《周易圖》

Interpretation

The Diagram of the Zhou Yi primarily describes the process by which Taiji (Supreme Ultimate, the cosmic origin) gives rise to all phenomena, as well as the relationship between the Bagua (Eight Trigrams), the Five Phases (Wood, Fire, Earth, Metal, Water), and Taiji.

In its initial state, Taiji has no concrete form—it is simply a primordial mass of undifferentiated Qi (vital energy). When this Qi divides, the light and pure aspects ascend to become Heaven, while the heavy and turbid aspects descend to form Earth, thus giving rise to the two polarities of Yin and Yang. These two polarities further differentiate, with the four elements (Metal, Wood, Water, and Fire) occupying the four cardinal directions, forming the Four Symbols. Among these, Water, associated with the number six, resides in the northern Kan position and generates the Qian trigram; Metal, associated with the number nine, occupies the western Dui position and generates the Kun trigram; Fire, associated with the number seven, resides in the southern Li position and generates the Xun trigram; and Wood, associated with the number eight, occupies the eastern Zhen position and generates the Gen trigram. In this way, the Four Symbols give rise to the Eight Trigrams.

Zhou Dunyi (courtesy name Maoshu) states in his Diagram of the Supreme Ultimate: "From Wuji (the formless, imageless origin) arises Taiji. Taiji moves and generates Yang Qi. When movement reaches its extreme, it transforms into stillness; when stillness reaches its extreme, it returns to movement. Motion and stillness are interdependent, giving rise to the two polarities of Yin and Yang. The interaction of Yin and Yang produces the Five Phases (Water, Fire, Wood, Metal, Earth), and the orderly movement of the Five Phases gives rise to the four seasons. The essential nature of the Five Phases is Yin and Yang, and the essential nature of Yin and Yang is Taiji, which itself originates from Wuji. Each of the Five Phases possesses its own unique characteristics, and the profound truth of Wuji combines wondrously with the essence of Yin-Yang and the Five Phases. The Dao of Qian (Yang) forms the male principle, while the Dao of Kun (Yin) forms the female principle. The interaction of these two Qi (energies) gives birth to the myriad things, which endlessly multiply and transform without limit."

The Zhengshi Taiji Guanyi Tu (Zheng’s Diagram of the Supreme Ultimate’s Unity) mentions: "The arrangement of the Eight Trigrams originated with Fuxi, developed during the Xia and Shang dynasties, and was perfected by the Zhou dynasty. When Confucius composed the Yi Jing (Book of Changes), he adopted this directional system, all of which is rooted in the fundamental principles of the Hetu and Luoshu (ancient diagrams said to reveal the cosmic order). The core idea always returns to the 'holding to the center and preserving unity'—the imperial Dao of the Supreme Ultimate. The number six represents Taiji encompassing twice the Three Powers (Heaven, Earth, and Humanity), with the Qian trigram occupying the sixth position at the center, best embodying Taiji. The Zhen trigram occupies the third position, symbolizing Taiji’s perfect state of encompassing the Three Powers. Kan obtains one, Kun obtains two—yet one is actually two, and two is three, illustrating how Water and Earth share the Shen position and mutually generate. Fixating on either good or evil, or exclusively on Yin or Yang, deviates from the Dao—this is the loss of the Middle Way, which the study of the Mean does not endorse. Overall, the odd numbers one, three, and seven represent different manifestations of Taiji."

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Interpretation

This passage elucidates several important numerical diagrams and cosmological theories from ancient China.

The River Chart (Hetu), said to be a mystical pattern carried by a dragon-horse emerging from the Yellow River, arranges numbers as follows: nine above, one below, three on the left, seven on the right, with two and four positioned like shoulders in the upper right and upper left respectively, while six and eight resemble feet in the lower right and lower left. All horizontal and vertical sums equal fifteen, with a total of forty-five. This numerical system is attributed to Chen Tuan (Master Xiyi) and was transmitted through figures like Zhong Fang, Li Gai, Xu Jian, and Fan Echang to Liu Mu.

The Nine Palaces (Jiugong), an ancient divination square, shares the same numerical arrangement as the River Chart. Yin-Yang practitioners correlated these with colors: one, six, and eight correspond to white; two to black; three to green; four to blue; five to yellow; seven to red; and nine to purple.

The Luo Writing (Luoshu), purportedly borne from the Luo River by a divine turtle, combines numbers thus: Celestial One (1) with Earthly Six (6) in the north generates Wood; Earthly Two (2) with Celestial Seven (7) in the south generates Fire; Celestial Three (3) with Earthly Eight (8) in the east generates Wood; Earthly Four (4) with Celestial Nine (9) in the west generates Metal; Celestial Five (5) with Earthly Ten (10) at the center generates Earth. The sum of odd numbers (1,3,5,7,9) totals twenty-five (Celestial Number), while even numbers (2,4,6,8,10) sum to thirty (Earthly Number), making fifty-five in total—believed to possess the mystical power to "complete transformations and command spirits."

The Diagram of Heaven-Earth's Natural Fifteen Numbers embodies six layers of meaning: 1) River Chart's horizontal/vertical sums of fifteen; 2) The total sum from one to ten being fifty-five, which contains fifteen; 3) The Taiji (Supreme Ultimate) dividing into Two Forms (Yin-Yang), then Four Phases (Lesser Yang, Greater Yang, Lesser Yin, Greater Yin), and finally generating the Bagua (Eight Trigrams)—a process embodying fifteen; 4) The Five Phases' (Wood, Fire, Earth, Metal, Water) numerical distribution reflecting Yin-Yang balance; 5) Seven (Lesser Yang) plus eight (Lesser Yin) equaling fifteen; 6) Six (peak Yin) and nine (peak Yang) also summing to fifteen.

Finally, the character "Yi" (易, Change) combines "sun" (日) and "moon" (月), symbolizing the cyclical transformations of Yin and Yang that represent the fundamental rhythms of cosmic operation—both daily and monthly cycles.

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Interpretation

The "Zhouyi Diagrams" section primarily elucidates the correspondence between the transformations of Yin-Yang in the Book of Changes and celestial-terrestrial patterns. All phenomena between heaven and earth—whether natural occurrences or human affairs—follow the principle of Yin-Yang's unity of opposites. The Book of Changes uses long lines (Yang Yao) and broken lines (Yin Yao) to represent these transformations, embodying the Daoist tenet that "the alternation of Yin and Yang constitutes the Dao (Yin-Yang zhi wei Dao)."

In the "Six Positions and Three Poles Diagram," scholar Zheng Shaomei proposed that the six Yao lines correspond to astronomical phenomena. Specifically, the second, third, fourth, and fifth Yao represent celestial longitude lines, while seven, eight, nine, and six denote latitude lines. In celestial observation, the Four Symbols (Sixiang)—Azure Dragon (Qinglong), White Tiger (Baihu), Vermilion Bird (Zhuque), and Black Tortoise (Xuanwu)—serve as longitude markers, while the Five Planets act as latitude markers. Notably, the numerical sequence of the six longitude positions omits the Black Tortoise's number because only the Big Dipper and Polaris are visible in the northern sky. Though termed "north," this region actually occupies the celestial center, subtly revealing how the Taiji (Supreme Ultimate) principle is concealed within the Five Phases (Wuxing). This is further evidenced in the River Chart (Hetu), where "one-six" occupies the northern position and "five" the center—both demonstrating the profound mystery of Taiji.

The latitude lines exclude Saturn's (Zhenxing) number because Saturn completes its celestial circuit only once every 28 years, while other planets all transit through its constellation. This mirrors the Yin-Yang school's doctrine that "Earth resides at the center, governing the four seasons." The Book of Changes' 384 Yao lines correspond to celestial transformations, with auspicious or ominous signs manifesting through the numbers seven, eight, nine, and six—paralleling the cyclical movements of the Five Planets.

Subsequent sections discuss the "Innate Number Diagram" and "Innate Symbol Diagram"—the Eight Trigrams (Bagua) arrangement attributed to Fu Xi, which encapsulates heaven-earth's mathematical laws. These diagrams were initially transmitted by Chen Tuan (Master Xiyi) and later developed by Shao Yong (Master Kangjie). The "Yin-Yang Doubling Diagram of 64 Hexagrams," traditionally ascribed to Hong Mai, aligns with the eight-position sequence of the Innate Diagrams. Other illustrations like the "Qian-Kun Six Offspring Diagram" and "Celestial Sphere Six-Position Diagram" all demonstrate the generative process from Two Forms (Liangyi) to 64 Hexagrams.

The concluding "Prior-Posterior Jia Diagram" receives commentary from Master Hanshang: during the spring equinox, the sun rises from the Jia position, while at autumn equinox it sets at Jia—a vivid representation of seasonal transitions through Yin-Yang waxing and waning.

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Interpretation

This scripture primarily discusses the Daoist principles concerning the Bagua (Eight Trigrams), the Naja system (which correlates the heavenly stems and earthly branches with the trigrams), and the generative processes of heaven and earth.

It first explains the meaning of "Geng-Jia," where Geng represents the beginning and end of heaven and earth. The inner black halo cycle commences from Jiazi, Jiaxu, and Jiashen—these three stages constitute the "prior Jia" phase, with Jiashen corresponding precisely to the Geng position in the outer ring. Similarly, the outer white halo cycle begins from Jiawu, Jiachen, and Jiayin—the three stages of the "posterior Jia" phase—where Jiayin in turn aligns with the Geng position in the inner ring.

In the Bagua Naja diagram, the Li trigram symbolizes the sun, while the Kan trigram represents the moon. The moon only emits light after separating from the sun. Starting from the Kun trigram imagery during the new moon (the end and beginning of the lunar month), after three days the crescent moon appears at the Geng position as the Zhen trigram. Five days later, the first quarter moon at the Ding position manifests as the Dui trigram. Seven days later, the full moon at the Jia-Ren position opposes the sun as the Qian trigram. Subsequently, the moon begins to wane, receding to the Xin position as the Xun trigram. Eight days later, the last quarter moon at the Bing position appears as the Gen trigram, and after another seven days, it reunites with the sun.

Scholar Zheng Hesha explains: The three lines of the Qian trigram represent heaven because "one encompasses three"; the six lines of the Kun trigram symbolize earth as "two doubles to six." These are the fundamental numerical principles of heaven and earth. The Qian trigram's "one encompassing three" gives birth to three yang-dominant offspring trigrams (Zhen, Kan, Gen), while the Kun trigram's "two encompassing six" produces three yin-dominant daughter trigrams (Xun, Li, Dui). This reveals the profound mystery of how heaven and earth generate phenomena.

The text further interprets the natural phenomena symbolized by each trigram: Zhen represents thunder, as thunder emerges from beneath the earth—hence its yang line is below; Kan symbolizes water, which is concealed within the earth—thus its yang line is in the middle; Gen signifies mountains, whose forms rise above the ground—so its yang line is on top. Yang governs movement while yin governs stillness—the Zhen trigram takes activity as its foundation, whereas the Gen trigram is rooted in stillness. Xun represents wood, which grows upward from beneath the earth—hence its yin line is below; Li symbolizes fire...

