《淮南鴻烈解》Vol. 6

The passage is currently being translated, and the designated area is being cropped.

Source note

This passage comes from the lower section of “Tianwen xun” in the Huainanzi and follows the format of Han-dynasty commentary such as Xu Shen’s Huainan Honglie jie—for example, “Recorded and submitted by your servant Xu Shen, Libationer for the Grand Commandant,” and small-character notes in parentheses. Below, I explain separately the general meaning of the text and the matters set out in the commentary.

General meaning of the text (lower Tianwen xun)

The relations among solar terms such as winter solstice and beginning of spring and the year, month, and day can be summarized as follows.

Regarding the year and solar terms: taking the year when the King of Huainan wrote the book as an example, the winter solstice was at bingzi and the beginning of spring at jiawu; it also records “renwu winter solstice” and so on, using the ganzhi (Heavenly Stems and Earthly Branches) to mark the positions of the solar terms as they move through the heavens. Regarding the combining of Yin-Yang Qi: two yin and one yang form “Qi two”; two yang and one yin form “Qi three.” Yin is coarse, hence its Qi is less; yang is refined, hence its Qi is more. Yin and yang combine to produce sound; the number of sounds is five, namely the five tones; when yin and yang combine again, the six pitch-standards arise. Doubling the tones corresponds to the number of days; doubling the pitch-standards corresponds to the number of earthly branches. Thus ten days make a xun (ten-day period), and twelve earthly branches make a month. The sun moves about 13 and 26/76 degrees (or 8/8), and about 29 and 499/940 days make one month; twelve months make one year. Within a year there remains an accumulated surplus of about 10 and 827/940 days, so seven intercalary months are inserted in nineteen years.

Regarding winter solstice and summer solstice: the winter solstice lies on one side of the zi-wu meridian, and the summer solstice at mao-you. Adding three days after the winter solstice can calculate the date of the summer solstice (note: three days after the winter solstice is the summer solstice of the following year). The year completes one circuit, and the sun’s position shifts about six days before returning to the start (note: if the winter solstice falls on a zi day this year, it falls on a wu day two years later).

Regarding the Five Phases taking charge and “fire-smoke”: according to the ganzhi, the periods are divided, each governing seventy-two days, and the color of “fire-smoke” symbolizes direction and the Five Phases. At renwu winter solstice, jiazi, Wood takes charge and the fire-smoke is blue-green (Wood color, east); at bingzi, Fire takes charge and the fire-smoke is red (south); at wuzi, Earth takes charge and the fire-smoke is yellow (Earth occupies the center).

The whole passage uses Yin-Yang, pitch standards, the movements of sun and moon, intercalation, and the Five Phases’ seasonal Qi to explain how the calendar, solar terms, and the Qi of heaven and earth correspond.

Parenthetical notes (plain language)

The first year of Huainan: the year when the King of Huainan wrote the book; some say it refers to Liu Chang, King of Huainan (Emperor Wen’s half-brother), who once arrogated the title “Eastern Emperor,” was moved and died in Yong; his four sons were all enfeoffed as marquises, and contemporaries made a ballad satirizing the brothers’ mutual intolerance; because of the ballad, Emperor Wen changed the enfeoffments of the four marquises, and therefore this year is recorded as “the first year of the accession of Liu An, King of Huainan.” Two yin and one yang / two yang and one yin: one interpretation says the upper obtains two and the lower obtains three, totaling five; hence “combining Qi to make sound,” and the number of tones is five. The sun’s degree count: in the denominator, some editions have “six” and some have “eight”; these are variant readings among transmitted editions. Adding three days to the winter solstice: three days after the winter solstice refers to the summer solstice of the next year. Shifting six days: if the winter solstice falls on a zi day this year, it falls on a wu day two years later; at the year’s end it completes the cycle and begins again. Colors of fire-smoke: blue-green is Wood and the east; red is Fire and the south; yellow is Earth and the center.

Reading note

The original text and commentary are interwoven. At its core is a Han-dynasty cosmology of seasonal Qi observation, pitch standards, and calendrics: using the ganzhi, the division of periods into seventy-two days, and the five colors of “fire-smoke,” it binds together celestial timing, phenology, and political ethics (as in the commentary on the Huainan affair).

When Gengzi is under restraint, Metal governs, and the smoke of fire appears white (the west belongs to Metal, whose color is white); this lasts seventy-two days.

When Renzi is under restraint, Water governs, and the smoke of fire appears black (the north belongs to Water, whose color is black); this lasts seventy-two days.

At the end of the year, it returns again to Gengzi under restraint; the yearly Qi shifts every six days. By numerical calculation, after seventy years it returns again to Jiazi. When Jiazi is under restraint, one should carry out a policy of gentleness and beneficence, support the myriad living beings, open doors and gates, and clear obstructions—one must not cut wood (Jia is Wood; Wood flourishes in the east, and so gentle beneficence is applied and creatures such as hibernating insects are allowed to remain hidden; things emerge through doors, and so one opens and closes the door leaves and clears obstructions; in spring Wood flourishes, and so one does not cut wood).

When Bingzi is under restraint, one should recommend the worthy and good, reward the meritorious, enfeoff marquises, and distribute goods and wealth (Fire governs; it images the brightness of Yang Qi, recognizes merit, and so there is enfeoffment of marquises and issuing of goods).

When Wuzi is under restraint, one should support the old, weak, widowers, and widows, provide relief through porridge and gruel, and broadly bestow grace (Earth governs; it images Earth’s nourishing of all things, and so grace is bestowed).

When Gengzi is under restraint, one should repair walls and fences, maintain city walls, review prohibitions, put weapons and armor in order, warn the hundred officials, and punish the unlawful (Metal governs; it images Metal’s cutting and decisiveness, and so those who do not follow the laws are punished).

When Renzi is under restraint, one should close doors and village gates, make a great search for guests (prohibiting the harboring of guests and sending out newly arrived guests), decide penalties and punishments, execute those who deserve death for their crimes, halt customs barriers and bridges, and prohibit migration outward (Water governs; it images winter’s closure and solidity, and so outsiders are prohibited from moving).

The Qi of Jiazi is dry and turbid; the Qi of Bingzi is dry and Yang; the Qi of Wuzi is damp and turbid; the Qi of Gengzi is dry and cold; the Qi of Renzi is clear and cold.

Bingzi clashes with (offends) Jiazi: hibernating insects emerge from the earth too early (because Wood Qi is overly warm), and so thunder sounds prematurely.

