《古易考原》

In ancient times, the legendary ruler Fuxi (also known as Paoxi) created the Eight Trigrams (Bagua) by observing the patterns of heaven and earth. He looked upward to study the movements of sun, moon and stars (celestial phenomena), downward to examine the characteristics of mountains, rivers and landforms (terrestrial features), while simultaneously observing the forms of birds and beasts along with the properties of all earthly things. Seeking patterns both within the human body and in external phenomena, he ultimately established the Bagua system to commune with the divine Virtue (De) and classify the essential qualities of all creation.

Specifically: Observing celestial phenomena, he created the Qian trigram (representing heaven), Li trigram (representing the sun), Zhen trigram (representing thunder), Xun trigram (representing wind), and Kan trigram (representing the moon with clouds and rain). From terrestrial features came the Kun trigram (representing earth), Dui trigram (representing marshes), Gen trigram (representing mountains), and Kan trigram (representing water). Animal characteristics were also incorporated: Qian corresponds to dragons and stallions, Kun to cows, Zhen to neighing horses, Xun to fowls, Kan to pigs and horse backs, Li to pheasants, crabs and tiger-leopards, while Gen represents dogs and rodents.

The text emphasizes how Confucius noted in the "Commentaries on the Yi" that Fuxi could comprehend the laws of heaven and earth through the trigram symbols alone. These symbols contain the fundamental principles governing all transformations, with later divination methods (using yarrow stalks) developing from this foundation. While the Three Dynasties (Xia, Shang and Zhou) primarily developed the divinatory applications of Yi studies, only Confucius truly understood the deeper meaning behind the trigrams. The author criticizes later scholars for misunderstanding this origin, mistakenly considering the Zhouyi as later additions—a view lacking fundamental understanding.

This scripture primarily explains the principles and process behind Fuxi's creation of the Eight Trigrams (Bagua). The text elaborates how the trigrams were established through observing the phenomena of heaven and earth: for instance, the Dui trigram symbolizes sheep, the Qian trigram represents tree fruits, the Zhen trigram embodies green bamboo and reeds, the Xun trigram signifies poplar trees, the Kan trigram corresponds to hard and thorny trees, the Li trigram denotes hollow and withered trees, and the Gen trigram stands for hard and knotty trees.

The method of creating the trigrams involved both observing nearby phenomena ("drawing from near at hand"), which encompassed not only the eight parts of the human body but also social relationships such as rulers and fathers, and observing distant phenomena ("drawing from afar"), which included not just everyday objects but also myriad things like round jade artifacts, metal, ice, and deep crimson colors. Initially, Fuxi created the eight fundamental trigrams (jinggua), from which the sixty-four hexagrams were later derived.

The text provides numerous examples of trigram combinations, such as the Qian trigram paired with others to form hexagrams like Guai, Dayou, and Dazhuang, or the Dui trigram combined to produce hexagrams like Lü, Kui, and Guimei, and so forth. The author emphasizes that the sage Fuxi's mind encompassed all phenomena of heaven and earth, observing plants, animals, and all things near and far, encapsulating universal principles within the trigrams. Through these symbols, he illuminated the divine virtue (De) and crafted objects in accordance with trigram principles.

Finally, the text critiques the Han Dynasty Confucian claim that the trigrams were based on the River Chart (Hetu), as well as the Song Dynasty Confucian assertion that one could derive trigrams merely by observing a rabbit. These views are dismissed as speculative, failing to grasp the essence of Fuxi's creation or Confucius's profound intent. It also firmly refutes the notion that Fuxi only created the three-line trigrams while the sixty-four hexagrams were later developed by King Wen of Zhou through doubling the trigrams.

This passage explains the combinatorial patterns of the ancient Bagua (Eight Trigrams, created by Fu Xi). Through systematic permutations, the author demonstrates how the overlapping of trigrams forms some of the sixty-four hexagrams.

First, the combinations with Qian (Heaven, one of the Eight Trigrams) as the base are explained: When Qian occupies the lower position, its pairing with each of the other seven trigrams produces distinct hexagram names. For instance, Qian below and Kun (Earth) above remains simply "Qian"; Qian below and Li (Fire) above forms "Dayou" (Great Possession); Qian below and Zhen (Thunder) above becomes "Dazhuang" (Great Strength), and so on. The author notes that when Qian is in the lower position, it dominates the configuration, while the upper trigram merely manifests Qian’s varying expressions.

Next, the combinations with Dui (Lake, another trigram) as the base are detailed: Dui below and Qian above forms "Lü" (Treading); Dui below and Dui above remains "Dui"; Dui below and Li above becomes "Kui" (Opposition), etc. Similarly, the author emphasizes that when Dui occupies the lower position, it governs the hexagram, with the upper trigram reflecting Dui’s transformations.

A particularly noteworthy distinction is made between the "primary trigrams" (the original Bagua) and "derived hexagrams" (composite forms). When a primary trigram appears alone, it is called a "primary trigram," but when combined with another, it becomes a "derived hexagram." For example, Qian standing alone is a primary trigram, while paired with another trigram, it forms a derived hexagram. This systematic approach reveals the rigorous logic underlying the Bagua system.

This passage explains how Fu Xi created the eight trigrams (Bagua) by using foundational trigrams like Li (representing fire), Dui (marshes), Xun (wind), and Kan (water) as bases, then combining them with other trigrams to form new hexagram names.

When the Li trigram occupies the lower position, its combinations yield distinct meanings: Li below with Dui above forms the "Ge" (Revolution) hexagram; Li below Li above remains the basic "Li" hexagram; Li below Zhen above becomes the "Feng" (Abundance) hexagram; Li below Xun above forms the "Jia Ren" (Family) hexagram; Li below Kan above creates the "Ji Ji" (After Completion) hexagram; Li below Gen above produces the "Shi" (Substance) hexagram; and Li below Kun above yields the "Ming Yi" (Darkening of the Light) hexagram. These are all variations of the Li trigram.

Similarly, when Xun occupies the lower position: Xun below Qian above forms the "Gou" (Encounter) hexagram; Xun below Dui above becomes the "Da Guo" (Great Exceeding) hexagram; Xun below Li above creates the "Ding" (Cauldron) hexagram; Xun below Zhen above forms the "Heng" (Constancy) hexagram; Xun below Xun above remains the basic "Xun" trigram; Xun below Kan above yields the "Jing" (Well) hexagram; Xun below Gen above produces the "Gu" (Corruption) hexagram; and Xun below Kun above becomes the "Sheng" (Ascending) hexagram. These are all variations of the Xun trigram.

For Kan in the lower position: Kan below Qian above forms the "Song" (Conflict) hexagram; Kan below Dui above creates the "Kun" (Oppression) hexagram; and Kan below Li above yields the "Wei Ji" (Before Completion) hexagram.

The commentator "Zhuo" (possibly an annotator) explains that in these hexagram combinations, the lower trigram serves as the host, while the upper trigram manifests its various transformational states. When the host trigram appears in the upper position, it ceases to be the host and instead becomes a variation of another trigram. This illustrates the Bagua's infinite capacity for mutual combination and transformation.

This passage explains the naming conventions for certain hexagrams formed by combining the Eight Trigrams (Bagua) in the Book of Changes (Yijing). When the Kan trigram (symbolizing water) occupies the lower position, its combinations with other trigrams produce the following hexagram names: paired with Zhen (thunder), it forms "Jie" (Release); with Xun (wind), "Huan" (Dispersion); with Gen (mountain), "Meng" (Darkening); and with Kun (earth), "Shi" (The Army). When Kan is doubled (both upper and lower), it remains "Kan," as it is one of the eight primary trigrams (Jingua).

The commentator Zhuo explains that hexagrams from "Song" (Conflict) to "Shi" (The Army) are all variations of Kan. When Kan occupies the lower position, it serves as the host trigram, while the upper trigram merely demonstrates Kan's different manifestations—hence they are collectively termed "Zuokan" (variations of Kan). However, when Kan appears in the upper position, it no longer acts as the host but becomes a variation of another trigram.

The same principle applies to Gen (mountain) in the lower position: paired with Qian (heaven), it forms "Dun" (Retreat); with Dui (lake), "Xian" (Influence); with Li (fire), "Lü" (Travel); with Zhen, "Xiaoguo" (Minor Excess); with Xun, "Jian" (Gradual Progress); and with Kan, "Jian" (Adversity). When Gen is doubled, it remains "Gen," another primary trigram. Hexagrams from "Dun" to "Qian" (Modesty) are all variations of Gen.

Lastly, several combinations with Kun (earth) in the lower position are listed: with Qian, "Pi" (Stagnation); with Dui, "Cui" (Gathering); with Li, "Jin" (Progress); with Zhen, "Yu" (Enthusiasm); and with Xun, "Guan" (Contemplation). These examples illustrate how the sixty-four hexagrams are systematically formed through upper-lower combinations of the eight primary trigrams.

This passage explains the arrangement principles of the eight trigrams (Bagua) in the Book of Changes (Yijing), consisting of Qian (Heaven), Kun (Earth), Zhen (Thunder), Xun (Wind), Kan (Water), Li (Fire), Gen (Mountain), and Dui (Lake). When the Kun trigram (symbolizing earth and yin softness) occupies the lower position with Xun (wind) above, this combination is called the "Bo hexagram"; yet the same Kun-below-Xun-above arrangement is sometimes directly referred to as the "Kun trigram" itself—this represents Fu Xi's original configuration when first creating the Kun trigram.

The scholar "Zhuo" (possibly an ancient Yijing commentator) explains that hexagrams ranging from "Pi" to "Kun" are essentially different manifestations of the Kun trigram. When Kun occupies the lower position, it dominates the configuration, with other trigrams superimposed above merely demonstrating Kun's variations. However, when Kun appears above other trigrams, it ceases to be dominant and instead becomes subordinate to those other trigrams.