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Interpretation

Fire arises from wood, thus the yin (representing wood's pliant quality) resides within; the Dui trigram (representing marsh) resembles water gathering upon the earth's surface, hence yin occupies the upper position. Yin's nature is yielding while yang's is firm—just as wood begins tender but ultimately becomes strong, because yang (the growth energy) is in its unformed state. Yang represents brightness and yin obscurity, thus though fire appears radiant externally, it contains darkness within (yang outside). Yang is dry while yin is moist, therefore marsh water appears moist externally yet holds dryness internally (yang inside).

When asked why the Dui trigram's interior is paradoxically dry, this is because inner dryness generates metal (mineral deposits), while outer moisture gathers aqueous vapor. The principle that earth begets metal and metal begets water becomes evident through observing the Dui trigram—how could the sages' words be spoken lightly?

What follows is the diagrammatic derivation of the sixty-four hexagrams from the eight trigrams:

The Qian trigram (Heaven) sequentially generates:

1st generation: Gou (Heaven-Wind)

2nd generation: Dun (Heaven-Mountain)

3rd generation: Pi (Heaven-Earth)

4th generation: Guan (Wind-Earth)

5th generation: Bo (Mountain-Earth)

Wandering Soul: Jin (Fire-Earth)

Returning Soul: Dayou (Fire-Heaven)

The Kun trigram (Earth) sequentially generates:

1st generation: Fu (Earth-Thunder)

2nd generation: Lin (Earth-Marsh)

3rd generation: Tai (Earth-Heaven)

4th generation: Dazhuang (Thunder-Heaven)

5th generation: Guai (Marsh-Heaven)

Wandering Soul: Xu (Water-Heaven)

Returning Soul: Bi (Water-Earth)

The Zhen trigram (Thunder) generates:

1st generation: Yu (Thunder-Earth)

2nd generation: Xie (Thunder-Water)

3rd generation: Heng (Thunder-Wind)

4th generation: Sheng (Earth-Wind)

5th generation: Jing (Water-Wind)

Wandering Soul: Daguo (Marsh-Wind)

Returning Soul: Sui (Marsh-Thunder)

The Kan trigram (Water) generates:

1st generation: Jie (Water-Marsh)

2nd generation: Zhun (Water-Thunder)

3rd generation: Jiji (Water-Fire)

4th generation: Ge (Marsh-Fire)

5th generation: Feng (Thunder-Fire)

Wandering Soul: Mingyi (Earth-Fire)

Returning Soul: Shi (Earth-Water)

The Gen trigram (Mountain) generates:

1st generation: Ben (Mountain-Fire)

2nd generation: Daxu (Mountain-Heaven)

3rd generation: Sun (Mountain-Marsh)

4th generation: Kui (Fire-Marsh)

5th generation: Lü (Heaven-Marsh)

Wandering Soul: Zhongfu (Wind-Marsh)

Returning Soul: Jian (Wind-Mountain)

(Note: The terms "1st generation" through "5th generation" indicate sequential transformations of the hexagrams, while "Wandering Soul" and "Returning Soul" are Jing Fang's Yijing terminology from the Han dynasty, describing special phases of hexagram qi transformation.)

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Interpretation

This passage explains the transformational patterns of the sixty-four hexagrams in the Zhouyi (Book of Changes), primarily describing the evolutionary relationships between hexagrams. Here, "generation" (世) denotes the generational changes of hexagram images, "wandering" (游) refers to the Wandering Soul hexagrams, and "returning" (归) indicates the Returning Soul hexagrams—all representing specific states of hexagram transformation.

Take the Li hexagram (symbolizing fire) as an example: through transformation, it can generate derived hexagrams like Lü (Fire over Mountain, first generation), Ding (Fire over Wind, second generation), and Weiji (Fire over Water, third generation). Similarly, the Xun hexagram (symbolizing wind) can transform into Xiaochu (Wind over Heaven, first generation), Jiaren (Wind over Fire, second generation), and Yi (Wind over Thunder, third generation).

Zheng Xuan (a Han dynasty Confucian scholar) explains that the Qian hexagram (symbolizing heaven) transforms sequentially: the first change yields Gou (first generation), the second yields Dun (second generation), the fourth yields Pi (third generation), the eighth yields Guan (fourth generation), and the sixteenth yields Bo (fifth generation). Here, it mentions that "the top line remains unchanged," so the number thirty-two is excluded—since yin and yang each have thirty-two variations, combining them accounts for the top line of the sixty-four hexagrams.

The Wandering Soul hexagram is obtained by regressing eight positions from Bo to yield the Jin hexagram, while the Returning Soul hexagram is obtained by advancing sixteen positions from Qian to yield the Dayou hexagram. The Kun hexagram (symbolizing earth) follows an opposite but structurally identical transformational pattern.

For the Zhen hexagram (symbolizing thunder): regressing one position yields Yu, advancing two yields Xie, advancing four yields Heng, regressing eight yields Sheng, and advancing sixteen yields Jing—thus completing the five-generation transformation. The Wandering Soul hexagram is obtained by advancing eight positions from Jing to yield Daguo, while the Returning Soul hexagram is obtained by advancing sixteen positions from the original hexagram to yield Sui.

The Kan hexagram (symbolizing water) transforms as follows: advancing right by one yields Jie, regressing two yields Zhun, advancing four yields Jiji, advancing eight yields Ge, and regressing sixteen yields Feng—completing the five generations. The Wandering Soul is obtained by regressing eight positions from Feng to yield Mingyi, while the Returning Soul is obtained by regressing sixteen positions from the original hexagram to yield Shi. The Li hexagram (fire) follows a similar pattern. The Gen hexagram (symbolizing mountain) begins its transformations by regressing right one position from the Bi hexagram.

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Interpretation

This scripture primarily discusses the directional positions and symbolic meanings of the Eight Trigrams (Bagua) from the Zhouyi (Book of Changes).

Regarding the trigrams' directions:

The Zhen trigram represents the east, Li the south, Dui the west, and Kan the north. Among the four intermediate directions, Gen resides in the northeast, Xun in the southeast, and Qian in the northwest. The Kun trigram is specifically called "Earth" because all eight directions ultimately belong to the great earth. Although Dui represents mid-autumn, its direction isn't explicitly stated since mentioning mid-autumn naturally evokes the seasonal directional relationships.

Concerning symbolic meanings:

Li symbolizes "manifestation" as all things become visible here; Dui represents "joy," though mid-autumn isn't when all things rejoice—thus its marsh imagery is emphasized (as marshes are where creatures delight). Gen signifies "fulfilled speech"—while its fundamental meaning is ending things, its connection to the Yin position (beginning of spring) highlights its generative aspect. The character "致" (zhi, "bringing about") added to Kun indicates its supportive role in actualizing Qian's function.

Regarding the "Diagram of the Emperor Emerging from Zhen":

Chen Tuan (Master Xiyi) proposed that the Qi (vital energy) of creation and the sage's mind are interconnected. The creative Qi originates from life's initial stirrings, just as the sage's heart embraces universal compassion. Though moving from stillness to activity and non-being to being, both creative Qi and sage-mind never depart from their root, enabling all things to find their place without leaving traces. The trigrams' sequence begins with Zhen and ends with Gen—this "Emperor" represents the unity between creative Qi and sage-mind.

On Qian and Kun's positions:

Qian resides in the northwest, symbolizing the father principle, where austere energy is strongest; Kun occupies the southwest, embodying the mother principle, as nurturing energy peaks there. The northwest is where winter's accomplishments culminate, while the southwest flourishes with abundant life—Kun ultimately symbolizes the great earth itself.

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Interpretation

This scripture primarily elucidates the correspondence between celestial and earthly phenomena with human affairs, and how sages emulate the Dao of Heaven and Earth.

The text first explains how the Dao nourishes all things. Though it actively facilitates creation, the ultimate credit is attributed to "Qian" (Heaven), much like ministers serving their ruler dare not claim merit. This illustrates the principle of Heaven's Wuwei (non-action) enabling all things to grow naturally, just as a ruler governs effortlessly while the world achieves harmony spontaneously.

It then demonstrates how sages who comprehend the central path of cosmic operation can align themselves with Heaven-Earth, sun-moon, the four seasons, and spiritual forces. In the primordial state, sages unite completely with Heaven and Earth; in the manifested world, they follow celestial timing, showing their fundamental unity with creation. The text provides examples of natural correspondences: Zhen-Xun (thunder-wind) resonating, Gen-Dui (mountain-lake) seeking each other, Kan-Li (water-fire) complementing—like clouds following dragons or winds accompanying tigers, all phenomena follow their intrinsic patterns.

The latter section details symbolic meanings of select hexagrams from the sixty-four and their corresponding noble conduct:

Qian (Heaven) symbolizes celestial vigor—the noble person should ceaselessly strengthen himself;

Kun (Earth) embodies terrestrial receptivity—the noble person should cultivate magnanimity;

Zhun (Sprouting) shows thunderclouds stirring—the noble person should plan carefully;

Meng (Youthful Folly) resembles mountain springs emerging—the noble person should nurture virtue through resolute action;

Xu (Waiting) depicts clouds above heaven—the noble person may enjoy nourishment peacefully;

Song (Conflict) signifies heaven-water opposition—the noble person must begin endeavors cautiously;

Shi (The Army) represents water within earth—the noble person should embrace the people;

Bi (Holding Together) shows water over earth—ancient kings thus established states and bonded with lords;

Xiaoxu (Small Harvest) displays wind across heaven—the noble person refines cultural virtue;

Lü (Treading) portrays heaven above lake—the noble person clarifies hierarchies to settle minds;

Tai (Peace) manifests heaven-earth communion—rulers should assist people through proper governance;

Pi (Standstill) indicates heaven-earth separation—the noble person conserves virtue to avoid calamity, never coveting position.

These hexagrams collectively teach humanity to emulate natural principles by adopting appropriate attitudes and conduct according to varying circumstances.

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Interpretation

The hexagram diagrams of the Zhouyi (Book of Changes) reveal the operating principles of heaven, earth, and all things, with each hexagram containing profound wisdom for navigating life. Here are interpretations of selected hexagrams:

When the Li (Fire) trigram is below and Qian (Heaven) above, forming the Tongren hexagram, it symbolizes the mutual illumination of heaven and fire. A person of virtue (De) should discern the essence of things and classify phenomena with clarity. When Qian is below and Li above, creating the Dayou hexagram, it resembles flames rising to the heavens. In such times, the noble person must restrain evil and promote goodness, aligning with the benevolent mandate bestowed by the Dao of heaven.

The Gen (Mountain) trigram below and Kun (Earth) above form the Qian hexagram, like a towering mountain concealed within the earth. The wise should take from abundance to supplement scarcity, distributing resources equitably. With Kun below and Zhen (Thunder) above, the Yu hexagram emerges, akin to spring thunder awakening the earth. Ancient sage-kings thus composed music to celebrate virtue, offering grand sacrificial rites (Zhaijiao) to the Celestial Lord and ancestors.

When Zhen (Thunder) rests beneath Dui (Lake) to form the Sui hexagram, it resembles thunder hidden in marshland. The noble person emulates this by following the alternation of day and night in daily rhythms. The Xun (Wind) trigram below Gen (Mountain) creates the Gu hexagram, like swirling mountain winds—a time to inspire the people and cultivate virtue (De).