Wuzi clashes with Jiazi: fetuses die prematurely, eggs are destroyed, and birds and insects suffer much injury.

Gengzi clashes with Jiazi: there will be military affairs.

Renzi clashes with Jiazi: there will be frost in spring.

Wuzi clashes with Bingzi: there will be peals of thunder (thunderbolts).

Gengzi clashes with Bingzi: there will be “yi” (injury; yi may refer to lightning).

Renzi clashes with Bingzi: there will be hail.

Jiazi clashes with Wuzi: there will be an earthquake.

Gengzi clashes with Wuzi: the five grains will suffer calamity.

Renzi clashes with Wuzi: summer cold and falling frost.

Jiazi clashes with Wuzi: shelled creatures do not develop (they cannot transform into shelled creatures).

Bingzi clashes with Wuzi: great drought, and gourds (melons) and chen (a kind of plant) wither and die from heat.

Vernacular Interpretation of the Huainan Honglie Jie

There is a kind of grass that grows where water and soil meet, thin as a sheet of paper, named Feng; when the weather is dry and hot, it withers, and this is called Han.

Anomalous correspondences when the stems and branches are paired (a summary the ancients made on the basis of calendrical calculations and phenology): when Renzi meets Gengzi, yang qi is too rigid, and fish find it difficult to grow and take proper form; when Jiazi meets Gengzi, plants and trees wither and then sprout again; when Bingzi meets Gengzi, plants and trees flourish again (as when plums and crabapples bloom and bear fruit again in the eighth and ninth months); when Wuzi meets Gengzi, the harvest is good at times and bad at times, hard to stabilize; when Jiazi meets Renzi, winter cannot store qi, and the earth qi instead issues outward; when Bingzi meets Renzi, there are anomalous signs of falling stars; when Wuzi meets Renzi, insects that should hibernate in winter come out of their holes and move about; when Gengzi meets Renzi, there is thunder in winter.

As for the four seasons, deities, and phenology: in the last month of spring, the third month, Fenglong (the thunder god) comes forth and sends rain. In the last month of autumn, the third month, the earth qi no longer stores itself within; it withdraws the “killing qi”; the hundred insects hibernate, quietly dwelling behind closed doors. Qingnü (the deity in charge of frost and snow, said in legend to be a jade-green goddess) comes forth and sends down frost and snow. The qi of the twelve double-hours (or twelve months) of the year circulates, and only at the end of the second month of midspring does it gather in what has been stored and close off the cold qi. Nüyi (the deity who governs growth and nourishment in spring and summer) beats drums and sings, harmonizing the seasons, so that the hundred grains, birds, and plants grow. In the first month of summer, grains ripen; the male cuckoo calls long, marking the critical farming season of the year.

In general, if Heaven does not issue Yin, the myriad things cannot be born and grow; if Earth does not issue Yang, the myriad things cannot mature. Heaven is round and Earth is square, and the Dao is in the center. The sun governs De and birth/issuing; the moon governs punishment and gathering—when the moon completes its circuit, the myriad things tend toward death; when the sun arrives, the myriad things revive. When one is far from mountains, the mountain qi is hidden; when far from water, the insects in the water hibernate; when far from trees, the leaves wither. If for five days in succession the sun is not seen, this means it has lost its place; even a sage would not recklessly explain it (“yu” here means “to speak”).

The course of the sun’s rising (mythic geography): the sun rises from Yanggu, bathes in Xianchi, brushes past Fusang, and this is called Chenming (“fu” means to pass by; it is the beginning of a day). Ascending Fusang and about to set out is called Feiming (bright about to come but not yet bright; “fei” is pronounced as in the “fei” of Nuogao). The following text continues with “arriving at…”; the original scroll breaks off here.

The sun rises from Qu'e, and this region is called Danming (just before dawn); when it reaches Zengquan, this corresponds to people's breakfast time; when it arrives at Sangye, it is Yanshi (a later morning meal); at Hengyang, it is Yuzhong (mid-morning leaning toward noon); at Kunwu (a legendary mound in the south), it is Zhengzhong (the sun at high noon); at Niaoci (in the southwestern mountains, where birds often roost), it is Xiaohuan; at Beigu (the Valley of Sorrow, a very deep gorge in the west and south where people standing above easily feel sorrow, hence the name), it is Bushi (the time of an afternoon extra meal); at Nüji (a place in the northwest inclined toward yin), it is Dahuan; at Yuanyu, it is Gaochong (near the xu hour, when the common people pound grain); at Lianshi (a northwestern mountain; as the sun is about to sink, it is as if all are pounding grain, hence the name Xiachong, “lower pounding”; “lian” may be read as “lan,” meaning ripe/rotted and about to be exhausted); at Beiquan, the sun chariot halts, the goddess who drives the sun rests, and the sun horses take their rest—this is called Xianche (the suspended chariot); at Yuyuan, it is Huanghun (dusk); at Menggu (a northern mountain, where Lu Ao once saw what seemed a heavenly realm), it is Dinghun (when the night colors have settled).

The sun sets at the edge of the waters of Yuyuan, and the next day it rises bright again on the bank of Menggu. The sun travels through the Nine Provinces and passes through seven lodges, a total course of about 507,309 li (from Yanggu to Yuyuan there are sixteen places, which together constitute the Nine Provinces and Seven Lodges). On this basis Yu established morning, day, dusk, and night.

At the summer solstice, yin Qi overpowers yang Qi, and the myriad things therefore withdraw and die; at the winter solstice, yang Qi overpowers yin Qi, and the myriad things turn upward and live. Day belongs to the yang division and night to the yin division: when yang Qi is abundant, daylight is long and night is short; when yin Qi is abundant, daylight is short and night is long.

The Heavenly Emperor opens out the four corner-cords and, with the Northern Dipper (Beidou), turns the celestial patterns. The moon each month moves past one earthly branch and returns to its original place: in the first month the Dipper's handle points to Yin, in the twelfth month to Chou; one year completes a circuit, ending and then beginning again. When it points to Yin, the myriad things stir and are about to be born, and the pitch pipe resonates with Taicu (clustered together but not yet emerged); when it points to Mao, plants and trees flourish, and the pitch pipe resonates with Jiazhong (seeds first sprout and are about to break through their shells).

