《易筮通變》

Book of Divinatory Changes: On Transformation and Mutability, Volume 1, Part 8, authored by Daoist Master Lei Siqi of Linchuan, primarily explores the origins and distinctions between turtle shell divination (bu) and milfoil stalk divination (shi).

The "Hong Fan" chapter of the Book of Documents records how ancient rulers selected specialized divination officials to resolve dilemmas. The Book of Odes similarly states that divination helps avoid errors. The "Monthly Ordinances" chapter in the Book of Rites mentions grand historians using animal blood on turtle shells for winter divination, suggesting these two methods were complementary. The Commentary on the Changes asserts that for investigating mysteries and foreseeing the future, nothing surpasses milfoil and turtle shells, maintaining that the Classic of Changes should preserve both divinatory functions.

While the "Great Announcement" and "Metal-Bound Coffer" chapters document the Duke of Zhou's turtle shell divinations, they omit milfoil methods. Other records claim only feudal lords used milfoil divination, with the Son of Heaven employing turtle shells exclusively - yet in travel contexts, the reverse appears. The "Explaining the Trigrams" commentary describes sages creating the Yi Jing by observing Yin-Yang transformations to establish hexagrams, articulating hard/soft lines to form judgments, ultimately revealing cosmic and human principles - all attributed to milfoil divination without mentioning turtle shells.

Though the "Great Expansion" number (dayan zhi shu) details milfoil stalk procedures, it remains silent on turtle shell techniques. The popular "coin-toss divination" allegedly originated with Jing Fang of the Han dynasty, while Tang scholar Jia Gongyan recorded using coins instead of stalks. Some even imitated turtle divination by shaking coins inside split shells, further blurring authentic traditions. The common term "divining hexagrams" (bu gua) itself conflates these distinct practices.

The Rites of Zhou records the Chief Diviner overseeing three turtle shell methods (jade, tile, and plain) under the Spring Offices, each yielding 120 crack patterns with thousands of interpretations. This demonstrates the rigorous ancient distinction between bu and shi that later generations gradually obscured.

This passage discusses the ancient systems and practical applications of divination (bu, using tortoise shells) and milfoil stalk divination (shi), emphasizing that these were two distinct predictive methods, each with its own framework and rules.

The Zhou dynasty established specialized divination offices: the Divination Master (Bushi) observed crack patterns on tortoise shells (zhao), while the Turtle Keeper (Guiren) managed six types of tortoise shells, interpreting auspicious or inauspicious signs based on their orientation, color, and shape. The Grand Diviner (Dabu), a senior official, mastered three methods of Yi divination: the Lianshan, Guicang, and Zhouyi systems—each containing eight primary trigrams and sixty-four hexagrams. The Milfoil Diviner (Shiren) performed nine types of milfoil divination to predict outcomes. For state affairs, milfoil divination was conducted first, followed by shell divination, with the results verified in spring. Shell divination relied on crack patterns, with recorded omens numbering up to 1,200 types, while Yi divination remained within the framework of sixty-four hexagrams.

The Hongfan records four possible outcomes between shell and milfoil divination: agreement between the two, shell divination yielding to milfoil, milfoil contradicting shell divination, or both contradicting human intentions. This demonstrates that bu and shi were originally independent methods, unlike their later conflation.

Several historical examples illustrate the exclusive use of shell divination: When Duke Hui of Jin was in Liang, Liang Ying's prolonged pregnancy prompted the father-son diviners Zhao Fu to predict twins—a boy named Yu (later held as a hostage) and a girl (who became a concubine). Duke Wen of Zhu divined on moving the capital to Yi; though inauspicious for the ruler, he prioritized the people's welfare and relocated, later dying as foretold. When the Marquis of Qi fell ill while preparing to attack Lu, the Lu diviner Chuqiu predicted through shell cracks that the Marquis would meet a violent end (later fulfilled when Duke Yi of Qi was assassinated).

These cases confirm that ancient bu and shi operated as separate systems: shell diviners did not use Yi-based milfoil methods, nor did milfoil diviners employ tortoise shells. For instance, when King Chu and Duke Ye used mei bu (a form of divination) to select a prime minister, the differing results between Shen Yin and Ziliang led to Ziliang's appointment. Such records prove that bu and shi were strictly distinguished as two independent predictive systems in antiquity.

This passage records several ancient divination cases that illustrate the differences between milfoil divination (using yarrow stalks) and turtle shell divination.

When Yin Zhu and Lord Ye discussed auspicious and inauspicious signs, they mentioned that when Prince Wei became prime minister, four situations would require renewed divination. However, Zi Guo argued that as the Lingyin (the highest-ranking official in Chu), encountering these four situations only necessitated milfoil divination, not turtle shell divination.

Several notable milfoil divination cases are then cited:

• When Bi Wan took office in Jin, he obtained the hexagram Zhun (屯) changing into Bi (比). Xin Liao interpreted this as highly auspicious, foretelling prosperous descendants.
• When Duke Mu of Qin attacked Jin, he obtained the hexagram Gu (蛊), which the diviner Tutu interpreted as predicting three initial defeats but ultimately capturing the ruler of Jin.
• Before the Battle of Yanling between Jin and Chu, the hexagram Fu (复) was obtained, foretelling injury to the Chu ruler.
• Before Duke Xian of Jin married his daughter Bo Ji to Qin, the hexagram Guimei (归妹) changing into Kui (睽) appeared. The historian Shi Su interpreted this as inauspicious, predicting Bo Ji would flee back to Jin after six years and die in Gaoliang.

These cases demonstrate that milfoil divination, with its complete hexagram images and line statements (yaoci), does not require additional interpretation from turtle shell cracks. The hexagram statements of Zhun, Fu, and Gu themselves contain full prophecies, highlighting the self-contained nature of the milfoil divination system.

This passage primarily discusses various scenarios of ancient divination practices (turtle shell divination and milfoil stalk divination) and their practical differences in application.

First, it mentions that some divination results didn't originate from the Zhouyi's (Book of Changes) hexagram statements. For instance, while the hexagram text for Guimei changing into Kui resembles the Zhouyi, it actually comes from the older Lianshan and Guizang systems of the Yijing. These ancient Yijing methods used the same divination techniques as the Zhouyi but featured different hexagram texts.

The text then cites the example of Cheng Ji (Ji You)'s birth in the State of Lu: Duke Huan of Lu simultaneously employed both turtle shell and milfoil stalk divination. The turtle shell reading predicted "a son named You who would assist the ruler," while the milfoil divination yielded the hexagram Dayou changing into Qian, with the interpretation "majestic as a father, noble as a sovereign." When the child was born, his palm indeed bore the character "You." This demonstrates that the two divination methods could be conducted independently, and milfoil interpretations didn't necessarily derive from the Zhouyi.