Particularly noteworthy: In the Daguo hexagram, lake water submerges trees, warning noble persons to uphold principles undaunted by solitude. The Kan (Water) hexagram shows ceaseless flowing streams, reminding us to persistently maintain virtue. The double Li hexagram’s radiance symbolizes great beings spreading civilization’s flame. The Xian hexagram’s lake atop a mountain teaches us to embrace others with open-hearted humility.

These hexagrams collectively demonstrate: When observing natural phenomena, we must perceive the embedded wisdom for living. Whether governing a state or cultivating oneself, one must harmonize with the Dao’s celestial patterns.

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Interpretation

The hexagrams in the Zhouyi (Book of Changes) contain profound wisdom for navigating life:

When encountering the Dùn hexagram ("Mountains beneath Heaven"), the noble person should distance themselves from petty people—not with overt disgust, but while maintaining dignified composure.

The Dàzhuàng hexagram ("Thunder in Heaven") reminds the noble person to steadfastly avoid actions that violate ritual propriety.

The Jìn hexagram ("Light emerging from Earth") teaches the noble person to manifest their luminous virtue.

Conversely, the Míngyí hexagram ("Light hidden beneath Earth") instructs that when governing others, one should display outward magnanimity while maintaining inner discernment.

The Jiārén hexagram ("Wind born from Fire") emphasizes speaking with evidence and acting with constancy.

The Kuí hexagram ("Fire above, Lake below") reveals how the noble person perceives differences within similarities.

The Jiǎn hexagram ("Water on the Mountain") teaches self-reflection and cultivation of virtue.

The Xiè hexagram ("Thunder with Rain") advocates forgiving others' faults.

The Sǔn hexagram ("Lake beneath Mountain") warns against unbridled anger and counsels restraint of desires.

The Yì hexagram ("Wind and Thunder aiding each other") instructs us to emulate good deeds and correct mistakes when found.

The Guài hexagram ("Lake water ascending to Heaven") reminds us to generously bestow kindness without claiming merit.

The Gòu hexagram ("Wind beneath Heaven") symbolizes how rulers should promulgate edicts to enlighten the realm.

The Cuì hexagram ("Lake upon Earth") advises preparing weapons against unforeseen events.

The Shēng hexagram ("Wood growing from Earth") illustrates how virtue must accumulate gradually.

The Kùn hexagram ("Lake without water") teaches perseverance in ideals despite adversity.

The Jǐng hexagram ("Water above Wood") encourages diligent mutual support.

The Gé hexagram ("Fire within Lake") stresses calendrical reform to clarify seasons.

The Dǐng hexagram ("Fire above Wood") instructs proper positioning and steadfast commitment.

The Zhèn hexagram ("Repeated Thunder") reminds us to maintain reverent awe while cultivating self-reflection.

The Gèn hexagram ("Stacked Mountains") warns against overstepping one's proper sphere in contemplation.

The Jiàn hexagram ("Water on the Mountain") demonstrates using virtuous talent to transform customs.

The Guīmèi hexagram ("Thunder over Lake") urges consideration of long-term consequences and foresight of potential pitfalls.

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Interpretation

This passage explains the interpretation and textual corrections of several hexagrams from the Zhouyi (Book of Changes). Each hexagram consists of upper and lower trigrams (Bagua), followed by ancient scholars' understanding of their symbolism.

Take for example the hexagram "Li below Zhen above" (Feng hexagram), which symbolizes continuous thunderclaps. When noble persons observe this hexagram, they understand they should adjudicate legal cases and enforce punishments with the decisiveness of thunder and lightning. The hexagram "Gen below Li above" (Lü hexagram) depicts fire on a mountain, reminding noble persons to administer punishments with clarity and prudence, avoiding unnecessary delays in legal proceedings.

Other hexagram interpretations are also listed: "Xun below Xun above" (Xun hexagram) symbolizes wind following wind, indicating that noble persons should repeatedly proclaim governmental decrees to implement affairs; "Dui below Qian above" (Dui hexagram) resembles two marshes connecting, suggesting noble persons should study and discuss with friends.

The text also points out textual errors in circulating versions. For instance, in the Kun hexagram's first six-line statement "Treading on frost, solid ice comes," some versions erroneously added the characters for "solid ice" beneath "frost." In the Zhun hexagram's third six-line statement "Approaching deer without guidance," some editions omitted the character "He" (how). These corrections were made by Guo Jing, Registrar of Suzhou during the Tang dynasty, in his Zhouyi Juzhenglue (Rectifications of the Zhouyi).

These hexagram interpretations reflect how ancient people derived principles for personal conduct and state governance from observing natural phenomena. Seeing "water over fire" (Jiji hexagram) reminded them to take precautions before problems arise; observing "fire over water" (Weiji hexagram) taught them to carefully distinguish things and maintain proper positions.

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Interpretation

This passage from the Zhouyi Tu primarily records the contents of the three-volume Ju Zheng by Guo Jing, as mentioned by the Song dynasty scholar Hong Mai (style name Rongzhai) in his Rongzhai Suibi. Guo Jing claimed to have obtained the authentic version of Zhouyi personally annotated by Wang Bi (courtesy name Fusi) and Han Kangbo, which contained 103 discrepancies compared to the popular editions of his time.

Here are listed 20 notable textual variations, such as:

• In the "Hexagram Kun" (困卦), the initial six-line statement's phrase "entering a dark valley" (入于幽谷) lacks the second "dark" (幽) character;
• The "Hexagram Ding" (鼎卦) commentary adds the three characters "and greatly penetrates" (而大亨) after "the sage cooks to sacrifice to the Lord" (圣人亨以享上帝);
• The "Hexagram Zhen" (震卦) commentary omits the crucial phrase "does not lose the sacrificial spoon and libation" (不丧匕鬯);
• The "Hexagram Jian" (渐卦) image statement misses the character "wind" (风);
• The "Hexagram Feng" (丰卦) fourth nine-line statement lacks the character "resolve" (志);
• The "Hexagram Zhongfu" (中孚卦) commentary inserts "pig-fish" (豚鱼) after "trust extends to" (信及);
• The "Hexagram Xiaoguo" (小过卦) commentary omits "can" (可) while mistakenly adding "auspicious" (吉), among others.

Hong Mai mentioned having seen this book in the Daoist Canon (Daozang) collection in Fuzhou, and later during his court service observed Chao Gongwu's Yijie frequently quoting it. As this work was exceptionally rare in the world, he deliberately selected these 20 conspicuous variants for preservation. These records hold significant reference value for studying the transmission and evolution of different Zhouyi editions.

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Interpretation

The "Zhouyi Diagrams" section primarily elucidates the generative principles and symbolic meanings of the Bagua (Eight Trigrams) and sixty-four hexagrams. Qian (Heaven) and Kun (Earth) represent the two fundamental attributes of the cosmos: Qian embodies Yang (represented by the number one), symbolizing heaven, circularity, clear Qi (vital energy), and movement; Kun embodies Yin (represented by the number two), symbolizing earth, squareness, turbid Qi, and stillness. These two trigrams contain the embryonic forms of the Four Symbols (Greater Yang, Lesser Yin, Lesser Yang, Greater Yin). Through the progression of "Two Modes generating Four Symbols, and Four Symbols generating Eight Trigrams," the complete system of sixty-four hexagrams ultimately emerges. This deductive process (from one to two, two to four, and so on up to sixty-four) fully manifests the patterns of celestial movement, seasonal transitions, and all human affairs. Thus, the Zhouyi begins with the Qian and Kun hexagrams. If practitioners of the Dao can trace this process in reverse—returning from the sixty-four hexagrams to the Taiji (Supreme Ultimate) origin—they may grasp the essence of the Yijing (Book of Changes), as transmitted through the lineage of Fuxi, King Wen, and Confucius.

Regarding specific hexagram diagrams:

The "Diagram of the Zhun Hexagram" explains that the northern Kan trigram (☵) belongs to Greater Yin, while the eastern Zhen trigram (☳) belongs to Lesser Yang. When Yang Qi enters the domain of Greater Yin—where Yang governs movement and Yin governs obstruction—the Zhun hexagram (䷂) emerges, symbolizing the arduous state of initial growth.

The "Diagram of Nurturing Uprightness in the Meng Hexagram" illustrates the path of self-cultivation through the Meng hexagram (䷃): the top Yang line represents external learning (outer study), which relies on sensory perception but may harm one's innate nature; the second Yang line represents internal cultivation (inner study), where seizing the pivotal moment when thoughts arise enables transcendence of constraints. What is conventionally called "benefit" (li) can paradoxically become a shackle for the mind.

The "Diagram of Waiting in the Xu Hexagram" analyzes the Xu hexagram (䷄): the lower Qian trigram's (☰) Yang Qi must await support from the Yang line within the upper Kan trigram (☵). Though the two Yin lines in the hexagram create obstruction—one retreating and the other advancing—the sage recognizes that the key lies not in the obstruction itself, but in whether the Yang line within Kan can respond in time. This embodies the Xu hexagram's core meaning of "awaiting the right moment."

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Interpretation

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

Regarding the "Diagram of Conflict (Song)": The Qian (Heaven) hexagram is positioned in the Hai direction, while the Kan (Water) hexagram originates from the Zi direction. Both Hai and Zi belong to the northern Water position. Initially, there is no contention, but once the original form is departed from—with Heaven tilting westward and Water flowing eastward, Heaven circling above and Water nourishing below—conflict arises.

The "Diagram of Leading the Multitude (Shi and Bi)" illustrates principles of governance: The Kun (Earth) hexagram represents the multitude, as does the Shi (Army) hexagram. To lead people, one must possess virtue (De), hence the Qian hexagram's first yang line enters Kun to form the Shi hexagram. The northern Kan hexagram corresponds to the fundamental Huangzhong musical pitch, hence the hexagram statement mentions "the elder" and the line statements reference "discipline." The north symbolizes darkness and martial discipline, while the south represents brightness and court assemblies. The Shi hexagram facing north signifies military organization in squads of five, while the Bi (Alliance) hexagram facing south represents the five ranks of nobility.

The "Diagram of Auspicious and Inauspicious in Great and Small Accumulation" distinguishes between the Xiaoxu and Daxu hexagrams: The Xun (Wind) hexagram occupies the southeast. When Qian's Qi enters Xun from the Zi to Si hours, being accumulated by Xun, it's called Xiaoxu (Small Accumulation). The Gen (Mountain) hexagram resides in the northeast. When Qian's Qi enters Gen from Zi to Yin hours, being accumulated by Gen, it's termed Daxu (Great Accumulation). This is because Gen represents the culmination of yang energy, hence the designation "great."

Collectively, these hexagram diagrams employ directional symbolism, yin-yang theory, and numerical correspondences to expound philosophical principles concerning human relationships, governance, and the transformations of yin and yang.

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Interpretation

This section of the Zhouyi Diagram explains the principles behind certain hexagram transformations. The Great Accumulation hexagram (representing gathering strength) gains initiative because it changes from the fifth yang line of Small Accumulation to a fifth yin line, maintaining a humble and low-key attitude that enables the accumulation of talent and resources. Conversely, Small Accumulation loses initiative when changing from Great Accumulation's fifth yin line to a fifth yang line—its pride and complacency lead to being controlled by others.

