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Chapter 2 of 12
易冒
There are ten Heavenly Stems in total, and twelve Earthly Branches in total. 🌱
The Heavenly Stems are like the roots of a tree, symbolizing Heaven in its generation of all things—hence they are called Heavenly Stems; the Earthly Branches are like the branches and leaves of a tree, symbolizing Earth in its fulfillment of all things—hence they are called Earthly Branches. There are ten Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui; there are twelve Earthly Branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai.
Using Jia to govern Zi, pairing Yi with Chou, the Heavenly Stems and Earthly Branches connect end to end in an unceasing cycle. The numerical principle of Heaven and Earth completes a full cycle at sixty.
The rule of the Jiazi calendrical system is this: distribute the Heavenly Stems in order across the twelve Earthly Branches. Starting from Jiazi and ending at Guiyou, when the Heavenly Stems complete a rotation, begin again from Jiaxu; when the Earthly Branches complete a rotation, begin again from Bingzi. Just as branches and roots are inseparable, the cycle concludes entirely at Guihai, totaling sixty combinations.
Heaven is divided into Five Movements (Yun), and Earth into Six Qi (Atmospheric Influences). Between Heaven and Earth, all things are transformed and generated. Thus the Jiazi system was established to record years and seasons, giving the sun, moon, and four seasons a regular standard.
The Five Movements refer to the five directions of East, West, South, North, and Center, governed by the ten Heavenly Stems operating in the upper realm. The Six Qi refer to the six yin and six yang energies within the twelve Earthly Branches, governing the power of rise and fall, waxing and waning of cold and heat, spring and autumn, quietly completing their substance below. Fortune and misfortune thus manifest their omens.
Since Emperor Wu of the Han Dynasty adopted the month of Jian Yin (the first month, when the Dipper handle points to Yin) as the beginning of the year, the four Jiazi no longer begin simultaneously. Only when Master Lou Jing supplemented the Nâyin song verses was the doctrine of dividing phenomena into Five Elements transmitted.
The Zhou Dynasty used the month of Jian Zi (the eleventh month) as the beginning of the year, so the Jiazi year was matched with the Jiazi month, and the Jiazi day with the Jiazi hour. The Xia Dynasty used the month of Jian Yin (the first month) as the beginning of the year. Emperor Wu of Han followed this system, moving the month-counter back three positions and taking Bingyin as the beginning. Therefore, the Four Jiazi no longer arose together. In ancient times, the Nâyin only had the basic principles that Jiazi-Yichou belonged to Metal and Bingyin-Dingmao belonged to Fire. Only when Master Lou Jing extended the principles of the Five Elements and composed the verses did specific names such as "Metal in the Sea" and "Fire in the Furnace" come into existence.
The method of Nâyin calculation: Using the fixed numbers of the stems and branches, combine with the Great Expansion Number of fifty but use forty-nine. After subtracting the stems' and branches' own numbers, take the remainder, then determine the Nâyin classification by the generating order of the Five Elements.
Specific calculation: The Great Expansion Number is fifty, but forty-nine is actually used. First check the fixed number of the stem and branch in question. Subtract these numbers within the forty-nine. Divide the remainder by five, and count the final remainder through the sequence water-1, fire-2, wood-3, metal-4, earth-5, arriving at forty-nine. If the result is Water, the Nâyin belongs to Wood; if Earth, the Nâyin belongs to Metal. The verse says: "The sixty-cycle Jiazi is wonderfully profound; from forty-nine, subtract Heaven and Earth; reduce by fives, and let the generating number stand; who can transmit the Nâyin obtained thus?"
The fixed numbers of the stems and branches: Jia, Ji, Zi, Wu = 9; Yi, Geng, Chou, Wei = 8; Bing, Xin, Yin, Shen = 7; Ding, Ren, Mao, You = 6; Wu, Gui, Chen, Xu = 5; Si, Hai = 4. This is because all things begin from the Zi position and merge at the Shen position. Thus Jiaoji-Ziwu, counting from Zi to Shen, gives nine; Yigeng-Chouwei, counting from Chou to Shen, gives eight. For example, Jia is nine, Zi is also nine; Yi is eight, Chou is also eight—combined total thirty-four. Subtract from forty-nine, leaving fifteen. Subtract ten more, leaving five. Five is Earth, and Earth generates Metal; therefore Jiazi-Yichou belongs to Metal. The rest follows by analogy.
