pairs with old yin where vitality is exhausted—like a withered willow flowering (yet bearing no fruit), signaling life force's depletion.

Kan (Abyss)'s judgment states "only the heart finds smooth passage," indicating a mind purified from attachments to good, evil, joy, or anger. Once contaminated by habitual tendencies, purity deteriorates. The entire Kan hexagram warns how petty men habituated to peril ultimately self-destruct, revealing the harm of malicious intent. Yin and Yang represent the beginnings of good and evil, movement and stillness respectively—when the mind stirs, evil thoughts arise (yang movement signifies good, yin stillness evil). The third yin line occupying a yang position (improper placement) and trapped between two yin lines demonstrates deeply ingrained bad habits. The fourth yin line correctly positioned between two yang lines symbolizes returning to innate sincerity, embodying simplicity and earnestness. Though the second and fifth yang lines occupy central positions, their immersion among yin lines inevitably taints them with bad habits. Thus Confucius noted their state of "not yet emerging from centrality" and "centrality not yet magnified."

This passage primarily explains the changing patterns of the Li (Fire/Brightness) and Xian (Resonance) hexagrams from the Yijing (Book of Changes), along with their underlying Yin-Yang philosophy.

In the Li hexagram, both the lower (inner) and upper (outer) trigrams are Li. The lower trigram represents the intrinsic luminous nature, while the upper trigram signifies the continuous manifestation of light. Just as the moon doesn't emit light itself but reflects sunlight to shine brightly, during the new moon (conjunction), the moon is enveloped by the sun's radiance before gradually revealing its luminosity—mirroring how the upper trigram encompasses the lower in the imagery of sun and moon following each other. Though Li symbolizes the sun, the overlapping of two Li trigrams creates lunar symbolism, hence called "double brightness," also illustrating how celestial bodies adhere to heavenly orbits.

The "yellow brightness" in the second six (Yin line at the central position of lower trigram) represents inner radiance, embodying the sincere and luminous essence. The fifth six (Yin line at the honored position) carries sorrowful symbolism, akin to the waning moon gradually distancing from the sun—where maximum brightness gives way to emerging darkness.

In the Xian hexagram (Mountain-Lake resonance), Yang energy occupies the central position. Like lake mist rising to the mountain while mountain springs flow back to the lake, it demonstrates the principle of mutual resonance between mountain and lake. The hexagram contains three Yang lines, with the fourth nine (Yang line at the center) symbolizing the human heart. However, being accompanied by two other Yang lines inevitably creates attachment, resulting in wavering thoughts.

The fifth nine (Yang line at the honored position) connects with the top six (Yin line), manifesting its effect through the top line's "cheeks and tongue" (symbolizing speech), while the fifth line itself remains obscure. The third nine (Yang line) links with the second six (Yin line), acting through the second line's "calf," while the third corresponds to the "thigh"—though the thigh follows the calf's movement, the back remains unmoved. Just as speech yields varying auspicious or ominous outcomes, different line interactions produce distinct effects.

Special mention goes to the first nine (initial Yang line) possessing perfectly balanced firmness and flexibility, earning Confucius's praise for its enduring adherence to the Middle Way. Though the fifth six occupies the central position, its pairing with a Yin line creates imagery of a woman's lifelong fidelity. The third nine's excessive Yang rigidity loses harmonious balance, while the initial and top lines deviate toward extremes, thus bearing ominous signs.

Finally, the yellow oxhide analogy illustrates: the second line (six-two) embodies central compliance like oxhide—only tough leather can bear heavy loads. The third nine in the outer trigram symbolizes leather; should it follow Qian (Heaven) into retreat, the second line would suffer misfortune, hence emphasizing the need to "hold fast" (metaphor for maintaining the Middle Way).

This passage explores the profound meanings behind several hexagrams from the Yi Jing (Book of Changes). It begins by explaining the relationship between "four yin" and "five yang": when a yin line (representing the yin principle) is positioned below and corresponds with the initial six, it's termed "mutual harmony," signifying the harmonious interaction between yin lines. When a yang line (representing the yang principle) is positioned below and corresponds with the second six, it's called "auspicious pairing," indicating the complementary union of yin and yang. The text emphasizes adhering to the correct path—severing ties with petty individuals to ensure good fortune.

The Dazhuang (Great Strength) hexagram features four yang lines below, symbolizing a solid foundation like a sturdy house, hence its name "Strength." The upper trigram is Zhen (Thunder), while the lower is Qian (Heaven). Zhen represents green bamboo, and when the third nine line of Qian transforms into Dui (Lake), with Dui in the west and Zhen in the east, a balanced east-west configuration emerges. This creates the imagery of a ram butting against a fence. When a ram pushes with its horns, its hooves also exert force; if the horns lack strength, the hooves become exhausted. The fourth nine line shares our nature—if it breaks through the fence to open a broad path, the ram may advance but with insufficient strength, while the three yang lines below form a solid axle.

In the Jin (Advance) hexagram, Qian symbolizes horses, yet Jin is dominated by Kun (Earth), with a yin line in the fifth position where horses shouldn't appear. Here, the horses are bestowed by Qian, representing the flourishing of feudal lords. Fire in heaven symbolizes the Son of Heaven (emperor), while both feudal lords and the emperor face south to govern—only with enlightened virtue (De) can they pacify the people, and only with pacified people can their positions be secure.