Vernacular Interpretation of the Huainan Honglie Jie

Below, according to the Twelve Earthly Branches, the corresponding pitch names and meanings are explained. Zi means “to breed”; its pitch is Huangzhong—the bell tone has turned yellow. Chou means “to knot”; its pitch is Dalü—the lü travels onward. Yin means “to unfold”; its pitch is Taicu—cu means to cluster. Mao means “luxuriant”; its pitch is Jiazhong—jia means to attach. Chen means “to shake or arouse”; its pitch is Guxi—xi means to remove the old and bring in the new. Si means “to settle”; its pitch is Zhonglü—lü means to fill out centrally and become great. Wu means “to oppose”; its pitch is Ruibin—bin means to be settled and submissive. Wei means “dark or unclear”; its pitch is Linzhong—zhong means to draw in and stop. Shen means “to groan”; its pitch is Yize—ze means to change its rule, and De has departed. You means “satiated”; its pitch is Nanlü—lü means to bear and embrace the great. Xu means “to extinguish”; its pitch is Wuyi—yi means to enter without satiety. Hai means “to close or block”; its pitch is Yingzhong—zhong means to respond with its bell.

With Mao and You added, Yin-Yang are distinguished and day and night are equal; hence it is said: the compass gives birth, the square kills, the balance lengthens, the weight stores, and the plumb line dwells in the center, as the root of the four seasons.

The Dao says: the compass begins with One. One alone does not generate, so it divides into Yin-Yang; Yin and Yang harmonize and the ten thousand things are born. Hence it is said: One generates two, two generates three, three generates the ten thousand things.

Heaven and Earth take three months as one season; therefore sacrifice uses three servings of rice as ritual, mourning uses three stamping leaps as measure, and military matters take three han as regulation. Using three to examine things, three times three is nine; therefore the Huangzhong pitch is nine inches and the gong tone is tuned. “Tuned” means harmonious. Extending by nine, nine times nine is eighty-one; thus the number of Huangzhong is established.

Yellow is the color of Earth’s De; zhong is where Qi is planted. At the winter solstice, De-Qi is Earth, and Earth’s color is yellow; hence it is called Huangzhong.

The numbers of the pitches divide at six into female and male, hence twelve bells correspond to the twelve months. Each of the twelve is completed by three; therefore set one and multiply by three eleven times; the accumulated fraction is 70,714, and the great number of Huangzhong is established.

Among the twelve pitches: Huangzhong is gong, Taicu is shang, Guxi is jue, Linzhong is zhi, and Nanlü is yu. Things are completed by three, tones are established by five; three and five make eight, hence egg-born creatures have eight apertures. When the pitches first arose, they copied the image of the phoenix.

Brief notes on terms: The Twelve Pitches are the twelve standard pitches of ancient music, correlated with the twelve months and Twelve Earthly Branches. Huangzhong is the first of the twelve pitches, the gong tone, associated with the winter solstice, Earth’s De, and numbers such as nine times nine = eighty-one. Gong, shang, jue, zhi, and yu are the five tones, correlated with the Five Phases and the numbers of the generation of things.

Tones and the Eightfold Generation: The tones of music are born from the “eight sounds” (instruments made of eight materials). Huangzhong (Yellow Bell) is Gong, and Gong is the ruler of all tones. Huangzhong occupies the zi position; its number is eighty-one; it governs the eleventh month and generates Linzhong downward.

Linzhong’s number is fifty-four; it governs the sixth month and generates Taicu upward. Taicu’s number is seventy-two; it governs the first month and generates Nanlü downward. Nanlü’s number is forty-eight; it governs the eighth month and generates Guxi upward. Guxi’s number is sixty-four; it governs the third month and generates Yingzhong downward. Yingzhong’s number is forty-two; it governs the tenth month and generates Ruibin upward. Ruibin’s number is fifty-seven; it governs the fifth month and generates Dalü upward. Dalü’s number is seventy-six; it governs the twelfth month and generates Yize downward. Yize’s number is fifty-one; it governs the seventh month and generates Jiazhong upward. Jiazhong’s number is sixty-eight; it governs the second month and generates Wuyi downward. Wuyi’s number is forty-five; it governs the ninth month and generates Zhonglü upward. Zhonglü’s number is sixty; it governs the fourth month. At this point it reaches its extreme and no longer generates.

The Five Notes and the Pitch Standards: Zhi generates Gong, Gong generates Shang, Shang generates Yu, Yu generates Jue, Jue generates Guxi, and Guxi generates Yingzhong. Yingzhong matches the proper tones, and so is “he” (harmony; he comes from sound; one account says it is harmony). Yingzhong generates Ruibin, which does not match the proper tones, and so is “miu” (discordant, inharmonious).

Seasonal Periods and Tones: On the day of the winter solstice, the tone resembles Linzhong and is relatively turbid; on the day of the summer solstice, it resembles Huangzhong and is relatively clear. The twelve pitch standards are correlated with the changes of the twenty-four periods of the year: on a Jiazi day, the zhi of Zhonglü; on a Bingzi day, the yu of Jiazhong; on a Wuzi day, the gong of Huangzhong; on a Gengzi day, the shang of Wuyi; on a Renzi day, the jue of Yize.

Measures and the Heavenly Dao: The ancients established weights and lengths on the basis of the heavenly Dao. The Huangzhong pitch pipe is nine cun long. All things are generated by three; three times nine is twenty-seven, and so the width of cloth is two chi and seven cun (ancient cloth was often this wide). Tones generate one another by eight, and so the measure of the human body is about eight chi; a xun is a doubling, and so eight chi make one xun. Where there is form there is sound; the number of sounds is five. Five times eight is forty, and so four zhang make one pi. A pi is the measure used by ordinary people for cutting cloth; one pi constitutes a standard. At the autumn equinox the fei (the awn of a grain ear) is fixed; when the fei is fixed, the grain ripens.

Measures and Pitch Numbers

Ding means cheng (maturation). When grain ripens it becomes solid; it is pronounced like mao in the Shijing phrase “there are cats and there are tigers”; the ancient graph was written miao.

In pitch pipes the number is twelve: thirteen biao make one su, and twelve su make one cun; pitch numbers correspond to the twelve chen, and note numbers correspond to the ten days (jia through gui are the ten days). Thus ten cun make one chi, and ten chi make one zhang.

Balances and Weights

A balance has two pans, left and right, so the calculation is doubled: twelve su make one fen (fen here denotes the division of light and heavy and is the unit of the zhu); twelve fen make one zhu; twenty-four zhu make one liang.

Heaven has four seasons to make one year; multiplying by four again gives sixteen, so sixteen liang make one jin. Three months make one season, and thirty days make one month, so thirty jin make one jun; four seasons make one year, so four jun make one shi.