The second section describes the cyclical movement of the trigrams. Heaven (Qian) is positioned in the south, Earth (Kun) in the north; Mountain (Gen) and Lake (Dui) share interconnected Qi; Thunder (Zhen) and Wind (Xun) mutually stimulate each other; while Water (Kan) and Fire (Li) remain non-conflicting. This arrangement follows an ancient immutable principle called "shu wang zhe shun" (recalling the past follows the smooth sequence)—the leftward rotation from the south proceeds in the order Heaven, Lake, Fire, Thunder; the rightward rotation follows Wind, Water, Mountain, Earth, both sequences operating from top to bottom.

The third section details trigram positioning: Heaven fixed in the south, Earth in the north; Mountain in the northwest exchanging Qi, Lake in the southeast exchanging Qi; Thunder stimulating in the northeast, Wind stimulating in the southwest; Water remaining non-conflicting in the west, and Fire non-conflicting in the east. This symbolic representation using natural imagery rather than direct trigram names reflects the expressive method commonly employed by ancient sages.

The Shuo Gua Zhuan (Explanation of the Trigrams) states that when the eight trigrams (Bagua) are arranged in mutual alternation, they can foretell future transformations. Thus, the Yijing (Book of Changes) employs reverse deduction for divination. It then explains the attributes of each trigram: Zhen (Thunder) stirs all things, Xun (Wind) disperses and spreads, Kan (Water/Rain) moistens and nourishes, Li (Sun) warms and illuminates, Gen (Mountain) brings stillness and stability, Dui (Marsh) gladdens all things, Qian (Heaven) governs and commands, and Kun (Earth) embraces and stores.

Here, it is worth noting that while Fu Xi’s arrangement of the sixty-four hexagrams is complete, the Shuo Gua Zhuan only mentions the eight trigrams, using them as a concise representation of the whole. The phrase "the eight trigrams mutually alternate" refers to the cyclical interaction of opposing trigrams—Heaven and Earth, Mountain and Marsh, Thunder and Wind, Water and Fire—forming a square matrix through their interwoven arrangement. The Song dynasty Yijing scholar Shao Yong (courtesy name Yaofu) interpreted the earlier mention of the eight trigrams as referring to the three-line single trigrams, and when they "mutually alternate," each trigram is superimposed with another to form the sixty-four hexagrams, thus interpreting "alternation" as "superposition." However, this is a misunderstanding, as "alternation" refers to horizontal combinatorial arrangements, while "superposition" implies vertical layering of trigrams.

The specific arrangement follows this pattern: Zhen (Thunder), with its stirring quality, is placed on the middle-left; Xun (Wind), with its dispersing quality, is on the middle-right—each with eight variations. Kan (Water/Rain), with its nourishing quality, follows Wind, while Li (Sun), with its warming quality, follows Thunder—each also divided into eight categories. Gen (Mountain), with its stabilizing quality, follows Rain, and Dui (Marsh), with its gladdening quality, follows Sun. Qian (Heaven), as the ruler, occupies the northern position, while Kun (Earth), as the storehouse, occupies the southern position. Although the trigrams' directional correspondences remain the same as in earlier descriptions, their sequence is now completely interwoven: whereas Heaven and Earth were previously placed first, here Li and Kan (Fire and Water) are positioned at the center, with Qian and Kun (Heaven and Earth) moved to the end. Mountain and Marsh, previously second, now become third, while Thunder and Wind, originally central, switch places with Heaven and Earth. This alternating arrangement reveals the deeper generative and controlling relationships between Heaven-Earth, Fire-Water, Mountain-Marsh, and Thunder-Wind.

This passage primarily explains the spatial arrangement and interlocking relationships of the Eight Trigrams (Bagua) — Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), and Kun (Earth). Positioned across the four cardinal directions, these trigrams form opposing pairs: Qian (Heaven) and Kun (Earth) face each other along the north-south axis; Dui (Lake) and Gen (Mountain) intersect diagonally between southeast and northwest; Li (Fire) and Kan (Water) oppose east-west; while Zhen (Thunder) and Xun (Wind) crisscross northeast and southwest. The sequence begins with Qian and proceeds through Dui, Li, Zhen, Xun, Kan, Gen, culminating in Kun, tracing a path from north to south and bottom to top — an arrangement described as "knowing the future requires reverse deduction" (zhi lai zhe ni).

The author critiques earlier scholars who mistakenly categorized Qian, Dui, Li, and Zhen as representing forward movement (shun), while Kun, Gen, Kan, and Xun signified backward movement (ni), arguing this interpretation lacks validity. Fuxi's original arrangement of the Eight Trigrams from Qian to Kun contained no inherent forward/backward distinction. Confucius (referred to as "the Master") merely employed circular movement (shun) and square arrangement (ni) as metaphors to elucidate the Zhouyi's principle that "wisdom preserves the past, while spiritual insight knows the future."

The text references Fuxi's 64 Hexagrams Square Diagram (formed by pairing the eight trigrams into sixty-four hexagram combinations), noting Confucian scholars once regarded it as an esoteric transmission preserved by occult specialists until Chen Tuan (Chen Xiyi) began teaching it openly, with Shao Yong (Shao Yaofu) later expanding its interpretation. The author maintains Confucius had already clarified these principles — Fuxi originally used the trigrams practically, while Confucius employed symbolism; without deep contemplation, their essence remains elusive.

Finally, the passage emphasizes how these two diagrams (likely the circular and square arrangements) embody yin-yang correspondences: the circle represents yang, movement, and Heaven; the square signifies yin, stillness, and Earth. The eight trigrams from "Heaven-Heaven" (Qian-Qian) to "Earth-Heaven" (Kun-Qian) demonstrate Heaven's fixed position in the south, while those from "Heaven-Earth" (Qian-Kun) to "Earth-Earth" (Kun-Kun) establish Earth's northern orientation. The "Heaven-Mountain" combination (likely Qian-Gen)...

This passage explains the correspondence between the eight trigrams (Bagua: Qian, Kun, Zhen, Xun, Kan, Li, Gen, Dui) of the ancient Book of Changes (Yijing) and natural phenomena. The mountain in the northwest (Gen trigram) shares Qi with Heaven's marsh (Qian and Dui), while the marsh in the southeast (Dui trigram) shares Qi with Heaven's thunder (Zhen). The thunder in the northeast (Zhen trigram) interacts dynamically with Heaven's wind (Xun), and the wind in the southwest (Xun trigram) interacts dynamically with Heaven's fire (Li). The fire in the east (Li trigram) does not conflict with Heaven's water (Kan), nor does the water in the west (Kan trigram) conflict with Heaven's fire (Li).

The circular arrangement of the sixty-four hexagrams (formed by pairing the eight trigrams) unfolds from south to north and top to bottom—this is called "shun" (順, following order). Among them, the Zhen trigram (thunder) governs the stirring of all things, and the Xun trigram (wind) governs their dispersal, embodying the characteristics of spring. The Kan trigram (water) nourishes all things, while the Li trigram (fire) warms them, embodying summer. The Gen trigram (mountain) halts growth, and the Dui trigram (marsh) brings maturity, embodying autumn. The Qian trigram (Heaven) commands all things, and the Kun trigram (Earth) gathers and stores them, embodying winter. The square arrangement of the sixty-four hexagrams unfolds from north to south and bottom to top—this is called "ni" (逆, reverse order).

The "Innate Diagram" (Xiantian Tu) transmitted by Shao Yong (Shaozi) of the Song Dynasty derives its principles from this arrangement. The text mentions three types of diagrams: first, the horizontally arranged trigram diagram; second, the circular trigram diagram; and third, the square trigram diagram. This is how Fuxi's system of trigrams was formulated by studying the patterns of Heaven and Earth.

This scripture primarily recounts how Fuxi (the legendary sage-king of antiquity) used milfoil divination to investigate the principles of heaven, earth, and all things. Confucius remarked that milfoil possesses a rounded and miraculous quality, capable of foreknowing the future. Its nature resembles the cyclical patterns of heaven and earth, thus it never contravenes the Dao of Heaven. Those who comprehend the patterns of all things can employ the Great Dao to benefit the world, their actions never straying from the proper path. Understanding how to follow the Mandate of Heaven dispels worry, while being content with one's lot and cultivating sincere benevolence nurtures universal compassion. Divine spirits (Shen) have no fixed form, just as the positions of lofty heaven and lowly earth are clearly distinct—all things naturally settle into their proper places of high and low, noble and base. Movement and stillness follow constant rules, hardness and softness can be discerned, things gather according to their kind, and from this arise auspicious and inauspicious outcomes. The heavens manifest stellar patterns, the earth takes on material forms, and through these transformations become evident. Hard and soft qualities rub against each other, the Eight Trigrams (Bagua) mutually stimulate—these constitute the profound mysteries of Fuxi's milfoil-based derivations of the Yi numbers.

It is precisely through this rounded, miraculous milfoil calculation that one can explore the patterns of heaven, earth, and all things within the hexagrams, foreseeing future fortunes and misfortunes. Thus the ancient text Guyi Kaoyuan subsequently expounds Fuxi's milfoil-based Yi principles.

Regarding the River Chart (Hetu, the mystical diagram said to have been borne from the Yellow River on a dragon-horse's back), the Xici commentary states: "The River brought forth the Chart, the Luo brought forth the Writing, which the sages took as their model." Heavenly numbers are odd (1, 3, 5, 7, 9), earthly numbers are even (2, 4, 6, 8, 10). The five heavenly numbers sum to 25, the five earthly numbers to 30, making the total of heaven and earth 55—these numbers can deduce transformations and commune with spirits. The sages modeled the milfoil divination on the River Chart and invented turtle shell divination based on the Luo Writing. The Hanshu Lüli Zhi (Treatise on Harmonics and Calendrics from the Book of Han) records that the River Chart was a star-like pattern formed by whorled hairs on a dragon-horse's back emerging from the Yellow River. All numbers under heaven begin at one and end at ten, cycling anew when exceeding ten. This passage mainly illustrates how ancient sages created systems for predicting fortune by observing natural phenomena.