The Mingyi (Darkening of the Light) hexagram employs the judgments and images to convey praise. The fifth line represents Jizi, the sixth King Zhou, and the third nine mentions "hunting in the south to capture the great chief," alluding to King Wu of Zhou. The imagery of "rescuing strong horses" subtly refers to King Wu's ministers. The fourth six line, originally part of Kun, shares the human position with the third line, symbolizing the submission of Prince Weizi and Jiang Taigong to the Zhou dynasty. Both the initial nine and top six lines reside in Kan (Water), hinting at imminent ascension. Through these hexagram transformations, the text elucidates the profound philosophy of yin-yang harmony and the proper relationship between ruler and minister.

This passage primarily interprets the meanings of several hexagrams from the Yijing (Book of Changes). It begins with the Jia Ren hexagram (composed of Li below and Xun above), explaining how this configuration embodies domestic order. The Li trigram represents illumination (brightness within), while Xun signifies orderly arrangement (harmony without), with their yin-yang pairing forming the familial relationships of parents and spouses. The text quotes Confucius describing parents as "stern rulers" within the household, while Jiao Yanshou (a Han dynasty Yijing scholar) interprets the top line as representing ancestral temples, the fifth line as the sovereign—suggesting that in the Jia Ren hexagram, the ruler's position corresponds to the father.

Next, it examines the Kui hexagram (Dui below Li above), symbolizing mutual suspicion between yin and yang. Here, yang lines occupy yin positions, their misplacement breeding distrust. The usual resonant relationships between lines are blocked, prompting the sages to resolve this tension through line statements, guiding yin and yang back to their proper places. The Kui hexagram uniquely emphasizes conveying profound meaning through concrete imagery.

The analysis then turns to the Jian hexagram (Gen below Kan above), where two yang lines are trapped amidst yin lines, symbolizing adversity. While the fourth line suggests movement back and forth, both the second and fourth lines deviate from the central path, whereas the fifth and second lines maintain centrality. The sages demonstrate that by cultivating this middle way, one can remain composed even in hardship. The fifth line, centrally positioned in the upper trigram, handles difficulties without oppressing subordinates; the second line, centered below, shoulders responsibility without evasion. The third line's yang energy loses centrality, requiring self-cultivation of virtue; the fourth line's yin imbalance necessitates connection with yang. The bottom line, being lowest, must build reputation through cautious action, while the top line, near the fifth, should enrich itself by following wisdom.

Finally, it notes how the yang line in the Kan hexagram (the solid center line) resembles the yang line at the base of the Zhen hexagram—initially enclosed within Kan's yin embrace. This illustrates the nascent state of yang qi's emergence.

This passage primarily explains the changing principles and symbolic meanings of several hexagrams from the "Book of Changes" (Yijing).

First, it discusses the "Jie" (解) hexagram: with Kan (Water) above and Zhen (Thunder) below, resembling a seed breaking through its shell to sprout. The phrase "obtaining a yellow arrow" symbolizes integrity, as only with uprightness can the new shoot grow properly. The Jie hexagram reveals disordered Yin-Yang and improper positioning, with the top line symbolizing the resolution of chaos. Like a noble person temporarily dwelling among petty individuals while maintaining lofty aspirations, ready to realize their ambitions when the time is ripe.

Next, it examines the shared characteristics of the "Sun" (损) and "Yi" (益) hexagrams: both emphasize acting in accordance with the times. Just as reducing when reduction is needed won't be seen as stinginess, and increasing when increase is appropriate won't be considered extravagant. The "turtle of ten friends" symbolizes divination results aligning with popular sentiment.

The analysis then turns to the "Guai" (夬) hexagram: five Yang lines seeking to expel one Yin line resembles five noble persons dealing with one petty individual, which should be straightforward. However, this Yin line clings to the fifth position, connecting with the fourth to form the Dui (Lake) trigram's symbolism—like a petty person manipulating a noble figure, making decisive action difficult. The "sheep" symbolism differs between the "Dazhuang" (大壮) and "Guai" hexagrams: the former shares affinity with Zhen trigram, while the latter differs from Dui trigram.

Finally, it explains several special hexagrams:

• The "Gou" (姤) hexagram, originally pure Qian (Heaven), transforms through one Yin line's change, like a dragon becoming a fish and losing its horns' power.
• Qian's Yang energy begins at the midnight hour (子时), meeting Xun (Wind) trigram at the si hour (巳时, southeast), when Yin energy starts germinating—hence the name "Gou" (encounter).
• The "Cui" (萃) hexagram symbolizes all things gathering by category, with Yang lines occupying noble positions: one representing the Son of Heaven, another feudal lords, below them governing the Three Dukes, ministers, and scholars—all maintaining ancestral temple order to prevent chaos.

These hexagram transformations collectively illustrate the waxing and waning of Yin-Yang, the dynamics between noble and petty individuals, and the importance of aligning with temporal circumstances in all developments.

This passage explains the principles of Yin and Yang line transformations in the Eight Trigrams (Bagua) of the Book of Changes (Yijing). It first mentions that the "initial line" (the bottom line of a hexagram) embodies the nascent state of things, while the "top line" (the uppermost line) symbolizes a situation where something reaching its final stage may lose support.

Taking the "Cui hexagram" as an example, it resembles the scene of all things maturing and gathering in autumn. Here, the top line of the Dui trigram (representing autumn) serves as a metaphor—when the Kun trigram (representing Yin energy) from the southwest moves to the west, Yin lines multiply. Although the two Yang lines govern the overall situation, the top Yang line will ultimately lose support.