Pitch Pipes and Calendar

In terms of pitch pipes: one pitch generates five notes, and twelve pitches make sixty notes; multiplying again by six—six sixes make thirty-six—gives 360 notes in all, corresponding to the number of days in a year. Thus the numbers of the pitch pipes and the calendar are the Dao of Heaven and Earth.

For pitches generated downward, double and divide by three; for pitches generated upward, multiply by four and divide by three. (Bell pitches generate one another upward and downward; the citations here are not explained in detail.)

Taiyin’s Original Era and the Yearly Jian

The original beginning of Taiyin: the first yuan is established at jia-yin; the first termination is established at jia-xu; the second termination at jia-wu; the third termination returns again to the jia-yin yuan. The yearly jian shifts one chen at a time; after the Beginning of Spring, when it reaches its chen, it moves in accordance with its proper sequence.

Three before and five after: the hundred affairs may be undertaken. (Before and after refer to before and after Taiyin.)

At the time established by Taiyin: hibernating insects head into their burrows and dwell there; magpies orient their nests and make an opening as a door. Taiyin is in Yin, the Vermilion Bird is in Mao, Gouchen is in Zi, Xuanwu is in Xu, the White Tiger is in You, and the Azure Dragon is in Chen.

The Twelve Jianchu Values

Yin is Jian (Establish), Mao is Chu (Remove), Chen is Man (Full), Si is Ping (Level; governs birth), Wu is Ding (Stable), Wei is Zhi (Grasp; governs sinking), Shen is Po (Break; governs balance), You is Wei (Danger; governs the ladle), Xu is Cheng (Completion; governs lesser De), Hai is Shou (Gather; governs great De), Zi is Kai (Open; governs Tai Sui), and Chou is Bi (Close; governs Taiyin).

Year Names and Stellar Lodgings

When Taiyin is in Yin, the year name is Shetige; its male counterpart is Suixing (the Year Star, Jupiter), which lodges in Dou and Qianniu; in the eleventh month it emerges with it at dawn in the east.

This passage discusses, in ancient astronomy and calendrics, the correspondence between Suixing (Jupiter) and Taiyin (here referring to the position among the twenty-eight lunar mansions through which the moon passes, and also to the year name and year order), and how the two positions Xing (Punishment) and De (Virtue/Power) are separately placed and when they conjoin. The following explains the general meaning in plain language.

The year names and their correspondences with Suixing and Taiyin are as follows. When Taiyin is in the branch Mao, the year name is Danyan (Dan is pronounced like Ming, as Yang Shen explicitly states). Suixing stays in the lunar mansions Xu Nu, Xu, and Wei, and in the twelfth month appears in the east at dawn at the same time as Taiyin. The three mansions Jing, Yu, and Gui are opposite Taiyin. When Taiyin is in the branch Chen, the year name is Zhixu. Suixing is in Yingshi and Dongbi, and in the first month appears in the east at dawn. Liu, Qixing, and Zhang are opposite. When Taiyin is in the branch Si, the year name is Dahuangluo. Suixing is in Kui and Lou, and in the second month appears in the east at dawn. Yi and Zhen are opposite. When Taiyin is in the branch Wu, the year name is Dunzang. Suixing is in Wei, Mao, and Bi, and in the third month appears in the east at dawn. Jiao and Kang are opposite. When Taiyin is in the branch Wei, the year name is Xieqia. Suixing is in Zi and Shen, and in the fourth month appears in the east at dawn. Di, Fang, and Xin are opposite. When Taiyin is in the branch Shen, the year name is Tuntan. Suixing is in Dongjing, Yu, and Gui, and in the fifth month appears in the east at dawn. Wei and Ji are opposite. When Taiyin is in the branch You, the year name is Zuoe (Zuo is pronounced like the word for “yesterday”). Suixing is in Liu, Qixing, and Zhang, and in the sixth month appears in the east at dawn. Dou and Qianniu are opposite. When Taiyin is in the branch Xu, the year name is Yanmao. Suixing is in Yi and Zhen, and in the seventh month appears in the east at dawn. Xu Nu, Xu, and Wei are opposite. When Taiyin is in the branch Hai, the year name is Dayuanxian. Suixing is in Jiao and Kang, and in the eighth month appears in the east at dawn. Kui and Lou are opposite. When Taiyin is in the branch Zi, the year name is Kundun (Kun is pronounced like Qun). Suixing is in Di, Fang, and Xin, and in the ninth month appears in the east at dawn. Wei, Mao, and Bi are opposite. When Taiyin is in the branch Chou, the year name is Chifenruo. Suixing is in Wei and Ji, and in the tenth month appears in the east at dawn. Zi and Shen are opposite.

On the conjunction and separation of Xing and De and the positions of the various spirits: in a Jiazi year, Xing and De conjoin and are both in the palace of the east. But the two cannot remain together for long; they often move to the direction that each does not overcome: roughly once every four years they separate, and after sixteen years they conjoin again. The reason they must separate is that Xing cannot enter the Central Palace (the palace where the Central Heavenly Emperor resides) and can only move to the Wood position. The place where Taiyin resides is called De, while the position is called Xing. De is the governing mainstay; when it doubles itself it turns to softness (excessively hard becomes soft)—this means that Yin-Yang and hardness and softness transform into one another. Xing must move to the Five-Phase position it cannot subdue: when Xing is in a Water position it moves to Wood; when in a Wood position it moves to Water; Metal and Fire each keep to their own place. Whenever the various spirits move, the Vermilion Bird is before Taiyin and Gouchen is behind Taiyin (the Vermilion Bird and Gouchen are both names of star officers; the ancients used them to mark the guarding positions before and behind Taiyin).

Brief background explanation, to aid reading. Suixing is Jupiter; the ancients took its twelve-year circuit of the heavens and paired it with the twelve year names and the twelve months to reckon years and divine auspiciousness and inauspiciousness. Taiyin in a certain earthly branch means using the twelve earthly branches to mark the position of the moon or the year order among the twenty-eight lunar mansions, corresponding one-to-one with the “year names.” Xing and De are terms of astrological observation and verification: De governs good fortune, Xing governs punishment; conjunction is auspicious, while separation requires separate placement to comply with the principle of mutual overcoming among the Five Phases. The “Central Palace” refers to the center of the celestial region; the Xing star should not remain there long, hence separation every four years and reconjunction after sixteen years. This is a systematic formulation of Han dynasty calendrical specialists and masters of the technical arts.