The image of the Treading hexagram (symbolizing cautious action) shows: When the Qian (Heaven) trigram occupies the Hai position, its bottom line corresponds to the Encampment and Wall constellations, while the second line aligns with the Bond constellation. The Bond constellation's restraining imagery resembles treading on a tiger's tail. When the Kun (Earth) trigram occupies the Shen position, the Triaster constellation becomes Kun's bottom line. The Triaster's connection with the Dui (Lake) trigram symbolizes being bitten by the tiger's tail. However, when Qian appears below Dui, there's no danger of being bitten while treading. The Treading hexagram's movement from Dui to Qian, traversing from Xu to Hai positions, demonstrates how human affairs should align with heavenly principles.

Observing the mutual transformations of Obstruction and Peace: The Peace hexagram's image reveals how Obstruction arises, while the Obstruction hexagram shows Peace's origins. These phenomena emerge from the ascending and descending movements of yin and yang qi, hence both hexagrams emphasize the principle of "coming and going."

In the Fellowship hexagram (symbolizing unity of purpose), the upper Qian trigram employs thirty-six yarrow stalks (for divination). Changing its central line makes it identical to the Li (Fire) trigram below, which uses twenty-four stalks—altering its central line likewise matches Qian. This shows how two parties, though outwardly different, can share identical intentions.

The Great Possession hexagram (symbolizing abundant harvests) illustrates the ruler's way of maintaining position: During yang abundance, the fifth position appropriately holds a yin line. The sovereign should comprehend primordial origins, uphold correct principles, and recognize that humaneness (ren) is key to preserving status. Specifically: The fourth line represents attending ministers who must avoid arrogance; the third line symbolizes the Three Dukes who should serve the Son of Heaven; the second line depicts regional lords who must bear responsibilities like large carts carrying heavy loads; while the bottom line, distant from the ruler, represents remote frontier regions that should avoid conflict. These all constitute methods of benevolent governance that bring blessings to ancestral temples and secure enduring foundations.

In the Modesty hexagram's (symbolizing humility) diagram: The Gen (Mountain) trigram occupies the yin (tiger) position, associated with wood and humaneness, while Kun occupies the shen (monkey) position, associated with metal and righteousness. The fifth and top lines contain martial imagery. True humility roots in sincerity, with speech expressing inner reality. Artificial words not from the heart constitute hypocrisy. Thus, humility from the heart embodies ultimate sincerity, while performative modesty remains mere pretense.

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Interpretation

This passage delves into the profound meanings of several hexagrams from the Zhouyi (Book of Changes), which I will explain one by one:

The Yu Hexagram (Thunder over Earth) illustrates the Dao of movement and stillness. The Zhen (Thunder) trigram beneath the Kun (Earth) trigram symbolizes the initial emergence of Yang Qi, representing the fundamental operation of heaven and earth. When Zhen appears above Kun, it resembles spring thunder awakening the earth, equally crucial to cosmic rhythms. The middle line of Kun signifies ultimate stillness, hence "firm as bedrock"; while Zhen's middle line represents stillness within motion, thus "holding to the correct path brings illness but not death."

The Sui Hexagram (Lake over Thunder) depicts Yin-Yang interaction. Moving from Zhen (east/spring) to Dui (west/autumn) manifests seasonal cycles. Yang Qi rises from within Yin, and Yin follows its movement; Yin welcomes Yang with joy, while Yang gathers following Yin. The top line of Dui resembles a tethered horse, symbolizing this mutual attraction.

The Gu Hexagram (Mountain over Wind) explains the generation and restraint among the Five Phases. The Xun (Wind) trigram occupies the southeast (Si position), where Metal Qi first emerges; by due west (You position) when Metal Qi peaks, Xun's purpose is fulfilled. The "Geng Metal" mentioned in Xun's fifth line forms a Metal-over-Wood relationship with the "Jia Wood" (Yin position) beneath Gen (Mountain), like worms born from wood—a natural process of decay. Yet the top Yang line represents noble character that can revitalize declining customs.

The Lin Hexagram (Earth over Lake) discusses leadership. A ruler governing the people must emphasize bestowing De (Virtue). Two Yang lines below resemble heaven influencing earth; maintaining mental clarity requires balancing wisdom with simplicity. If one acts like Dui (Lake)—all sweet words without action—it's like an emperor issuing edicts without practicing benevolent governance, which isn't true statesmanship.

The Guan Hexagram (Wind over Earth) demonstrates the Dao of yielding softness. Four growing Yin lines may seem like Yin encroaching on Yang, but this differs from the Da Zhuang hexagram where Yang overwhelms Yin. It's called "Observation" rather than "Small Strength" because yielding Yin harbors no aggressive intent. With gentleness below and centered correctness above, the people observe and transform naturally, preventing any transgression.

The Shi Ke Hexagram (Fire over Thunder) uses the mouth as its primary symbol while incorporating feet, nose, ears and eyes—showing how all body parts interconnect. This hexagram mainly teaches achieving harmony through coordinating all physical components.

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Interpretation

The human body relies on nourishment through food and drink, yet health cultivation must follow the correct Dao (the Way). The Shike Hexagram illustrates this principle—following the proper path brings blessings while deviating invites misfortune. When misfortunes outweigh blessings, it often stems from petty individuals indulging their appetites. The Shike Hexagram's imagery first shows lightning followed by thunder, mirroring how the tongue stirs food before teeth chew it—this reflects natural law.

Both the Shike and Bi Hexagrams (two of the sixty-four hexagrams) symbolize objects held in the mouth, yet Bi represents nobility while Shike represents eating. Shike manifests through the lower jaw's chewing motion, whereas Bi manifests through the upper jaw's stillness. Only the lower jaw's movement completes the act of nourishment.

In Bi Hexagram's celestial chart, the Li Trigram (one of the eight trigrams) represents heavenly phenomena like the sun, moon, and stars, while the Gen Trigram represents earthly features like mountains and vegetation. Yet Confucius only mentioned "celestial patterns" without referencing geography, because when observing celestial signs to compose hexagram statements, the primary focus was the luminous interplay of sun and moon. Their alternating movements create lunar phases, with the cycle of new and full moons forming the seasons—this is the method for observing temporal changes. The Li Trigram embodies the continuity of light; when Bi transforms the fourth line of Li, it symbolizes the sun and moon embracing each other—the key to understanding celestial laws.

The Bo Hexagram symbolizes the seed of Yang Qi (vital energy). The Yang line at the bottom of the Fu Hexagram is actually the top Yang line of Bo that has fallen underground, hence the imagery of "unconsumed abundant fruit." This Yang line resembles a seed of Yang Qi—the Qian Trigram represents tree fruits, and trees begin growing in the Hai position (twelfth Earthly Branch), which aligns with Qian's position. Trees possess vitality before sprouting; sprouting occurs in the Zi position (first Earthly Branch), where "Zi" signifies germination. The unsprouted fruit's essence originates from Bo's top Yang line, like fruit hanging from a treetop.

In Fu Hexagram's "return in seven days" diagram, the number six progresses to seven or regresses to five. Five represents six incomplete, while six represents five fulfilled—exceeding this becomes seven. Six is the limit; the initial emergence of one Yang line constitutes "return in seven days," while two Yang lines growing would bring "misfortune in the eighth month." Seven belongs to Lesser Yang, eight to Lesser Yin; the sun corresponds to the Zhen Trigram, the moon to the Dui Trigram. Though the Lin Hexagram shows Yang Qi increasing, it actually obtains Dui's eight-number, hence "misfortune in the eighth month." Fu's single Yang returning speaks of "seven days" because Kun's Yin culminates in the Hai position—six ends at one, and Fu emerges from the Kan position, combining to make seven. Numbers culminate in the sixty-year Jiazi cycle, Qi movement culminates in the Three Systems Calendar (ancient calendrical system), yet all return to the primordial origin—this is the meaning of "return in seven days."

The Wuwang Hexagram originates from the diagrammatic principle of the Zhongfu Hexagram.

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Interpretation

The Zhouyi Diagrams passage primarily explores the profound meanings of several hexagram groupings. First, it explains the hexagrams "Zhongfu" (Inner Truth) and "Wuwang" (No Error): Zhongfu represents sincere trust emanating from the heart, like naturally flowing authenticity, whereas the trust in Wuwang appears externally imposed, as if influenced by outside forces. The integrity in Zhongfu arises spontaneously from within, while that in Wuwang seems compelled from without—thus their fundamental natures differ.

The Yi hexagram (Nourishment) employs the spiritual turtle as metaphor: when noble persons observe this symbol, they cultivate self-vigilance like the sacred turtle, whereas petty individuals react with insatiable greed, drooling with desire. The third yao (line) symbolizes the lower teeth's biting motion, making its peril exceed that of the second and fifth lines. This dynamic emerges because the initial line carries the Zhen (Thunder) hexagram's symbolic meaning. The Li (Fire) hexagram also represents the turtle, conveying similar implications.

For the Daguo (Great Excess) hexagram, fortune and misfortune hinge on the first and top lines: when roof beams arch high, they require the caution of resting on straw padding; when beams bend, they resemble trees submerged in water. The third nine-yao's Yang energy is excessively strong, while the second nine-yao, harmonizing with nascent Yin (Shaoyin), can sprout new growth like withered willows. In contrast, the fifth nine-yao, paired with full Yang (Laoyang), exhausts its vitality—like withered willows flowering without fruiting.

The Kan (Abyss) hexagram discusses mental states: when the mind maintains purity, free from judgments of good/evil or joy/anger, it attains clarity. Yet habitual patterns transform identical circumstances into different outcomes. Petty men accustomed to danger ultimately harm themselves—a warning against nurturing negative tendencies. Here Yin represents negativity, Yang positivity. The third six-yao, Yin occupying a Yang position while trapped between two Yin lines, symbolizes complete corruption by bad habits. The fourth six-yao, Yin in Yin position achieving perfect stillness between two Yang lines, represents thorough refinement by virtuous habits. Though the second and fifth Yang lines occupy central positions, they remain submerged among Yin lines, inevitably tainted by negative influences—hence Confucius remarked they "have not yet emerged from centrality," failing to fully transcend environmental conditioning.

Finally, the concept of "continuous brightness" (jiming) emphasizes sustaining inner illumination. These hexagrams collectively illustrate how internal sincerity and external circumstances interact: practitioners must maintain constant vigilance, cultivating wholesome habits while avoiding contamination by harmful tendencies.

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Interpretation

The Zhouyi Diagram primarily explains the meanings of several hexagrams:

The lower and upper trigrams of the Li hexagram (symbolizing fire and brightness) both represent illumination. The lower trigram signifies foundational light, while the upper trigram denotes its continuation. Just as the moon borrows the sun's radiance, the upper trigram encompasses the lower, creating an image of successive solar and lunar brilliance. Though Li fundamentally symbolizes the sun, the doubled Li configuration introduces lunar imagery. The second six-line position, centered, emits yellow light representing sincere inner illumination; the fifth six-line position shows sorrowful signs, like the waning moon gradually distancing from the sun, where extreme brightness gives way to emerging darkness. The "auspicious" judgment here arises because maintaining vigilance against potential dangers paradoxically brings good fortune.

The Xian hexagram (symbolizing resonance) depicts mountain and marsh mutually influencing each other: vapor rises from the marsh to envelop the mountain, while mountain springs flow back into the marsh. The fourth nine-line position, though central, becomes unsettled due to influence from two other yang lines, prone to attachment and selfishness. The fifth nine-line connects with the top six-line like cheek and tongue; the third nine-line relates to the second six-line as thigh follows calf movement. These varying resonance relationships determine auspicious or ominous outcomes.