This passage explores the numerical mysteries in the ancient Book of Changes (Yijing), specifically explaining the generative principles behind the numbers in the "River Chart" (Hetu), a legendary mystical diagram said to have been carried by a dragon-horse. The numbers of Heaven and Earth are divided into celestial numbers (Yang numbers) and terrestrial numbers (Yin numbers). The celestial numbers are the five odd digits: one, three, five, seven, and nine, while the terrestrial numbers are the five even digits: two, four, six, eight, and ten.

The calculation of celestial numbers proceeds as follows: Beginning with celestial one (1), by the time celestial three is added, the sum becomes 4 (1+3). With the inclusion of celestial five, the total rises to 9 (1+3+5). At celestial seven, it reaches 16 (1+3+5+7), and finally, with celestial nine, the sum becomes 25 (1+3+5+7+9). The combined total of these five fundamental celestial numbers is 25, with 5 serving as the core number, while the remaining 20 are derived from it.

Similarly, the terrestrial numbers are calculated: terrestrial two is 2, and by terrestrial four, the sum becomes 6 (2+4). With terrestrial six, it increases to 12 (2+4+6), then to 20 (2+4+6+8), and finally to 30 (2+4+6+8+10). The total of these five fundamental terrestrial numbers is 30, where 5 is the core number, and the other 25 are derived from it.

When the celestial and terrestrial numbers are combined, they total 55 (25 + 30). Here, 10 is the foundational number (celestial 5 + terrestrial 5), while the remaining 45 are derived. Though the numbers may appear numerous, they fundamentally do not exceed the root number of 10. Celestial numbers, originally odd and Yang in nature, can transform into Yin; terrestrial numbers, originally even and Yin, can transform into Yang. These 55 numbers interact and transform endlessly.

Because of their profound and mystical nature, the ancient sage Fuxi established the "Great Expansion Number" (Dayan zhi shu), a major numerical principle for divination, using yarrow stalks to derive hexagrams. The divination method is as follows: Prepare 50 yarrow stalks, though only 49 are actually used. These are divided into two piles to symbolize Heaven and Earth, with one stalk set aside to represent humanity, thus forming the "Three Powers" (San Cai)—Heaven, Earth, and humanity. The stalks are then counted in groups of four to symbolize the four seasons, with the remainders representing intercalary months. Since there are two intercalary months in five years, the division process is repeated twice to complete a single divination.

This passage explains how the ancient sage Fuxi developed the method of divination using yarrow stalks based on the numerical patterns of the Hetu (the River Chart, a mystical diagram said to have been borne from the Yellow River by a dragon-horse).

In the Hetu, there are five heavenly numbers (odd numbers) which sum to twenty-five when expanded, and five earthly numbers (even numbers) which sum to thirty when expanded. However, this does not exhaust the profound mysteries of numerical derivation. Fuxi further deduced from the Hetu a larger numerical combination of ninety-nine. The specific calculation method is as follows: 1 plus 2 equals 3, 2 plus 3 equals 5, 3 plus 4 equals 7, and 4 plus 5 equals 9—the sum of these four odd numbers is 24. Then, 5 plus 6 equals 11 (with 10 at the center), 6 plus 7 equals 13, 7 plus 8 equals 15, 8 plus 9 equals 17, and 9 plus 10 equals 19—the sum of the tens digits of these five numbers is again 24.

The text mentions the "Great Expansion number fifty" (Dayan zhi shu wushi), referring to the fixed base number in the derivation process, though only forty-nine yarrow stalks are actually used in divination. Although the final derivation yields ninety-nine, none of these numbers exceed the fundamental range of 1 to 10 in the Hetu. Confucius used the character "yan" (expansion) to reveal the principle of derivation in the Hetu, and the character "da" (great) to highlight Fuxi's profound emulation of the Hetu's patterns—this wisdom is as infinitely subtle as the workings of nature itself.

The reason forty-nine is used in divination instead of fifty is that fifty represents the static essence in the Hetu's derivations, while forty-nine represents dynamic change. In terms of numerical arrangement, the left and right sides both consist of the five heavenly numbers—1, 3, 5, 7, and 9 (symbolizing the pure Yang energy of the Qian hexagram). The twenty-four on each side represents the division of Yin and Yang, while the central one represents the single yarrow stalk suspended during divination. The four odd numbers—3, 5, 7, and 9—correspond to the "dividing into four" (she si) step in the divination process.

This passage discusses the mathematical principles behind ancient divination using yarrow stalks (a herbaceous plant used for fortune-telling). When performing divination with forty-nine stalks, the ancients would first set aside one stalk unused, symbolizing Taiji (the Supreme Ultimate, the origin of the cosmos). However, the author questions this interpretation, arguing that Taiji as the root of all things cannot be isolated and left unused.

The author criticizes the Jin dynasty practice of interpreting the Zhouyi (Book of Changes) through Lao-Zhuang philosophy. By designating one stalk as representing Taiji while using the remaining forty-nine for divination, they essentially set aside the fundamental principle of the universe while letting concrete phenomena operate independently—a complete violation of reason. In reality, that single stalk is identical to the other forty-nine; what justification elevates it to the sacred status of Taiji?

The text then mentions that the Hetu (River Chart, a mythical diagram said to have been borne from the Yellow River by a dragon-horse) originally contained fifty-five numbers. Yet when using forty-nine stalks for divination, five numbers are missing—how can this be called "Dayan" (the Grand Derivation, complete cosmological unfolding)?

Finally, it cites perspectives from Han dynasty scholar Liu Xin and Song dynasty philosopher Shao Yong: Fuxi created the Eight Trigrams (Bagua) based on the Hetu, while Yu the Great established the Hongfan (Great Plan) governance system after receiving the Luoshu (Luo Writing, borne from the Luo River by a divine turtle). Shao Yong maintained that circular patterns symbolize celestial movements and calendrics, while square patterns represent terrestrial divisions—all being connected to the Hetu and Luoshu mysteries.

This scripture primarily explains the origin and symbolic significance of the Hetu (River Chart) and Luoshu (Luo Writing). Legend tells of a dragon-horse emerging from the Yellow River, its whorled coat hairs forming circular dot patterns that arranged into the ten-numbered Hetu. Similarly, a divine turtle appeared in the Luo River, its shell cracks forming the nine-numbered Luoshu. While ordinary horses' coat patterns and turtle shell cracks today may show similar markings, they no longer possess complete numerical arrangements.

The Hetu represents celestial phenomena, with its numbers arranged in a circular pattern totaling twenty-five—the number of Heaven. The Luoshu represents terrestrial phenomena, with numbers arranged in a square pattern totaling thirty—the number of Earth. Combined they make fifty-five, symbolizing the numbers of Heaven and Earth. Fu Xi created the yarrow stalk divination method based on the Hetu, while Yu the Great established nine governance principles (jiuchou) according to the Luoshu. These were regarded as auspicious omens heralding the appearance of sage-kings.

Specifically: The heavenly numbers—one, three, five, seven, and nine (all odd)—sum to twenty-five; the earthly numbers—two, four, six, eight, and ten (all even)—sum to thirty. Though these Heaven-Earth numbers can generate infinite variations through calculation, they never transcend the framework of these five fundamental numerals. The numerical systems of Hetu and Luoshu embody the ancient cosmological view of "taking five as foundation."

This scripture discusses the numerical arrangement principles of the Hetu (River Chart, the mystical diagram said to have been borne from the Yellow River by a dragon-horse) and its derived mathematical system. The author criticizes Han Dynasty Confucian scholars for misinterpreting the phrase "five positions mutually obtain yet each has its correspondence," arguing they erroneously split the decimal numbers into heavenly numbers and earthly numbers.

The text details Fuxi's (the legendary sage-king of antiquity) method for deriving the Hetu numbers: adding adjacent numbers in sequence, such as one plus two yielding three, two plus three yielding five, etc. It particularly emphasizes that the number "one" occupies the central position, combining with surrounding numbers to form the key number forty-nine. Among these, five number pairs that sum to ten (like five plus six, six plus seven, etc.) constitute the "Great Expansion's Ti numbers" (fundamental structural numbers), while the surrounding twenty-four numbers plus the central one make forty-nine as the "Great Expansion's Yong numbers" (practical application numbers).

The author stresses that ancient calculations exclusively used the Yong numbers rather than the Ti numbers. Through the computational method of "guayi fen'er shesi" (an ancient divination technique involving yarrow stalk division), this purely yang method without yin elements originates from the purity of heavenly numbers. Fuxi employed precisely this method to guide people's lives. Finally, citing a certain scholar named Zhuo, the text mentions Confucius' admiration for the exquisite numerical system of the Hetu, considering it the fundamental principle that accomplishes all things.

This passage reveals the unique cosmological thinking in ancient numerology, where mathematical principles were integrated with universal concepts. The numerical arrangements were believed not only to possess computational functions but also to contain the profound mysteries of celestial and terrestrial operations.

This passage explains the ancient divination practice of yarrow stalk casting (she shi) and the principles of the Eight Trigrams (Bagua). The ancients believed yarrow stalks—used for divination—possessed mystical properties of perfect integration. The number forty-nine (seven times seven) represented completeness, while the Eight Trigrams symbolized the wisdom of proper orientation, with sixty-four hexagrams (eight times eight) representing spatial directions. Through the transformations of the six lines (yao) in a hexagram, the interplay of strength and yielding could be revealed, showing people auspicious or inauspicious signs.

The sages (specifically referring to Fuxi here) used this method to purify their minds, gathering their concern for the world into silent contemplation. They could foresee future fortune or misfortune through the yarrow stalks' magic while grasping the patterns of development through the wisdom of hexagrams. Thus, they avoided constant worry over the people's welfare, maintaining inner tranquility.