The single Yin line beneath the Xun trigram (representing wind) shares the same nature as the three Yin lines of the Kun trigram—both embody the descending quality of Yin energy. Yang energy, represented here by the two Yang lines, naturally ascends. When the initial line attaches to these two ascending Yang lines, and the three Yang lines connect as one, it forms the hexagram image of "yun sheng" (smooth ascension). Here, "yun" signifies being trusted by others.

When the Kun trigram governs in the Hai position (one of the Earthly Branches), Hai also symbolizes the state where trees are newly sprouted but not yet formed. Upon reaching the Zi position, with the Zhen trigram (representing thunder) beneath Kun—Zhen also belonging to wood—it resembles trees just beginning to sprout roots. If the Xun trigram lies beneath Kun, its two Yang lines possess stronger ascending momentum than Zhen's single Yang line, hence it's called "sheng" (ascension).

When the Sheng hexagram reaches the Chou position and arrives at Mao, the wood energy becomes vigorous—this is described from the perspective of the upper trigram's position. The fifth line represents the heavenly position, not something easily attained. Yet "zhen" (correct steadfastness) means adhering to the proper path, just as sage-kings like Yao, Shun, Yu, and Tang ascended to heavenly positions by following the correct way, as steadily as climbing steps. Without maintaining correctness, how could one avoid stumbling?

This scripture analyzes the changing line positions in the Yijing hexagrams of Kun (Hardship), Jing (Well), Ding (Cauldron), Ge (Revolution), and Zhen (Thunder), revealing the correspondence between natural laws and human affairs.

The Kun hexagram corresponds to the ninth lunar month, when the Dui (Lake) trigram governs as it meets the Earthly Branch Xu. Here, marsh waters are blocked by soil, hence the hexagram shows "a lake without water." Composed by overlapping Dui (representing mid-autumn) and Kan (winter), Kun's first yin line symbolizes early autumn vines yet to wither—like entangled kudzu. The third yin line at the autumn-winter transition depicts vines shedding leaves, leaving only thorns akin to tribulus. The bottom yin line beneath Kan signifies deep winter when frost exterminates vegetation, leaving mere deadwood—thus all three yin lines use plant imagery.

In the Jing hexagram, yang lines represent spring water originating from primordial yang energy. Kan's yang line in the north symbolizes cold springs, embodying the principle "northern direction generates cold, which generates water." Xun's two yang lines show one descending underground to form valleys rather than wells, while another—though at the human position—lies below the well curb (甃), harder to draw than the overflowing fifth line. Wells favor fullness while cauldrons abhor overfilling, reflecting their distinct virtues. The Ding hexagram depicts complete handles (铉), ears, and legs, yet its first line shows "overturned legs," balanced by the fifth line's "golden ears."

Though Ge contains imagery of cauldrons transforming raw food (like tripods cooking), its core symbolism is the crucible—Li fire melting Dui metal to forge revolution. Ge precedes Ding because cauldrons require smelting. When Xia dynasty cast the Nine Tripods, Shang Tang and Zhou Wu inherited and renewed them, forming the hexagram's revelation of "Tang-Wu revolution."

In Zhen's six lines: the first teaches how vigilance enables calm laughter; the second warns against chasing lost possessions, cultivating inner stillness and outer detachment; the third line's "trembling unease" (震苏苏) urges fault-correction and discernment to avoid missteps—all key to mind-cultivation. The upper trigram (lines 4-6) then discusses concrete actions.

This passage elucidates the symbolic meanings of the Gen (Mountain) and Jian (Gradual Progress) hexagrams from the Yijing (Book of Changes), as well as the imagery of yin-yang union in the Guimei (Marrying Maiden) hexagram.

The Gen hexagram (symbolizing mountain and stillness) employs bodily metaphors: it mentions "cheeks" rather than directly referring to the "mouth," "torso" instead of "abdomen," and "spine" (yin) rather than "ascending" (ji), precisely to capture the imagery of turning one's back and remaining motionless. Viewed holistically, the lower trigram does not distinguish between calves and toes, while the upper trigram does not separate torso from cheeks. The four yin lines are arranged like vertebrae, with the top yang line representing shoulders and the middle yang line symbolizing the waist. The Nine at the Third line is Gen's ruling line—a yang line in a yang position—whose restless nature resembles the waist, driving all bending, stretching, and daily movements, though actual motion is governed by the heart. Thus, the sages describe this state as "smoke in the heart." The Six at the Second line, a yin line in a yin position, embodies stillness like the calves; when the heart desires movement but the legs cannot act, discontent naturally arises.

The Jian hexagram (symbolizing gradual progress) combines Gen below and Xun (Wind) above, coinciding with the lunar January period when wild geese migrate north after the Spring Equinox—hence all six lines employ goose imagery. As geese follow yang energy's movement, and the Gen-Xun combination is confined to the yang-oriented north-south axis (zi-wu), the metaphor is apt. The Third line at Gen's apex and the Top line at Xun's summit represent northern and southern migratory routes. The Third line's solitary yang constrained by multiple yin lines coincides with both the geese's northward return and mating season, producing the imagery of "a husband departing for war while his wife conceives." The Third and Fourth lines (human positions in the hexagram) interact through yin-yang energy exchange, enabling conception, whereas the Fifth and Second lines—separated by heaven/earth positions and gender distinctions—cannot conceive.