Three different sequences of divination practice are then illustrated: First, when Duke Xian of Jin sought to make Lady Li his principal wife, turtle divination first showed inauspicious signs, followed by an auspicious milfoil reading. The diviner advised following the older turtle shell's warning, citing the oracle text that "exclusive favor breeds turmoil," but Duke Xian disregarded this, ultimately leading to Crown Prince Shensheng's death and national turmoil. Second, when the Marquis of Wei had a dream, milfoil divination was performed first, followed by turtle divination which used the metaphor "a fish with red tail" to predict Wei's downfall - a prophecy later fulfilled. Third, before attacking the Li Rong tribe, Duke Xian of Jin only conducted turtle shell divination, where historian Su interpreted the cracks as "victory without blessing," using the omen of "bones stuck in teeth" to foretell internal and external conflicts.

These examples reveal ancient practical applications: divination methods could be used separately or jointly; turtle oracle texts (zhaoci) and milfoil hexagram statements (guaci) belonged to different systems; and different sequences (turtle first or milfoil first) might yield divergent conclusions for the same matter. The key distinction lies in their fundamental methodologies - turtle divination primarily interprets crack patterns while milfoil divination analyzes hexagram transformations.

This passage primarily discusses the distinction between ancient divination methods (卜 bu) and milfoil stalk divination (筮 shi), while questioning the credibility of the Confucius divination story recorded in the Family Sayings of Confucius (家语).

The text first cites a historical anecdote: Duke Xian of Jin ignored admonitions to attack the Li Rong tribe. Although the turtle shell divination showed auspicious signs, it ultimately led to national turmoil. This illustrates that relying solely on oracle bone divination (卜辞) without incorporating milfoil stalk divination (筮法) may result in misjudgment.

It then questions the story in Family Sayings where Confucius supposedly divined and obtained the Bi hexagram (贲卦, Mountain over Fire). Confucius allegedly interpreted this as symbolizing excessive ornamentation, conflicting with his advocacy for simplicity. However, the author raises several doubts: first, Zi Zhang mistakenly referred to the milfoil method as turtle shell divination; second, the Bi hexagram's commentary (彖辞) explicitly emphasizes the positive meaning of "observing celestial patterns to understand seasonal changes, and observing human culture to civilize the world," which contradicts Confucius' alleged reaction; third, the Family Sayings account conflicts with the original Zhouyi text.

The author favors the records in Zuo's Commentary (左传), noting that during the Spring and Autumn period, milfoil divination (筮) and turtle shell divination (卜) were strictly distinguished. Although the ancient Lianshan and Guicang versions of the Yi are lost, the Rites of Zhou (周礼) confirms they shared the same system of deriving 64 hexagrams from the eight trigrams with the Zhouyi, contrary to popular misconceptions that conflate "divining hexagrams" (卜卦) as a single practice. The passage concludes by suggesting that the Book of Changes might have survived Qin Shihuang's book-burning precisely because it was conflated with divination practices.

This passage examines the evolution of ancient divination practices and the unique value of the Zhouyi (Book of Changes). The author notes that the Grand Diviners (Taibu) of antiquity originally mastered 120 methods of interpreting omens with 1,200 accompanying verses, all of which were later lost. During Emperor Wen of Han's reign, records still mentioned the "Great Horizontal" (Daheng) turtle shell divination, but even this disappeared in later eras. When Gao Yang of Northern Qi sought to usurp the throne, Li Mi used the "Great Horizontal" omen to flatter him—a maneuver the author dismisses as mere sycophancy.

The author laments the loss of divination texts due to their overwhelming complexity (360 methods with 3,600 verses), making complete preservation impossible. In contrast, the Zhouyi, with its concise system of 64 hexagrams and 384 lines (yao), achieved profound subtlety through continuous refinement by ancient sages. Contemporary commentators, however, often focus narrowly on hexagram and line statements while neglecting the divinatory principle of "adapting to change" (wei bian suo shi). How can one truly comprehend the Yijing without grasping this dynamic application?

The latter section explains the functions of hexagram images (xiang) and line statements: sages created symbolic hexagrams by observing all phenomena under heaven, and formulated line judgments by studying patterns of movement. Hexagram images exhaustively represent all situations, while line statements propel transformative action. Through flexible application, the Yi's full potential is realized, giving rise to civilization. The interplay of the Eight Trigrams (Bagua) generates infinite symbolic combinations, and the stacking of six lines reveals the principles of change.

(Note: "Great Horizontal" refers to major transverse cracks on turtle shells, considered auspicious signs; "Grand Diviner" was an official position overseeing divination; Lianshan and Guicang were legendary pre-Zhouyi divination texts.)

The interplay of Yin and Yang, hardness and softness, gives rise to transformation. Through the attached statements (the hexagram and line texts), auspicious and inauspicious signs are determined, revealing the patterns of movement within all things.

The eight trigrams manifest omens through their symbolic images, while the line statements and hexagram judgments express conditions through words. Changes and transformations serve to pursue benefits and avoid harm. Judgments of fortune and misfortune shift according to circumstances—when the line images transform within the hexagram, their auspicious or ominous nature manifests externally. The accomplishment of merit lies in responding to change, and the wisdom of sages is embodied in these divinatory texts.

The Book of Changes (Yijing) uses hexagram and line statements to illuminate the patterns of movement in all things under heaven. These texts serve to determine fortune and misfortune, with the key to discernment lying precisely in their wording. Thus the principles of this classic are ever-flowing and changing, never fixed in form, cycling endlessly through the six virtual positions (the six lines of a hexagram), rising and falling without constancy, as hardness and softness mutually transform. One must not approach it as rigid dogma, but rather adapt to its transformations.

Hexagrams have their magnitudes, and statements their degrees of peril or ease. Each line text points toward a particular direction of change—the character "zhi" (之) especially emphasizes this transformative tendency. The Book of Changes speaks of transformation, observing change to comprehend the patterns of movement in all things. During divination, when a line changes and causes the hexagram to transform, pointing toward a new symbolic configuration, this is what we call the "resultant hexagram" (zhi gua).

For illustration: During the Spring and Autumn period, when the young Chen Jingzhong was divined for by the Grand Historian of Zhou using the Zhouyi, they obtained Guan (䷓) changing to Pi (䷋), specifically through the transformation of Guan's fourth line. The Grand Historian, citing Guan's fourth line text—"Observing the glory of the state, it benefits one to be a guest of the king"—prophesied he would come to possess a state. Another example: when Duke Wen of Jin escorted King Xiang of Zhou back to his capital, the divination yielded Da You (䷍) changing to Kui (䷥), through the transformation of Da You's third line. The diviner Bu Yan, referencing Da You's third line text—"The duke presents his offerings to the Son of Heaven"—judged this to be highly auspicious.

(Supplementary note: "Resultant hexagram" is a technical divination term referring to the new hexagram formed when a particular line changes in the original hexagram. Ancient practitioners would analyze the relationship between original and resultant hexagrams, combined with line statements, to determine auspicious or inauspicious outcomes.)

This passage recounts several historical anecdotes of divination using the Zhouyi (Book of Changes):

When Cui Zhu, a high official of Qi, sought to marry the widow Dongguo Jiang (also known as Tang Jiang) of the deceased Lord Tang, he consulted the Zhouyi and obtained the Hexagram Kun (困, "Distress") changing into Daguo (大过, "Great Excess")—specifically, Kun's third line transforming to form Daguo. The court diviners all declared this auspicious, but Minister Chen Wenzi pointed to Kun's third line statement: "The husband follows the wind, yet the wind will cause the wife to fall—this marriage must not proceed." The line further states: "Distressed among stones, grasping thorny vines; returning home to find no wife—a dire omen," interpreted as: being trapped among stones signifies obstructed action, clutching thorns injures the hands, and losing one's wife leaves one homeless. Despite these warnings, Cui Zhu insisted on marrying Tang Jiang, ultimately leading to his clan's destruction.