The text particularly emphasizes that only sage-kings like Fuxi—both wise and benevolent—could comprehend the Dao of Heaven and understand the people's needs, inventing this extraordinary tool of yarrow divination to guide them. When using the yarrow stalks, one must observe purification rituals (zhai for focused concentration, jie for eliminating distractions) to communicate with the divine. In practice: closing the hands around the stalks represents the Kun hexagram (symbolizing contraction), while separating them represents the Qian hexagram (symbolizing expansion). This opening and closing embodies transformation. The stalks are repeatedly divided until an odd number (representing the solid yang line "seven") or even number (representing the broken yin line "eight") appears, with three such changes determining the final hexagram.

The author criticizes scholars like Liu Xin for mistakenly believing the Eight Trigrams were derived from yarrow stalks. In truth, yarrow divination and the trigrams are two complementary systems. This diagram clarifies Confucius's original intent, urging readers to deeply contemplate their distinctions.

This passage explains the fundamental principles and symbolic meanings of divination in the Book of Changes (Yijing). When ancient practitioners used yarrow stalks (a divination tool) for prognostication, the act of dividing and combining the stalks mirrored the transformations of Heaven and Earth.

Initially, all forty-nine stalks remain undivided in their container, representing the primordial "Taiji" (Supreme Ultimate) state before the separation of Heaven and Earth. When the stalks are removed from the container and divided, they manifest the two polarities of Yin and Yang—Qian (Heaven) and Kun (Earth). This resembles opening the container: closing the lid symbolizes Kun (Earth), while opening it signifies Qian (Heaven). The "Yi Gate" in ancient cities derived its name from this concept of the two polarities joining together.

Through four rounds of division (known as the "four transformations"), four symbolic states emerge: Lesser Yang (7), Lesser Yin (8), Greater Yang (9), and Greater Yin (6). These represent the transformations of hardness and softness, maturity and youth. Like the ridgepole and rafters of a house, these four images form a complete structure. As each image develops further, they give rise to the Eight Trigrams (Qian, Kun, Zhen, Xun, Kan, Li, Gen, Dui).

After eighteen transformations, both the inner and outer trigrams are determined, allowing the diviner to interpret auspicious or inauspicious omens based on the hexagram. Once the outcome is discerned, people can decide how to act, thereby accomplishing great undertakings. Just as the movements of Heaven and Earth and the succession of seasons follow their inherent patterns, these transformations obey natural laws. The sun (extreme Yang) and moon (extreme Yin) serve as the most visible celestial symbols, while wealth and honor represent the most tangible pursuits in human life.

The entire divination process simulates the patterns of nature—from chaos to order, from simplicity to complexity—ultimately guiding people to seek auspicious outcomes, avoid misfortune, and achieve success in their endeavors.

This passage primarily discusses how ancient sages utilized divination (using yarrow stalks and tortoise shells) to benefit all under heaven. The text states that sages possessed divinatory wisdom, employing hexagram imagery to create tools, guide the people, and accomplish great undertakings. Only those sagacious and profoundly wise, endowed with divine martial virtue (De) yet refraining from wanton slaughter, could truly achieve this.

The text particularly emphasizes the mystical properties of yarrow stalks and tortoise shells. When Heaven bestowed these two sacred objects, the sages modeled their divination practices upon them. The River Chart (legendary patterns appearing in the Yellow River) was used with yarrow stalk divination, while the Luo Writing (legendary markings from the Luo River) was employed with tortoise shell divination. By observing these celestial and terrestrial transformations, sages predicted auspicious and inauspicious signs, guiding people to pursue fortune and avoid misfortune.

The passage later describes Fu Xi's creation of the sixty-four hexagrams in sequence. The author critiques Shao Yong's (Master Shao) interpretation, considering his explanation of Taiji (Supreme Ultimate), Liangyi (Two Forms), and Sixiang (Four Images) overly mechanistic. The original classic simply states "Taiji generates Liangyi, Liangyi generates Sixiang, Sixiang generates Bagua (Eight Trigrams)," without suggesting the trigrams would continue doubling to produce sixteen, thirty-two, and ultimately sixty-four hexagrams. Shao Yong proposed that Yin-Yang interactions produce the Four Images, whose further interactions generate additional hexagrams, but this interpretation deviates from the canonical meaning.

The core message throughout is this: Ancient sages observed natural phenomena and employed divinatory tools to benefit the common people and guide productive living. Simultaneously, the text critiques certain later scholarly interpretations of the Yijing (Classic of Changes), advocating a return to the original meaning of the classics.

This passage elucidates the origins and evolution of the Book of Changes (Yijing). It explains how the interplay of Yin-Yang forces in heaven and earth gave rise to the Eight Trigrams (Bagua), whose further combinations generated the sixty-four hexagrams. This process mirrors a tree's growth from roots to branches and finally leaves, with divisions becoming increasingly intricate as they extend outward. Zhu Xi maintained that the alternating odd-even patterns within these hexagrams emerged naturally rather than through deliberate human design.

The text notes that Shao Yong (Master Kangjie) first transmitted the study of Primordial Changes (Xiantian Yi), considering it the Book of Changes from Fu Xi's era. However, the author confesses harboring doubts since childhood that only deepened with age. He critiques earlier interpretations of the character "Yi" (易) as inadequate—arguing it encompasses not just the transformations of hexagram symbols (the "Yi of diagrams"), but also the numerical variations of yarrow stalks used in divination (the "Yi of counting stalks").

A philological investigation follows, refuting claims that "Yi" didn't exist in Fu Xi's time. Citing the Zhou dynasty Rites of Zhou (Zhouli), the author notes the Grand Diviner's stewardship over three versions: the Lianshan of Xia, Guicang of Shang, and Zhouyi of Zhou. This confirms "Yi" as an enduring title since antiquity—though bearing different names across dynasties, all were fundamentally variant editions of the same classic.

Through this exposition, the text reveals both the Book of Changes' gradual complexification and scholars' divergent theories about its genesis, offering a window into ancient methodologies for deciphering cosmic patterns.

This passage primarily discusses the origins and core concepts of the Book of Changes (Yijing). Regarding the term "易" (Change), the author suggests it did not originate during the Zhou dynasty but traces back to the era of Fu Xi, though written records were absent at that time. The Eight Trigrams (Qian, Kun, Gen, Xun, Zhen, Li, Kan, Dui) created by Fu Xi, along with numerical systems like 7, 8, 9, and 6, were gradually refined by later generations.

The text focuses on explaining the concept of "Taiji" (Supreme Ultimate). Originally meaning the central beam of a house, Taiji was extended to signify the supreme origin of all things. Han Kangbo (an Eastern Jin dynasty scholar of the Yijing) annotated that all existence begins from "nothingness," hence Taiji gives rise to the Two Modes (Yin-Yang). Taiji itself is the nameless ultimate existence, the limit state from which all things emerge. Kong Yingda (a Tang dynasty Confucian scholar) further elaborated: Taiji represents the undifferentiated primordial Qi before heaven and earth separated, equivalent to the Daoist concepts of "Taichu" (Great Beginning) or "Taiyi" (Great Unity). This aligns with Laozi's statement that "the Dao begets the One."

When this chaotic primordial Qi divides, it forms heaven and earth—hence "Taiji generates the Two Modes," corresponding to Laozi's "the One begets the Two." The term "Two Modes" is used instead of "heaven and earth" to emphasize fundamental forms and maintain conceptual continuity with the subsequent "Four Symbols." Zhu Xi (a Song dynasty Neo-Confucian philosopher) viewed this as a natural law: a single origin necessarily differentiates into opposing aspects.

The author concludes that while Han Kangbo and Kong Yingda's Daoist-influenced interpretations of the Yijing may be debatable, their framework illustrates traditional cosmogony: the Dao first generates heaven and earth, which then produce the Five Phases (Wood, Fire, Earth, Metal, Water), from which all things arise. This synthesis bridges the Yijing's Taiji philosophy with Daoist theories of the Dao.

This passage examines different interpretations regarding the origins of the Eight Trigrams (Bagua) and the theory of Two Forms (Yin-Yang), raising doubts about Zhu Xi's (Master Zhu) viewpoints.

Concerning the formation process of the Eight Trigrams, Zhu Xi proposed a progressive development from simplicity to complexity: first came the two strokes of Yin and Yang (initial lines), which then generated four-line combinations, eventually evolving into eight-line configurations. However, the author points out an inherent contradiction—if the original Yin and Yang strokes bore no distinction in magnitude, how could the resulting Eight Trigrams fully manifest the Dao of Heaven, Earth, and Humanity?

Regarding the origin of the "Two Forms" (Yin-Yang symbols), the author's textual research reveals that ancient Confucian scholars believed Fu Xi, when drawing the trigrams, first created the solid line "—" (Yang Yao) to symbolize Yang and the broken line "--" (Yin Yao) to symbolize Yin, which later generations termed the Two Forms. Yet after thoroughly examining the Ten Wings (Confucius' ten commentaries on the Yijing), the author notes Confucius only stated that "Fu Xi first created the Eight Trigrams," never mentioning "Fu Xi first created the Two Forms." From which classic does this notion of "first drawing Yin and Yang lines" actually originate?

The author further analyzes: according to Zhu Xi's "Horizontal Diagram" theory of trigram arrangement, starting from one Yin and one Yang line, sixty-four hexagrams would require four successive divisions (dichotomies). This would create an imbalance in the bearing relationships between Yin and Yang lines—a single Yang line would need to support thirty-two strokes above it, as would a single Yin line, which is clearly unreasonable. If, as some claim, "the Two Forms are so mystical that one stroke can transform into thirty-two forms," then the sages' Horizontal, Square, and Circular Diagrams should all follow this principle—yet in reality, they do not.

(Note: The "Horizontal Diagram," "Circular Diagram," and "Square Diagram" mentioned refer to schematic arrangements of hexagrams created by Song dynasty scholars to illustrate the generative principles and transformational patterns of the Eight Trigrams in Yijing studies.)

This passage discusses the origins and transformational patterns of the sixty-four hexagrams in the Book of Changes (Yijing). The author contends that the original arrangement of the hexagrams was not the primal method used by the sages (referring to Fuxi), but rather a later modification.