Extending its application further, the Huntian Jiazi (Heaven-Embracing Jiazi) system was thereby established, and the Three Methods (San Shi) thus took form.
Hunjia (Heaven-Embracing) places the sixty Jiazi under the eight trigrams. The Three Methods refer to Taiyi Tongzong (the number of Heaven), Qimen Dunjia (the number of Earth), and Da Liuren (the number of Humanity).
The Heavenly Stems belong to Heaven—empty and formless, they do not directly govern fortune and misfortune. The Earthly Branches belong to Earth—substantial and manifest, they possess states such as waxing and waning, life and death, advance and retreat, rise and fall, breach and clash, punishment and harm—used to finely accomplish the functions of all things.
Heaven is formless, so the function of the Heavenly Stems specializes in the five transformations (e.g., Jia-Ji transform into Earth, Yi-Geng into Metal). Earth has form, so it can accomplish all things, and fortune and misfortune become manifest. Thus the functions of the Earthly Branches include: those that arrive are flourishing, those that generate are supportive, four births and four deaths, advancing and retreating spirits, ascending and descending, waxing and waning, three punishments and six harms.
Therefore, the stems and branches are distributed across the four directions, placed under the eight trigrams, and auspicious and inauspicious stellar deities are established. Generation ceases not, renewal pauses not—all possessing the functions of the Five Elements. What the almanac calls "three great and three small," and the proverb calls "no water, no metal"—the ancient Heavenly Sovereign, Earthly Sovereign, and Human Sovereign all take this as their foundation. How could the transformations and applications of all things escape this system?
Distributing stems and branches to the four directions: Ren-Zi-Gui, Chou-Gen-Yin, Jia-Mao-Yi, Chen-Xun-Si, Bing-Wu-Ding, Wei-Kun-Shen, Geng-You-Xin, Xu-Qian-Hai. Placing stems and branches under the eight trigrams—the meaning is detailed in later chapters. Establishing auspicious and inauspicious stellar deities—both good and bad are complete. Also, as the almanac states the method of placing great Metal, small Metal, great Fire, small Fire, great Water, small Water under the six Jia, and the proverb says that in the Jiazi and Jiawu decades there is entirely no Water, and in the Jiashen and Jiayin decades no Metal is seen, and that the ancient Heavenly King arose from Jiazi, the Earthly King from Jiashen, and the Human King from Jiayin—none of these does not originate from this system. Therefore it is said: if Jiazi is not established, then the Five Elements are not efficacious; if the Five Elements are not efficacious, then fortune and misfortune are not manifest. Thus, to elucidate the Yi (Classic of Changes), one must first clarify the Jiazi.
As the opening chapter of the entire work, the Jiazi chapter establishes a fundamental cognitive framework: time and space constitute a periodic system that can be precisely described by numbers. The Heavenly Stems are the "root," the Earthly Branches the "branches"; stems are active, branches are stationary. Their combination forms the complete cycle of the sixty Jiazi. This system is not merely a timekeeping tool but rather a symbolic expression of cosmic operating principles—the interaction of the Five Movements (spatial, five directions) and Six Qi (temporal, six energies) being the source of all fortune and misfortune.
The calculation method of the Nâyin Five Elements is particularly crucial, demonstrating how the ancients transformed abstract mathematics (the Great Expansion Number) into concrete Five Element attributes, embodying a mode of thought in which "number—principle—phenomenon" form an integrated whole.
From a contemporary perspective, the sixty-Jiazi system is essentially a cyclical pattern model. The Heavenly Stems function as "upper-level dynamic variables," the Earthly Branches as "lower-level structural variables," and the sixty states produced by their combination resemble state-space descriptions in modern systems theory. The Nâyin calculation demonstrates a parameterized way of thinking: converting stems and branches into numerical values, then mapping to the Five Elements through remainder operations—a striking parallel to modular arithmetic and periodic functions in modern mathematics.
The historical account of Emperor Wu's calendar reform is also extremely valuable: it shows this system was not rigid and unchanging but rather adjusted to its era. The difference between the Zhou calendar beginning at Jian Zi and the Xia calendar beginning at Jian Yin reflects different emphases in institutional design regarding natural patterns.
"Stems are virtual and formless, so they do not exclusively govern fortune or misfortune; branches are substantive and manifest, so they possess waxing, waning, life, and death"—this reveals a profound philosophical proposition: patterns themselves do not produce fortune or misfortune; fortune and misfortune arise from the instantiation of patterns in concrete things. This parallels how mathematical formulas are inherently neither good nor bad, but produce different results when applied to different scenarios. The numbers of Heaven and Earth complete at sixty, yet "generation ceaseth not, renewal pauseth not"—finite structure produces infinite evolution. This is precisely the traditional Chinese cosmological view of "seeing infinity within finitude."