In the Guimei hexagram (symbolizing a maiden's marriage), the Zhen (Thunder) trigram resembles green bamboo—solid below and hollow above, evoking a basket's form. Structurally similar to the Tai hexagram, Guimei's human-positioned Second lines interweave, creating imagery of overlapping sleeves. The human body's left (yang) and right (yin) sides unite like sleeves crossing. The younger sister (di), represented by a yang line below, contrasts with the sovereign's yin line above. The Yijing privileges yang (noble, virtuous) over yin (humble, perilous), hence the observation that "the sovereign's sleeves lack the maiden's splendor"—precisely the marital symbolism revealed through yin-yang line positions in Guimei.

This passage delves into the profound meanings and transformational principles of several hexagrams from the Yijing (Book of Changes). It begins by explaining the "Guimei" hexagram (symbolizing marriage), pointing out that improper conduct is akin to forcibly drawing eastern Yang energy into western Yin positions, causing Wood (represented by the Zhen trigram) to be overcome by Metal (represented by the Dui trigram). Action should be taken when the moon is waxing but not yet full; if one waits until full moon when Yin energy peaks, it will suppress Yang energy, much like juniors bullying elders or the lowly disrespecting the noble. Thus, the hexagram's line statements warn that military campaigns at this time bring misfortune with no benefit, as such actions deviate from the Dao and are unworthy of sages.

Next, it discusses how Fuxi arranged the eight trigrams, placing Zhen (thunder) in the east and Li (fire) in the south, representing the stirring of lesser Yang energy in the east and the flourishing of great brightness in the south. King Wen of Zhou combined Zhen and Li to form the Feng hexagram (symbolizing abundance), indicating how lesser Yang's vibratory movement reaches the south to unite with great brightness, creating prosperity. Yet King Wen's line statements caution: at the zenith of brightness comes decline, hence the advice to maintain the midday sun's state; excessive brightness paradoxically brings darkness, like seeing stars at noon or during a solar eclipse. While King Wen used only "sun" and "dipper" as metaphors, Confucius in the Commentary further explained with lunar imagery, as Feng corresponds to the fifth and sixth lunar months when the sun reaches the Willow constellation and the Big Dipper points to the noon position, making stars indeed visible.

The analysis then turns to the Lü hexagram (symbolizing travel and wandering): the second Yin line gains wealth and servants through adhering to the Middle Way; the fourth Yang line achieves harvest through balancing firmness and yielding, yet neither compares to the fifth Yin line. Li's brightness manifests through following wisdom, hence the auspiciousness of nurturing cows, while the top Yang line losing its ox signifies lost illumination. Positioned between the Guai and Qian hexagrams, Lü shows excessive Yang energy becoming transient guest energy. Though the top Yang line gains power, it's like placing oneself on blazing fire unaware of nest-burning danger; the third Yang line's eagerness to cling to power ignores impending disaster; while the second Yin and fourth Yang lines gain benefits through gentle conduct, the former must pay to avoid calamity, and the latter remains discontented—all warning against profit-driven journeys. As for the fifth Yin line, despite possessing Li's cultural elegance, losing arrows while shooting yields nothing, proving blocked paths bring no gain.

This passage explains the principles of hexagram transformation in the Yijing (Book of Changes), focusing on Xun (Wind/Wood) and Dui (Marsh/Joy). Using a bed as metaphor: Xun's four solid (yang) lines resemble neatly arranged bed planks, while its two broken (yin) lines act as supporting legs. The ninth line in second position corresponds to the bed's eastern side, while the top ninth line represents the western side—hence both reference "Xun beneath the bed," illustrating how legs support the structure.

The fifth yang line symbolizes the dragon's flight and tiger's transformation—the flying dragon representing yang Wood (Jia) and the transforming tiger representing yin Metal (Geng), both manifestations of Qi's dynamic changes. The top yang line loses its axe (symbolizing excessive yang dominance), while the second yang line's mention of diviners (Shi-Wu) indicates strong centrality without proper positioning. The third yang line's frequent frowning stems from being off-center. This demonstrates that true mastery of strategic adaptation belongs solely to the fifth yang line, which occupies both central and correct positions.

Kan (Water)'s initial yin line corresponds to winter solstice, while Li (Fire)'s initial yang line matches summer solstice, with Zhen (Thunder) and Dui marking spring and autumn equinoxes respectively. Dui's lower two yang lines (peak yang) represent July, its middle balanced lines signify August, and upper yin-dominated lines indicate September. Dui's fourth line discusses "autumn tones" (Shang Dui), reflecting the five musical notes: Zhen as Jue (角), Li as Zhi (徵), and Kan as Yu (羽). The fifth line's "yin overcoming yang" (Fu Bo) reveals Zhen's decisiveness, Li's encounters, and Kan's cyclical return.

Yang Qi emerges in the eleventh month (Zi, Water) and peaks by the fourth month (Si, Wind). Zi belongs to Kan-Water, Si to Xun-Wind—when Xun overlaps Kan, it forms Huan (Dissolution). Before summer solstice, yang energy expands outward while retaining inner generative power—this is Kan's single yang line, representing the primordial Qi of all existence. Yang governs Qi while yin governs form; yang's outward dispersal manifests as sweat and blood, while yin's internal differentiation creates limbs and organs—all transformations of original Qi. Human life originates from Kan-Water's primordial Qi (innate Jing), which vaporizes as sweat, flows as blood, and nourishes the entire body.