Regarding the interpretation of the "Four Images" (old Yin, old Yang, young Yin, young Yang), the author notes that previous scholars added one broken and one solid line to each odd or even trigram, totaling four lines, to symbolize the progression of Yin and Yang from young to old. However, the author argues that the Four Images should be positioned above the initial line and below the three-line structure of the trigrams, not in other positions.

The term "Two Modes" (Liangyi) derives its character "yi" from the preceding context of "closing and opening doors," representing the opposition of Yin and Yang. The "images" in the Four Images follow the concept that "what manifests is called an image," with the number seven symbolizing young Yang, eight young Yin, nine old Yang, and six old Yin.

When Confucius spoke of "the Changes having Four Images," he aimed to demonstrate the signs of fortune, misfortune, regret, and remorse through the hexagram images. If the Four Images are fixed at the position of the second line, then the Qian (Heaven) and Dui (Lake) trigrams correspond to old Yang, Li (Fire) and Zhen (Thunder) to young Yin, Kun (Earth) and Gen (Mountain) to old Yin, and Xun (Wind) and Kan (Water) to young Yang. According to the divination methods recorded in the Zuo Commentary, old Yang and old Yin undergo transformation, while young Yang and young Yin remain unchanged.

The specific transformational patterns are as follows: the Qian hexagram transforms into Li, and Dui transforms into Zhen, but Xun and Li remain unchanged (since young Yin does not transform); Kun transforms into Kan, and Gen transforms into Xun, but Xun and Kan remain unchanged (since young Yang does not transform). In this way, the four trigrams Qian, Dui, Kun, and Gen disappear, while Zhen, Li, Xun, and Kan reappear, forming the process by which the Four Images are generated.

This passage primarily discusses the generative principles of the Eight Trigrams (Bagua) and critiques previous misunderstandings regarding the formation of hexagram imagery in the Book of Changes (Yijing).

Concerning the generation of the Eight Trigrams, the author points out: Earlier scholars mistakenly believed that simply superimposing yin and yang symbols onto the Four Images (old yang, young yin, young yang, old yin) could produce the Eight Trigrams. In reality, adding an odd-numbered (yang) line to another odd-numbered line forms the pure yang of old yang; adding an even-numbered (yin) line to an odd-numbered line creates young yin (yin containing yang); adding an odd-numbered line to an even-numbered line produces young yang (yang containing yin); while adding an even-numbered line to another even-numbered line forms the pure yin of old yin. However, if this superimposition method were extended to six-line hexagrams, it would result in illogical situations like "supreme old yin" or "supreme old yang," demonstrating the imprecision of this theory.

Regarding the essential nature of the Eight Trigrams, the author emphasizes: The trigrams created by Fu Xi each consist of three complete and independent lines. The Qian (Heaven) trigram, from bottom to top, comprises three unbroken yang lines (odd-numbered strokes), while the Kun (Earth) trigram consists of three complete yin lines (even-numbered strokes). Contrary to what some scholars claim, these trigrams do not share line strokes with other trigrams. The length and form of each line in the Eight Trigrams must be entirely consistent—there can be no instances where certain strokes are shared between trigrams, as this would violate the original intent of the sages in creating the trigrams.

Addressing the sixteen-line theory, the author refutes the notion that "adding one yin and one yang line to each trigram generates sixteen-line figures." By referencing the Book of Changes passage stating "the Eight Trigrams determine fortune and misfortune," we can deduce that the Four Images generate not only the inner Eight Trigrams but simultaneously produce the outer Eight Trigrams as well. This proves the inherent completeness of the Eight Trigrams system—it requires no expansion through additional line strokes. The earlier sixteen-line theory lacks both classical foundation and alignment with the principles of Yijing studies.

This passage discusses the generative principles of the Bagua (Eight Trigrams, the eight fundamental symbols used in ancient divination), critiquing the theories of sixteen and thirty-two trigrams proposed by the Song dynasty scholar Shao Yong (Shaozi). The core argument is that the formation of the Bagua is already fully contained within the fundamental principle of "the Four Images generating the Eight Trigrams" (where the two polarities of Yin-Yang give rise to the Four Images, which in turn produce the Eight Trigrams). The eighteen variations of the inner and outer trigrams (referring to their overlapping combinations) are sufficient to determine auspicious and inauspicious outcomes, without needing to double them into sixteen or thirty-two trigrams as Shao Yong suggested.

The author highlights several key issues: First, Shao Yong's claim that "eight divides into sixteen, and sixteen divides into thirty-two" finds no basis in the classics of Fuxi (the legendary sage who created the Bagua) or Confucius (the Master). Second, this doubling theory fails to hold up in actual trigram diagrams (such as the square and circular diagrams)—the dimensions of the trigrams are fixed in length and width, so how could strokes suddenly be added or removed to inflate their numbers?

Most importantly, Confucius explicitly stated that "the Eight Trigrams determine auspiciousness and inauspiciousness." Inserting claims like "generating sixteen" or "generating thirty-two" between the Bagua and their function of determining outcomes completely distorts the sages' original intent. Thus, the author firmly maintains that theories extending beyond the Bagua and the sixty-four hexagrams (complete symbols composed of six lines) neither align with Fuxi's foundational principles nor Confucius' interpretations, rendering them entirely unreliable.

Finally, the passage notes that in the authentic sixty-four hexagram system, the sixth line (the topmost stroke) of each hexagram is the decisive factor. The Song dynasty Confucians' theories about trigram generation are, in reality, already encompassed within the transformations of this final line.

This passage discusses Fuxi's original method of creating the sixty-four hexagrams, criticizing later scholars' misinterpretations of hexagram formation. The author argues that certain scholars' approach—starting from six-line hexagrams and progressively reducing them (removing thirty-two five-line hexagrams, then forty-eight four-line figures, and so on)—completely violates the original intent of both Fuxi and Confucius (referred to as "the Master"), fragmenting the hexagram system into incoherence. The proper method should restore Fuxi's primordial principles of hexagram generation.

The text mentions "Kun's mode" (坤仪), which refers to the meditative state of holding yarrow stalks and closing the doors during divination, symbolizing the receptive Kun hexagram (representing stillness and containment). "Taiji" (太极) denotes the central gathering point of the yarrow stalks, representing the cosmic origin. "Qian's mode" (乾仪) describes dividing the stalks equally and suspending one portion, symbolizing the creative Qian hexagram (representing initiation and movement).

In actual divination practice: obtaining the number nine is called "the image of Greater Yang" (太阳之象), corresponding to the Qian hexagram. If all eighteen transformations yield seven, this produces the pure Yang hexagram of Qian below Qian above. If the third and top lines yield eight while the rest yield seven, this forms the Dui hexagram. Obtaining the number eight is called "the image of Lesser Yin" (少阴之象), corresponding to the Li hexagram. Should the second and fifth lines yield eight with the remainder yielding seven, this creates the Li below Li above configuration. These specific stalk-divination (揲蓍) methods all aim to recover the foundational meaning behind Fuxi's creation of the hexagrams.

This passage explains the relationship between the "Four Images" (shaoyang [lesser yang], shaoyin [lesser yin], taiyin [greater yin], and taiyang [greater yang]) in ancient divination and their transformations within the Bagua (Eight Trigrams). Different numerical results obtained through yarrow stalk divination (the ancient method using milfoil stems) correspond to different trigram transformations.

When the number seven is obtained, it corresponds to the shaoyang image. For instance, if the first and fourth lines of the Zhen trigram (representing thunder) yield seven while the other lines yield eight, it forms the hexagram of Zhen below Zhen above. If the top line yields nine or six, it transforms into the Xun trigram (representing wind).

Obtaining the number eight corresponds to the shaoyin image. For example, if the first and fourth lines of the Xun trigram yield eight while the other lines yield seven, it forms the hexagram of Xun below Xun above. If the top line yields nine or six, it transforms into the Zhen trigram.

The number seven also relates to the Kan trigram (representing water). If its second and fifth lines yield seven while the others yield eight, it forms the hexagram of Kan below Kan above. If the top line yields nine or six, it transforms into the Li trigram (representing fire).

Obtaining the number six corresponds to the taiyin image. For instance, if the third and top lines of the Gen trigram (representing mountain) yield seven while the others yield eight, it forms the hexagram of Gen below Gen above. If the top line yields nine or six, it transforms into the Dui trigram (representing marsh).

The Kun trigram (representing earth) is unique—all eight transformations yield eight, forming the hexagram of Kun below Kun above. If all lines yield six, it transforms into the Qian trigram (representing heaven).

Through the deduction of these four fundamental numerical symbols (seven, eight, nine, six), sixty-four hexagram variations can be derived. If seven or eight is obtained, it corresponds to the hexagram statements attributed to King Wen; if nine or six is obtained, it corresponds to the line statements attributed to the Duke of Zhou. In this way, a single trigram can transform into all sixty-four hexagrams.

The Yijing (Classic of Changes) was originally a sacred text created by six sages beginning with Fuxi. Fuxi first delineated the eight trigrams (Bagua)—Qian (Heaven), Kun (Earth), Zhen (Thunder), Xun (Wind), Kan (Water), Li (Fire), Gen (Mountain), and Dui (Lake)—then compounded each trigram by superimposing another, thereby deriving the sixty-four hexagrams. For instance, the Qian trigram (representing Heaven), originally composed of three solid lines, retained its name when another three lines were added beneath it. The same principle applied to the other seven trigrams, collectively forming the foundational "canonical trigrams."

When the Dui trigram (representing Lake) was superimposed upon Qian, the resulting configuration could no longer be called either Qian or Dui, and was thus named the Guai hexagram (symbolizing resolution). This became the first variation of the Qian hexagram. The Qian sequence contains nine such variations, and each of the other seven trigrams similarly yields its own set of transformations, collectively forming the complete sixty-four hexagrams. Their names and pronunciations were all established by Fuxi himself. Throughout the Xia, Shang, and Zhou dynasties, successive sages preserved Fuxi's original trigrams and hexagram names without alteration.