At the birth of Shusun Muzi, his father Zhuangshu consulted the Zhouyi, obtaining the Hexagram Mingyi (明夷, "Darkening of the Light") changing into Qian (谦, "Modesty")—Mingyi's first line transforming. The diviner Chuqiu interpreted: Mingyi's first line states "light exists but does not shine forth," like the sun at dawn; "hanging wings" symbolize the sun's movement; "the nobleman sets forth, fasting for three days" foretold future slander. Later, Shusun Muzi indeed suffered during the Jianniu Rebellion, fulfilling the divination's prediction.

When Duke Xiang of Wei's primary consort bore no heir, his favored concubine Zhou'e gave birth to Meng Zhi. Kong Chengzi dreamed that Kangshu (founder of the Wei state) instructed him to enthrone Yuan (Meng Zhi's younger brother). Later, Zhou'e bore another son named Yuan. As Meng Zhi had a foot disability, Kong Chengzi consulted the Zhouyi about the succession, obtaining the Hexagram Zhun (屯, "Difficulty at the Beginning") changing into Bi (比, "Alliance"). The diviner Shi Chao explained that the phrase "yuan heng" (元亨, "supreme success") referred to Yuan—Kangshu had already designated Yuan as heir in the dream, so the younger Yuan should inherit rather than the elder Meng Zhi.

These stories exemplify the ancient tradition of using Zhouyi divination to resolve uncertainties, where hexagram transformations and line interpretations often accurately foreshadowed future fortunes.

This passage illustrates practical divination cases using the "Yijing" (Book of Changes) in ancient times. When deciding whether to establish feudal lords or select heirs, divination was employed to consult the will of heaven. For instance, during King Wu of Zhou's reign, the enfeoffment of Kang Shu (the king's younger brother) was determined through combined divination and dream interpretation.

During one divination session, the hexagram Zhun (Hexagram 3 of the 64 hexagrams) appeared with its bottom line changing into the hexagram Bi (derived from Zhun's changing line). The line statement for Zhun's bottom line reads: "Hesitating to advance. Favorable to abide in steadfastness. Favorable to establish feudal lords," which consequently determined the heir's selection.

Another case involves Nan Kuai, a senior official of Lu during the Spring and Autumn period, who consulted the Yijing before plotting rebellion. He obtained the hexagram Kun transforming into Bi, with the line statement: "Yellow lower garment. Supreme good fortune." Mistaking this for an extremely auspicious sign, he was corrected by divination expert Zifu Huibo, who explained that such fortune only manifests when acting with loyalty and sincerity—yellow representing centrality and correctness, while the lower garment symbolizes humility. True good fortune requires all three qualities: centrality, humility, and virtuous action. Nan Kuai's subsequent rebellion indeed ended in failure.

These examples demonstrate that Yijing divination isn't merely about simplistic fortune-telling. The crucial methodology lies in interpreting the changing lines' statements after obtaining the transformed hexagram. Ancient masters of the Yijing didn't just use it for divination; they emphasized aligning one's life with the hexagrams' sequence and cultivating mind-heart through line statements. The complete practice involves observing hexagram images and studying texts during peaceful times, while examining transformations and contemplating omens when taking action—this constitutes the comprehensive way of Yijing study.

The passage concludes with a military example: When Chu besieged Zheng, Jin general Xun Huanzi considered withdrawing upon hearing Zheng had made peace with Chu, to avoid exhausting resources. Minister Sui Wuzi quoted the Yijing's Shi (Army) hexagram transforming into Lin, citing the line: "The army must maintain discipline, otherwise inauspicious," demonstrating how changing line statements guided real-world decisions. This again proves the practical significance of transformed hexagrams' line statements.

Youji of Zheng, upon returning from Chu, reported to Zizhan: "The King of Chu is nearing his end. He neglects to cultivate virtuous governance (De), covets endlessly among the feudal lords, and indulges his desires—how can this last? The line statement in the Yi Jing (Book of Changes) for the transformation from the Fu hexagram (Hexagram 24) to the Yi hexagram (Hexagram 27) says, 'Straying without return brings calamity'—this precisely describes the King of Chu."

This refers to the transformation of the top line of the Fu hexagram into the top line of the Yi hexagram. When Manman, a nobleman of Zheng, spoke with Prince Boliao about his ambition to become a high minister, Boliao remarked to others, "One who lacks virtue (De) yet craves high position—this is already forewarned in the line statement for the transformation from the Feng hexagram (Hexagram 55) to the Li hexagram (Hexagram 30)." This refers to the top line of the Feng hexagram transforming into the top line of the Li hexagram, which states: "A towering house overshadows the home; peering through the door, one sees no one. For three years, no one appears—calamity." A year later, the people of Zheng indeed executed Manman.

These three examples all illustrate principles by citing the transformation of a single line within a hexagram. When Cai Mo answered Duke Xian of Wei’s question about the appearance of dragons in the suburbs of Jiangdu, he directly quoted the line statements of the Qian hexagram (Hexagram 1):

• The first line (yang line at the bottom) transforming into the Gou hexagram (Hexagram 44) states, "Hidden dragon: do not act."
• The second line transforming into the Tongren hexagram (Hexagram 13) states, "Dragon appearing in the field."
• The fifth line transforming into the Dayou hexagram (Hexagram 14) states, "Flying dragon in the heavens."
• The top line transforming into the Guai hexagram (Hexagram 43) states, "Arrogant dragon: there will be regret."
• The top line of the Kun hexagram (Hexagram 2) transforming into the Bo hexagram (Hexagram 23) states, "Dragons battle in the wilderness."

Though these line statements do not refer to actual dragons, their underlying principles are consistent. The six transformations cited here all involve the mutual changes between the Qian and Kun hexagrams, using comparison to clarify the patterns of transformation. The Yi Jing comprises sixty-four hexagrams and three hundred eighty-four lines, all of which follow this logic. This sufficiently demonstrates that the Yi Zhuan’s (Commentary on the Changes) statement—"each line statement points to a specific meaning"—is not arbitrary but deliberately established for hexagram transformations. This is precisely how one observes the movements and changes of all things under heaven, grasps their patterns, establishes rituals accordingly, discerns fortune and misfortune, and ultimately acts in harmony with change.

The so-called "adaptation to change" refers to the transformations of hexagram images. Thus, when the lines shift within a hexagram, fortune or misfortune manifests externally; achievement lies in transformation, and the sage’s wisdom is embodied in the line statements. Hexagrams have distinctions of magnitude, statements vary in difficulty and ease, and each line indicates the direction of change. Scholars observe these transformations to establish hexagram images, rely on numerical principles to deduce line statements, delve into their subtleties, and study their ultimate transformations—until they attain spiritual communion and harmonize with the Dao and its Virtue (De).