The above faithfully follows the original correspondences among lunar mansions, month order, and year names, without adding or deleting doctrinal content; proper terms have been briefly explained in parentheses or in context.

The Array Aligns with Heaven and Earth

In the formation: at the front are the "Three Xuanwu," at the back are the "Five Baihu," and the stars of the "Six Xu" are arranged relying on the position of "Gouchen." Such an arrangement means the Qi of Heaven and Earth overlap and harmonize (the word "xi" means harmony and correspondence).

The Firmness and Yielding of the Ten Heavenly Stems

When discussing the day's Heavenly Stem and Earthly Branch: Jia is firm, Yi is yielding, Bing is firm, Ding is yielding... and so on up to Gui. Each Heavenly Stem has a distinction of firm and yielding.

The Five Phases and the Twelve Earthly Branches

Wood is born in Hai, flourishes in Mao, and dies in Wei—the three Earthly Branches Hai, Mao, and Wei all belong to Wood. Fire is born in Yin, flourishes in Wu, and dies in Xu—Yin, Wu, and Xu all belong to Fire. Earth is born in Wu, flourishes in Xu, and dies in Yin—Wu, Xu, and Yin all belong to Earth. Metal is born in Si, flourishes in You, and dies in Chou—Si, You, and Chou all belong to Metal. Water is born in Shen, flourishes in Zi, and dies in Chen—Shen, Zi, and Chen all belong to Water. These are the positions of "birth, flourishing, and death" of the Five Phases in the twelve Earthly Branches.

The Numbers of the Five Victories and the Movement of "Shen"

The principle of the Five Victories: birth is one, flourishing is five, and end is nine; five times nine is forty-five. Therefore, the "Shen" (spirit) moves once every forty-five days; with three corresponding to five, after eight moves the year ends.

Taiyin in Warfare and the Dao of Heaven

In all military operations, take Taiyin (the Moon) as the master: the left front is punishment, the right rear is virtue; strike the opposing direction of Gouchen, then in battle you will surely win, and in attack you will surely conquer. To know the Dao of Heaven, take the Sun as the guiding principle.

The sixth month corresponds to the position of the "Heart" mansion (Xinxiu), moving leftward in a circular course, and then divided into twelve months, matching the movement of the Sun. When Heaven and Earth respond in multiple layers, then afterwards there will be no disaster.

The Twelve Months and the Twenty-Eight Lunar Mansions (Establishing Stars)

The lunar mansions "established" in each month are: In the first month, establish in Ying Shi; in the second month, in Kui and Lou; in the third month, in Wei; in the fourth month, in Bi; in the fifth month, in Dong Jing; in the sixth month, in Zhang; in the seventh month, in Yi; in the eighth month, in Kang; in the ninth month, in Fang; in the tenth month, in Wei (Tail); in the eleventh month, in Qian Niu; in the twelfth month, in Xu.

(Note: Ancient editions may have "Xing Yue Jian Ying Shi" etc., which agrees with the Yue Ling (Monthly Ordinances) saying "In the first month of spring, the Sun is in Ying Shi; in the second month, in Kui and Lou; in the third month, in Wei." One should take the mansion where the Sun resides as the meaning of "establishing Ying Shi in the first month," rather than treating the erroneous character "Xing" as an independent phrase.)

Degree Divisions of the Twenty-Eight Lunar Mansions

The divisions of the twenty-eight lunar mansions are: Jiao 12 degrees, Kang 9, Di 15, Fang 5, Xin 5, Wei 18, Ji 11 (Dou 26), Qian Niu 8, Xu Nü 12, Xu 10, Wei 17, Ying Shi 16, Dong Bi 9, Kui 16, Lou 12, Wei 14, Mao 11, Bi 16, Zi Xi 2, Shen 9, Dong Jing 30, Yu Gui 4, Liu 15, Qi Xing, Zhang and Yi each 18, Zhen 17—these are the divisions of the twenty-eight lunar mansions.

Field Allocation of the Lunar Mansions and Place Names

Jiao and Kang belong to Zheng; Di, Fang, and Xin belong to Song; Wei and Ji belong to Yan; Dou and Qian Niu belong to Yue; Xu Nü belongs to Wu; Xu and Wei belong to Qi; Ying Shi and Dong Bi belong to Wei; Kui and Lou belong to Lu; Wei, Mao, and Bi belong to Wei (state of Wei); Zi Xi and Shen belong to Zhao; Dong Jing and Yu Gui belong to Qin; Liu and Qi Xing belong to Zhou; Zhang and Yi belong to Chu. These are the correspondences between the lunar mansions and the nine provinces.

Vernacular Interpretation of Relevant Passages from the Huainan Honglie

The Zhen Position, Suixing, and Clash-Baleful Influences

If Suixing (Jupiter, the Year Star) travels in the position of the Zhen lunar mansion corresponding to the state of Chu, then the five grains will be abundant. If Suixing ought to be in its proper position but is not, has left its track for another place, or corresponds to the opposing position, then that year will often have calamities; the ruler is prone to danger, and the state is prone to the peril of collapse and ruin.

The Qi Governed by Taiyin (the Moon) in the Four Seasons

Taiyin governs spring, when it is fitting to practice the Qi of soft compliance, kindness, and mild coolness (spring belongs to the De of Wood; the De of Wood is close to benevolence, so softness and coolness are appropriate). It governs summer, when it is fitting to bestow gifts and make things clear and manifest (summer belongs to the De of Fire; the De of Fire inclines to Yang, so broad giving and open display are appropriate). It governs autumn, when it is fitting to make preparations and put weapons in order (autumn belongs to the De of Metal; Metal governs cutting and severing, so military preparations should be readied). It governs winter, when it is fitting to be fierce, resolute, hard, and strong (winter is the time of pure Yin, closed and solidified; water and marshes freeze, so fierceness and hardness are its image).

The Cycle of the Yearly Movement

Roughly every three years the image of the seasonal ordinances changes, and every six years the constant norm changes; therefore there is often one famine every three years, one decline every six years, and one period of health and abundance every twelve years.