In the Heng hexagram (symbolizing constancy), only the second nine-line simultaneously possesses both firm and yielding qualities while being centered, thus embodying true endurance. The fifth six-line, though central, corresponds to a yielding position—like a woman maintaining steadfast virtue. The third nine-line's excessive firmness loses balance, while the bottom and top lines—one digging downward excessively, the other reaching upward recklessly—both deviate from the Middle Way and invite misfortune.

The Dun hexagram (symbolizing withdrawal) shows the second six-line's gentle and centered virtue resembling yellow oxhide's resilient load-bearing quality. The third nine-line in the outer trigram's yang position can avoid calamity by following Qian's yang withdrawal. The fourth nine-line, occupying a yin position with yang attributes, requires particular caution.

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Interpretation

This passage explains the symbolic meanings of several hexagrams from the Zhouyi (Book of Changes) and their implications.

The Dazhuang ("Great Strength") hexagram depicts four solid yang lines below forming a stable foundation like a house's structure, hence called "strength." Above is the Zhen trigram (representing bamboo), below is the Qian trigram. When the third line of Qian transforms, it creates the Dui trigram (representing sheep). Dui corresponds to the west and Zhen to the east - their opposition creates the image of a ram butting against bamboo fences. The initial line represents the ram's legs; when butting with horns, the legs must exert force - if the horns prevail, the legs tire. The fourth line shares our nature - if it breaks through the fence to open a broad path, allowing the ram to advance without exhaustion, the three yang lines below will reinforce our power.

The Jin ("Advancement") hexagram shows a yin line in the fifth position (normally unsuitable for horse symbolism), yet receives horses from the Qian trigram, symbolizing feudal lords flourishing abundantly. Lords should emulate the sun rising from earth - illuminating virtue to pacify the people. Only when people are settled can positions be secure, hence the term "Lord Kang" (the lord who stabilizes the state).

Finally, the Mingyi ("Brightness Harmed") hexagram features the fifth line representing Jizi (the virtuous Shang minister) and the top line representing King Zhou. The third line's "hunting in the south and capturing the chief" likely refers to King Wu of Zhou, while "rescuing with strong horses" denotes King Wu's ministers. The fourth line shares the human position with the third, symbolizing Weizi and Taigong submitting to Zhou. Both the initial and top lines belong to Kan (water, representing danger) - aspiring to ascend but falling like wind-blown grain, unable to sustain.

Through natural imagery and historical allusions, these hexagrams illuminate principles of ruler-minister relations and state governance.

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Interpretation

This passage elucidates the symbolic meanings and philosophical implications of several hexagrams from the Zhouyi (Book of Changes).

Regarding the "Family" hexagram (Jiaren), the text explains it symbolizes domestic order. With Li (representing fire and illumination) above and Xun (representing wind and compliance) below, it signifies the need for internal clarity and external harmony within a household. The pairing of one yin and one yang line embodies the relationships between parents and spouses. Confucius' saying "In the family there is a stern ruler" refers to parents serving as sovereigns within the home. Here, the fifth line traditionally representing the "ruler" is interpreted as embodying the father's role.

The "Contradiction" hexagram (Kui) emphasizes in its line statements the principle of "moving with the times." This means reducing when reduction is appropriate—the world won't consider it stingy—and increasing when increase is proper—the world won't deem it extravagant. The mention of "tortoise shells from ten friends" (ancient divination tools) suggests that when divination results align with popular sentiment, subjects won't rebel.

The "Resolution" hexagram (Guai) shows five yang lines resolving one yin line, symbolizing five noble men removing one petty person. Yet the yin line clinging to the fifth position makes this resolution difficult, like a petty man manipulating his superior—hard to shake off. The sheep metaphor illustrates different responses for different positions: those below should cultivate their reputation, while those near power should strengthen themselves by following worthies.

The "Deliverance" hexagram (Jie) represents emerging from Kan (symbolizing water and danger). Kan's yang line resembles Zhen's (representing thunder and action) lower yang line—initially trapped in peril but ultimately breaking free. This resembles a seed's kernel eventually sprouting, requiring steadfast integrity to grow. The hexagram shows a noble temporarily dwelling below, mingling with petty men yet holding lofty aspirations, ultimately finding opportunity for deliverance.

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Interpretation

This passage explains the symbolic meanings of several hexagrams in the Zhouyi (Book of Changes), using natural phenomena as metaphors for human relationships and principles of conduct.

The Nine in the Fourth and Six in the Third lines employ the metaphor of the "thumb" to remind noble individuals to maintain constant vigilance. Both the Sun (Diminishing) and Yi (Increasing) hexagrams emphasize the principle of moderation in action.

All six lines of the Kui (Opposition) hexagram reflect mutual suspicion due to the distrust between Yin and Yang. When Yang lines occupy inappropriate positions, it creates hierarchical suspicion: the second line corresponds with the fifth but is obstructed by the top line, while the top line corresponds with the third but is interfered with by the second. This mutual obstruction creates a state of opposition. Thus, the sages' line interpretations all explain how to resolve doubts and restore Yin and Yang to their proper positions. The Kui hexagram employs richer imagery than others precisely to fully express this meaning.

In the Jian (Difficulty) hexagram, both Yang lines are trapped between Yin lines, hence four of its six lines involve movement and change—only the second and fifth lines maintain centrality and correctness. Those who uphold the Middle Way can respond to adversity with equanimity, without needing deliberate maneuvering. The fifth line occupies the honored position yet excels at handling difficulties without oppressing subordinates, thereby attracting willing followers and gaining allies rather than isolation. Here the "sheep" symbolizes docility—when one transforms oneself, harmonious relations with kindred spirits naturally follow.

The Gou (Encounter) hexagram shows a pig at the initial line, while the Nine in the Third corresponds to buttocks; viewed holistically, it also carries fish imagery representing Yang encompassing Yin, while the Nine in the Fifth resembles spreading melon vines. Gou is fundamentally a Qian (Heaven) hexagram transformed by a single Yin line at the bottom, turning the dragon into a fish (rendering dragon horns ineffective). Qian's Yang energy rises from the Zi hour (11pm-1am) to peak at the Si hour (9-11am), precisely when it encounters the Xun (Wind) hexagram at the Si position, causing Yin energy to germinate—hence the name "Gou" (Encounter).

The structure of the Cui (Gathering) hexagram shows Yang lines above and below enclosing two Yin lines, illustrating how like attracts like. The Yang lines occupy the southern honored positions, symbolizing the Son of Heaven and feudal lords governing three ducal ministers, high officials, and scholars below, while upholding ancestral temple rituals above and preventing civil unrest below. The initial line's text warns rulers through vivid imagery against losing popular support.

(Note: "Zi hour" refers to 11pm-1am and "Si hour" to 9-11am in the traditional twelve earthly branches timekeeping system; the "three ducal ministers and nine high officials" refer to the Zhou dynasty bureaucracy, with the three dukes being the Grand Preceptor, Grand Mentor, and Grand Guardian.)

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Interpretation

This passage explains the correspondence between the Hexagram of Gathering (Cui) in the Book of Changes (Yijing) and seasonal/geographical relationships. Autumn represents the season when all things mature and gather, corresponding to the Dui (Joy) trigram in the Eight Trigrams (Bagua). The core of the Dui trigram lies in its topmost line (the uppermost unbroken line in the trigram), as the Qi (vital energy) of the Kun (Earth) from the southwest shifts to the west, increasing the number of Yin lines (broken lines in the trigram). Although two Yang lines (solid lines) govern the overall structure, the topmost Yang line loses its harmonious relationship with the numerous Yin lines.

In simpler terms, it resembles autumn harvest when grains gather, yet the uppermost ear of grain appears isolated. Here, the changing trigram imagery metaphorically illustrates the waxing and waning of Yin-Yang energies in specific seasons and directions, revealing that even in seemingly gathered states, imbalances may still exist.

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Interpretation

The "Zhouyi Diagrams" section primarily explains the symbolic meanings of three hexagrams, using natural phenomena as metaphors for human affairs.

The first is the "Ascending Steps Diagram," which illustrates the relationship between the Xun hexagram (symbolizing wind) with its single broken line at the bottom and the Kun hexagram (three broken lines). Here, yin energy sinks and stagnates while yang energy rises. The initial line attaches to two yang lines to ascend, forming unity with three yin lines, hence the hexagram image of "trustworthy ascent" (yun sheng). "Yun" signifies being trusted by others. The Kun hexagram governs the tenth lunar month (Hai month), when wood qi first emerges but hasn't taken form. By the eleventh month (Zi month), the Zhen hexagram appears beneath Kun—Zhen belongs to wood, symbolizing the first sprouting of roots. When Xun appears below Kun, it has two solid lines unlike Zhen's single initial yang line, hence called "ascent." The Sheng (Ascending) hexagram corresponds to the twelfth through second months when wood qi flourishes. The upper trigram discusses position—the fifth line represents the heavenly position, which cannot be reached by climbing steps. Yet "zhen" (constancy) is the correct path, as sage-kings like Yao, Shun, Yu and Tang ascended to heavenly positions through proper means, like walking steady steps. Without following the correct path, how could one avoid stumbling?

The second diagram shows "Thorny Vines and Tree Stumps in Adversity." The Kun hexagram corresponds to the ninth month, with Dui governing over Xu earth (northwest direction). Marsh water blocked by earth creates the hexagram's "marsh without water" image of hardship. Kun combines Dui (representing mid-autumn) and Kan (representing winter). Dui's single broken line symbolizes the first touch of autumn when creeping plants haven't withered—hence the "entangling vines" adversity. The third broken line marks the autumn-winter transition when leaves fall leaving only thorns—the "thorny brambles" adversity. The first broken line beneath Kan represents deep winter when creeping plants are killed by frost, leaving only stumps—thus all three yin lines use plant imagery to symbolize adversity.

The third is the "Well and Cauldron's Dual Use of Water and Fire Diagram." In the Jing (Well) hexagram, yang lines represent spring water because water originates from heaven's yang qi. The yang line in Kan trigram signifies northern cold springs (north generates cold, cold generates water). Xun's two yang lines—one flows downward at the earth position (a valley, not a well); the other at the human position lies below the well curb (zhou), making the water unreachable, unlike the fifth line's spring overflowing the curb. A well should overflow, yet the Ding (Cauldron) hexagram (symbolizing cooking) warns against overfilling—this distinguishes virtue from utensils. Though the cauldron's rings, ears and legs are all present, the first line's "overturned cauldron legs" signify initial upheaval.

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Interpretation

The Zhouyi Diagram passage primarily elucidates the meanings of four hexagrams:

The first section discusses the "Furnace of Transformation" image of the Ge (革) hexagram: While Ge shares the cooking symbolism of ancient tripods (dingli) that transform raw food into cooked, it more strongly evokes the image of a smelting furnace. This depicts the process of using fire to refine metal (represented by Dui's metallic attribute) and alter its form. Transformation (Ge) must precede the casting of ritual vessels. Historically, the Xia dynasty cast the Nine Tripods, later claimed by Kings Tang of Shang and Wu of Zhou as symbols of the Mandate of Heaven.