Fuxi's symbolic system functions like the progenitor of a lineage—all subsequent developments trace back to this source. Sages including Yu of Xia, Tang of Shang, King Wen of Zhou, the Duke of Zhou, and Confucius each expanded upon Fuxi's foundation. They composed various Yijing commentaries reflecting their understandings, some beginning with Gen (Mountain), others with Kun (Earth) or Qian (Heaven). The Duke of Zhou and Confucius primarily inherited and developed the Zhouyi tradition centered on the Qian hexagram.

Though simple and unadorned, Fuxi's system contains inexhaustible profundity, encompassing the essential wisdom later elaborated in the Three Dynasties' classics. Those expansive later texts ultimately serve to illuminate the principles first encoded in Fuxi's Yi. His system resembles the primordial Qi that permeates the four seasons, while the Three Dynasties' interpretations manifest as the distinctive characteristics of spring, summer, autumn and winter.

Regarding the Lianshan Yi (Linked Mountains Classic) of the Xia dynasty, Confucius noted it perpetuated an earlier tradition from the Lianshan clan. Ancient commentaries explain "Lianshan" as resembling continuous mountain mists, but this interpretation seems questionable since the original text mentions no clouds. The Xiang commentary on the Gen hexagram states "Gen means joined mountains"—suggesting "Lianshan" more likely refers to interconnected mountain ranges.

This passage primarily discusses different versions of the ancient Book of Changes (Yijing) and their divination methods. The original text maintains that the Gen trigram (one of the Eight Trigrams [Bagua], symbolizing mountain) has represented mountains since the era of Fu Xi. The Lianshan Yi (Linked Mountains Classic) of the Xia Dynasty took Gen as its first trigram, named "Lianshan" (Linked Mountains) because both inner and outer trigrams were Gen, symbolizing interconnected mountains. Adding interpretations like "issuing clouds" would deviate from its original meaning. Regarding the Xia Dynasty's Lianshan Yi, only its title and the fact that Gen was its first trigram remain verifiable today—the sequence of the remaining sixty-four hexagrams is no longer traceable.

Concerning divination methods, Fu Xi created techniques using yarrow stalks (shi divination) and turtle shell oracle bones based on the River Chart (Hetu) and Luo Writing (Luoshu)—mystical diagrams from ancient legend. When Yu the Great controlled the floods, he obtained the Luo Writing and employed it for systematic governance. Specialized diviners (buren for shell cracks and shiren for stalks) were appointed, each practicing distinct methods. If three diviners produced conflicting results, majority opinion prevailed: two auspicious and one inauspicious meant accepting the auspicious outcome, while two inauspicious and one auspicious meant accepting the inauspicious.

The text also explains the terms "zhen" (constancy) and "hui" (regret): the inner trigram (lower trigram) is called zhen, while the outer trigram (upper trigram) is called hui. For instance, "zhen Zhun hui Yu" means the original hexagram is Zhun (3) changing into Yu (16). These terms frequently appear in the Zhouyi (Zhou Changes), with expressions like "beneficial constancy" (li zhen) and "regret vanishes" (hui wang) deriving from this system. These methods were first established by Fu Xi and later refined during the Xia, Shang, and Zhou dynasties.

Lastly, the Shang Dynasty's Guicang Yi (Returning to the Hidden Classic) is mentioned, said to originate from the earlier Guicang lineage, with the Shang Dynasty preserving its name.

The Guicang (one of the three ancient Yi classics, traditionally attributed to the Yellow Emperor) centers on the principle that all things ultimately return to their source to be reborn anew. Just as the earth embraces all, everything eventually returns to be stored within it. The Kun hexagram symbolizes the earth, and Guicang embodies this very law of the earth—hence the scripture begins with the Kun hexagram. As the Shuogua Zhuan states, "Kun stores all things." Of the Shang dynasty's Yi classic, only these two features—the title and the placement of Kun as the first hexagram—remain known today; the sequence of the remaining sixty-four hexagrams has been lost to time.

The Book of Rites: Evolution of Rites records Confucius telling Ziyou about "the order of Kun and Qian," suggesting that Guicang likely placed Kun before Qian. Later, King Wen of Zhou deemed it improper for Kun to precede Qian, so the Zhouyi reversed their order. As for the arrangement of the other hexagrams, reconstructing their sequence is even more challenging. Though the positions of Qian and Kun were swapped, the principle of pairing Yin and Yang likely remained consistent with the Zhouyi, though the specific proximity of hexagrams may have differed.

Some hexagram lines in the Zhouyi reference Shang dynasty events: the sixth line of Tai mentions "Di Yi giving his sister in marriage," the sixth line of Mingyi refers to "Ji Zi's enlightened concealment," the sixth line of Guimei again notes "Di Yi giving his sister in marriage," while the third line of Jiji records "Gaozong's three-year campaign against the Guifang," and the fourth line of Weiji states, "Zhen's campaign against the Guifang, rewarded by the great state after three years." Earlier scholars believed these were records of verified divinations, hence their inclusion in the line statements.

The Rites of Zhou notes that the Grand Diviner (the official in charge of divination) mastered three methods of interpreting omens and three Yi classics: the jade, tile, and primal crack methods each had 120 omens and 1,200 prognostications; the Lianshan, Guicang, and Zhouyi each contained eight primary trigrams and sixty-four hexagrams. The ancients held that "nothing surpasses the yarrow stalks and tortoise shell," underscoring their supreme importance in divination. Fuxi's original trigram sequence was Qian, Dui, Li, Zhen, Xun, Kan, Gen, Kun, and the sixty-four hexagrams followed this order. The Xia dynasty's Lianshan Yi began with the Gen hexagram, but its full sequence is lost; the Shang dynasty's Guicang Yi started with Kun, but its arrangement is also unknown, including whether it adhered to the primary trigram sequence.

Ancient courts appointed officials to oversee the three Yi classics, responsible for nine divination categories: Shi Geng (consulting on change), Shi Xian (consulting on resonance), Shi Shi (consulting on method), Shi Mu (consulting on critical matters), Shi Yi (consulting on transformation), and six other divination techniques.

This passage explains the methods and principles of ancient divination. When performing divination, yarrow stalks (a divination tool) are used for calculation. The main steps involve: taking the stalks from the container and holding them in hand, called "closing the door" (he hu); randomly dividing them and hanging/arranging the remainders, called "opening the door" (pi hu). This opening and closing constitutes "one transformation" (yi bian).

Through three transformations, a single line (yao) of the hexagram is formed. Nine transformations create the inner trigram (lower gua), and eighteen transformations complete the entire hexagram, at which point the outer trigram (upper gua) is added.

During divination, the lines formed through three transformations may yield the numbers seven, eight, nine, or six, known as the "four images" (si xiang). If seven or eight is obtained, the inner trigram is "zhen" (the primary hexagram), while the outer trigram is "hui" (the changing hexagram). If nine or six is obtained, the original hexagram is "zhen," and the changing hexagram is "hui." The divination process involves consulting two individuals' interpretations, with possible outcomes including great agreement, auspiciousness, or cases where the turtle shell (divination) agrees but the yarrow stalks disagree.

The text then lists some of the 64 hexagrams from the Zhouyi (Book of Changes) and their transformational relationships. For example, the Qian hexagram does not reverse (remains unchanged), while the Kun hexagram does not correspond (lacks resonance). The Zhun hexagram reversed becomes the Meng hexagram; the Xu hexagram reversed forms the Song hexagram (with missing characters in the original text); the Shi hexagram reversed yields the Bi hexagram, and so on. It is specifically noted that among the first 30 hexagrams of the "Upper Canon," aside from Kun, Yi, Daguo, Kan, and Li (six hexagrams in total), the remaining 24 can be reversed to form 12 pairs of hexagrams.

These divination methods all originate from Fu Xi, who used the mystical circular yarrow stalks to seek the wisdom of the square hexagrams. The transformations of the hexagram lines all follow the rules established by Fu Xi. These methods were already in use during the Xia dynasty, and later generations continued to inherit Fu Xi's divination system.

This passage primarily explains the concepts of hexagram transformations and the notions of "coming and going, ascending and descending" in the Zhouyi (Book of Changes). It mentions that King Wen of Zhou, when arranging the sequence of the sixty-four hexagrams, reorganized the earlier Fu Xi's innate sequence by pairing hexagrams in opposing pairs. By observing these mirrored relationships between paired hexagrams, one can comprehend the meaning of "coming and going."

For example, the Tai hexagram (symbolizing prosperity) and the Pi hexagram (symbolizing stagnation) form a pair of mutually inverted hexagrams. In the Tai hexagram, the three yang lines are inside, and the three yin lines are outside, described as "the small goes and the great comes." Conversely, in the Pi hexagram, the three yin lines are inside, and the three yang lines are outside, termed "the great goes and the small comes." Here, "going" refers to movement from the inside outward, while "coming" refers to movement from the outside inward.

Confucius (the Master) expanded on this concept further, using phrases like "the firm ascends and the yielding descends" (yang lines above, yin lines below) or "the yielding ascends and the firm descends" (yin lines above, yang lines below) to describe hexagram structures. These observations are derived from comparing the arrangements of paired hexagrams and do not imply that one hexagram literally transforms into another or that the line positions undergo actual changes.

The author particularly emphasizes that this interpretive method should not conflate the transformation patterns of "seven and eight" (lesser yang and lesser yin) with those of "nine and six" (greater yang and greater yin). Moreover, when King Wen and Confucius explained the eight pure hexagrams (such as Qian and Kun, which do not pair with others), they did not use the language of "coming and going, ascending and descending," indicating their original intent was quite clear.

Finally, it is noted that discussions of "coming and going" originated from the hexagram statements of Tai and Pi. Confucius's later elaborations were all developed based on this principle. However, it must be understood that this does not mean the three yin lines departing from Tai are the same as the three yin lines entering Pi, nor that the three yang lines entering Tai are the same as the three yang lines departing from Pi. Rather, these relationships are understood through the perspective of the two hexagrams being mutual inverses.