This passage from Yishi Tongbian (The Divination Method of Change and Its Universal Mutations) discusses the relationship between Daoist cultivation and the principles of the Yijing (Book of Changes). It conveys that by cultivating De (Virtue/Power) — the foundation of Daoist practice — one can comprehend universal principles, thoroughly investigate the patterns and nature of phenomena, and ultimately attain enlightenment about Tianming (the Mandate of Heaven, which in Daoism refers to the origin and laws of life). When a practitioner fully masters both the ti (essence) and yong (application) of the Yijing — grasping its fundamental theories while skillfully applying them — this represents the highest attainment.

The term "yishi" refers to divination methods using the Yijing, while "tongbian" emphasizes penetrating the principles of transformation. The entire passage illustrates how Daoist practitioners should integrate moral cultivation with Yijing studies, using profound inquiry into cosmic patterns to realize life's ultimate truths. Through this synthesis of Dao (the Way) and Change, one aligns with the dynamic interplay of Yin-Yang and the Five Phases, embodying Wuwei (non-action) while navigating existence's perpetual flux.

The Book of Changes (Yijing) originally used Yin-Yang symbols (with the solid line representing Yang as an "odd" number and the broken line representing Yin as an "even" number) to construct the hexagrams. The Qian hexagram (pure Yang) gave rise to three Yang hexagrams (odd-numbered): Zhen, Kan, and Gen. The Kun hexagram (pure Yin) gave rise to three Yin hexagrams (even-numbered): Xun, Li, and Dui. Although Yang hexagrams contain more Yin lines and Yin hexagrams contain more Yang lines, this is merely a numerical odd-even relationship. Initially, the terms "nine" and "six" were not used to designate the lines.

When the sages created the Book of Changes, they established the hexagrams by observing the transformations of Yin and Yang (the Dao of Heaven manifests as Yin-Yang) and generated the line images by applying the qualities of firmness and yielding (the Dao of Earth manifests as yielding-firmness). Each hexagram consists of six lines (six yao), and through the alternating application of Yin-Yang and firmness-yielding, a complete system is formed across the six positions. Here, the terms "line" and "position" refer to the hexagram lines themselves; originally, there was no distinction between "nine" and "six."

It was only when all the lines of the Qian hexagram (pure Yang hexagram) were Yang lines that the line statements were marked with "nine," giving rise to the phrase "using nine." Similarly, when all the lines of the Kun hexagram (pure Yin hexagram) were Yin lines, the line statements were marked with "six," giving rise to the phrase "using six." Later scholars adopted this convention, treating "nine" and "six" as fixed terms, but rarely investigated their origins.

In reality, "nine" and "six" are numerical concepts. The Commentary on the Changes (Yizhuan) states, "To exhaust the numbers and know the future is called divination; to comprehend transformation is called undertaking affairs." This indicates that "nine" and "six" are tools for divining transformations. The numbers of Heaven and Earth total fifty-five (twenty-five for Heaven and thirty for Earth). Through the combinations and transformations of the odd numbers one, three, five, seven, and nine (numbers of Heaven) and the even numbers two, four, six, eight, and ten (numbers of Earth), the generative and completion numbers of the Five Phases are formed: one and six correspond to Water, two and seven to Fire, and so on. These numerical combinations can deduce transformations and communicate with spirits, but they are not directly equivalent to the "nine" and "six" designations in the line statements.

(Additional note: The phrase "varying by threes and fives" refers to the transformations of the Three Powers (San Cai) and the Five Phases (Wuxing). "Generative numbers and completion numbers" are ancient numerological concepts: one to five are generative numbers, and six to ten are completion numbers, which combine to form the attributes of the Five Phases.)

This passage explains the correspondence between numbers and Yin-Yang transformations in the Book of Changes (Yijing). Ancient sages used numbers to represent the patterns of Yin-Yang alternation: Metal corresponds to the combination of three and eight, Wood to four and nine, and Fire to five and ten (where ten is a symbolic number). Earth permeates between nine and six, though its specific function remains subtle.

In the numerical arrangement, the first five digits are "substance numbers" (本体之数 tishu), while the latter five are "function numbers" (用数 yongshu). The generative principle behind these numbers is as follows: Heaven numbers (odd) one, three, and five sum to nine; Earth numbers (even) two and four sum to six. By tripling the Heaven number and doubling the Earth number, we derive the pivotal numbers nine and six.

The transformational logic operates thus: one plus five yields six (old Yin), two plus five yields seven (young Yang), three plus five yields eight (young Yin), and four plus five yields nine (old Yang). These four numbers—six, seven, eight, nine—mutually transform to form the foundation of Yin-Yang alternation. While people generally recognize the distinction between mature and nascent Yin-Yang states, they typically only observe that Yijing hexagrams use nine for Yang lines and six for Yin lines, unaware that seven actually represents Yang and eight represents Yin during the actual drawing of hexagrams.

This numerical transformation manifests in divination methods: when using yarrow stalks, four operations complete one transformation (bian), and eighteen transformations complete one hexagram. Every three transformations accumulate into a single line, judged by the parity combination of four and eight. If one four and two eights appear in three transformations, a Yang line is drawn (symbolizing the trigrams Zhen, Kan, or Gen); if one eight and two fours appear, a Yin line is drawn (symbolizing Xun, Li, or Dui). This simulates the principle of Yin-Yang interaction generating the six offspring trigrams. Should three transformations all yield four, the Qian (Heaven) trigram is drawn; if all yield eight, the Kun (Earth) trigram appears. This method of deducing hexagrams through numerical changes embodies the essential Yijing principle of "varying through threes and fives, interweaving their numbers."

This passage explains the correspondence between numbers and hexagram transformations in ancient yarrow stalk divination. The numbers seven and eight represent unchanging lines (the basic components of a hexagram), where seven corresponds to a yang line (symbolizing masculine strength) and eight to a yin line (symbolizing feminine receptivity). In contrast, nine and six denote changing lines: nine marks a transforming yang line, while six indicates a transforming yin line.

When drawing hexagrams, the unchanging seven and eight are typically marked at the beginning to signify the hexagram’s fundamental nature. The changing lines—nine and six—are distributed throughout the hexagram without separate notation, embodying the dynamic interplay of yin and yang. This transformation lies at the heart of the Book of Changes (Yijing), revealing the profound principles behind "using nine" (yong jiu) and "using six" (yong liu).

The Qian Zao Du (a commentary on the Yijing) states: "When yang moves, it advances; when yin moves, it retreats." Thus, seven represents yang in its stable state, while nine signifies its transformation. Similarly, eight represents yin in its stable state, and six denotes its transformation. Chao Yuezhi, a Song Dynasty scholar of the Yijing, argued that ancient hexagram drawing originally used odd and even numbers to denote yin and yang. Later, through yarrow stalk divination, the naming system of seven, eight, nine, and six emerged: old yang transforms into nine, old yin into six, young yang into seven, and young yin into eight.

In the Zhouyi (the Book of Changes), seven and eight correspond to the ancient concepts of odd and even. When nine or six appears in a hexagram, it signals transformation. For example, if all six lines are nine, the Qian (Heaven) hexagram transforms into Kun (Earth). Conversely, if all six lines are six, Kun becomes Qian. This is the rule governing "using nine" and "using six."