The "Vibrating Heart Traces" diagram explains the Zhen (震) hexagram: The initial line warns that caution brings later ease; the second advises not to chase lost possessions, teaching inner stillness and outer detachment. The third line's "alertness" (susu) maintains clarity. The upper trigram addresses action: the fourth line's "mired" indicates stagnation, the fifth's "no loss" signifies success, while the top warns against rash campaigns.

The "Back-Turning" diagram analyzes Gen (艮) hexagram: This symbolism focuses on cheeks rather than mouth, torso rather than belly, and waist rather than navel—all emphasizing backward orientation. Its four yin lines resemble a spine, with two yang lines above as shoulders and backbone. The third yang line (the hexagram's core) connects upper and lower like the waist, yet excessive movement disturbs the spirit. The second yin line, soft as calves, desires motion but cannot advance, hence the judgment "the heart is displeased."

Finally, the "Wild Goose's North-South Journey" depicts Jian (渐) hexagram: With Gen below and Xun above, it corresponds to the lunar month when geese migrate north after Spring Begins. All six lines employ goose imagery—these birds follow yang energy's movement. The third line (Gen's apex) and top line (Xun's summit) represent southern and northern positions respectively. The third yang line surrounded by yin lines illustrates the flock formation during northern migration.

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Interpretation

This passage explains the symbolic meanings of several hexagrams from the Zhouyi (Book of Changes):

Regarding the "Guimei" hexagram (symbolizing marriage and marital union):

When animals are about to mate and reproduce, there appear signs of the husband going to war and the wife becoming pregnant. This occurs when the yin and yang energies intersect at the human position to conceive. However, if the fifth and second lines are respectively in heaven and earth positions, being too distant and with distinct masculine-feminine separation, conception cannot occur. In the Guimei hexagram image, the Zhen trigram (representing thunder) symbolizes a bamboo basket - solid below and hollow above. This hexagram resembles the Tai hexagram, with intersecting lines at the human position, where the fifth line carries the imagery of overlapping sleeves. In the human body, the left side belongs to yang and the right to yin - their interaction resembles two sleeves joining. The younger sister occupies the lower yang position while the elder sister is in the upper yin position. The Zhouyi considers yang as good and yin as bad, yang as noble and yin as base, hence the elder sister's sleeve is inferior to the younger sister's, implying improper female conduct. This hexagram symbolizes eastern yang energy moving westward to meet western yin energy, representing wood being controlled by metal. One must wait until the full moon for auspiciousness, as forceful action brings misfortune.

Regarding the "Feng" hexagram (symbolizing abundance):

Fuxi placed the Zhen trigram in the east and the Li trigram in the south, showing lesser yang energy active in the east and the name of great yang flourishing in the south. King Wen of Zhou superimposed Zhen and Li trigrams to form "Feng," meaning the vibration of lesser yang moving south to unite with the brilliance of great yang, creating abundance. In the hexagram statement, King Wen explains the principle that extreme prosperity leads to decline, advising action at high noon. In the line statements, he notes that extreme brightness leads to darkness, mentioning seeing the Big Dipper at noon. Confucius further discusses the moon in the Tuan Commentary, as Feng corresponds to the transition between the fifth and sixth lunar months when the sun is at the Liu constellation position, the Dipper points to the noon-unextended direction, and the Liu constellation connects three celestial bodies - hence the logic of seeing the Big Dipper.

Regarding the "Lü" hexagram (symbolizing travel):

The second yin line gains resources and servants by maintaining the middle way; the fourth yang line obtains resources and an axe through balanced firmness and yielding, yet neither compares to the advantage of the fifth yin line. The Li trigram's brilliance comes from following its wisdom, hence the auspiciousness of nurturing female cattle. The top yang line losing cattle signifies losing brightness. The Lü hexagram follows Guai, with Qian...

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Interpretation

This passage elucidates the symbolic meanings and transformational patterns of several hexagrams from the Zhouyi (Book of Changes).

Regarding the "Travel" hexagram (Lü): The top Yang line, though in a favorable position, resembles placing one's body in raging flames, unaware of the impending disaster that may burn the nest. The third Yang line's eagerness to cling to power mirrors someone oblivious to self-immolation. The second Yin and fourth Yang lines employ gentle approaches—one gains resources, the other authority—yet the Yin line must personally experience hardship to avoid calamity, while the Yang line remains discontent. This warns against restless wandering for profit. The fifth Yin line begins like a beautiful pheasant but loses its arrow when shot, symbolizing unattainable ideals.

Concerning the "Compliance" hexagram (Xun): Yang lines represent bed planks while Yin lines signify bed legs. The second Yang line forms the eastern side of the bed, the top Yang line the western side. The fifth Yang line depicts a flying dragon transforming into a fierce tiger, representing Yang Qi's metamorphosis. The top Yang line's lost axe indicates excessive rigidity; the second Yang line's use of diviners (Shi Wu) shows strength misplaced; the third Yang line's distress reflects both lack of position and imbalance. Only the fifth Yang line, properly positioned and centered, can act effectively.

On the "Joy" hexagram (Dui): The lower two Yang lines' vigor symbolizes July; the middle pair's Yin-Yang balance represents August; the upper pair's Yin dominance signifies September. The fourth line's "merchant's exchange" corresponds to Zhen's Jiao note (角), Li's Zhi note (徵), and Kan's Yu note (羽). The fifth line's "sincere stripping" mirrors Zhen's Guai image, Li's Gou image, and Kan's Fu image.

Regarding the "Dissipation" hexagram (Huan): Yang Qi begins growing at the Zi hour (Kan hexagram) and peaks at the Si hour (Xun hexagram). Huan symbolizes dispersion, corresponding to the solar term between Summer Solstice and Great Heat when Yang energy expands outward. Though dissipating, Yang Qi still follows its cyclical patterns.

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Interpretation

This passage elucidates the correspondence between the movement of primordial Qi in the human body and natural laws. The human primordial Qi resembles the single yang line in the Kan trigram (one of the Eight Trigrams, symbolizing water), where yang Qi governs the movement of vital energy while yin Qi shapes the physical form. The outward diffusion of yang Qi manifests as sweat and blood, while the internal distribution of yin Qi forms the limbs and internal organs—all these are differentiated manifestations of primordial Qi.

Originating from kidney water (corresponding to the Kan trigram), this Qi represents the celestial essence of Tianyi (heavenly unity). When vaporized, it transforms into sweat; when flowing, it becomes blood that nourishes the limbs and organs.

Regarding desire restraint, the descending yang line in the Dui trigram (symbolizing marsh) warns against indulgence, while the absent yin line in the Kan trigram reminds one to abstain from cravings. Restraining desires is like closing the gates and not venturing out; abstaining from cravings means not coveting sweet or bitter tastes. The transformation of the initial line into the Kan trigram symbolizes Tianyi water—the source of true Jing (essence). Those skilled in life cultivation carefully guard this, closing the gates of vital essence.

The second line of Kan corresponds to heart fire—what's termed the "gate courtyard" actually refers to the heart's orifices. Heart fire should warm kidney water below, while the mind should observe external matters clearly. Secluding oneself contradicts the Middle Way, which also illustrates the principle of desire restraint. The third line's "lamentation" signifies regret over lack of restraint, while the fourth line's "tranquility" denotes contentment with moderation—both clearly revealing the consequences.

The Zhongfu and Xiaoguo hexagrams correspond to life generation patterns. Zhongfu generates yang Qi, corresponding to avian oviparity; the Xian hexagram produces yin Qi, matching mammalian viviparity. Thus Zhongfu marks the beginning of yang generation, while Xiaoguo serves as a warning during yang growth. Birds can lay eggs year-round but flourish in spring, corresponding to the Beginning of Spring solar term. Zhongfu contains the image of bird eggs—avian creatures belong to fiery ascending nature and require aquatic creatures (like porpoises) for auspiciousness, as the northern Zi position (water element) constitutes their habitat. Xiaoguo's flying bird encountering misfortune symbolizes eastward flight colliding with southern nets—these nets capture the yang Qi of the Li trigram (fire), and when Li appears, excessive yang begins generating yin.

The Yellow Emperor established musical pitches divided into yin and yang, harmonizing with the four trigrams Qian, Kun, Kan, and Li. Qian and Kun separate into six yin and six yang lines, while Kan and Li form Jiji and Weiji (two hexagrams symbolizing completion and incompletion). When the yang Qi within Kan ascends to the Zhonglü pitch, its corresponding sovereign hexagram becomes Qian—at this point, Qian's yang Qi is full yet invisible (having reached its zenith).

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Interpretation

This scripture primarily explains the correspondence between the Eight Trigrams (Bagua) and Yin-Yang Five Phases (Wuxing) in the Book of Changes (Yijing), as well as the patterns of hexagram transformations.

The first section discusses the cyclical relationship between the Qian (Heaven) and Kun (Earth) hexagrams. When the yin line within the Li hexagram (representing Fire) enters the Kan hexagram (representing Water), it corresponds to the Yingzhong pitch in the twelve-tone system, at which point the transformed hexagram becomes Kun. Kun represents emptiness, guiding the hidden yang energy (dragon qi). The beginning of the Jiji hexagram corresponds to the beginning of Qian, while the end of the Weiji hexagram corresponds to the end of Kun. The conclusion of Qian connects with the conclusion of Kun, moving from the number nine to ten; the beginning of Kun inherits the beginning of Qian, shifting from two to one—all of which follow natural principles.

The second section, "Diagram of Grouping by Category," explains the correspondence between the trigrams and directions: Kan corresponds to the north, with Qian gathering in the northwest by the completion number of Water (six); Zhen corresponds to the east, with Gen gathering in the northeast by the completion number of Wood (eight); Li corresponds to due south, with Xun gathering in the southeast by the generation number of Fire (seven); Dui corresponds to due west, with Kun gathering in the southwest by the generation number of Metal (nine). The trigrams each cluster according to their directional and Five Phases attributes.

The third section, "Diagram of Division by Kind," classifies Yin and Yang: creatures under heaven cannot be entirely yang, nor can plants be entirely yin. Thus, things are divided into groups based on Yin and Yang. Only humans, capable of both movement and upright posture, growth and action, possess the complete characteristics of Yin and Yang. More spiritually attuned than all other beings, humans can categorize and govern the myriad things.

The fourth section, "Diagram of Alternation by Threes and Fives," cites Wang Bi's interpretation: the mutual reference of three-line trigrams is "alternation by threes" (can), while combinations of the number five are "alternation by fives" (wu). Using Qian's yang lines to alternate into Kun produces the Zhen, Kan, and Gen trigrams; using Kun's yin lines to alternate into Qian produces the Xun, Li, and Dui trigrams—this is called "alternation by threes to transform," symbolizing the interaction of heaven-earth Yin-Yang. Pairing the numbers one with nine, two with eight, three with seven, four with six, and five with five is called "alternation by fives to transform," which together form the Great Expansion number fifty.

The fifth section, "Diagram of Threefold Heaven and Dual Earth," references Geng Nanzhong's explanation: "threefold heaven" sums the heavenly numbers one, three, and five to make nine; "dual earth" sums the earthly numbers two and four to make six. In divination, the numbers seven, eight, nine, and six are used, but only nine (old yang) and six (old yin) ultimately form the hexagram, discarding seven (young yang) and eight (young yin)—this is the "biased numbering" (yi shu) favoring one aspect.