This passage primarily discusses the principles of hexagram transformations in the Yijing (Book of Changes), explaining the patterns of hexagram evolution through celestial-terrestrial orientations and the movement of Yin-Yang Qi.

The text observes that this year's three-Yang Qi is essentially the same as the three-Yang Qi from the first month of last year, just as this year's three-Yin Qi corresponds to last year's seventh-month three-Yin Qi. The Yin and Yang energies between heaven and earth perpetually exist—they merely conceal themselves in different directions, awaiting opportune moments to manifest or withdraw, rather than being newly generated. This cyclical flow of Yin and Yang has remained constant from ancient times to the present.

The author illustrates hexagram transformations with examples: the Tai hexagram (Earth over Heaven) evolves from the Guimei hexagram, involving changes in the fourth and third lines; the Pi hexagram (Heaven over Earth) derives from the Jian hexagram, with transformations occurring in the fourth and third of its nine lines. These changes manifest not only in line position shifts but also in the relative significance between line images.

The discussion then turns to the formation of the Song hexagram (Water over Heaven): it transforms from the Dun hexagram (Mountain under Heaven), changing from four Yang and two Yin lines to an altered initial line. Here, the firm (Yang) line moves to the second position while the yielding (Yin) line advances to the third. Zhu Xi maintained that such hexagram transformations originated from records in the Tuanzhuan (Commentary on the Judgments).

The text further examines transformation patterns in the Sui hexagram (Lake over Thunder) and Gu hexagram (Mountain over Wind): Sui demonstrates firm lines descending with yielding lines following, whereas Gu shows firm lines ascending while yielding lines descend. The author critiques earlier Confucian scholars' rigid applications of the "six offspring hexagrams" (referring to the six basic hexagrams beyond Qian and Kun), particularly rejecting their claims about line exchanges between Pi's initial line and Sui's top line, or between Tai's initial line and Gu's top line.

Finally concerning the Shihe hexagram (Fire over Thunder), earlier scholars believed it transformed from the Pi hexagram with a yielding line rising from the first to the fifth position—a view the author disputes.

(Note: In this context, "firm" denotes Yang lines and "yielding" indicates Yin lines; "three-Yang" refers to trigrams composed of three Yang lines, while "three-Yin" means three-Yin trigrams; "lines" are the fundamental components of hexagrams, divided into unbroken Yang lines "—" and broken Yin lines "--")

This passage primarily discusses the principles of hexagram transformations in the Zhouyi (Book of Changes), explaining the patterns of hexagram evolution through the shifting positions of strong (yang) and yielding (yin) lines.

Regarding the "Bi Hexagram" (Hexagram of Adornment), it describes how the yielding line ascends from below to adorn the strong line, while the strong line in turn moves upward to embellish the yielding line. This transformation originates from the Tai Hexagram (Hexagram of Peace), where the upward movement of strong lines isn't arbitrary. The differentiation between strong and yielding lines manifests through this process of yang lines ascending while yin lines descend.

In analyzing the "Wu Wang Hexagram" (Hexagram of Innocence) and "Da Xu Hexagram" (Hexagram of Great Accumulation), the text explains that the strong line in Wu Wang descends from the top position of Da Xu to become the ruling line of the inner trigram. Conversely, the strong line in Da Xu develops upward based on the initial line of Wu Wang, forming a pattern that honors the worthy. These transformations become clear through comparative study.

The changing patterns of "Xian Hexagram" (Hexagram of Influence) and "Heng Hexagram" (Hexagram of Constancy) are equally evident: Xian shows yielding lines ascending and strong lines descending, evolving from the Pi Hexagram (Hexagram of Standstill), while Heng demonstrates strong lines ascending and yielding lines descending, developing from the Tai Hexagram.

The four hexagrams of Jin (Advance), Ming Yi (Darkening of the Light), Jia Ren (Family Members), and Kui (Opposition) all contain the characteristics of the Li Trigram (Fire). Generally, upward development of lines signifies auspiciousness while downward movement often indicates adversity, reflecting the sages' emphasis on illumination.

The auspicious and inauspicious orientations in Jian Hexagram (Obstruction) and Xie Hexagram (Release) are clearly defined: southwest proves favorable as it attains the Middle Way, while northeast brings misfortune through entrapment. Success comes either through encountering virtuous individuals or timely action.

The transformational principles of Sun Hexagram (Decrease) and Yi Hexagram (Increase) reveal that Sun decreases below to benefit above, symbolizing upward development, while Yi decreases above to benefit below, representing grace flowing from superior to inferior. Both patterns align perfectly with the Dao of nature.

These interpretations of hexagram transformations exemplify how the Zhouyi reveals developmental patterns through line position changes, requiring careful contemplation to grasp their profound meanings.

This scripture primarily examines several key issues concerning the transformations of hexagrams in the Zhouyi and the interpretation of line statements.

First, it explains the relationship between the Tai (Peace) and Pi (Stagnation) hexagrams, noting that while they appear interconnected, each possesses distinct meanings. The Cui (Gathering) hexagram represents convergence, as its lines show firm and yielding elements in mutual response; the Sheng (Ascending) hexagram symbolizes upward movement, as its yielding fourth line rises in accordance with the temporal circumstances. The text critiques certain scholars (Zhang and Xu) for overinterpreting line transformations, arguing they fail to grasp even the fundamental hexagram structures.

Regarding the rules of hexagram transformation, it clearly states: A complete hexagram consists of six lines, and transformations occur only when encountering "nine" (old yang) or "six" (old yin). The diagram of hexagram changes devised by the Duke of Zhou (rules for using nine and six) demonstrates that each hexagram can evolve into sixty-four possible states, but genuine transformation requires first obtaining changing lines through divination.

The specific transformation principles are: Obtaining a "nine" indicates a yang line changing to yin, while obtaining a "six" means a yin line transforming into yang. Taking the Qian (Heaven) and Kun (Earth) hexagrams as examples: When the first line of Qian changes, it becomes Gou (Encounter); when Kun's first line changes, it becomes Fu (Return). Changing the second line yields Tongren (Fellowship) and Shi (Army) respectively; the third line transforms into Lü (Treading) and Qian (Modesty); the fourth line becomes Xiaoxu (Small Accumulation) and Yu (Enthusiasm); while the fifth line shifts to Dayou (Great Possession) and Bi (Closeness). This system of transformations embodies the Zhouyi's core principle: "When exhausted, it changes; when changed, it penetrates."

This passage explains the transformational patterns of the sixty-four hexagrams in the Zhouyi (Book of Changes). It begins with the interactive transformations between the Kun hexagram (representing Earth) and Qian hexagram (representing Heaven), as well as the formation process of the Bo hexagram (symbolizing decline). The Duke of Zhou (founding statesman of the Zhou dynasty) used these hexagram images to expound philosophical principles.

The text details three primary methods of hexagram transformation: two-line changes, three-line changes, and four-line changes. The fifteen possible two-line transformations include combinations like the simultaneous change of the bottom and top lines, which produces either the Daguo or Yi hexagram, while altering the bottom and fifth lines generates the Ding or Zhun hexagram. Each transformation corresponds to specific hexagram combinations.

Three-line changes are more complex, comprising twenty possible combinations. For instance, simultaneous transformation of the bottom, second and top lines produces either the Xian or Sun hexagram, while changing the bottom, second and third lines yields the Pi or Tai hexagram (symbolizing obstruction and prosperity respectively). These transformations follow strict correlative relationships.

Four-line changes have fifteen combinations. Transforming the bottom, third, fifth and top lines simultaneously creates either the Xiaoguo or Sun hexagram, while altering the bottom, second, fourth and top lines generates the Jian or Kui hexagram. These systematic transformation rules form the foundational framework for hexagram derivation in the Zhouyi.

(Note: A yao is the basic unit composing a hexagram—each horizontal line is called a yao, numbered from bottom to top as the bottom, second through top yao. Hexagram transformation refers to the process where yin yao become yang or vice versa, generating new hexagram configurations.)

This passage explains the principles of hexagram transformation in the Yijing (Book of Changes), focusing on the calculation methods for "changing hexagrams" (the different hexagram patterns formed through line transformations).

First, it describes the combinatorial patterns of hexagram changes: from single-line transformations to all six lines changing, each produces a distinct number of new hexagram configurations. For instance, five changing lines yield six new hexagram possibilities, while transforming all six lines has only one outcome (Qian transforming into Kun or vice versa). The Duke of Zhou in the Xici commentary only mentioned the specific transformation rules for "using the nine" and "using the six" in the Qian and Kun hexagrams.

Next, it explains the divination methods for different quantities of changing lines: With one changing line, consult the line statement of that specific transforming line in the original hexagram. For two changing lines, examine both transformed lines but prioritize the upper one. With three changing lines, consider both the original and transformed hexagram statements (the Tuan commentaries). For four changing lines, focus on the two unchanging lines in the transformed hexagram. When five lines change, analyze the sole unchanging line in the new hexagram.

Wang Shi (likely Wang Bi) supplemented that divination should distinguish between "zhen" (the original hexagram) and "hui" (the transformed hexagram). For example, with two changing lines, the first transformed line represents zhen while the second signifies hui; with three changing lines, the transformation process should be divided into three stages for interpretation. Xia Shi (possibly Yu the Great) maintained that unchanging elements must also be incorporated into the analysis.

These rules form a complete system of hexagram transformation. Later, Jiao Gan's Yilin (Forest of Changes) applied these principles systematically, using mutual transformations among the sixty-four hexagrams to derive 4,096 possible hexagram combinations.

This passage primarily discusses the application rules of line statements (explanatory texts for hexagram lines) and the "hexagram ruler" (key line positions determining hexagram interpretation) in Zhouyi divination.

