by An Liu
[The territorial allotments of the earthly branches are as follows:]
zi with Zhou wu with Qin
chou with Di wei with Song
yin with Chu shen with Qi
mao with Zheng you with Lu
chen with Jin xu with Zhao
si with Wey hai with Yan [3/28/22–24]
[The stem and branch correlations of the Five Phases are as follows:]
[stems] [branches] [phases]
jia and yi yin and mao Wood
bing and ding si and wu Fire
wu and chi the four seasons Earth
geng and xin shen and you Metal
ren and gui hai and zi Water [3/28/26–27]
3.38
Water produces Wood; Wood produces Fire; Fire produces Earth; Earth produces Metal; Metal produces Water.
If the child gives birth to the mother, this is called Rightness.
If the mother gives birth to the child, this is called fostering.
If the mother and child each give rise to the other, this is called concentration.
If the mother vanquishes the child, this is called control.
If the child vanquishes the mother, this is called obstruction.
If one employs victory to smite and kill, the victory will be without recompense.
If one employs concentration to pursue affairs, there will be achievement.
If one employs Rightness to carry out fixed principles, one’s fame will be established and it will not diminish.
If one employs fostering to nurture the myriad creatures, there will be luxuriant growth and prosperity.
If one employs obstruction to pursue affairs, there will be destruction, extermination, death, and extinction [of the state]. [3/28/26–29]
3.39
The gods of the Northern Dipper are both female and male. In the eleventh month, at the beginning [of the year], they are established [together] in zi. Every month they shift by one chronogram. The male goes leftward, the female rightward. In the fifth month they coincide in wu and devise recision. In the eleventh month they coincide in zi and devise accretion. [3/29/1–2]
3.40
The chronogram in which taiyin is located58 is called an “oppressive day.” On oppressive days it is not possible to pursue the hundred [normal] affairs. Earth and Heaven59 move with slow dignity; the male knows the female by the sound [of her singing]. Thus [the chronogram in which taiyin is located] is known as the “extraordinary chronogram.” [3/29/2–3]
The numbers [of the sexagenary cycle] begin with jiazi. Offspring and mother seek each other out. The place where they come together is called a concurrence. Ten stems and twelve branches make a sexagenary cycle.
In all there are eight concurrences. If the concurrence is [at a point in the cycle] before [the stem–branch combination in which taiyin is located], there will be death and destruction; if the concurrence is later [in the cycle], there will be no calamity. [3/29/5–6]
[The territorial allocations of the “eight concurrences” are as follows:]
jiaxu is Yan gengchen is Qin
yiyou is Qi xinmao is the Rong tribes
bingwu is Yue renzi is the Dai tribes
dingsi is Chu guihai is the Hu tribes
[The territorial allocations of the “lesser conjunction” cyclical pairs are as follows:]60
[wuchen is . . .] yiyou is . . .
wuxu is . . . yimao is Wei
[yisi is . . .] wuwu is . . .
yihai is Hann wuzi is . . .
The eight concurrences [together with the eight lesser conjunctions] [thus correspond to] the world. [3/29/8–10]
When taiyin, the Lesser Year, the asterisms [= lunar lodges], the branches, the stems, and the five [directional] gods all coincide on the same day, there will be clouds, vapors, and rain. The state and ruler match [the prognostication]. [3/29/12]
3.41
Of those prized by the heavenly spirits, none is more prized than the Bluegreen Dragon. The Bluegreen Dragon is otherwise called the Heavenly Unity, or otherwise taiyin. [The country corresponding to] the place where taiyin dwells cannot retreat but can advance. [The country corresponding to] the place beaten against by the Northern Dipper cannot withstand attack. [3/29/14–15] When Heaven and Earth were founded, they divided to make yin and yang.
Yang is born from yin;
yin is born from yang;
they are in a state of mutual alternation. The four binding cords [of Heaven] communicate with them.
Sometimes there is death;
sometimes there is birth.
Thus are the myriad things brought to completion.
[Of all creatures that] move and breathe, none is more prized than humans. [The bodily] orifices, limbs, and trunk all communicate with Heaven.