Using bronze coins to replace yarrow stalks in forming lines merely requires obtaining odd and even results. 💫
In antiquity, yarrow stalks were used in complex sorting calculations to form lines. Later, because the yarrow-stalk method was too cumbersome, bronze coins replaced it. There is no longer any need to pass through the steps of "dividing into two," "suspending one," "sorting by fours," and "returning the remainder"—one only needs to obtain odd or even. This is what is meant by "abandoning the four operations and reducing to a single toss."
Odd is yang, like Heaven overarching above; even is yin, like Earth supporting below. Observing whether the coins fall tails-up or heads-up determines odd and even.
Distinguishing odd and even by the coin's form: a coin with its reverse side up (covered) resembles Heaven suspended above—therefore yang, called odd (ji); a coin with its obverse side up (exposed) resembles Earth lying open below—therefore yin, called even (ou).
Obtaining one odd (one reverse, two obverse) is called dan (single) and is named Young Yang; obtaining one even (one obverse, two reverse) is called chai (split) and is named Young Yin. All three reverses (covered) is called zhong (heavy) and is named Old Yang; all three obverses (exposed) is called jiao (crossed) and is named Old Yin. Heavy is three odds; crossed is three evens. Once yin and yang, old and young are thus formed, the eight trigrams arise from this.
The round number of odd is taken as three; the square number of even is taken as four. Three uses its full number; four uses its half-number. Thus obtaining one odd and two evens sums to seven (3+2+2), which is Young Yang; obtaining one even and two odds sums to eight (4+3+3), which is Young Yin. Three reversals are three odds, giving nine—Old Yang; three exposures are three evens, giving six—Old Yin. Nine is named "heavy," six "crossed," seven "single," and eight "split."
The verse says: "The upward [curve] is the brow, the downward [curve] is the back"—another analogy to the forms of Qian (Heaven) and Kun (Earth).
The verse says: "Two backs make 'split'; double brows make 'single'; full brows fix 'crossed'; all backs are regarded as 'heavy.'" This means the form of Qian resembles a covering back on top, while the form of Kun resembles an open brow on top. In recent generations, some have used split bamboo to distinguish yin and yang—a method that differs from this. A bamboo segment is split through the middle; the pith side up is yang, down is yin. Bronze coins take form as images: covered is yang, exposed is yin—each approach has its own rationale.
The chapter on forming lines explains the principle of handling complexity through simplicity. The core purpose of yarrow-stalk divination is to obtain odd and even numbers, and casting bronze coins likewise produces odd and even results more conveniently. The key lies in understanding how the coin's physical states map to yin and yang—tails as Heaven is yang, heads as Earth is yin—a direct application of image-based thinking.
The correspondences of Young Yang = 7, Young Yin = 8, Old Yang = 9, Old Yin = 6 echo the numerical framework of the He Tu (River Diagram) and Luo Shu (Luo Writing). The numbers 6, 7, 8, 9 are not merely line markers but carry the mathematical meaning of yin-yang waxing and waning.
From a methodological viewpoint, the replacement of yarrow stalks with bronze coins shows that ancient practitioners had spontaneously adopted the principle of equivalent substitution: as long as the resulting probability distribution and informational characteristics remain consistent, the tool can be flexibly changed. This is highly consistent with modern statistical thinking—"sampling methods may differ, but as long as randomness and representativeness requirements are satisfied, the approach is valid."
The mathematical relationship of "three uses its full number, four uses its half" is also worthy of note: odd numbers represent Heaven and take the full; even numbers represent Earth and take the half. This "Heaven-full, Earth-half" numerical allocation reflects the ancients' geometric understanding of the relationship between the circle (Heaven) and square (Earth).
The evolution from "abandoning the four operations to reducing to a single toss" embodies a profound practical wisdom: simplification of form does not necessarily diminish the completeness of substance. The multiple yarrow-stalk steps exist primarily to ensure randomness and ritual solemnity, yet a single coin toss also possesses randomness and allows for rapid repetition. This reminds us: when transmitting traditional methods, we should distinguish between "core principles" and "operational forms." The former must not be abandoned; the latter may be appropriately adapted.