Regarding the use of line statements, ancient scholars believed that the line texts attributed to the Duke of Zhou were originally created for "nine and six" lines (representing changing yin and yang), not for "seven and eight" lines (representing unchanging lines). The Zhouyi originally didn't use the numbers seven and eight, so how could one use seven and eight to substitute for nine and six line statements? When all six lines change, the Qian (Heaven) and Kun (Earth) hexagrams should be interpreted by looking at their top and bottom lines, while other hexagrams should refer to the judgment text (hexagram statement) of the transformed hexagram. All hexagram statements were originally established for unchanging seven-eight situations—how could they be used to divine changing circumstances? Only Qian and Kun hexagrams can be interpreted by their top and bottom lines. This references Zhu Xi's perspective based on records in the Zuo Zhuan such as "Gen's eight" and "Zhen Zhun Hui Yu both being eight," but since the Zuo Zhuan contains records using both the Xia-Shang Yi and Zhou Yi systems, complete verification remains difficult.

The text details selection rules for determining key line positions in various hexagram configurations:

The Twelve Sovereign Hexagrams (representing twelve months) each have their ruling lines: Fu and Gou hexagrams focus on the first line; Lin and Dun on the second; Tai and Pi on the third; Dazhuang and Guan on the fourth; Guai and Bo on the fifth; Qian and Kun on the top line.

Among the doubled trigrams (hexagrams formed by doubling the eight trigrams): Zhen and Xun focus on the fourth line; Kan and Li on the fifth; Gen and Dui on the top line.

In combined hexagram configurations: Heng and Yi hexagrams focus on the first line; Jiji and Weiji on the second; Xian and Sun on the third. Hexagrams without opposing counterparts (like Yi or Daguo) formed by Zhen, Xun, Gen, and Dui combinations focus on the top line, while Zhongfu and Xiaoguo focus on the fourth line. Hexagrams with opposing counterparts (like Sui or Gu) focus on the first line; Jian and Guimei on the third.

For hexagrams containing Kan and Li trigrams, focus on their central lines. Hexagrams like Song, Kun, Jie, Huan, Meng, Shi, Tongren, Ge, Feng, Jiaren, Bi, and Mingyi all take the second line as primary. Hexagrams like Xu, Jie, Zhun, Jing, Jian, Bi, Dayou, Kui, Shike, Ding, Lü, and Jin all take the fifth line as primary.

Hexagrams dominated by Zhen and Xun trigrams focus on the original trigram's fourth line—for example, Yu and Xiaoxu focus on the fourth line; Sheng and Wuwang on the first. Hexagrams dominated by Gen and Dui trigrams focus on the original trigram's third line—for example, Qian and Lü focus on the third line; Daxu on the top line.

Special note: Kun hexagram's statement "later finds its lord" refers to Kun's ruler being the top line; Mingyi's initial nine line statement "the host has words" indicates Mingyi's ruler is the second line.

This passage elucidates the special usage of the character "I" (我) in the Zhouyi (Book of Changes). In the Chunqiu (Spring and Autumn Annals), the narrative typically takes the state of Lu as its subject, referring to it as "I." Similarly, when the term "I" appears in the hexagram statements and line texts of the Zhouyi, it consistently refers to the host line (the most pivotal line within a given hexagram).

Several concrete examples illustrate this principle: In the Meng (Hexagram 4, "Youthful Folly"), the second line serves as the host line, hence the use of "I." In Xiaoxu (Hexagram 9, "Small Accumulation"), the fourth line is the host line, so "I" appears there. For Guan (Hexagram 20, "Contemplation"), the fourth line is the host, while the third line observes the fourth's movement to determine advance or retreat. In Yi (Hexagram 27, "Nourishment"), the top yang line (line 6) is the host—though the initial yang line (line 1) understands self-cultivation methods, it still looks upward to line 6. Yi (Hexagram 42, "Increase") designates the initial yang line (line 1) as host, hence "I" appears there. Finally, in Jing (Hexagram 48, "The Well"), the fifth line serves as host, accounting for the "I" reference.

These examples demonstrate that the term "I" in the Zhouyi is never used arbitrarily but specifically denotes each hexagram's host line. This linguistic convention parallels the Chunqiu's practice of using "I" for the state of Lu, reflecting the meticulous precision of classical texts in their terminology. By identifying which line "I" refers to in a given hexagram, we gain more accurate insight into the meaning of its statements and line texts.

This passage explains the meanings of several hexagram lines from the Yijing (Book of Changes) in modern terms:

The Nine in the Fifth line of the Ding (Cauldron) hexagram describes the predicament of a noble person whose talents go unrecognized. This line symbolizes pristine virtue (represented by pure food in the cauldron), but positioned above the Dui (Lake) trigram (symbolizing the mouth), it's like food placed at the lips yet uneaten—implying a worthy person remains unappreciated, thus evoking compassion.

The Nine in the Second line of Ding states: The cauldron is filled with nourishment (representing inner fulfillment), but my companion ("qiu" meaning a matching counterpart) is temporarily indisposed and cannot partake. Spoken from the perspective of the hexagram ruler (the dominant line), though this line's moral substance makes it my ideal match, temporary yin-yang imbalance prevents union. A virtuous scholar shouldn't compromise principles to seek audience with rulers; rather, leaders should actively seek worthy counsel—hence this signifies good fortune.

The Nine in the Fourth line of Lü (Travel) expresses: As the hexagram ruler occupying an improper position, like a traveler displaced from proper lodging, one feels unsettled.

The Nine in the Second line of Zhongfu (Inner Truth) describes: "I have fine wine (the 'jue' wine vessel), which I wish to share with you." This is the hexagram ruler (Nine in the Fourth) addressing the Nine in the Second, indicating that the Nine in the Fifth (symbolizing the sovereign) holds supreme authority we should jointly revere and follow. Since the Fourth line approaches the Fifth and the Second corresponds with the Fifth, this encouragement arises naturally.

The Six in the Fifth line of Xiaoguo (Minor Excess) states: "Dense clouds in the west bring no rain." Here the hexagram ruler (Nine in the Fourth) explains: The Nine in the Third acts like clouds obscuring the Kan (Water) trigram, preventing rainfall; the Six in the Fifth lies in the west (Dui's position in the eight trigrams' compass), beyond the inner trigram hence called "suburbs." Since the Fourth doesn't correspond with the Fifth, yin and yang cannot harmonize, making rainfall impossible.

Finally, regarding the "interlocking hexagrams" principle in the Xiantian Diagram (the pre-heaven sequence created by Song dynasty scholar Shao Yong): Conventional interpretation holds that interlocking merely extracts four lines from six to form new hexagrams, but the reality is more profound. Observing the Xiantian Diagram reveals that through octave-skipping contraction (a specific sequencing pattern), sixteen interlocking hexagrams emerge naturally.

[Note: The original small-text annotations in parentheses explain technical terms like "interlocking hexagrams," clarifying the mathematical patterns of hexagram overlap and combination.]

This passage explains the combinatorial principles governing the arrangement of the sixty-four hexagrams in the Zhouyi. On the left side, beginning with the Qian (Heaven) and Guai (Resolution) hexagrams, the sequence progresses through eight hexagrams to reach Guimei (Returning Maiden), then another eight to Jiaren (Family) and Jiji (After Completion), followed by eight more to Yi (Nourishment) and Fu (Return). The right side commences with Gou (Encounter) and Daguo (Great Crossing), proceeds through eight hexagrams to Weiji (Before Completion) and Xie (Release), then another eight to Jian (Gradual Progress) and Jian (Obstruction), concluding with eight more to Bo (Peeling) and Kun (Earth).

Each side features two hexagrams that combine in sets of three to form the sixty-four hexagrams. Through these interconnections, the hexagrams can ultimately be distilled into sixteen principal configurations, which further consolidate into four core hexagrams: Qian, Kun, Jiji, and Weiji. This elucidates why the Zhouyi begins with Qian and Kun and concludes with Jiji and Weiji.

Zhu Xi (possibly referring to the Neo-Confucian scholar) explains that the middle layer contains sixteen hexagrams on each side. The lower trigrams follow a pairwise sequence adhering to the Qian-1 and Kun-8 order, while the upper trigrams cycle around this same Qian-1 to Kun-8 sequence. The innermost layer arranges the lower trigrams in the order Qian, Li (Fire), Kan (Water), Kun, with the upper trigrams cycling through Qian, Kan, Li, Kun.

The author notes that Confucius, in the Zagua Zhuan (Miscellaneous Hexagrams Commentary), selected eight hexagrams from the middle layer: Daguo, Gou, and Guai due to their correlation with the inner Qian hexagram; Yi was chosen for its connection to the inner Kun hexagram; Jian and Jiji for their relationship to Weiji; and Guimei and Weiji for their ties to Jiji. Qian and Kun were excluded as they appear at the beginning; Bo and Fu were omitted due to excessive Yin energy; Kui and Xie were passed over in favor of Weiji and Guimei; while Jiaren and Jian were excluded because Jiji and Jian had already been selected.

Three hexagrams were chosen to represent Qian, while Kun was represented solely by Yi. Jiji was paired with Guimei, and Weiji with Jian, reflecting Qian’s supreme status. The placement of Jiji and Weiji at the end of the Zhouyi embodies the text’s cyclical philosophy of beginnings and endings. The sequencing of Guai and Fu after Jiji and Weiji reflects Confucius’ organizational logic in the Zagua Zhuan. Just as the Xia, Shang, and Zhou dynasties each had distinct naming conventions, Confucius’ nomenclature in the Zagua Zhuan follows the principle of "appearing miscellaneous yet never transgressing order" (杂而不越).

This excerpt comes from Guyi Kaoyuan (Investigations into the Ancient Yi), Volume 3, collated and published in 1607 by Zhang Guoxiang of the Zhengyi (Orthodox Unity) Daoist tradition during the Wanli era of the Ming Dynasty. At the time, Zhang held the title of "Zhengyi Sigiao Ningcheng Zhidao Chanxuan Hongjiao Dazhenren" (Great Perfected of Orthodox Unity Succession, Focused on the Dao, Expounding Mysteries and Vast Teachings), overseeing all Daoist affairs in the empire.