The passage concludes with an example: When Mu Jiang, the mother of a ruler of Lu during the Spring and Autumn period, was exiled to the Eastern Palace, she consulted the oracle and obtained the Gen (Mountain) hexagram transforming into Sui (Following). The diviner interpreted this as a sign that she should leave quickly. However, Mu Jiang cited the Zhouyi's explanation of Sui—"supreme success, beneficial perseverance"—and reflected that her own moral failings made her unworthy of a favorable outcome. This illustrates that divination involves not only interpreting hexagram changes but also assessing one's virtue (De).

This passage explains the principles of hexagram transformation in ancient divination (shi), focusing on the Zhouyi's divinatory rule that "seven and eight constitute the body, while nine and six constitute the function."

It first observes that pursuing prosperity at the expense of one's fundamental integrity cannot be considered true benefit, nor can abandoning proper position to curry favor be deemed true steadfastness. If one lacks even these four basic virtues (yuan, heng, li, zhen), how can misfortune be avoided? Calamity inevitably follows.

The text then details the divination method: among the three versions of the Yi (Lianshan, Guicang, and Zhouyi) recorded in the Rites of Zhou, though their names differ, their divinatory techniques remain identical. Here, seven and eight represent the unchanging body of the hexagram, while nine and six signify transforming lines. Taking the Gen hexagram as an example: when its bottom line changes, it becomes Bi; when the third line changes, Bo; the fourth line yields Lü; the fifth produces Jian; and the top line transforms into Qian. Should five of a hexagram's six lines all change, the diviner faces difficulty in judgment—in such cases, one follows the unchanging yin line (eight) to determine the outcome, termed "Gen transforming into Sui."

The passage criticizes Du Yu's (Du Shi) misinterpretation, where he mistakenly considered "encountering eight as inauspicious" and thus advocated using Zhouyi's changing lines for divination instead. In truth, seven and eight represent the fixed, unchanging lines of a hexagram's structure and are never referred to as nine or six. The text cites an example from the Discourses of the States: when Prince Chong'er of Jin performed divination, his first reading yielded Zhun transforming into Yu, both containing eights (referring to unchanging yin lines in both hexagrams); his second reading yielded Tai without any moving lines—further evidence that seven and eight represent the bodily aspect of hexagrams.

Wei Zhao's commentary confirms this: within Zhun's lower trigram (Zhen), two yin lines remain unmoving, just as Yu's upper trigram (Zhen) also contains two unchanging yin lines—hence "both are eight." The same applies when Tai hexagram appears without moving lines. This demonstrates that seven and eight represent the unchanging yin aspect within hexagram imagery.

This passage examines the transformation principles between yin lines (representing even numbers and passive qualities) and yang lines (representing odd numbers and active qualities) in Yijing divination. In original practice, stationary yin lines were marked as "eight" while stationary yang lines as "seven," though the received Zhouyi text only records "nine" (changing yang) and "six" (changing yin).

The author observes that scholars often focus on the "using nine" and "using six" expressions while overlooking the transformative relationship between seven-eight and nine-six. In reality, when the stationary yang line "seven" begins to change, it upgrades to "nine" while retaining yin qualities; the stationary yin line "eight" transforms downward to "six" while preserving yang attributes. This dynamic proves crucial in hexagram interpretation, as evidenced by divination records in the Zuozhuan which consistently explain lines based on their transformations.

The text cites Cai Mo's explanation to Duke Xian of Wei about dragon symbolism to illustrate this principle: when Qian (Heaven) hexagram transforms into Gou (Encounter), the "hidden dragon" line appears; when changing into Tongren (Fellowship), the "dragon seen in the field" emerges. These line statements only manifest after seven-eight transforms into nine-six. Otherwise, why would Qian's lines already contain fixed statements like "hidden dragon" when simply marked "nine," or Kun's top line directly state "dragons fight in the wild" without requiring hexagram transformation?

Particularly noteworthy are Qian's "using nine" line stating "seeing headless dragons, auspicious" and Kun's "using six" declaring "favorable for perpetual perseverance"—both expressions fundamentally depend on line transformations. Through analyzing these classical examples, we clearly discern the pattern where stationary seven-eight numbers transform into changing nine-six numbers, which constitutes the essential key to understanding the principles of line mutation.

This passage primarily explains the meanings of "using nine" (用九) and "using six" (用六) in the Yijing (Book of Changes) and their application in divination.

First, it clarifies that the method of explanation following the Kun hexagram (坤卦) follows the same principle as mentioned earlier: all instances where "nine" is used to denote changing lines follow the same pattern, though this requires deeper understanding. The reason each line first references its original hexagram before being verified through the hexagram statement is to illustrate that when the yang number seven changes forward, it becomes nine, while when the yin number eight changes backward, it becomes six.

By examining the hexagram statements cited in the Yizhuan (Commentaries on the Yijing), we see that whether a line becomes nine or six depends entirely on whether seven or eight undergoes transformation. Hence, the rules of "using nine" and "using six" emerge. Specifically: in the Qian hexagram (乾卦), from the first line to the top line, all must wait for the yang number seven to change before being called nine; in the Kun hexagram, from the first line to the top line, all must wait for the yin number eight to change before being called six.

Chao Yuezhi (a Song dynasty Yijing scholar) argued that the appearance of nine or six in the lines signifies transformation. If all six lines are nines, the Qian hexagram transforms into Kun; if all six lines are sixes, the Kun hexagram transforms into Qian. The Qian Zao Du (a Han dynasty apocryphal text) reiterates this: when yang moves forward, seven changes to nine, symbolizing the growth of Qi; when yin moves backward, eight changes to six, symbolizing the waning of Qi. It also states that Qian declines after thirty-two generations, while Kun grows after thirty-two generations.

The Yizhuan states that "Qian and Kun are the gates of change," because by entering through these gates, all other hexagrams must follow this pattern to determine the transformations of each hexagram and thus establish the names of nine and six. Therefore, "using nine" and "using six" do not appear in other hexagrams but are uniquely present in Qian and Kun. These rules are not only established for Qian and Kun but actually apply to all other hexagrams as well.

The divination method stipulates: if none of the six lines change, the judgment is based on the original hexagram's tuanci (hexagram statement); if five lines change and only one remains unchanged, the judgment is based on the tuanci of the unchanged line in the transformed hexagram (not the line statement), because that line has not changed and cannot be called nine or six.

Ouyang Xiu (styled Yongshu) explained: What does it mean when Qian says "using nine" and Kun says "using six"? It means that seven and eight are not used. The lines of Qian are seven or nine, and nine will change; the lines of Kun are eight or six, and six will change. The Yijing uses transformation for divination, hence the naming of lines as nine and six. Zhu Xi (styled Yuanhui) strongly agreed with this interpretation and further elaborated: What do Qian and Kun's "using nine" and "using six" mean? The lines of Qian are seven...

This scripture primarily explores the mysteries of the numbers "nine and six" (九六) versus "seven and eight" (七八) in Yijing (I Ching) divination. During divination using yarrow stalks (the ancient divination tool), the numbers seven and eight appear more frequently, while nine and six are relatively rare, sometimes even absent. This phenomenon exists across all sixty-four hexagrams, being most pronounced in the Qian (Heaven) and Kun (Earth) hexagrams.