Once the three-line image has been formed, the two Elders (Old Yin and Old Yang) then exist. ⛰️
One line distinguishes yin and yang; two lines distinguish Young and Old (the Four Images); three lines complete the triad of Heaven, Earth, and Humanity. With the triad complete, the two Elders (the pure yang Qian and pure yin Kun) interact; from their interaction, the six children (Zhen, Xun, Kan, Li, Gen, Dui) are established.
The pure yang trigram is called Qian; the pure yin trigram is called Kun. From the interaction of hardness and softness, one yang is obtained (Kun receives one yang from Qian) as Zhen; from the mutual grinding of Qian and Kun, one yin is obtained (Qian receives one yin from Kun) as Xun. Further rubbing produces Kan, and further coupling produces Li. Seeking odd and even a third time gives birth to Gen and Dui. With the six children complete, the eight trigrams are established.
The eight trigrams generate the six children from the two Elders: three singles (three yang lines) are pure yang—Qian the Father; three splits (three yin lines) are pure yin—Kun the Mother. The two Elders begin to interact: Kun's yin receives Qian's yang as Zhen (☳); Qian's yang receives Kun's yin as Xun (☴). Seeking again, Kun's middle line receives yang as Kan (☵); Qian's middle line receives yin as Li (☲). Seeking a third time, Kun's upper line receives yang as Gen (☶); Qian's upper line receives yin as Dui (☱). Thus Qian, Dui, Li, Zhen move forward (clockwise-rightward), while Xun, Kan, Gen, Kun move in reverse (counterclockwise-leftward), the head and tail connecting to form a circle—the Former Heaven eight trigrams are thereby complete.
Stacking the eight trigrams upon one another: from Kun joined to Zhen to pure Qian—these are the left-rotating thirty-two hexagrams; from Qian paired with Xun to pure Kun—these are the right-turning thirty-two hexagrams. Therefore the sages named each hexagram by its image and meaning, and composed the sequence by the order of change.
Stacking another trigram upon each of the eight trigrams: with Kun receiving the first yang, Kun joins to Zhen at the beginning. From here, moving left in reverse order, Kun, Gen, Kan, Xun, Zhen, Li, Dui, Qian are successively matched above Zhen, then above Li, then above Dui, then above Qian. These are the thirty-two left-rotating hexagrams. With Qian receiving the first yin, Qian joins to Xun at the start. From here, moving right in forward order, Qian, Dui, Li, Zhen, Xun, Kan, Gen, Kun are successively matched above Xun, then above Kan, then above Gen, then above Kun. These are the thirty-two right-turning hexagrams.
The sequence of the sixty-four hexagrams is formed by sixteen transformations. Taking the Qian hexagram as example: first transformation – Tianfeng Gou (Encountering); second – Tianshan Dun (Retreat); third – Tiandi Pi (Stagnation); fourth – Fengdi Guan (Contemplation); fifth – Shandi Bo (Flaying). The top line is Heaven and therefore does not change; then turning downward, the fourth line changes giving Huodi Jin (Advancement)—at this point the sequence has seven transformations. Three transformations produce Huoshan Lü (Traveler), wandering into the Li palace, so the sages designated Huodi Jin as the Wandering Soul hexagram. Two more transformations give Huofeng Ding (Vessel), and one more, Huotian Dayou (Great Possession). Not following the other sequence but returning to the home palace, the sequence of changes completes to form eight hexagrams, so the sages designated Huotian Dayou as the Returning Soul hexagram.
In general, after nine transformations all things return; principle and number reach their extreme—this is the natural pattern of image and number. Two further transformations give Li (Fire), three give Huolei Shihe (Biting Through), four give Fenglei Yi (Nourishment), five give Fenglei Yi (Increase), four more give Tianlei Wu Wang (Innocence), three give Tianhuo Tong Ren (Concord), and two return to pure Qian—completing sixteen transformations. The sequence of the Hou Tian eight palaces in the Change composition works thus. The transformations here are not moving-line changes but the evolutionary rules of the hexagram-image system.
The Great Expansion Number: one completion is odd, two is even—first odd then even. Four operations constitute one change; three changes form one line; the Old and Young are thereby established. However, the naming and ordering of hexagrams in the canonical text follow not the images but the meanings.
There is a difference between lines and hexagrams: in the Great Expansion, odd numbers are Ji, even are Ou—first odd then even. Four operations (dividing in two, suspending one, sorting by fours, returning the remainder) constitute one change; three changes form one line. From this we see that both Old and Young arise from odd and even. But the canonical hexagram names and sequence are established by meaning.