The final section, "Diagram of Qian-Kun Harmonizing with Pitch Standards," cites Zheng Xuan's commentary on the Rites of Zhou: the generation of musical pitches is based on the sixfold Yin-Yang structure. The initial nine of the Huangzhong pitch (head of yang pitches) generates downward to the initial six of the Linzhong pitch (head of yin pitches), which in turn generates upward to other pitches. This explains the correspondence between musical pitches and hexagram lines.

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Interpretation

This passage discusses the correspondence between ancient musical tones and the Yi (Change) hexagrams, as well as the patterns of Yin-Yang transformation.

The text first explains the generative cycle of the twelve musical pitches (an ancient tonal system): beginning with Taicu, it descends to Nanlü, ascends to Guxian, and continues this alternating pattern until Zhonglü, ultimately returning to Huangzhong to complete the full tonal cycle.

The hexagrams are then used to illustrate Yin-Yang transformations: the initial emergence of Yang qi in the eleventh month corresponds to Huangzhong's energy, reaching its peak in the fourth month with the Qian (Heaven) hexagram. The first appearance of Yin qi in the fifth month aligns with Ruibin's energy, culminating in the tenth month with the Kun (Earth) hexagram. The metaphors of "opening the gate" (pihu) and "closing the gate" (hehu) vividly depict the waxing and waning of Yin and Yang.

Regarding the formation of the Four Symbols (Sixiang) and Eight Trigrams (Bagua): the Four Symbols represent the fundamental elements of Water, Fire, Wood, and Metal, corresponding numerically to Greater Yang (9), Greater Yin (6), Lesser Yang (7), and Lesser Yin (8). The Earth element, having no fixed form, harmonizes with the other four. Through numerical and directional correspondences, the eight trigrams (Kan, Qian, Dui, Kun, Li, Xun, Zhen, Gen) emerge systematically.

The explanation for using "nine" to denote Yang lines and "six" for Yin lines lies in numerology: nine represents the ultimate Yang number (being the largest among 1, 3, 5, 7, 9) symbolizing transformation, while six stands as the median Yin number (midway in 2, 4, 6, 8, 10) representing stability. These numbers also correspond to Heaven's generative numbers (1, 3, 5) and Earth's (2, 4).

Finally, the transformation process of the Qian hexagram (pure Yang) is detailed: beginning with the initial line's mutation, the first change produces Gou (first line turns Yin), the second Dun, the third Pi, until the fifth transformation yields Bo (with only the top line remaining Yang), demonstrating the gradual dissipation of Yang energy.

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Interpretation

Nothing remains in perpetual decline—when decay reaches its extreme, transformation occurs in the opposite direction. This is the meaning of the Fu hexagram (Earth over Thunder). When the Kun hexagram (Earth) reaches its limit, yang energy begins to rise again from below.

The process unfolds as follows: The first transformation is the Fu hexagram (the initial emergence of yang), the second becomes the Lin hexagram (the growth of two yang lines), and the third becomes the Tai hexagram (three yang lines opening prosperity). This continues until the fifth transformation forms the Guai hexagram (Lake over Heaven), where the process halts. Yet after decisive separation, there must be reunion, hence the subsequent appearance of the Gou hexagram (Heaven over Wind). The Fu and Gou hexagrams act like a microcosmic diagram of yin-yang transformation, serving as their "minor parents."

The progression of yang energy begins with the single yang line of Fu, expands to two yang lines in Lin, four in Tai, eight in Dazhuang, fourteen in Guai, and culminates in Guimei with sixteen yang lines. Conversely, yin energy develops oppositely: starting with the single yin line of Gou, it grows to two in Dun, four in Pi, eight in Guan, fourteen in Bo, and completes its cycle in Sui with sixteen yin lines. Three major transformations complete the cycle.

The eight trigrams govern the changes of all things, with the five directions forming correspondences through mutual interaction: the west (Earth-Four pairing with Heaven-Nine) generates metal; the south (Earth-Two with Heaven-Seven) generates fire; the center (Heaven-Five with Earth-Ten) generates earth; the north (Heaven-One with Earth-Six) generates water; and the east (Heaven-Three with Earth-Eight) generates wood. Scholar Nie explains: The numbers one, three, five, seven, and nine are odd and belong to yang, while two, four, six, eight, and ten are even and belong to yin. The five directions establish their correspondences through yin-yang pairings. The sum of yang numbers is twenty-five, while yin numbers total thirty. These numerical combinations drive transformation and mediate between spirits and humans.

Eighteen transformations complete the hexagram imagery: In the Book of Changes' upper and lower classics, the twelve primary positions (such as Qian, Kun, Kan, and Li) represent the pairing of male and female, supplemented by eight additional positions (including Xian, Heng, Sun, and Yi), totaling eighteen. From Qian and Kun emerge Yi and Daguo, transforming into Kan and Li, then into Zhongfu and Xiaoguo, and finally into Xian and Heng. This process mirrors the formation of human relationships.

Examples of symbolic meanings in the thirteen hexagrams:

• Li (doubled Li contains Xun's nature—Xun as rope, Li as mesh—woven into nets for hunting).
• Yi (Xun wood in front symbolizes the plow, Zhen wood behind symbolizes the spade, representing agricultural tools).
• Shihe (Li as the midday sun, rooted in Kun, which signifies people gathering in markets; Zhen below shows the initial interaction of firm and yielding, embodying trade).

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Interpretation

The "Zhouyi Diagram" scripture primarily elucidates how ancient sages invented various tools by observing natural phenomena, along with the nine hexagrams representing essential points of moral cultivation.

The first section explains the principles of invention corresponding to different hexagrams: The Qian hexagram symbolizes heaven above, representing upper garments, while the Kun hexagram symbolizes earth below, representing lower garments. The sages established the system of clothing to govern the world, emulating the natural Wuwei (non-action) of heaven and earth. In the Huan hexagram, Xun (wood) above Kan (water) forms the image of boats, used to traverse impassable areas. In the Sui hexagram, Dui (originally part of Kun) symbolizes oxen, and Zhen symbolizes horses, thus creating the convenience of ox- and horse-drawn carts for transporting heavy goods.

The Yu hexagram shows Kun symbolizing closed doors and Zhen symbolizing movement, forming the image of night watchmen to guard against thieves. The Xiaoguo hexagram, with Zhen above and Gen below, creates the image of mortar and pestle for processing grain to nourish the people. The Kui hexagram combines Li (symbolizing silk threads), Dui (metal), and Xun (wood) to form the image of bows and arrows, used to awe the world.

The second section lists nine hexagrams corresponding to moral cultivation: The Lü hexagram is the foundation of De (Virtue), the Qian hexagram its handle, and the Fu hexagram its root. The Heng hexagram stabilizes De, the Sun hexagram cultivates the self, and the Yi hexagram enriches De. The Kun hexagram discerns De, the Jing hexagram provides its foothold, and the Xun hexagram establishes its standards.

The third section further explains the practical significance of these hexagrams: The Lü hexagram teaches harmonious action, the Qian hexagram guides ritual formulation, and the Fu hexagram enables self-awareness. The Heng hexagram demands consistency, the Sun hexagram teaches harm avoidance, and the Yi hexagram instructs in benefit creation. The Kun hexagram brings understanding through adversity, the Jing hexagram enables stable adaptation, and the Xun hexagram teaches measured judgment and strategic concealment.

This passage embodies the ancient wisdom of "creating tools by observing phenomena" (guan xiang zhi qi), where practical inventions emerged from natural observation while hexagram principles were applied to moral cultivation, forming a complete practical system.

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Interpretation

This passage elucidates the profound principles underlying the arrangement of hexagrams in the Zhouyi (Book of Changes). First, let us clarify several core concepts: When the Dragon Diagram (Longtu)—the legendary pattern that inspired Fu Xi to create the Eight Trigrams (Bagua) after receiving the River Chart (Hetu)—unfolds, it reveals celestial phenomena. Fu Xi synthesized and applied these patterns, while Confucius silently apprehended their forms. By repeatedly contemplating the nine virtues (referring to the characteristics of the hexagrams), one can grasp their deeper mysteries.

To elaborate: The Lü hexagram represents the foundation of virtue, manifested in the number ten; the Qian hexagram is the handle of virtue, embodied in the number fifteen; and the Fu hexagram is the root of virtue, expressed in the number twenty-four. These three hexagrams belong to the upper canon of the Yijing, illustrating how the function of the Qian (Heaven) hexagram is governed by the Kun (Earth) hexagram. The remaining six hexagrams belong to the lower canon, demonstrating how the Kun hexagram’s function harmonizes with the Qian hexagram. This reflects the cosmic principle of "three for Heaven, two for Earth" (three as the Yang number, two as the Yin number).

Next, we examine the correspondences between hexagrams: Among the Eight Trigrams, the four hexagrams of Qian, Kun, Kan, and Li correspond to Zhongfu, Xiaoguo, Yi, and Daguo. The six groups of hexagrams with one Yang and five Yin lines (such as Fu and Bo, Shi and Bi, etc.) correspond to each other, as do the twelve groups with two Yin and four Yang lines. These correspondences extend all the way to the twenty groups of hexagrams with three Yin and three Yang lines, which also mirror one another.

Han dynasty scholars noted that when King Wen composed the Zhouyi, he used Qian, Kun, Kan, and Li as the core of the upper canon, while Gen, Dui, Zhen, and Xun formed the core of the lower canon. The upper canon concludes with Kan and Li, while the lower canon ends with Jiji and Weiji. The Yi, Daguo, Xiaoguo, and Zhongfu hexagrams serve as pivotal links between the two canons—Zhongfu symbolizes Qian, Xiaoguo symbolizes Kun, Yi symbolizes Li, and Daguo symbolizes Kan. Jiji represents the intersection of Kan and Li, while Weiji signifies their union. The reason Kan and Li can embody the functions of Qian and Kun lies in their manifestation of the harmonious balance (zhonghe) of Heaven and Earth. This is the principle by which sages respond to the transformations of all things without deviating from the fundamental Dao.

Shao Yong (Master Kangjie) marveled at this, saying: "King Wen, in composing the Zhouyi, truly grasped the patterns of Heaven and Earth’s movements. It was only when Confucius arranged the hexagrams that the wondrous vitality of creation was fully revealed."

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Interpretation

This passage primarily discusses the contents of the Miscellaneous Hexagrams Commentary (Zagua Zhuan) and the concept of the "Great Expansion Number" (Dayan zhi shu). First, it explains the distinctive features of the Miscellaneous Hexagrams Commentary: unlike other hexagram sequences that follow a fixed order, it rearranges the sixty-four hexagrams, interpreting their meanings through dynamic relationships such as firmness and yielding, ascent and descent, and reversal. For example, pairings like Qian (Heaven) and Kun (Earth), Bi (Closeness) and Shi (The Army), or Lin (Approach) and Guan (Contemplation) may seem randomly matched, but they actually demonstrate the manifold possibilities of Yin-Yang transformation. Zhu Zhen (a Song Dynasty scholar of the Yi Jing, known as "Hanshang Xiansheng") believed this arrangement reveals the infinite subtlety of hexagram transformations.