Suixing, the Various States, and the Stems and Branches

The branch visited by Suixing corresponds to the various states: in a Jia year, Qi; Yi, the Eastern Yi; Bing, Chu; Ding, the Southern Yi; Wu, the state of Wei; Ji, Han; Geng, Qin; Xin, the Western Yi; Ren, Wey; Gui, Yue. For the branches: Zi, Zhou; Chou, Di; Yin, Chu; Mao, Zheng; Chen, Jin; Si, Wey; Wu, Qin; the Wei branch, Song; Shen, Qi; You, Lu; Xu, Zhao; Hai, Yan. Also: Jia and Yi, Yin and Mao belong to Wood; Bing and Ding, Si and Wu belong to Fire; Wu and Ji occupy the four seasons and belong to Earth; Geng and Xin, Shen and You belong to Metal; Ren and Gui, Hai and Zi belong to Water. Water generates Wood, Wood generates Fire, Fire generates Earth, Earth generates Metal, and Metal generates Water. When the child generates the mother, it is "yi"; when the mother generates the child, it is "bao"; when child and mother mutually accord, it is "zhuan"; when the mother overcomes the child, it is "zhi"; when the child overcomes the mother, it is "kun". Acting by "zhi" brings victory without recompense; undertaking affairs by "zhuan" brings success; conducting principle by "yi" establishes a name that does not fall; raising and nurturing by "bao" makes the ten thousand things flourish; initiating affairs by "kun" brings defeat, ruin, and death.

The Male and Female of the Northern Dipper and Conjoined Branches

The deity of the Northern Dipper has male and female aspects. In the eleventh month, when Zi is established, the male star starts from the first branch and moves left, while the female star moves right; in the fifth month they conjoin at Wu and plan punishment, and in the eleventh month they conjoin at Zi and plan De. The branch where Taiyin resides is the "Yan day"; on a Yan day it is not fitting to undertake any affair. Kanyu, the art of divining auspicious and inauspicious signs, proceeds slowly; the male knows the female by sound, and thus there is discernment of good and bad fortune. The counting of branches begins from Jiazi; child and mother seek each other, and where they conjoin is called a "conjunction"; ten days and twelve branches complete one cycle of sixty days, and there are eight conjunctions in all. If a conjunction is before the year, it governs death; if it is after the year, there is no calamity. For example, Jiaxu conjoins with Yan, Yiyou with Qi, Bingwu with Yue, Dingsi with Chu, Gengshen with Qin, Xinmao with Song, and so on (each conjunction governs the state listed in the original text).

Vernacular Interpretation of the Huainan Honglie Jie

First Paragraph (Ganzhi, Star Deities, and the Ruler)

In the text, labels such as “Rong, Renzi,” “Dai, Guihai,” “Hu, Wuxu, Jihai,” “Han, Jiyou, Jimao,” and “Wei, Wuwu, Wuzi” refer to correspondences among the Ganzhi (Heavenly Stems and Earthly Branches), year-names, and the field-allocation of the realm; together they are called the “Bahe Tianxia (Eight Unions of the World).”

When the days presided over by the five celestial deities—Taiyin (Great Yin), the Small Year Star, the sun, and Chen—converge, and if on that day there are cloud vapors, wind, or rain, calamity is often borne by the ruler.

Among the celestial deities, the most honored is the Azure Dragon (also called Tianyi, or Taiyin). One must not turn one’s back on the direction in which Taiyin is located; one may only face it. Where the Northern Dipper points and what it “strikes” must not be opposed.

Second Paragraph (Yin-Yang and the Resonance Between Heaven and Humanity)

Heaven and Earth establish Yin-Yang through their dividing boundary: Yang is born from Yin, and Yin is born from Yang; only when Yin-Yang interweave do the Siwei (the four bonds—the bonds of the four directions and of above and below) become open. Whether death or life, the myriad things are formed through this.

Among creatures that crawl and have mouths able to make sound, none is more honored than the human. The apertures and four limbs all communicate with Heaven and Earth. Heaven has nine layers, and humans too have nine apertures; Heaven has four seasons to regulate the twelve months, and humans too have four limbs to correspond to the twelve joints; Heaven has twelve months to regulate the three hundred sixty days, and humans too have twelve major joints (limb joints) to correspond to the three hundred sixty days. Therefore, to act without complying with the Dao of Heaven is to go against the vital impulse.

Reckoning from the winter solstice to the first day of the first month of the following year: if the interval reaches fifty days, the people’s food will be sufficient; if it falls short of fifty days, then for each day short there is a decrease of more than one dou; if it exceeds fifty days, then for each day over there is an increase of one sheng—all these are related to what the year deity governs in that year.

Third Paragraph (Year Names and Harvest Prospects—Shetige, Danyan, and Zhixu)

In the year of Shetige (“ge” means that the myriad things receive Yang Qi and arise): the year is at Yin. The early part of the year is wet, and the later part dry; rice is prone to disease, silkworms do not mature, beans and wheat are relatively good; the common people’s ration is about four sheng per day. Yin corresponds to Jia among the Heavenly Stems, and the year name is also called Yanpeng (the sharp tips of the myriad things wish to emerge but are blocked and not yet penetrating; hence it is called Yanpeng).

In the year of Danyan (“dan” means exhausted, “yan” means stopped: Yang Qi pushes the myriad things to arise, while Yin Qi is exhausted and stops): the year is at Mao. The year’s prospects are calm and even; rice, beans, wheat, and silkworms are all good; the people’s ration is about five sheng per day. Mao corresponds to Yi, and the year name is Zhanmeng (the myriad things are armored and obstructed, and only afterward emerge; hence it is called Zhanmeng).

In the year of Zhixu (“zhi” means hibernating, “xu” means unfolding: all things that lay hidden and hibernating scatter, unfold, and emerge): the year is at Chen. The early part is dry, the later part wet; there is minor famine, silkworms are shut down, wheat ripens; the people’s ration is about three sheng per day. Chen corresponds to Bing, and the year name is Rouzhao (the myriad things grow branches and spread leaves; hence it is called Rouzhao).

Note (for Reading the Original Text)

Shetige, Danyan, Zhixu, and the like are the twelve year-names used in ancient Year Star (Jupiter) reckoning. They correspond one-to-one with the earthly branches Yin, Mao, Chen, and so on, and were mostly used for divining the year and agricultural affairs. “People’s food X sheng” refers to the grade of grain sufficiency or shortage for the year as reckoned by the calendar and to the order of magnitude of the daily ration available per person; it is a term of political and agricultural divination, not a concrete archaeologically measured figure. The main purport of the whole passage is that celestial phenomena, year names, Yin-Yang, and the structure of the human body correspond to one another; both the ruler and the people’s harvest prospects depend on whether they comply with Heaven and on the year in which Tai Sui (the Year God) is located.