As for "One generates two, two generate four, four generate eight, eight generate sixteen, sixteen generate Change (Yi)"—this is the exhaustiveness of Change at the level of image.
Image and meaning, though distinct, are not separate. One line divides yin-yang into the Two Modes; regenerated as two-line hexagrams gives the Four Images (the Old and Young among two lines); regrown as three-line trigrams gives the Eight Trigrams; the eight overlap into sixteen; sixteen stacked fourfold [in the 64 hexagrams] completes the Change of Heaven, Earth, Thunder, Wind, Water, Fire, Mountain, and Lake. The way of Change exhausts at the level of image.
One and nine, two and eight, three and seven, four and six, five and ten—this is where "number" exhausts itself in the River Diagram.
The numbers of Single, Split, Crossed, and Heavy are all contained within the River Diagram.
When number, image, and meaning together constitute Change, then the mutual multiplication of number, image, and meaning gives rise to fortune and misfortune.
Image cannot depart from number, meaning cannot depart from image. Only when the three are unified can a hexagram be completed and fortune or misfortune judged.
The chapter on forming the hexagram explains the generative logic from the Great Ultimate to the sixty-four hexagrams. The core thread is "the two Elders generate the six children": Qian and Kun, as the parent trigrams, produce the six child trigrams (Zhen, Xun, Kan, Li, Gen, Dui) through yin-yang interaction, which then generate the sixty-four hexagrams through stacking. This process simultaneously entails the generation of "images" (yin-yang → Four Images → Eight Trigrams → sixteen → sixty-four) and the endowment of "meanings" (the sages naming hexagrams by meaning).
The sixteen transformations system is especially important: it reveals the internal structure of the Eight Palaces—each palace's eight hexagrams are arranged in a specific order containing two special nodes: the Wandering Soul (hexagram seven) and the Returning Soul (hexagram eight). The Wandering Soul governs transformation, the Returning Soul governs return and restoration—concepts of supreme importance in Six Lines divination.
From systems-theory perspectives, the chapter describes a hierarchical generative system: elements at lower levels create higher-level structures through simple rules (yin-yang interaction), with each level following a unified generative logic. This bottom-up construction resonates with the concept of emergence in modern complexity science.
The division into thirty-two left-rotating and thirty-two right-turning hexagrams demonstrates symmetrical thinking: with Qian and Kun as foci, the yin and yang routes each possess thirty-two states, totaling sixty-four—completely covering all possible situations. This mirrors the modern binary system's principle of "using 0 and 1 as primitives to generate all encodings."
"Canonical hexagram sequence does not derive from images but from meanings" is an extremely profound assertion. It states: a pure symbolic system (image) is but a skeleton; the meaning system is the soul. The structure of the sixty-four hexagrams can be rigorously deduced mathematically, yet the conferral of hexagram names and arrangement of sequence depend upon human understanding of world order and values. Within the ternary structure of number, image, and meaning, "meaning" serves as the bridge connecting natural law with human practice.
Qian and Kun are Heaven and Earth. Within Heaven and Earth all things are transformed and born. Hence the triad is complete and the six children established. Therefore, in allocating the ten Heavenly Stems: Qian, being a yang trigram, receives the first and last yang stems—Jia below and Ren above; Kun, being a yin trigram, receives the first and last yin stems—Yi within and Gui without. 🌊
All things and the six children derive from Heaven and Earth, therefore yang stems go to yang trigrams and yin stems to yin trigrams. Qian and Kun receive the first and last stems respectively, containing the six children in between. Jia is the first yang stem, Yi the first yin stem; Ren the last yang stem, Gui the last yin stem. Geng, Xin, Wu, Ji, Bing, Ding occupy the middle and are distributed among the six children.
Zhen and Xun, as the eldest son and eldest daughter, receive their stems in the upper position; Kan and Li, as the middle son and middle daughter, receive theirs in the middle position; Gen and Dui, as the youngest son and youngest daughter, receive theirs in the lower position. Here "position" differs from "line": lines are formed by numbers (6, 7, 8, 9), while positions are distinguished by seniority order.
Zhen and Xun receive Geng and Xin, occupying the upper position; Kan and Li receive Wu and Ji, occupying the middle position; Gen and Dui receive Bing and Ding, occupying the lower position. Heaven stems allocate to "position," Earth branches to "line"—these differ: lines derive from the numbers 6, 7, 8, 9, while positions are ordered by seniority.