The ancients believed that "three represents Heaven and two represents Earth" (参天两地) forms the origin of the nine and six numbers: multiplying three by three yields nine (used in the Qian hexagram's "Use Nine"), while adding two three times yields six (used in the Kun hexagram's "Use Six"). Hexagram images are established through the transformations of Yin and Yang—the Dao of Heaven lies in Yin-Yang, the Dao of Earth in hardness and softness, and the Dao of humanity in benevolence and righteousness. Within the six lines of a hexagram, the arrangement of odd and even numbers forms fixed patterns—when static, they are called "lines" (画), but when changing, they become "yao" (爻).

The author points out that although past scholars like Zhu Xi discussed this issue, none truly clarified the fundamental principle behind the numbers nine and six. Classical texts such as the Qian Zao Du (a Han dynasty Yijing commentary), often dismissed by Confucian scholars, actually contain much valuable material. Finally, the text emphasizes that when studying hexagrams, one must carefully distinguish between "lines" (static hexagram images) and "yao" (changing lines)—this distinction lies at the heart of Yijing divination's profundity.

The hexagrams of the Book of Changes (Yijing) consist of six alternating yao positions, each representing the dynamic interplay of Yin and Yang from bottom to top. The firmness of Yang and the yielding of Yin shift and flow through these six empty positions without fixed patterns—their transformations adapting fluidly to the needs of change. Sometimes the heavenly number three is multiplied to yield nine (representing old Yang), while the earthly number two yields six (old Yin). The principles of "using nine" and "using six" generate transformations in the lines, giving rise to new hexagrams. What doubt can there be in applying these numbers?

The sages, penetrating the mysteries of all phenomena and observing the movements of the world, drew analogies through symbolic imagery to discern their interconnected patterns. By attaching judgments to the lines, they revealed auspicious or inauspicious outcomes—thus completing the hexagram's structural system. Their expressions, though concise, contain profound meaning, illuminating these truths clearly for all generations. Yet some scholars cling only to the names of these concepts without grasping their essence, applying them throughout their lives yet remaining oblivious to their true significance. Confused, they invent their own interpretations, believing they possess unique insights, and even compose treatises—a truly lamentable state. For this reason, I have taken care here to elucidate these principles in detail.

(Note: In this passage, "nine" signifies the number of old Yang and "six" that of old Yin—key numerals in Yijing divination for determining line changes. "Taking three from heaven" and "taking two from earth" refer to ancient mathematical methods for deriving hexagram imagery.)

The tenth chapter of the lower scroll of Yishi Tongbian (Comprehensive Changes of Divination) was composed by the Linchuan Daoist master Lei Siqi, primarily exploring the mysteries of "derived numbers." The text points out: The natural numbers of heaven and earth originally total fifty-five (twenty-five heavenly numbers plus thirty earthly numbers), yet in the Great Expansion numbers used for divination, only fifty are employed. What does this missing five signify?

The author traces records from the Liezi and the Yiwei Qianzaodu (Apocryphal Treatise on the Changes: Chiseling Open the Path of the Qian Hexagram), revealing that cosmic generation occurs in five stages: Taiyi (the state without Qi), Taichu (the beginning of Qi), Taishi (the beginning of form), Taisu (the beginning of substance), and finally Hunlun (the undifferentiated chaotic state where Qi, form, and substance are not yet separated). This "Five Ultimates" (Wutai) culminates in the Hunlun stage, which is none other than Taiji (the Supreme Ultimate). Taiji already encompasses the previous four stages within itself. Thus, the Great Expansion number fifty actually represents the virtualization of the "Five Ultimates" prior to Taiji, retaining only the fifty transformations that follow Taiji for divination purposes.

The six statements in the Yizhuan (Commentary on the Changes), including "That which generates life after life is called Change," precisely elucidate this principle: Taiji as the origin of transformation ("the One"), through the interaction of Qian and Kun, Yin and Yang ("forming images" and "imitating patterns"), employs numerical derivation ("exhausting numbers to know the future") to comprehend the laws of transformation ("comprehending change"), ultimately reaching the realm of unfathomable mystery ("what Yin and Yang cannot fathom is called Shen [Spirit]"). This numerical system preserves the primordial Taiji while manifesting the subtleties of practical application.

The "Taiji" (Supreme Ultimate) mentioned in the Yijing (Book of Changes) is the fundamental origin of all things, and the concept of "unceasing generation" lies at the heart of its philosophy. While the text states that "the Qian hexagram symbolizes formation," it does not directly mention Taiji because Taiji is actually the ultimate source of Yin-Yang transformation.

Taiji, as the root of Yin-Yang transformation, can be understood as "One"—the starting point of all morphological changes in existence. The "One" symbolized by the Qian hexagram divides to produce "Two," represented by the Kun hexagram. This is analogous to the divination practice using fifty yarrow stalks, where one stalk is deliberately set aside to symbolize Taiji's foundational role—that unused stalk represents Taiji, while the remaining forty-nine signify the transformations of heaven, earth, and all things.

During divination, the forty-nine stalks are divided into two piles (symbolizing the two polarities of heaven and earth), then one is taken out (representing humanity, completing the triad of heaven-earth-human), and finally counted in groups of four (symbolizing the four seasons). This corresponds to the number forty in the Hetu (an ancient astrological diagram). Although the total number in heaven and earth is fifty-five, only fifty are used in divination because the number "five" has no fixed position among the Four Symbols (Lesser Yang, Greater Yang, Lesser Yin, Greater Yin), and "ten" has no fixed position in the Eight Trigrams.

The uniqueness of the number five lies in its ancient written form, which resembles the interweaving of Yin and Yang. The Earth phase (one of the Five Phases) corresponds to both five and ten—from one to five to ten, ultimately returning to one. Precisely because the Earth phase has no fixed direction, the number five is absent in the Four Symbols, and ten is absent in the Eight Trigrams. In fact, the numbers one through four of the Four Symbols, through progressive combination (e.g., one plus one equals two, two plus one equals three, etc.), can fully derive the system of the Eight Trigrams.

This passage explains the numerical principles underlying divination in the Book of Changes (Yijing). It begins by describing the generative pattern of the Eight Trigrams (Bagua): using the foundational number four in combination with five produces the four key numbers six, seven, eight, and nine (representing old Yin, young Yang, young Yin, and old Yang, respectively). These forty-eight trigrams, through the pairings of one with nine, two with eight, three with seven, and four with six, ultimately converge to the number forty, excluding the fixed positions of "five for Heaven and ten for Earth."

The core explanation focuses on the origin of the "Great Expansion number fifty": multiplying Heaven's five by Earth's ten yields exactly fifty. The operational method is as follows: the one of the northern Kan trigram combines with five to form six (corresponding to the northwestern Qian trigram); the three of the eastern Zhen trigram combines with five to form eight (corresponding to the northeastern Gen trigram)—this establishes the primary directions first, then aligns with the secondary directions. The two of the southwestern Kun trigram combines with five to form seven (corresponding to the western Dui trigram); the four of the southeastern Xun trigram combines with five to form nine (corresponding to the southern Li trigram)—this establishes the secondary directions first, then aligns with the primary directions. Thus, when Yang numbers (odd) gain five, they become Yin numbers (even), and when Yin numbers gain five, they become Yang numbers, clarifying the distinction between Yin-Yang and forming the arrangement of the Eight Trigrams.