Huainan Honglie Jie, Scroll Nine, Section 41: A Plain-Language Reading

This section draws on prophetic portents, celestial signs, and the rise and fall of dynasties to discuss why the Son of Heaven must observe signs of good and ill fortune, why ministers should offer remonstrance discreetly, and how usurpation differs from the lawful transmission of the throne.

1. Divination and Caution

Someone asks about divination: when the Son of Heaven first ascends the throne or succeeds to it, must he examine signs of good and ill fortune? The ancients saw unusual phenomena, such as the Pleiades entering the constellation Gua, and took them as a warning to be cautious and fearful of excessive elevation. This is what the question concerns.

Yet usurpers and pretenders, too, invoke claims that something “fell from heaven” or “thundered in the suburbs.” It is not certain that a ruler who holds power for only a day can truly wield the Eight Powers and command the allegiance of all the states. The royal position ultimately depends on Heaven. The ruler must therefore look down and observe the proper order of Yin and Yang, for which the Seven Stars serve as markers. The warning is not limited to water disasters: when the Three Stars undergo mixed changes, ominous influences may become confused. The signs say that the king must solemnly heed Heaven’s charge and must not take it lightly. How could he fail to investigate them?

2. Usurpation, Seizure of the Throne, and the Failure to Finish Well

Some conspire with the ruler; a great schemer waits for an opening, brings the ruler down, frightens the people, and suddenly takes the throne. When Cai Nian held power, the Way gradually became neglected and distant; the head of the Bureau of Personnel suddenly fell ill and declined. The two Qin states and Chu together installed a ruler from an earlier age as Son of Heaven. Without the proper relationship between ruler and minister, this was usurpation. Wang Mang may have been made heir apparent, but the new capital had no successor in reserve; all under Heaven looked on as he was executed.

In Wei, even the ruler’s dogs and horses wept, and the realm’s achievements in hegemony were exhausted. Greed for profit led one to point eastward and perish on the road; Heaven offered no help. Consider the Three Legitimate Lines of Succession: both Yin and Zhou reached the end of their cycles, and each saw a succession of three rulers before a change of dynasty. At the end of Yin there were two rulers, which is a cause for regret. The Son of Heaven of the Xin dynasty died in Jian Palace, and passersby all grieved. Heaven and Earth were brought to ruin, and the Son of Heaven lay dead. When an usurping Son of Heaven and his ministers overturn the proper order, the princes throughout the realm may all fail to unite in war for their own advantage.

One should follow the way of Yin and Zhou. There has never been a ruler who devoured the years of his reign only to become a commoner. The descendants of the Wu and Hou houses perished in one place; those who later came to bury them at Houwei perished elsewhere. The King of Yan, after his death, was reduced to the status of a commoner. The King of Huaiyang was strangled; the wife of the King of Liang, Xiao, was deposed and set up over a well, while the great Wu was confined in the palace. Zhong of Qin, who succeeded the two kings, suffered greatly; the three groups were gathered and wiped out, and the line ended in the second generation. More recently, a brave member of the Wang house was killed by a violent usurper; the waters of the Xing River bore witness to the injury done to the ruler. Such is the fate of those whose achievements do not end well.

3. The Feudal Lords, Reducing Their Fiefs, and the Han Dynasty

If one should instead honor the great Wu through the feudal lords, then the system by which Tang, Yu, Yu, Ji, Wen, and Wu successively became Son of Heaven would surely not have brought the princes to ruin through the hope of eradicating them. In the early Han, the feudal lords were powerful. The founding emperor had already had meritorious ministers killed, yet the great era had not run its full course. After Emperor Gaozu, the lords’ power was reduced; the dynasty’s decline reached the generation after his own, in less than forty years. Although the kings were stripped of their titles and reduced in rank, their lines did not thereby become extinct.

The Han did not enfeoff as many of its sons and younger brothers as Yin and Zhou had. By the end, its descendants were scattered, and some were so insignificant that their lines did not endure. All three Han rulers had heirs, and the throne passed from father to son, with empresses and maternal relatives involved. Even in the disorderly time of the Red Eyebrows, the circumstances resembled those of Jie of Xia and Xin of Yin; in the end, however, the dynasty returned to the Han house.

At first, Emperor Gengshi entered the capital. The Red Eyebrows then advanced west into Chang’an, where Liu Penzi was installed as Han emperor, taking advantage of the earlier ruler’s removal. [The remaining text is corrupt and unreadable.]

Huainan Honglie Jie: A Plain-Language Reading

In the year Dahuangluo (“great” and “abundant”: all things flourish intensely and then scatter in profusion), there are minor military disturbances. The silkworm harvest is poor, wheat is good, and beans are blighted; the people have about two sheng of grain per person. The year is associated with Ding and is called Qiangyu: under Ding, all things are at the height of their strength, hence the name Qiangyu.

In the year Dunqiang (all things are vigorous and flourishing; dun means abundant, qiang means strong), there is a great drought. The silkworm harvest is good, rice is blighted, beans and wheat are good, and the grain crop fails. The people have about two sheng of grain per person. The year is associated with Wu and is called Zhuyong: in the central position of Wu, all things multiply and flourish in the four directions, hence the name Zhuyong. The original text says “Wu is in the position of Wu,” which appears to be a scribal error; Wu is generally paired with its own year name.

In the year Xieqia (harmony and union: Yin Qi seeks to bring all things into harmony), there are minor military disturbances. The silkworm harvest and rice are good, but beans and wheat fail. The people have about three sheng of grain per person. The year is associated with Wei and is called Tuwei: under Wei, all things each come into their own nature. Tu means to distinguish, and wei to separate.

In the year Tuntan (tun means great, tan means extended: all things extend and refine their vital energy), the year is mild, with light rain. The silkworm harvest, beans, and wheat are good. The people have about three sheng of grain per person. The year is associated with Shen and is called Shangzhang: under Geng, Yin Qi rises and all things complete their growth, hence the name Shangzhang.

In the year Zuoe (falling and scattering: all things tumble and fall away), there is major warfare and the people are sick. The silkworm harvest fails, beans and wheat fail, and insects infest the grain. The people have about five sheng of grain per person. The year is associated with You and is called Chongguang: under Xin, all things ripen and shine brightly, hence the name Chongguang.

In the year Yanmao (yan means to cover, mao means to envelop: all things are covered over), there is a minor famine and warfare. The silkworm harvest fails, wheat fails, and chang—a crop of uncertain identity—is poor. The people have about seven sheng of grain per person. The year is associated with Xu and is called Xuan Yi: under Ren, the year comes to an end and all things are stored away, hence the name Xuan Yi.