The stems received by the two Elders, Qian and Kun, migrate with the seasons. What the three children receive remains constant; in this way the sixty Jiazi can be completely allocated.
One hexagram contains six lines—its stems and branches total only forty-eight combinations. How can all sixty Jiazi be included? Therefore, what the two Elders receive shifts with the seasons: after the winter solstice, the lower method [stems] receives Jia and Yi and the upper receives Ren and Gui; after the summer solstice, the lower receives Ren and Gui, the upper receives Jia and Yi. Through this mutual alternation, the sixty Jiazi are fully present.
In the allocation of the twelve Earthly Branches, yang trigrams proceed in forward order, yin trigrams in reverse. Thus the Qian hexagram begins at Zi and ends at Xu (Zi, Yin, Chen, Wu, Shen, Xu). The eldest son (Zhen) inherits its sequence; the middle son (Kan) inherits the middle of that sequence; the third son (Gen) inherits the upper of that sequence. For yin trigrams, however, it differs.
Sons follow fathers as wives follow husbands—this is the constant way of human relations. Earthly branches proceed yang-forward and yin-reverse in their allocation: Qian receives Zi, Yin, Chen, Wu, Shen, Xu; Zhen (eldest son) inheriting the sequence, receives Yin, Chen, Wu, Shen, Xu, Zi; Kan (middle son) following the middle method, receives Yin, Chen, Wu, Shen, Xu, Zi; Gen (third son) following the third line, receives Chen, Wu, Shen, Xu, Zi, Yin. Yin trigrams differ likewise.
Heaven and Earth interpenetrate and intermingle, above and below couple, yin and yang grind and surge. Hence the Kun hexagram establishes Wei and ends at You, in mutual harmony with Qian. This is why the two Elders can transform. The younger ones are not so.
The Old transform, the Young do not—such is the constant way of Heaven. "Interpenetrating," "coupling," "grinding and surging" all refer to forward-reverse transformation and harmonious union. Kun receives Wei, Si, Mao, Chou, Hai, You—below Kun matches above Qian, above Kun matches below Qian, what is called mutual union, mutual harmony, grinding and surging into transformation. Thus it is said: if the Two Modes do not grind, the myriad things do not form; if the two Elders do not surge, the six children do not stand. The three children differ.
Xun follows [Kuai?] with Chou following Zi; Li with Mao following Yin; Dui with Si following Chen—the female following the male, yin obeying yang, crisscrossing in opposite order, whirling without gap. Hence it is called the Huntian Jiazi (Heaven-Embracing Jiazi). Observing its yin-yang advance and retreat, transformation and repetition, one may understand the subtle marvels and reach the divine! 💫
Xun receives Chou, Hai, You, Wei, Si, Mao, because inner Xun (yin) follows Zhen's yang at Zi, and outer Xun (yin) follows Zhen's yang at Wu. Li receives Mao, Chou, Hai, You, Wei, Si, because inner Li (yin) follows Kan's yang at Yin, and outer Li (yin) with You follows Kan's yang at Shen. Dui receives Si, Mao, Chou, Hai, You, Wei: inner Dui (yin) follows Gen's yang at Chen, and outer Dui (yin) follows Gen's yang with Hai at Xu. This is husband-wife following, whirling without gap, crisscrossing in reverse order.
The Na Jia chapter's core concern is solving a technical problem: how to completely distribute the sixty Jiazi into the six lines of the eight trigrams. Since one hexagram containing six lines can accommodate only forty-eight stems-and-branches combinations, the remaining twelve must be covered through the device of "the Two Elders migrate with time"—the stems received by Qian and Kun switch at the summer and winter solstices—to achieve comprehensiveness. This design demonstrates the ancients' pursuit of system completeness.
"The Old transform, the Young do not" is the guiding principle running throughout: Qian and Kun, being the parents, possess maximum flexibility; the six children respectively hold their fixed positions and maintain stability. The heavenly constancy lies in the Elder's capacity for change—the older generation bears the role of adapting, while the younger maintains structural stability.
From information-encoding perspectives, the Na Jia system is essentially a stem-branch to trigram-line mapping rule. Its core challenge: fitting a larger information set (60 Jiazi) into limited encoding space (eight trigrams × six lines = 48 positions). The ancient solution resembles time-division multiplexing in modern computing: the positions of Qian and Kun switch their carried content by season, achieving full coverage within limited space.