Heaven has nine layers; man also has nine orifices.
Heaven has four seasons, to regulate the twelve months;
Man also has four limbs, to control the twelve joints.
* * *
This diagram of the stems, branches, lunar lodges, and Five Phases is in the form of the Earth plate of a shi cosmograph, showing significant alignments with the “pointer” of the Northern Dipper engraved on the rotating Heaven plate (not depicted here).
Heaven has twelve months, to regulate the 360 days;
Man also has twelve joints, to regulate the 360 nodes.61
A person who undertakes affairs while not obeying Heaven is someone who deviates from what gave birth to him. [3/29/17–20]
3.42
Take the arrival of the winter solstice and count to the first day of the first month of the coming year. [If] there are a full fifty days, the people’s food supply will be sufficient. [If] there are fewer [than fifty days], [the people’s rations] will be reduced by one pint per day. [If] there is a surplus [above fifty], [the people’s rations] will be increased by one pint per day. This is what controls the harvest. [3/29/22–23]
* * *
Translation of the diagram of the stems, branches, lunar lodges, and Five Phases.
The year Shetige: A year of early moisture and late drought. Rice plants are sickly and silkworms do not mature. Legumes and wheat flourish. The people’s food ration is four pints [of grain per day]. Yin in jia is called “impeded seedlings.”
The year Ming’e: The year is harmonious. Rice, legumes, wheat, and silkworms flourish. The people’s food ration is five pints. Mao in yi is called “flag sprouts.”
The year Zhixu: A year of early drought and late moisture. There is minor famine. Silkworms are obstructed, and wheat ripens. The people’s food ration is three pints. Chen in bing is called “pliant omen.”
The year Dahuangluo: A year of minor warfare. Silkworms mature in small numbers, wheat flourishes, and legumes are sickly. The people’s food ration is two pints. Si in ding is called “strengthen the frontier.”
The year Dunzang: A year of great drought. Silkworms mature, rice is sickly, and wheat flourishes, but the crops do not yield. The people’s food ration is two pints. Wu in wu is called “manifestly harmonious.”
The year Xiexia: A year of minor warfare. Silkworms mature, rice flourishes, and legumes and wheat do not yield. The people’s food ration is three pints. Wei in ji is called “differentiate and separate.”
The year Tuntan: The year is harmonious. The lesser rains fall in season. Silkworms mature; legumes and wheat flourish. The people’s food ration is three pints. Shen in geng is called “elevate and make manifest.”
The year Zuo’e: A year of great war. People suffer illness, silkworms do not mature, legumes and wheat do not yield, and crops suffer insect damage. The people’s food ration is five pints. You in xin is called “redoubled brightness.”
The year Yanmao: A year of minor famine and warfare. Silkworms do not mature, wheat does not yield, but legumes flourish. The people’s food ration is seven pints. Xu in ren is called “umbral blackness.”
The year Dayuanxian: A year of great warfare and great famine. Silkworms r
upture their cocoons; legumes and wheat do not yield; crops suffer insect damage. The people’s food ration is three pints. [Hai in gui is called . . .]62
The year Kundun: A year of great fogs rising up and great waters issuing forth. Silkworms, rice, and wheat flourish. The people’s food ration is three bushels. Zi in jia is called “dawning brilliance.”