Transformations in Xun's top line and Dui's bottom line both generate Kan-Water. Water-Qi ascends to moisten Xun-Wood's foliage and descends to permeate Dui's marshes. This mirrors the body's fluid dynamics: rising as nourishing fluids, descending as vital essence—different manifestations of the same primordial Qi.

This scripture expounds the Daoist principles of yin-yang balance and desire moderation in health cultivation practices.

The first section employs hexagrams from the Classic of Changes (Yijing) as metaphors: The "Confined" (Kun) hexagram represents a state when marsh waters dry up, symbolizing the dissipation of human vital essence (Jing). The "Joyous" (Dui) hexagram with its yang line leaking below warns against indulging desires, while the "Abysmal" (Kan) hexagram with missing yin lines above cautions against excessive cravings. The text particularly emphasizes the health-preserving wisdom of "not crossing the threshold" - where the first line suggests safety in staying indoors, yet the second line paradoxically indicates danger in such confinement, teaching practitioners to discern the proper timing for restraining desires. Cultivators must comprehend the principles of essence circulation and vigilantly guard its gateways, which forms the crux of life-nourishment.

The second section discusses yin-yang transformations through the "Inner Truth" (Zhongfu) and "Influence" (Xian) hexagrams: Zhongfu symbolizes nascent yang energy, likened to avian oviparity, while Xian represents developing yin energy, comparable to mammalian viviparity. The seasonal egg-laying patterns of birds - most vigorous in spring - mirror the yang energy's sprouting during the Spring Commencement. Winter Solstice bird eggs signify the budding yang energy, yet since fire nature ascends, it requires water nature (symbolized by river fish) for harmonious balance to achieve auspiciousness. The "Small Exceeding" (Xiaoguo) hexagram's flying bird encountering the "Radiance" (Li) hexagram's danger illustrates how excessive yang energy inevitably generates yin energy, like birds flying eastward into southern nets.

The third section correlates the Yellow Emperor's pitch-pipe system with the Qian-Kun-Kan-Li hexagrams: Pure yang (Qian) and pure yin (Kun) differentiate into six yin and six yang manifestations, while Kan and Li form the "Already Fording" (Jiji) and "Not Yet Fording" (Weiji) states. When yang energy within Kan rises to the Zhonglü pitch, it corresponds to Qian's fullness; when yin energy within Li descends to the Yingzhong pitch, it mirrors Kun's emptiness. Jiji's commencement aligns with Qian's beginning, while Weiji's conclusion matches Kun's termination - using musical harmonics to illustrate the cyclical interplay of yin-yang energies.

Through these Yijing transformations, the scripture demonstrates that health cultivation requires mastering yin-yang equilibrium, practicing desire moderation, safeguarding vital essence, and following natural rhythms.

This passage explains the correspondence between the twelve months in the Book of Changes (Yijing) and the twelve musical pitches, along with the interactions between hexagram symbols. It describes the principle of Yin-Yang mutual generation (Yang generates Yin below, Yin generates Yang above), using various hexagram combinations to interpret natural phenomena and human activities.

The Li hexagram (symbolizing the sun) above represents noon, while the Kun hexagram (symbolizing earth and common people) below represents marketplaces. When Kun interacts with Qian (symbolizing heaven), it creates the phenomenon of trade circulation. Though Qian and Kun appear to embody Wuwei (non-action), they function through their six subsidiary trigrams—just as governing the world is like wearing clothes: Qian above represents the upper garment, Kun below represents the lower garment (skirts or trousers).

Specific hexagrams explain artifact creation: The combination of Qian (metal) and Xun (wood) symbolizes wooden boats floating on Kan (water); the sharp energy of Li (fire) represents carving wood into oars. Kun (ox) combined with Zhen (feet) signifies driving an ox-cart; Zhen (horse) with Xun (thighs) represents horseback riding. Kun is the carriage, Zhen the axle, and the top sixth line at the outermost position symbolizes pulling heavy loads or long-distance travel.

The Yu hexagram contrasts with the Qian hexagram. In Qian, Gen (gate) at the third line changes to the fourth line, forming a double gate. Gen represents hands, Kan hard wood, and Zhen sound—combined, this depicts striking hard wood to produce sound (like nightwatch clappers). Kun signifies closing gates, but Kan symbolizes approaching thieves, indicating bandit attacks.

The combination of Dui (metal) and Xun (wood) represents using metal tools to carve wood into pestles, while Xun wood entering Kun earth symbolizes hollowing the ground to make mortars. Kan's concave nature resembles a mortar's shape—the pestle moves above while the mortar stays still below, their trigrams corresponding to create the convenience of pounding. When Kan transforms into Xun, it symbolizes people crossing waters safely.

The Kui hexagram contrasts with the Jia Ren hexagram. In Jia Ren, Xun is wood, Li is silk, and Kan is bowstrings—together forming wooden bows. Dui metal sharpens Xun wood into arrows; Dui's decisiveness combined with Qian's strength can awe the world.

The Da Zhuang hexagram evolves from Dun: First changing into Zhong Fu, where Gen is dwelling and Dui is mouth, symbolizing cave dwellings. Second changing into Da Xu, where Qian above represents the sky and Xun's penetration transforms into Gen's stillness, symbolizing living in the wild. Third changing into Da Zhuang, with Zhen wood above as roof beams and Qian heaven below as eaves, while Xun wind hides and Dui marsh flows, awaiting wind and rain. Reaching Da Zhuang means no more bending.