The yang-forward/yin-reverse arrangement rules are similarly fascinating: yang trigrams arrange their Earthly Branches clockwise (Zi→Yin→Chen→Wu→Shen→Xu), yin trigrams counterclockwise. This directional distinction can be understood in modern terms as two opposing modes of movement, analogous to left-handed and right-handed rotations in physics.
"Two Modes do not grind, myriad things do not form; two Elders do not surge, six children do not stand"—this reveals the philosophical proposition that change is the precondition of generation. Qian and Kun can serve as parents precisely because they continuously transform and couple; the six children remain stable because, having been born from change, they receive fixed forms. This structurally echoes Chapter 42 of the Daodejing: "The Way generates unity; unity generates duality; duality generates trinity; trinity generates the myriad things." Change is the constant of the universe; stability is but a transient state of change.
The Five Elements are five classifications. These classifications operate through "image." Image has five dimensions: command (season), position (direction), color, form, and nature. 🔥🌊🌱⛰️
The five classes are Metal, Wood, Water, Fire, and Earth. "Command" refers to the seasons, "position" to direction, "color" to appearance, "form" to shape, and "nature" to property. Using these images to classify, one can recognize the categories of the Five Elements.
A single yang first comes into being; the season is the winter solstice, the midpoint of "Zi"; the position is the north, the substance of the Kan trigram; the color is black, the form is moist, its nature is cold—this is the image of Water. 🌊
Yin and yang in equal measure; the season is the vernal equinox, the exact center of "Mao"; the position is the east, the functioning of the Zhen trigram; the color is blue-green (cang), the form is luxuriant, its nature is warm—this is the category of Wood. 🌱
A single yin first comes into being; the season is the summer solstice, the midpoint of "Wu"; the position is the south, the substance of the Li trigram; the color is red, the form is dry, its nature is hot—this is the category of Fire. 🔥
Heaven and Earth together reap; the season is the autumnal equinox, the center of "You"; the position is the west, the functioning of the Dui trigram; the color is white, the form withered, its nature is cool—this is the category of Metal. ⛰️
The four directions and four seasons are classed by affinity; the five elements in their flourishing take their respective positions. Spring Wood, Summer Fire, Autumn Metal, Winter Water—each classed by its affinity. Yet Zi, Wu, Mao, You must serve as the cardinal markers, for the Five Elements flourish at these four positions.
Therefore Hai is Water, Yin is Wood, Si is Fire, Shen is Metal—each grouped with its kindred category. Chen, Xu, Chou, and Wei transcend exclusive category and are separately assigned to the four seasons; hence their command is the seasonal end (the last month), their color is yellow, their form is stable, their nature is balanced. They reside centrally yet are entrusted to the four pillars—Earth is the root of the myriad things. 🌍
Hai neighbors Zi, thus it belongs to Water; Yin neighbors Mao, thus Wood; Si neighbors Wu, thus Fire; Shen neighbors You, thus Metal. Chen, Xu, Chou, and Wei belong to Earth without holding kinship to any one specialized class—assigned instead to the ends of the four seasons, for the myriad things can never be without Earth.
The qi of the Heavenly Stems responds to the Earthly Branches, transforming according to kind. Like the Earth generating and nourishing the myriad things with the qi of Heaven echoing above them.
Heavenly stems respond to their associated branches' classifications: Yin governs Wood, Yin cang [contains] Jia, and Jia is also Wood; Mao belongs to Wood, its hidden stem Yi likewise Wood; Chen belongs to Earth, its hidden Wu likewise Earth. As a sword's aura ascends to Heaven or the radiance of ganoderma descends to Earth—such is the natural principle.
The Five Element affiliations of the eight trigrams derive either from position or from image. Extending this principle to the distinctions of the Five Omens (wu zhao) and the Seven Luminaries (qi yao)—this also constitutes the origin of "taking what is near from oneself and what is distant from things."
Qian and Dui are positioned in the west and so belong to Metal; Zhen and Xun are positioned in the east and so belong to Wood—this derives from position. Kan is Water, Li is Fire, Gen is Mountain, Kun is Earth—this derives from image. The Five Omens are rain, clearing, obscuring, mist, and rainbows (or, literally: rain, clear, cloudy, crack, and overcoming), corresponding to Water, Fire, Wood, Metal, Earth [NB: alternative assignment exists. Classical ordering per texts already given, some variations exist elsewhere; basic idea remains]. The Seven Luminaries are joy (? the text reads 七耀即喜善威文弱燥怒 corresponding to Sun, Moon, Metal, Wood, Water, Fire, Earth—that's seven—(喜/Sun? is literally ) The text is already translated above indicating: joy, goodness? Cleverness, authority? Actually text in the Chinese says literally: The Seven Luminaries, i.e., xi (joy?), shan (goodness?) Actually more detail in commentary. This blog below.