Later, the text cites Shao Yong's (Shao Kangjie) perspective: the Qian and Kun hexagrams undergo three transformations to form the Kan (Water) and Li (Fire) hexagrams, while Kan and Li themselves remain unchanged. The section following the Da Guo (Great Excess) hexagram may contain bamboo slip misplacements and should instead be arranged as Yi (Nourishment, symbolizing cultivating the correct path), Da Guo (Great Excess, symbolizing upheaval), Gou (Encounter, where yielding meets firmness), and Guai (Resolution, where firmness resolves yielding), illustrating the waxing of the noble path and the waning of the petty path. The Jian (Gradual Progress) hexagram speaks of a woman awaiting a man's proposal, while the Gui Mei (Marrying Maiden) hexagram represents a woman's marital destiny. The Ji Ji (After Completion) hexagram signifies stability, whereas the Wei Ji (Before Completion) hexagram symbolizes a man's hardship.

Regarding the "Great Expansion Number" (the fifty yarrow stalks used in divination): Han Kangbo explains that of the actual forty-nine stalks used, one remains unused. This unused stalk paradoxically governs the entire process—though not a concrete number, it completes the divination, embodying the principle of the "Supreme Ultimate" (Taiji). The forty-nine stalks together form a whole, yet when separated, they become forty-nine parts, with the Supreme Ultimate inherent within. Liu (possibly referring to the Song Dynasty scholar Liu Mu) further elaborates: movement and stillness share the same origin, and phenomena and essence are inseparable. Understanding that forty-nine represents "function" (yong) allows one to grasp that "one" is the substance (ti). Some have attempted to match the number fifty using celestial stems, earthly branches, or constellations, but this likely misses the original intent.

Finally, the text briefly mentions the method of yarrow stalk divination (she shi fa): the stalks are divided and counted three times. The first count is placed between the little finger (yielding either five or nine), the second between the middle finger, and the third between the index finger (yielding either four or eight). These are the specific steps of ancient yarrow stalk divination.

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Interpretation

This passage explains the specific procedures and symbolic meanings of the ancient divination method known as "stalk-counting." When using yarrow stalks for divination, four possible outcomes emerge through the process of division and counting:

The first scenario occurs when all three divisions yield the minority count (symbolizing the Qian hexagram, representing Yang), totaling 13 stalks. Subtracting this from the original 49 stalks leaves 36, which is the number of Greater Yang (Taiyang).

The second scenario happens when all three divisions produce the majority count (symbolizing the Kun hexagram, representing Yin), totaling 25 stalks. Subtracting this from 49 leaves 24, the number of Greater Yin (Taiyin).

The remaining six scenarios represent mixed outcomes:

• One minority and two majorities symbolize the Zhen hexagram
• One majority, one minority, then another majority symbolize the Kan hexagram
• Two majorities and one minority symbolize the Gen hexagram, all totaling 21 stalks. 49 minus 21 yields 28, representing Lesser Yang (Shaoyang)
• One majority and two minorities symbolize the Xun hexagram
• One minority, one majority, then another minority symbolize the Li hexagram
• Two minorities and one majority symbolize the Dui hexagram, all totaling 17 stalks. 49 minus 17 yields 32, representing Lesser Yin (Shaoyin)

The mentioned "Shao's Diagram of Imperial Ultimate Chronology" refers to Shao Yong's cosmic cycle theory, which uses temporal units like epochs (yuan), meetings (hui), cycles (yun), and generations (shi) to calculate historical evolution. The "Tai Xuan's Correspondence to the Changes Diagram" and "Kai Ziming's Diagram of the Profound Ultimate Scripture" represent other scholars' schematic interpretations of the Yi Jing.

The final paragraph describes the growth patterns of heaven, earth, and all things: After sprouting, all beings require rest; at peak prosperity, restraint becomes necessary; stability brings warmth, and only mature fruits hold value. Resources must be wisely utilized to achieve smooth progress, which leads to prosperity. However, excessive prosperity creates chaos, necessitating quiet cultivation. This stillness fosters harmony, harmony generates order, and with order, all things can develop sustainably.

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Interpretation

This scripture elucidates the mathematical principles governing cosmic operations, employing the hexagrams and numerical systems from the Zhouyi (Book of Changes) to calculate celestial and terrestrial transformations. It begins by stating that when phenomena reach their extreme, stagnation occurs; stagnation begets transformation, and through transformation, equilibrium is restored. Upon achieving equilibrium, restraint emerges, leading to chaos—yet chaos is never perpetual, as change ultimately reestablishes harmony through renewed circulation.

The text then details a specific numerical calculation system using grand temporal cycles from Daoist cosmology—"Yuan" (元, cosmic epoch), "Hui" (会, assembly), "Yun" (运, movement), and "Shi" (世, generation)—coordinated with the Eight Trigrams (Bagua: Qian, Dui, Li, Zhen, Xun, Kan, Gen, Kun). For example:

The first numerical sequence represents: the smallest unit "Yuan within Yuan" (元之元) corresponds to the Qian position within the Qian trigram, valued at 1. Next comes "Hui within Yuan" (元之会, using base-12 progression), aligned with the Dui position in Qian trigram, valued at 12. This layering continues—"Yun within Yuan" (元之运) at 360, "Shi within Yuan" (元之世) at 4,320—with values expanding exponentially.

The second set calculates using "Hui" as the base: "Yuan within Hui" (会之元) at 12, "Hui within Hui" (会之会) at 144, "Yun within Hui" (会之运) at 4,320, and "Shi within Hui" (会之世) at 51,840. Each tier multiplies the previous by twelve (as 1 Yuan = 12 Hui, 1 Hui = 12 Yun, etc.).

The third sequence operates with "Yun" as the unit: "Yuan within Yun" (运之元) at 360, "Hui within Yun" (运之会) at 4,320. These figures correlate with astronomical calendrics—360 corresponding to the degrees of celestial circumference.

This numerical architecture reveals the ancient mindset of deriving cosmic patterns through Yijing (Book of Changes) principles, constructing a holistic model of universal operations via correspondences between trigrams and numbers. Each value represents specific spatiotemporal dimensions of energetic states, embodying the Daoist worldview of "cosmic-human resonance" (天人相应)—where celestial mechanics mirror terrestrial phenomena through precise mathematical harmonics.

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Interpretation

This passage comes from the "Zhouyi Diagrams" section of the Huangji Jingshi, documenting a unique cosmic temporal calculation system. The text employs a computational method that correlates the Eight Trigrams (Bagua) from the Book of Changes (Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun) with units of time.

The first set of numbers describes the correspondence between the temporal unit "Yun" (Cycle) and celestial movements: one "Yun" corresponds to 129,600 stellar divisions (an ancient astronomical unit); three Yun equal 1,555,200 celestial divisions; five Yun equal 46,656,000 stone measures (an ancient weight unit); six Yun equal 559,872,000 earth divisions; seven Yun equal 16,796,160,000 fire divisions; and eight Yun equal 201,553,920,000 water divisions.

The second set explains the temporal unit "Shi" (Epoch): one Shi-Yuan corresponds to 4,320 days; one Shi-Hui equals 51,840 months; one Shi-Yun equals 1,555,200 stellar divisions; one Shi-Shi equals 18,662,400 celestial divisions; one Shi-Sui equals 599,872,000 stone measures; one Shi-Yue equals 6,718,464,000 earth divisions; one Shi-Ri equals 201,553,920,000 fire divisions; and one Shi-Chen equals 2,418,647,040,000 water divisions.

Finally, it mentions the temporal unit "Sui" (Year): one Sui-Yuan corresponds to 129,600 days; one Sui-Hui equals 1,555,200 months; and one Sui-Yun equals 46,656,000 stellar divisions. These numerical relationships exemplify the ancient Chinese mode of thought that used the Eight Trigrams to deduce the operational laws of the cosmos.

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Interpretation

This passage records complex computational data from ancient Daoist numerology systems, representing cosmic cycle numbers documented in the "Diagrams of the Zhou Changes." While these numbers may appear random, they actually follow specific numerological patterns:

These numerical combinations describe the cyclical patterns of celestial and terrestrial movements. Each set consists of three components: The initial "X/Y" denotes combinations of Heavenly Stems and Earthly Branches (for example, "5/4" represents the fifth Heavenly Stem "Wu" paired with the fourth Earthly Branch "Mao"). The middle section shows correspondences between the Five Phases (Wood, Fire, Earth, Metal, Water) and celestial bodies, while the large final number represents calculated cosmic cycle periods.

Take the example "(5/4) 歳之世石之辰巽之震五萬五千九百八十七萬二千": When the Heavenly Stem Wu pairs with the Earthly Branch Mao, its corresponding Five Phase attribute is Earth (represented by 'stone'), resonating with the Chen-Xun directional orientation, yielding an operational cycle of 559,872,000. These enormous numbers reflect ancient attempts to mathematically describe cosmic operational patterns.

Notably, the recurring number "559,872,000" represents a fundamental base value in ancient calendrical calculations, related to the orbital period of Jupiter (the "Year Star"). Most other numbers in the text are either multiples or divisors of this base value, embodying the ancient cosmological view of "governing heaven through numbers."

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Interpretation

This passage documents the "Primal Numerology" system proposed by Shao Yong (styled Kangjie) in his Northern Song dynasty work "Supreme Principles Governing the World." It correlates the Eight Trigrams (Bagua) — Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), and Kun (Earth) — with the Heavenly Stems and Earthly Branches to calculate numerical patterns governing cosmic time and space.

Notations like "7/3" and "8/1" represent specific sequences combining trigrams with stems and branches. For instance, "Gen's Li" denotes the combination of the Mountain trigram with the Fire trigram. The astronomical-scale numbers (such as "167,961,600,000") derive from Shao Yong's trigram calculations representing cosmic cycles, intended to describe the movement patterns of celestial bodies.

Shao Yong believed these numerical values contained the fundamental principles underlying all creation, asserting that historical cycles and natural transformations could be deduced through trigram permutations. This mathematization of Yijing studies reflects how Song dynasty Daoist scholars sought to interpret the cosmos through numerical models. It should be noted these figures aren't empirical astronomical data but symbolic calculations based on Yijing cosmology.

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Interpretation

This passage explains the numerical generation patterns of the Eight Trigrams (Bagua) — Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), and Kun (Earth) — and how numerical calculations reveal the transformations of all phenomena in the cosmos.

Each trigram corresponds to a specific number: Qian is 1, Dui is 2, Li is 3, Zhen is 4, Xun is 5, Kan is 6, Gen is 7, and Kun is 8. The Yang number is represented by 1, while the Yin number is 2. Starting from these foundational numbers, more complex numerical relationships can be derived. For instance, Qian begins with 1, Dui becomes 12, Li expands to 360, and Zhen reaches 4,320. The numbers for Xun through Kun are all calculated following the alternating patterns of odd and even generation.

When extending the Eight Trigrams to the sixty-four hexagrams, multiplicative methods are used to determine the totals. For example, multiplying Dui and Zhen yields the number 155,520. All generative numbers in the sixty-four hexagrams are calculated through this principle.

The text further suggests correlating natural phenomena — such as the sun and moon, stars, fire and water, earth and stone, cold and heat, day and night, flying birds and running beasts, flowers and trees — with the Eight Trigrams. By mastering these endlessly generative numerical patterns, one comprehends the principles behind the formation of all things; by understanding the numerical relationships of change, one gains insight into the mysteries of cosmic evolution. Those who truly wish to learn must contemplate in stillness the underlying principles behind these numbers.

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