The Dayi Xiangshu Goushen Tu (Great Changes Symbol Numerology Depth-Charting Diagrams) primarily discusses the relationship between hexagram transformations in the Yijing (Book of Changes) and the cultivation of virtue (De), as well as the mysteries of celestial-terrestrial yin-yang numerical principles.

Hexagram Transformations Section:

The Daguo hexagram (symbolizing excess) derives from the Dun hexagram (symbolizing withdrawal). The first transformation generates the Song hexagram (with Qian [Heaven] manifest and Kun [Earth] concealed). In the second transformation, Xun (symbolizing Wood) and Dui (symbolizing Metal) interact through conquest—Metal overcomes Wood. The third transformation forms the Ding hexagram, where Li (Fire) represents the eyes and Dui (Marsh) signifies dissipation. The transformation of the top yang line resonates with the lower trigram, while Kan (Water) and Dui form the Jie hexagram (symbolizing moderation). Changes in the lower trigram indicate the loss of temporal boundaries.

Nine Virtues Section:

The Lü hexagram (Heaven over Marsh) is the foundation of virtue; Qian (Earth over Mountain) is its handle; Fu (Earth over Thunder) is its root. Heng (Thunder over Wind) stabilizes virtue; Sun (Mountain over Marsh) refines it; Yi (Wind over Thunder) enriches it. Kun (Marsh over Water) discerns virtue; Jing (Water over Wind) provides its grounding; Xun (Wind over Wind) regulates it.

Hexagram Characteristics Section:

Lü achieves harmony at its peak; Qian embodies nobility and illumination; Fu, though subtle, distinguishes phenomena clearly. Heng manages complexity without fatigue; Sun transforms difficulty into ease; Yi grows continuously without artifice. Kun finds renewal through exhaustion; Jing remains steadfast yet adaptable; Xun balances while remaining concealed.

Hexagram Functions Section:

Lü harmonizes action; Qian establishes ritual propriety; Fu fosters self-awareness. Heng maintains constancy; Sun averts calamity; Yi initiates beneficial endeavors. Kun mitigates resentment; Jing clarifies righteous principles; Xun enacts strategic flexibility.

Numerical Relationships Section:

The upper canonical hexagrams follow a 3×3=9 pattern, while the lower canonical hexagrams follow 6×3=18. Specific hexagram counts: Lü (10), Qian (15), Fu (24), Heng (2), Sun (11), Yi (12), Kun (17), Jing (18), Xun (27). The nine hexagrams total 136; tripled, this yields 408. The celestial cycle counts 360 degrees, with the remainder 48 representing yin-yang advance/retreat. Yang Qi advances 48 units monthly from Fu to Qian (six months), while Yin Qi retreats 48 units monthly from Gou to Kun (six months)—demonstrating the nine hexagrams' numerical application.

Celestial-Terrestrial Numerical Generation:

Heaven's One (yang number) below generates Earth's Six (yin number); Earth's Two above generates Heaven's Seven. Heaven's Three on the left generates Earth's Eight; Earth's Four on the right generates Heaven's Nine. These numbers interweave and combine, forming the intricate transformations of all phenomena between heaven and earth.

This passage elucidates the patterns of hexagram transformations in the Book of Changes (Yijing). The mutual interaction of Yin and Yang energies gives birth to all things, generating the myriad phenomena between heaven and earth. As stated in the Great Commentary (Xici): "Through the transformations of three and five (参伍以变), and by interweaving their numerical patterns (错综其数), one comprehends the Dao of change, forming the textures of heaven, earth, and all creation."

The union of male and female symbolizes the twelve primary positions of the upper and lower classics, with the four hexagrams Qian (Heaven), Kun (Earth), Kan (Water), and Li (Fire) representing fundamental directions. The hexagrams Xian (Influence), Heng (Duration), Sun (Decrease), and Yi (Increase) derive eighteen directional positions. The transformations between Qian and Kun produce the Yi (Nourishment) and Daguo (Great Excess) hexagrams, which in turn transform into Kan and Li. These then give rise to Zhongfu (Inner Truth) and Xiaoguo (Small Excess), ultimately forming symbols of human relationships.

All sixty-four hexagrams originate from the interplay of one Yin and one Yang, progressing from the purely Yang Qian hexagram to the purely Yin Kun hexagram. The arrangement follows this pattern: first Qian (pure Yang) and Kun (pure Yin), then two Yang and two Yin pairings, followed by four Yang and four Yin, then sixteen Yang and sixteen Yin, and finally thirty-two Yang and thirty-two Yin, completing the sixty-four hexagrams. This illustrates the principle that "one Yin and one Yang constitute the Dao (道)."

The text also describes the cyclical movement of the Heavenly Stems and Earthly Branches: the thirty-day period from Jiawu to Guihai is called "prior Jia," during which a black qi halo persists from the Shen hour (3-5 PM) to the Si hour (9-11 AM). The thirty-day period from Jiazi to Guisi is called "posterior Jia," marked by a white qi halo extending from the Yin hour (3-5 AM) to the Hai hour (9-11 PM).