The year Chifenruo: A year of minor warfare and early moisture. Silkworms do not hatch. Rice plants are sickly, legumes do not yield, but wheat flourishes. The people’s food ration is one pint. [Chou in yi is called. . . .]63 [3/29/25–3/31/8]
3.43
To establish the directions of sunrise and sunset, first set up a gnomon in the east. Take one [other] gnomon, and step back ten paces from the first gnomon. Use it to sight in alignment toward the sun when it first emerges at the northern edge [of its position on the eastern horizon?] When the sun is just setting, again plant one gnomon to the east [of the second gnomon], and use the gnomon to the west of it to sight in alignment toward the sun when it sets at the northern edge. Then establish the midpoint of the two eastern gnomons; this along with the western gnomon fixes a true east–west line. At the winter solstice, the sun rises at the southeastern binding cord and sets at the southwestern binding cord. At the spring and autumn equinoxes, it rises exactly in the east and sets exactly in the west. At the summer solstice, the sun rises at the northeastern binding cord and sets at the northwestern binding cord. At the zenith it is exactly in the south. [3/31/10–14]
3.44
If you wish to know the numerical values for the east–west and north–south breadth and length [of the earth], set up four gnomons to form a square one li on each side. Ten or a few more days before the spring or autumn equinox, use the two gnomons on the northern edge of the square to sight in alignment on the rising sun when it first appears [above the horizon]. Wait until [the day when the gnomons] coincide [with the rising sun]. When they coincide, then this corresponds to the true [east] position of the sun. Then immediately also use the south[west]ern gnomon to sight on the sun in alignment. Take the amount by which [this sighting] is within the forward gnomons as the standard. Divide the width and length [between the gnomons [i.e., one li]] by this, and from this you will know the numerical value of [the width of the earth] from east to west. For example, observe the [alignment of the southwestern gnomon with] the rising sun to be one inch within the forward gnomons, and let one inch equate to one li. One li equals 18,000 inches, so the distance from [the point of observation] eastward to the sun is 18,000 li. Or [on the same day] observe the setting sun; [the alignment of the sun with the southeastern gnomon] lies one-half inch within the forward gnomons. For one-half inch, one obtains one li. Divide the number of inches in one li by one-half inch; one obtains the answer of 36,000 li. Thus one obtains the numerical value of the distance from [the point of observation] westward to the sun. Add [the two figures] together for the numerical value of the distance from east to west. This number represents the span between the extreme end points [of the earth].
If the alignment [of the gnomons on the northern edge of the square] occurs before the spring equinox or after the autumn equinox, you are to the south [of the midline of the earth]. If the alignment occurs before the autumn equinox or after the spring equinox, you are to the north. If the alignment occurs exactly on the equinox, then you are midway between north and south.
If you wish to know true south from a position in the exact center, [observe that] if the alignment [of the gnomons on the northern edge of the square] does not occur before the autumn equinox, the position is exactly between north and south. If you wish to know the distance to the extreme limits of south and north from a position in the center, use the southwestern gnomon to sight in alignment on the sun. When the sun at the summer solstice first rises, sight on the north[west]ern gnomon, and [you will see that] the sun is an equal distance to the east, [aligned with] the northeastern gnomon. The distance to the east is 18,000 li, so the distance from the center to the north is also 18,000 li. Double this to obtain the numerical value of the distance from south to north.
The amount by which [a position] departs from the center is larger or smaller, [proportional to the] amount by which [the sight line] is within or outside the forward gnomons. If [that line] is one inch inside the gnomons, the sun is closer by one li. If [the line] is one inch outside the gnomons, the sun is more distant by one li. [3/31/15–24]
3.45
If you wish to know the height of heaven, plant a gnomon one zhang [i.e., ten feet] tall in the south [and another] in the north, at a distance of a thousand li. Measure their shadows [at noon] on the same day. [Suppose that] the northern gnomon [casts a shadow of] two feet, and the southern gnomon [casts a shadow of] one foot, nine inches. Thus by going a thousand li to the south, the shadow is shortened by one inch.64 Going twenty thousand li [to the south], there would be no shadow. That would be directly beneath the sun. A shadow two feet long results from a height of ten feet, so going south one [li] [increases] the height by five [li] Thus if one measures the li from [the northern gnomon] to a point directly beneath the sun and then multiplies that by five, it makes 100,000 li, and that is the height of heaven. Or if you suppose that the [length of] the shadow is equal to [the height of] the gnomon, then the height [of heaven] would be equal to the distance [southward to a point directly beneath the sun].65 [3/32/1–4]
Translated by John S. Major
1. Conventionally translated as “cosmos” or “universe,” yuzhou more precisely means, as Angus C. Graham put it, “process enduring in time” and “matter extending in space” (“Reflections and Replies: Major,” in Chinese Texts and Philosophical Contexts: Essays Dedicated to Angus C. Graham, ed. Henry Rosemont [La Salle, Ill.: Open Court Press, 1990], 279). “Space-time,” a term borrowed from modern physics, captures the idea very well.