The application of the number ten is as follows: the nine of the southern Li trigram and the one of the northern Kan trigram sum to ten; the seven of the western Dui trigram and the three of the eastern Zhen trigram sum to ten—this is the pairing of Yang numbers, establishing the primary directions. The eight of the northeastern Gen trigram and the two of the southwestern Kun trigram sum to ten; the six of the northwestern Qian trigram and the four of the southeastern Xun trigram sum to ten—this is the pairing of Yin numbers, establishing the secondary directions. In this way, a central five is virtually positioned, and all combinations conform to the transformational number fifteen (note: each row of the Luoshu magic square sums to fifteen), causing Yin and Yang to interact and the Eight Trigrams to stimulate and transform each other.

Finally, the passage explains why forty-nine yarrow stalks are used in divination: four symbolizes the four seasons, and the profound function of fifty lies precisely in this. The specific operation involves placing the numbers one, two, three, and four above and six, seven, eight, and nine below. By combining five with Heaven's one to form six (four times six equals twenty-four, corresponding to the tally number of old Yin Kun trigram) and five with Earth's two to form seven (four times seven equals twenty-eight, corresponding to the tally numbers of the young Yang Zhen, Kan, and Gen trigrams), these numerical transformations constitute the mathematical foundation of Yijing divination.

This passage explains the concrete procedures and numerical principles of ancient divination using yarrow stalks (a method of prediction). At its core, it describes how specific methods of dividing the stalks yield hexagram images.

During divination, the yarrow stalks are divided into left and right portions (symbolizing heaven and earth), then counted in groups of four. After each counting, four possible remainders may appear: 4, 5, 8, or 9. Among these, 4 and 8 are foundational numbers, while 5 and 9 result from adding the "suspended one" (a single stalk set aside to represent humanity) to these base numbers.

The text emphasizes the relationships between these numbers: heavenly numbers are multiples of three (3×8=24), while earthly numbers are multiples of four (4×9=36). The Lesser Yang (represented by the Xun, Li, and Dui trigrams) uses the unchanging numbers 7 and 8, which sum to 15, representing the fixed structure of the hexagram. The Greater Yang (Qian trigram) and Greater Yin employ the changing numbers 9 and 6, which also sum to 15, representing the transformative aspects of the hexagram.

The passage critiques common errors among contemporary diviners: they mistakenly included the "suspended one" stalk in their total counts, resulting in remainders of 5 or 9 during the first transformation. The correct method requires counting the "suspended one" separately, ensuring remainders of only 4 or 8. A complete hexagram determination requires three such transformations (totaling 18 operations).

These numbers and operations correspond to principles found in the Hetu (the ancient River Chart diagram), where 4 represents the four seasons and 40 corresponds to the formation of the eight trigrams. The entire divination process mirrors the cyclical patterns of seasonal changes and the transformations of heaven and earth.

This passage examines the mathematical principles underlying the ancient divination method of the "Great Expansion Number" (Dayan zhi shu), specifically addressing controversies regarding the division and counting of yarrow stalks (shecao) used in the process. The author critiques earlier misinterpretations by Kong Yingda in his commentaries.

The central debate revolves around the calculation method for the "hanging one" (guayi) step—where one stalk is set aside during each division. The correct understanding maintains that exactly 48 stalks remain actively used in the division (derived from the total 50 minus the "hanging one" and the "unused Supreme Ultimate [Taiji] stalk"). Through 18 transformations (grouped in sets of three changes, totaling six groups), the hexagram is determined. Previous scholars erroneously included the "hanging one" stalk within the count of 49, causing systemic confusion in the calculations.

The author further explains the composition of the Great Expansion Number 50: The yarrow stalks, as divination tools, embody round and numinous qualities—represented by 7×7=49 (symbolizing their spiritual nature). Hexagrams manifest square and wise qualities—represented by 8×8=64 (symbolizing their intellectual nature). The sum of 7 and 8 yields 15, a number reflected in the changing lines of the Qian hexagram (using 9) and Kun hexagram (using 6), where 9+6=15. The multiplicative relationship from 5 to 10 (5×10=50) forms the complete framework of the Great Expansion system.

The conclusion emphasizes that from the Heaven-Earth generative numbers 1 through 10 (summing to 55) to the Great Expansion Number 50 and its operational number 49, each figure has precise mathematical foundations and practical applications. Due to the longstanding misunderstanding of the "hanging one" principle, this crucial divination method remained misinterpreted for centuries without proper correction.

This scripture primarily discusses the philosophical principles and operational procedures of divination in the Book of Changes (Yijing). At its core, it explains how the use of yarrow stalks (ancient divination tools) embodies the transformative patterns of heaven, earth, and all things.

First, it elucidates the principle that "the Taiji (Supreme Ultimate) generates the Two Modes (Yin-Yang)": In divination, one prepares 50 yarrow stalks but uses only 49, leaving one unused to symbolize Taiji (the cosmic origin). The 49 stalks are divided into left and right piles representing the Yin and Yang modes. One stalk is then taken from the left and set aside, forming the pattern of the "Three Powers" (heaven, earth, and humanity). In this process, the unused stalk symbolizes heaven, the divided piles symbolize earth, and the removed stalk symbolizes humanity, embodying the mathematical principle of "coordinating heaven and earth."

Next, it describes the formation of the Four Images and Eight Trigrams: The Yin and Yang modes each further divide into mature and young Yin and Yang, forming the Four Images of Great Yang, Lesser Yang, Great Yin, and Lesser Yin. By observing the transformations of Yin and Yang in the yarrow stalks, the hexagram images are established, with the interplay of firm and yielding lines generating the changes of the hexagram lines. It emphasizes that these steps carry profound meaning: drawing the hexagrams is not arbitrary, nor are the line changes randomly produced. Instead, they reveal the mysteries of heaven, earth, and all things through the numerical changes of the yarrow stalks, driving the evolution and transformation of phenomena.

Finally, it quotes the Commentaries on the Changes (Yizhuan): "The nature of the yarrow stalks is round and spiritually potent, the nature of the hexagrams is square and wise, and the changes of the six lines are simple yet capable of foretelling fortune and misfortune." The Great Expansion number (the fifty used in divination) manifests the patterns of heaven and earth through the yarrow stalks, with the unused "one" symbolizing the substance of Taiji—precisely the embodiment of "the Changes have Taiji." The entire divination process is, in fact, a simulation of the cosmic process of generation and transformation.

This passage explains the generative principles of the Eight Trigrams (Bagua) from the Book of Changes (Yijing) and their divination methods. The Supreme Ultimate (Taiji, cosmic origin) first divides into Two Modes (Yin-Yang), which then transform into the Four Images (Sixiang) - Old Yin, Old Yang, Young Yin, and Young Yang (four fundamental states). Through three layers of Yin-Yang interaction (represented by "three lines"), these Four Images further evolve into the Eight Trigrams (Qian, Kun, Zhen, Xun, Kan, Li, Gen, Dui).