Yang hexagrams are dominated by odd numbers—thus one Yang line with two Yin lines, where Yang represents the ruler and Yin the people. Yin hexagrams are governed by even numbers—two Yang lines with one Yin line, where Yin symbolizes the ruler and Yang the people. In Yang hexagrams, the single Yang line above signifies the ruler, while the two Yin lines below represent the people—this is the natural order. In Yin hexagrams, two Yin lines above denote rulers, with one Yang line below as the people—this is the inverted order, hence called "the way of petty persons."

The Zhen (Thunder), Kan (Water), and Gen (Mountain) hexagrams belong to the Yang category yet contain more Yin lines because they derive from Kun (pure Yin), all structured as one Yang and two Yin. The Xun (Wind), Li (Fire), and Dui (Lake) hexagrams are Yin yet contain more Yang lines, originating from Qian (pure Yang), all structured as one Yin and two Yang.

Multiplying three by the heavenly-earth number fifteen yields forty-five; multiplying by five gives seventy-five; multiplying by seven produces one hundred and five. The Nine Palaces numbers culminate at one hundred and five, making one hundred and six the limit. Intermediate odd numbers like three, five, and seven are selected for calculations.

Finally, the text explains the governing functions of the eight trigrams: Qian presides over creation and covering, Kan over cold and transformation, Gen over moisture and change, Zhen over movement and dynamism, Xun over wind and fluctuation, Li over heat and summer, Kun over form and bearing, and Dui over dryness and alteration.

In the Bagua (Eight Trigrams) arrangement of the Yijing (Book of Changes), the four trigrams of Kan (north), Zhen (east), Qian (northwest), and Gen (northeast) belong to the Yang category, while the four trigrams of Li (south), Dui (west), Xun (southeast), and Kun (southwest) belong to the Yin category. This illustrates the principle of "like attracting like": the number six corresponds to Qian and Kan trigrams, nine to Kun and Dui, seven to Li and Xun, and eight to Zhen and Gen. When things are categorized by their kind, harmonious grouping brings good fortune while mismatched combinations create misfortune—this is the fundamental principle governing auspicious and inauspicious outcomes.

From the Zi hour (beginning with Qian) to the Si hour completes one cycle, while from the Wu hour (beginning with Kun) to the Hai hour forms another. The Yang lines total 292 strokes, amounting to 1,728; the Yin lines total 192 strokes, amounting to 1,152. Combined, these sum to 2,880. Through four calculations, this derives the total of 11,520, revealing the underlying pattern governing day-night transitions.

The upper canon of the Yijing contains thirty hexagrams, while the lower canon has thirty-four. The Li trigram holds special significance as it integrates characteristics of all other trigrams, demonstrating infinite subtle functions through the dynamic interplay of firm and yielding, ascent and descent—a distinct approach from the sequence presented in the Xugua Zhuan (Sequence of Hexagrams Commentary). As Han Kangbo observed, hexagrams may correlate through similarities or illuminate through contrasts, with all sixty-four interweaving to form a complete system.

The generative principle of the Taixuan Jing (Classic of Supreme Mystery) unfolds thus: One Primordial (Yi Yuan) generates Three Directions (multiplying one by three), Three Directions generate Nine Provinces (three by three), Nine Provinces generate Twenty-Seven Divisions (three by nine), Twenty-Seven Divisions generate Eighty-One Houses (three by twenty-seven), Eighty-One Houses generate Two Hundred Forty-Three Manifestations (three by eighty-one), Two Hundred Forty-Three Manifestations generate Seven Hundred Twenty-Nine Eulogies (three by two hundred forty-three), and Seven Hundred Twenty-Nine Eulogies generate Twenty-Six Thousand Two Hundred Forty-Four Divinatory Stalks (thirty-six by seven hundred twenty-nine). The entire Taixuan system symbolizes an annual cycle, with seventy-two stalks representing one day, calculated from the eleventh month.

All calendrical calculations originate from the winter solstice, while hexagram-Qi correlations (guaqi) begin with the Zhongfu hexagram. The foundational layer is "Primordial of Primordials, Day of Days, Qian of Qian," representing the ultimate One. The second layer, "Convergence of Primordials, Month of Days, Dui of Qian," corresponds to the number twelve. The third layer, "Primordial of Convergences, Day of Months, Qian of Dui," likewise corresponds to twelve.

This scripture employs the Daoist symbolic numerical system, constructing a comprehensive cosmic spatiotemporal calculation model through temporal units like "yuan, hui, yun, shi" and the arrangement of Bagua (Eight Trigrams) symbols such as "Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder)."

The numbers follow specific patterns: for instance, "360 days-stars of Qian transforming into Li" indicates calculating the solar cycle (days-stars) using the "yuan" unit, where the numerical value corresponding to Qian trigram transforming into Li trigram is 360. This number subtly corresponds to the degrees of the celestial sphere. Subsequent figures like 4,320 and 51,840 are multiples of 360, embodying the Daoist cosmological view that "nothing is beyond its vastness, nothing within its minuteness."

The fractional notations in parentheses, such as "51,840," represent ancient numerical writing conventions. These astronomical-scale calculations reflect Daoism's attempt to grasp cosmic patterns through mathematical modeling. Here, "Dui" signifies the Lake trigram, "Xun" represents Wind, and "Kan" symbolizes Water—each trigram transformation corresponds to specific numerical relationships.

This integrated system combines the hexagrams of the Yijing (Book of Changes), calendrical astronomy, and numerical divination, exemplifying how Daoism materializes abstract philosophy into mathematical models. What appears as complex numerical sequences essentially demonstrates the mathematical laws governing cosmic generation and evolution.