2. Gong Gong is a mythical figure of high antiquity, sometimes described as the “minister of works” to the ancient thearchs but also depicted as a rebel and fomenter of disorder.
3. Zhuan Xu is a divine thearch and god of the north, from whom many aristocratic lineages of the Bronze Age claimed descent. See also chap. 5, n. 46.
4. Mount Buzhou, conceptualized as the central peak of Mount Kunlun and therefore located to the northwest of China (see the introduction to chap. 4 and fig. 4.1), is the pivot of Heaven and Earth. Zhou means “to circle” in the sense of “to circumambulate” or “to orbit”; it does not mean “to revolve on its own axis.” Thus the common translation of “Unrotating Mountain” for Buzhou is not correct. The sense of the term is that the mountain rests unmoving at the very center of the universe, which rotates around it.
5. The same phrase, yin yang xiang bo , occurs five times in 4.19 and once in 17.174. The context of 17.174 requires a slightly different translation: “yin and yang erode each other.”
6. See 10.27: “When an eagle hovers above the river, fish and turtles plunge and flying birds scatter. By necessity they distance themselves from harm.”
7. A device intended to collect dew by condensation.
8. Reading er as er . Essentially the same statement appears in 6.2. See chap. 6, n. 18.
9. That is, the Gulf of Bohai, a shallow body of water located off northeastern China and partly enclosed by the Liaodong and Shandong peninsulas.
10. Reading ling bu shi as in the Yiwen, in place of the ling bu shou of the Huainanzi text. My thanks to Michael Loewe (private communication) for suggesting this emendation. For the concept of “unseasonable ordinances,” see chap. 5.
11. “Chariot Frame,” Xuanyuan , is the personal name of the Yellow Emperor, after the name of his supposed birthplace in Henan. The compound word means “axle and shafts”—that is, the basic frame of a chariot.
12. The Pool of Xian is a constellation. The word xian is open to various interpretations, but in this compound it seems to be the name of the legendary figure Shaman Xian, Wuxian . For further discussion, see Major 1993, 199. See also
chap. 11, n. 35.
13. The “asterisms” (xing ) of this passage are the lunar lodges (xiu ). For the lunar lodges and the English translations of their names used in this work, see app. B.
14. Tai Hao, Gou Mang, and the other planetary gods and “assistants” are mythical figures; many also appear in the poems of the Chuci. For further identifications, see the “Glossary of Names” in Hawkes 1985, 322–45.
15. This and the following four paragraphs are quoted verbatim from the Mawangdui manuscript text known as “Wuxingzhan.” See Xi Zezong , “Zhongguo tianwenxue shi de yige zhongyao faxian—Mawangdui Hanmu boshu zhong de ‘Wuxingzhan’” — (An important discovery for the history of Chinese astronomy—the Mawangdui silk manuscript “Prognostications of the Five Planets”), in Zhongguo tianwenxue shi wenji (Beijing: Science Press, 1978), 14–33. On the motions of the five planets, 3.7 through 3.11 are similar to but less detailed than the corresponding sections of the “Wuxingzhan.”
16. Yan Di , the “Flame Emperor,” is a semidivine figure who figures variously in different myths. In some stories he is credited with having invented the use of fire for humankind, and in others he is depicted as a rebel against the legitimate authority of the Yellow Emperor, who is sometimes identified as his half brother.
17. Each of the “four hooks” defines two points on the horizon, and Jupiter passes through two lunar lodges for each of those points. Thus four hooks equal eight points and therefore the “two times eight is sixteen” of the text. See Major 1993, 34, fig. 2.2.
18. These wind names are repeated in 4.18. A different list of wind names, perhaps representing an alternative tradition, is found in 4.1.
19. Changhe is the name of the Gate of Heaven, the portal through which communication between Heaven and Earth is possible. See 4.3.
20. Mount Buzhou is the pivot of Heaven, around which the cosmos rotates. See 4.3 and chap. 4, n. 10.