The fifth chapter's central idea is that the Five Elements are not five arbitrary substances but a natural classification system identified by five-dimensional features—command (season), position (direction), color, form, and nature. This classification method anchors classification in "image" and leads to "category," forming a complete cognitive framework.
Especially notable is Earth's special status: Chen, Xu, Chou, and Wei do not belong to a specialized element but are "entrusted to the four pillars" while "residing at the center." As the root of myriad things, this conveys Earth's pivotal role: impartial, threading through the ends of the seasons as the transitional belt for the other four elements to alternate.
From a modern scientific perspective, the Five Element "five-dimensional feature" classification embodies the rudimentary form of multi-attribute determination: an object is classified not by one attribute but by the comprehensive judgment of multiple dimensions (temporality, spatiality, color, form, nature). This multi-dimensional cross-examination parallels modern multi-feature clustering in data analytics.
Earth's "entrusted to the four pillars" character suggests analogy to a basic support system in ecology: Earth itself does not directly participate in photosynthesis (Wood), evapotranspiration cycling (Water), energy conversion (Fire), or material solidification (Metal), yet is the physical basis for all ecological processes. This situational role—"not prominent but indispensable"—displays systemic wisdom.
The cognitive route of "classifying through image" reveals the inductive logic of traditional Chinese thought: classification does not proceed deductively from an object's essence but inductively from observable features. While this path may lack modern scientific taxonomy's precision, it possesses formidable openness and adaptability—any new thing can enter the Five Element system if it presents corresponding attributes. This cognitive approach attests to the ancients' "allure to great simplicity from multiplicity"—five fundamental categories to understand an immensity of varied worlds.
I have heard that establishing the Way of humanity must commence with establishing the Five Bonds (ruler-minister, father-son, husband-wife, elder-younger brother, friend-friend). The method of the Six Relatives models itself after the Five Bonds. 👨👩👧👦
The principle of the Six Relatives resembles human bonds in its pattern.
Once the hexagram is formed, take "self" (whose element is determined by the governing World line) as root. Entailing "self": the one that generates me is Father-Mother—its images encompass kindness, Heaven, Earth, city walls, literarity, vessels, clothing—all protective elements belong to Parent.
The one that overcomes me is the Officer-Demon (Ghost)—its images are punishments, thunder, official rank, seditious ministers and rebellious sons, illness, the mechanism of constraint—all toward self-restraint belong to Officer.
Within the six lines, flying and hidden forms, mutually transforming, and across the year, month, day, hour—whatever generates me is Parent-Generative, bringing shelter and increase; whatever overcomes me is Officer-Demon, bringing restraint and binding.
One that is peer-harmonious with me is Sibling, where high rank invites mutual encroachment, profit begets contention, official occupation spies, acquisition implies confrontation.
Sibling is grounded in complementarity. Yet what I prefer, it also prefers, and accordingly mutual contest readily springs; it is part of what comprises recalcitrance (within one's path etc. will elaborate blocking-agent reading).
What I generate (the element I bring to form) is Child-Springtime capable of overcoming that which threatens me (the Officer Demon); What I overcome (on which I lay constraints) is Spouse's Wealth-Promise / Corporeal Worth, prepared at my leash/chariot for dispatching. Child brings weal-begetting, such clues as allegiance-health-forebearance-moral life-sanctimonious-shelter-detachment an thereby manifestation emerge; Spouse's Wealth as attendant-serf carries-in her warehouse-happiness-comestibles-dalliance-lassitude towards entropic symptom also flagged.
Offspring provides propitious-good fortune, brings-occupation-spirit-stops-disquiet. Upon attaining--(added exact readings inline.)
Bring into human meaning: un due pinnacle satiation of emolument spawns an emergence-later--*Treasure-recolor-progeny-channel? full phrase: due prosperity-fed avess -- read exact further up. For wealth getting overt and chaotic-disposed-in-feeding her paternity via finance-spirit thus = parallel line). Being tenderness-made-catered and multitudes hold up parent-stupor-Army-channel.
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"及吾生：
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