In the year Dayuanxian (yuan means to store, xian means to welcome: as all things come to their end in Hai, great and small alike hide deep in caves to await the Yang Qi), there is a great disaster and a severe famine. The silkworm season begins—or possibly undergoes some change—beans and wheat fail, and insects infest the grain. The people have about three sheng of grain per person.

In the year Kundun (kun means mixed, dun means formless: Yang Qi is mixed and undifferentiated, and the sprouts of all things begin to emerge), a great fog rises…

Note: This is an ancient set of divination entries linking year names and the sexagenary cycle with agriculture, warfare, and famine. It belongs to the same system of year names found in the “Treatise on Astronomy” of the Huainanzi, including Xieqia and Tuntan. The figures for “grain per person” indicate the degree of food scarcity. The statement “Wu is in the position of Wu and is called Zhuyong” does not match the usual name associated with the Wu year and may reflect an error in compilation or transmission. It should be checked against the year-name table elsewhere in the work.

Vernacular Explanation

Year of Water Virtue: Mulberry, rice, beans, and wheat are still fairly good; the common people’s grain ration comes to about three dou (a rough calculation for a famine year).

The Heavenly Stem is Gui, called Zhaoyang: Yang Qi first sprouts, and the myriad things arise in harmony and generation, hence the name Zhaoyang.

The year of Chifenruo (“fen” means to rouse, “ruo” means to accord; Yang Qi rouses the myriad things and none fails to follow its nature; red is the color of Yang): there are minor wars, drought and flood; silkworms do not emerge, rice suffers disease, beans do not grow, wheat is still passable, and the common people’s grain ration is about one sheng.

Determining Orientation by Measuring the Sun’s Shadow (Morning and Evening Method in the First Month)

On the morning and evening of the first day of the first month (or, according to one account, during the first month): first set up a gnomon in the east, take another gnomon and retreat ten paces from the first, and sight the sun with them. At sunrise, the sun’s shadow enters straight from the north side (the north edge). Again set up a gnomon in the east, and use the western gnomon to sight the setting sun; the shadow likewise enters from the north side. Then the midpoint between the two eastern gnomons, opposite the single western gnomon, is true east-west.

At the winter solstice, the sun rises at the southeast quarter and sets at the southwest quarter. At the spring and autumn equinoxes, it rises due east and sets due west. At the summer solstice, it rises at the northeast quarter and sets at the northwest quarter. From this one can know the obliquity of the sun’s path according to the solar terms.

Knowing the Measurements of East, West, South, North, and Extent

Set up four gnomons to form a square, one li on each side. More than ten days after the spring or autumn equinox, observe the sunrise from the north gnomon at dawn; when the front and rear gnomons form a straight line with the sun, then it is directly aligned with the sun. Observe again from the south gnomon; using the shadow length that “enters the front gnomon” as the divisor, divide the gnomon spacing and the gnomon height by it, and one can calculate the distance from this place to the east (or west).

For example, when observing sunrise and sunset, if the shadow falls one cun inside the front gnomon, then one cun corresponds to one li; since one li comprises 18,000 cun, one is about 18,000 li east of this place. If the shadow enters only half a cun into the front gnomon, half a cun equals one li, so one is about 36,000 li west of this place. Combining the east-west li figures gives the breadth across; viewed together with the distances to the north and south poles, one can infer the scale of the earth.

Verification of Deviation and Straightness

If before the spring equinox it is already “straight,” or after the autumn equinox it is not straight, this place deviates south. If before the autumn equinox it is already straight, or after the spring equinox it is not straight, this place deviates north. If it is straight at both the spring and autumn equinoxes, this place is the north-south center. Measuring again from the midpoint: if it is still not straight at the autumn equinox, it is still in the north-south center. From the midpoint, to know the distance to the north and south poles: observe the sun from the southwest gnomon; at summer solstice sunrise, when it forms a straight line with the north gnomon, this is the measuring method determined by the east and north gnomons (paired with the east-west method above to infer the extreme distance).

Note: This section belongs to the Huainan tradition’s arts of calendrical calculation, Qi observation, and determining li by shadow measurement. It uses erected gnomons to measure sunrise and sunset directions and shadow lengths, inferring east-west breadth and whether the latitude is south or north. It shares a common source with the later armillary sphere and the idea of Qi observation in calendrical systems. The “li” in the text is an idealized mathematical li of that time and should not be equated one-to-one with the modern kilometer.

This passage concerns how the ancients used gnomon shadows to measure the sun (setting up a pole to measure its shadow) in order to infer the dimensions of heaven and earth; it belongs to the calendrical-astronomical kind of discussion in the Huainanzi.

The li-distances east-west and north-south. The direction opposite the northeast is due east; one account says east and west are each 18,000 li. From the “exact center” of heaven and earth northward and southward are likewise each 18,000 li. The full north-south length is twice this number. Here one does not use the set of li-distances “calculated from the center”; rather, one adds or subtracts according to the shadow lengths of two shadow-measuring poles, one in front and one behind (one pole erected at each). If the front pole’s shadow is one cun shorter than the rear pole’s, then the sun is said to be northward in position, equivalent to being one li nearer; if the front pole is one cun longer than the rear, then it is said to be southward, equivalent to being one li farther. This is the method of converting shadow difference into ground distance.

How to infer “how high heaven is.” Erect a shadow-measuring pole one zhang high, with one due south and one due north, a thousand li apart. On the same day measure the shadows: the northern pole’s shadow is two chi, the southern pole’s shadow is one chi nine cun—at a thousand li to the south, the shadow is one cun shorter than in the north. By analogy: twenty thousand li to the south, the sun is at zenith, and there is no shadow (the point directly under the sun). When the shadow length is two chi and the pole height is one zhang, the ratio is one unit of shadow to five units of pole height (at the same moment and under the same set of proportions). Therefore take the north-south li distance “from here to the point under the sun” and multiply it by five, obtaining one hundred thousand li; this is what the text calls the height of heaven. It also says: if the shadow length and the pole height are equal, then “height” and “distance” are equal—that is a statement under another ideal ratio.

Brief notes on technical terms. Biao is the vertical pole used for measuring shadows. Li, cun, chi, and zhang are ancient units of length and distance. Rixia is the place directly under the sun, where the sun is overhead and casts no shadow. “Heaven is 100,000 li high” is a cosmological scale derived in Huainan-system texts through shadow geometry; it is a theoretical calculation of that era, not a modern measured value.