This passage employs the symbolic numerical system of the "Book of Changes" (Yijing) for cosmological calculations, primarily concerning the correspondence between astronomical calendrics and hexagram transformations. The terms "Zhen (Thunder), Li (Fire), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth), Qian (Heaven), Dui (Marsh)" represent the Eight Trigrams (Bagua), symbolizing eight natural phenomena. The numerical combinations denote temporal cycle conversions in ancient calendrical systems.

Phrases like "the Zhen trigram transforming into Li across generations, cycles and celestial periods" describe correspondences between specific temporal units (generation/30 years, cycle/12 years, celestial period/2-hour mark) with astral phenomena (stars) and trigrams (Zhen, Li), where subsequent numbers indicate calendrical values. Here, "generation" signifies thirty years, "cycle" twelve years, "celestial period" a two-hour mark, "year" one solar cycle, "month" one lunar cycle, and "day" one diurnal cycle—all being traditional Chinese time measurements.

These numerical operations embody the Daoist synthesis of astronomical calendrics with Yijing cosmology, using hexagram transformations to calculate temporal patterns. Fractional expressions like "155/15,200" likely represent certain cyclical proportions. The entire content belongs to the specialized calculations of ancient numerology (shushu xue), requiring knowledge of the "Supreme Principles Governing the World" (Huangji Jingshi) and other classical symbolic-numerological systems to fully comprehend its deductive logic.

This scripture records astronomical calendrical calculations from the ancient Daoist text Dayi Xiangshu Goushen Tu, employing a special numerical coding system to document celestial cycles. Fractions like "6/3" and "5/4" represent proportional divisions of time units, while terms such as "monthly motion" and "annual eras" denote different temporal measurement dimensions (e.g., months, years).

Kan (Water), Li (Fire), Xun (Wind), and Zhen (Thunder) are names from the Bagua (Eight Trigrams), Daoism's fundamental symbolic system, corresponding to natural elements. Numerical sequences like "55,908/1,872,000" represent accumulated year counts in ancient calendrics for calculating the cycles of celestial bodies. For instance, the figure 167,961,600 following "year of years, stone of stones, Xun of Xun" likely indicates a grand cycle of certain celestial motion.

This numerical recording method reflects Daoism's "cosmological mathematics" tradition, using precise calculations to comprehend the patterns of cosmic movement. References to earth, stone, fire, and water are not literal but signify different computational dimensions or celestial attributes. The entire passage essentially functions as an esoteric code for ancient Daoist astronomers to compute celestial phenomena, the exact correlations of which modern scholars continue to decipher.

This scripture documents an intricate Daoist numerology system primarily employing correlations between the Eight Trigrams (Qian/Kun/Zhen/Xun/Kan/Li/Gen/Dui) and the Five Phases (Water, Fire, Wood, Metal, Earth). The seemingly random numerical sequences actually conceal specific patterns:

The text first presents eight sets of paired numerical combinations (e.g. "6,0071,008/1,464,000"), each corresponding to distinct hexagram configurations. For instance, "Water-phase month Kun-Dui" signifies the combination of Water element with Kun (Earth) and Dui (Lake) hexagrams, while "Fire-phase star Gen-Li" represents Fire element paired with Gen (Mountain) and Li (Fire) hexagrams. These numbers likely relate to Zhou天 celestial cycles in Daoist cultivation, seasonal calculations, or alchemical timing in Neidan practice.

The latter section explains the system's organizational logic: beginning with the foundational "Ten Pures" (possibly referring to the Ten Heavenly Stems or pure hexagram states), then progressively "descending by one" (reducing one variable), "descending by two" (reducing two variables), until reaching the final "Five Harmonies" (five-element coordination). This graduated reduction mirrors the Daoist cultivation principle of "proceeding from simplicity to complexity, then returning to simplicity."

It's crucial to note these numbers often carry symbolic rather than arithmetic significance in Daoist practice—they may represent celestial cycles, elixir refinement timings, or cosmological measurements. Without complete methodological explanations, modern scholars find it challenging to fully reconstruct their original applications.

Human nature is originally complete and flawless, beginning from a state of pristine purity, ultimately capable of harmonizing with the celestial patterns of Heaven and Earth. The fundamental Qi (vital energy) that creates and transforms the cosmos—what Daoism considers the primordial energy constituting all things—is in essence identical to the original mind of sages. While the creative Qi originates from the sprouting growth of all beings, the sage's mind forever embraces the aspiration to aid the world and save humanity.

This creative Qi and the sage's mind, though shifting from stillness to movement and transforming from formlessness to form, enable all things to flourish smoothly and find their proper place. Why is it that people under Heaven never perceive the traces of their operation? Because although this creative Qi and sage's mind are in motion, they never depart from their source; though manifesting as concrete phenomena, they remain unattached to form. All creatures and common people receive their nourishment and guidance unknowingly, just as the sequence of the Bagua (Eight Trigrams) begins with Zhen (symbolizing thunder's movement) and culminates in Gen (symbolizing mountain's stillness).

The reason we call this principle "Di" (the Supreme Sovereign) is precisely because the creative Qi and the sage's mind share the same origin as one unified whole. This profound truth is the very mystery that the "Dayi Xiangshu Goushen Tu" (Great Change's Symbol Numerology Revealing Profundities Diagram) seeks to unveil.