Each trigram consists of three lines (yao), collectively representing the Three Powers (Sancai) of heaven, earth, and humanity. The complete trigram system comprises sixty-four hexagrams, but sixteen belong to "wandering and returning souls" (special transitional states) and are excluded from standard divination calculations. Thus, only forty-eight yarrow stalks (divination tools) are used in practice.

During divination, fifty stalks are initially taken, though only forty-nine are actually used (symbolizing the Taiji). Through steps like "dividing into two" (separating the stalks into two piles) and "hanging one" (removing a single stalk), the process eventually yields six lines forming a hexagram. This method employs multiples of four to correspond with the four seasons (Sishi) and eight solar terms (the eight major divisions of the twenty-four solar terms), mirroring how the Four Images generate the Eight Trigrams.

Finally, the text notes that each of the Three Powers (heaven, earth, humanity) possesses dual attributes—Yin-Yang, soft-hard, and benevolence-righteousness—hence each hexagram uses six lines (two for each Power). The entire divination process, through the division and recombination of yarrow stalks, simulates the cyclical patterns of the cosmos.

This passage explains the concrete procedures of the Dayan divination method, an ancient practice using yarrow stalks. At its core is the operational sequence known as "four operations complete the change" (si ying cheng yi):

First, the 49 yarrow stalks are randomly divided into left and right portions (division into two). Then one stalk is taken from the right portion and set aside (hanging one). Next, the left and right portions are each counted off in groups of four stalks (counting by fours), with the remainders (returning the odd) placed between the fingers. This complete process constitutes "one operation," which must be repeated four times to determine a single hexagram line.

The text meticulously details the calculation rules for remainders: If the right portion yields a remainder of 1, the left must yield 3 (totaling 4); if the right yields 3, the left yields 1; when both sides yield 2, they total 4; when both yield 4, they total 8. It particularly notes that although the remainder 8 appears even, it actually consists of two 4s—just as the Kun hexagram (yin) originates from the differentiation of the Qian hexagram (yang).

After completing the four operations, all used stalks are gathered back to their initial state, completing the full "four operations complete the change" cycle. The four steps are: division into two, hanging one, counting by fours, and returning the odd. Through this rigorous mathematical derivation, the final hexagram emerges for divining auspicious or inauspicious outcomes.

This passage explains the ancient divination method using yarrow stalks (known as "she shi fa"). The process involves performing three consecutive operations, each time dividing the stalks into two groups, setting aside one stalk, then counting them in groups of four. The remainders are recorded after each operation.

After completing the three operations, the judgment is made based on the total sum of remainders:

• If all three remainders are 4 (called "lesser"), totaling 12, with 36 stalks remaining, this corresponds to the Qian hexagram (old yang)
• If all three remainders are 8 (called "greater"), totaling 24, with 24 stalks remaining, this corresponds to the Kun hexagram (old yin)
• Two greater and one lesser remainders (total 20) with 28 stalks remaining correspond to Zhen, Kan, or Gen hexagrams (young yang)
• Two lesser and one greater remainders (total 16) with 32 stalks remaining correspond to Xun, Li, or Dui hexagrams (young yin)

The sequence of remainders further determines the specific hexagram:

• For young yang hexagrams: 4-8-8 indicates Zhen (yang at bottom line), 8-4-8 indicates Kan (yang at middle line), 8-8-4 indicates Gen (yang at top line)
• For young yin hexagrams: 8-4-4 indicates Xun (yin at bottom line), 4-8-4 indicates Li (yin at middle line), 4-4-8 indicates Dui (yin at top line)

Typically, young yang (Zhen/Kan/Gen) is represented by an unbroken yang line, while young yin (Xun/Li/Dui) by a broken yin line. Only when all three operations yield 4 (total 12) is it specially called old yang (Qian hexagram), represented as a "changing" line (yang transforming into yin). These judgment methods simulate the transformational patterns of the eight trigrams, where young yang/yin represent incomplete transformations, while old yang/yin signify fully matured states.

This passage explains the specific method of yarrow stalk divination in ancient times, focusing on the formation process of the Eight Trigrams (Bagua) and sixty-four hexagrams in the Book of Changes (Yijing).

Each trigram consists of three lines (yao, each representing yin or yang), requiring three transformations to determine a single line. In practice, this involves four operations: dividing the yarrow stalks, setting aside a portion, counting the stalks, and recording remainders (collectively called the "four operations"). Repeating this process three times determines the nature of a single line (yin or yang). Through nine transformations (three lines × three transformations), a three-line trigram is formed, known as the "minor completion."

To form a complete six-line hexagram (one of the sixty-four hexagrams), the above process must be repeated twice, totaling eighteen transformations. Here:

• The yang line (represented by the number nine) is fundamentally yang but contains yin qualities
• The yin line (represented by the number six) is fundamentally yin but contains yang qualities

This mutual containment of yin and yang embodies the principle of transformation in all things.

The text also mentions that the total stalk count (calculation number) for the Qian hexagram (pure yang) is thirty-six, while for the Kun hexagram (pure yin) it is twenty-four. Combined, they make sixty, corresponding to the sixty-year sexagenary cycle. The entire divination process is rigorous and complex, requiring eighteen transformations to complete the derivation of a single hexagram, demonstrating the ancient sages' wisdom in observing natural transformations.

This passage explains the computational principles and symbolic significance of the "Great Expansion Number" (Dayan zhi shu) in ancient divination. The Earth phase of the Five Phases (representing the center) governs the four seasons, with each season presiding over eighteen days, totaling seventy-two days across all seasons. Through eighteen transformational operations, each comprising four steps (called "four camps"), the total also amounts to seventy-two steps. Five sets of seventy-two days make three hundred and sixty days, corresponding to a solar year.

In divination practice, forty-nine yarrow stalks (divination tools) are used. The first nine transformations establish the basic forms of the Eight Trigrams (Bagua), while the subsequent nine transformations deduce the patterns of change among the sixty-four hexagrams and their three hundred eighty-four lines through the interaction of Yin-Yang and hardness-softness. This method of deduction can simulate all transformations between heaven and earth—through the mutual pushing of hard and soft, the oscillation of Yin and Yang—it exhaustively encompasses all possible changes under heaven.

The wonder of yarrow stalks lies in their perfect responsiveness to change, the wisdom of hexagrams in their stable manifestation of patterns, while the transformations of the six lines truthfully reflect celestial mandate. Though this divination method appears motionless, it resonates with and comprehends all affairs under heaven. Thus it can be used to understand human hearts, accomplish great works, resolve doubts, and even communicate with divine spirits.

The conclusion emphasizes these numbers and symbols are never arbitrarily set: using only forty-nine of fifty stalks, observing Yin-Yang changes to establish hexagrams, deducing hard-soft relationships to generate lines—all serve to accurately model the operating principles of heaven and earth. Those who truly master this method can illuminate the Dao of heaven, comprehend spiritual mysteries, and fulfill the ultimate purpose of the "Great Expansion Number"—the most profound divination art.