邝楚嘉，笔名嘉言一得，广东揭阳人，独立研究者。1996 年起研习中国传统历法。三十年下来，主要做三件事：节气按太阳黄经定在哪个时刻，干支从哪一天换岁，历法时间与季节方位怎么对应。文字尽量说白话，推算一步步摆出来。
天象数据全部离线回推，用 NASA JPL DE421 高精度星历；历法编算依 GB/T 33661—2017《农历的编算和颁行》。古书说法打架的地方，两说并列写出，不下断语。站里没有星占、谶纬，也不谈个人吉凶。
主要成果是《中国历法公共数据集》（CC BY 4.0）：二十四节气交节时刻（1900—2052）、历代历法改革年表（52 部）、干支纪日对照表，全部公开，可核验、可引用。
ORCID：0009-0002-7650-833X ｜ OpenAlex：A5151908354（25 篇）｜ 数据集 DOI：10.5281/zenodo.22788686 ｜ OSF：osf.io/8mj2z ｜ GitHub：github.com/Kuangchujia
Chujia Kuang (邝楚嘉), pen-name Jiayan-Yide (嘉言一得). Independent researcher in Jieyang, Guangdong, China. I have studied the traditional Chinese calendar since 1996. Thirty years on, the work comes down to three things: at which instant a solar term falls by the sun's ecliptic longitude, on which day the sexagenary year turns, and how calendrical time maps onto season and direction. I write plainly and lay the computation out step by step.
Sky data are recomputed offline from the NASA JPL DE421 ephemeris; the calendar follows GB/T 33661-2017, Calculation and Promulgation of the Chinese Calendar. Where the old books disagree, both readings are given side by side and no verdict is passed. The site carries no astrology, no apocrypha, and nothing on individual fortunes.
The main output is the Chinese Calendar Public Dataset (CC BY 4.0): solar-term instants, 1900-2052; a chronology of 52 calendrical reforms; and a ganzhi day-count concordance. All of it is public, open to checking and citation.
ORCID: 0009-0002-7650-833X | OpenAlex: A5151908354 (25 works) | Dataset DOI: 10.5281/zenodo.22788686 | OSF: osf.io/8mj2z | GitHub: github.com/Kuangchujia
In 1978, at Leigudun in Suixian, Hubei, present-day Suizhou, an archaeological team lifted a wooden box out of a Warring States tomb. The lid was taken off: on a ground of black lacquer a ring of characters had been painted in vermilion, twenty-eight of them, with a large seal-script 「斗」, the Dipper, in the middle. Outside the ring, one at each end, a dragon was painted on the east and a tiger on the west. The box is now known as the twenty-eight-mansion diagram clothes box. No account of where the twenty-eight mansions came from can get around it, because it is early; and one further sentence is habitually added to it: on this box there are the twenty-eight mansions, and there are also the four images.
Fig. 1 Painted lacquer box with the twenty-eight lunar mansions. Warring States period; 71 x 47 x 40.5 cm. A red “dou” (Dipper) character at the centre of the lid, the twenty-eight mansions arranged around it, the Azure Dragon and the White Tiger on the two sides; “zhi hu” carved at a corner, marking it as a clothes box. Hubei Provincial Museum. Source: Google Arts & Culture, “Zeng Houyi: Lacquerware” (images provided by Hubei Provincial Museum) Copyright remains with the original photographer or institution; please contact this site for removal if needed.
That sentence is worth weighing. What an excavated object supplies is a terminus ante quem, a lower bound, at the latest; not a terminus post quem, from when. The twenty-eight names on this lid can still be read one by one, and the dragon and the tiger are plainly drawn. But “four images” means four creatures, and on this lid only two are visible. Beneath the term lie three separate layers: a closed list of twenty-eight names, the division of that list into four groups of seven, and the pairing of each group with one animal. The three need not arrive together. Working backwards from the box, the earliest hard evidence for animal-plus-direction is the Xishuipo tomb at Puyang, Henan, whose clam-shell dragon, tiger and Dipper are dated by radiocarbon measurement on shell, tree-ring corrected, to 6460±135 years before present, and which contains not one star name. The four creatures are written down side by side only in the Eastern Han. The lower bounds therefore lie at three different depths, from about six and a half thousand years ago down to the Eastern Han, and the lacquer box reaches only the second of them. The piece is descriptive and carries no prediction.
Fig. 2 The Mawangdui silk manuscripts. Silk manuscripts from Han tomb no. 3 at Mawangdui, Changsha. Related material shown for reference, not the Wuxing zhan or Tianwen qixiang zazhan themselves. Source: Wikimedia Commons，Mawangdui Silk Texts 1.JPG（Public domain） Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Keywords: Marquis Yi of Zeng; lacquer box; twenty-eight mansions; four images (四象); Xishuipo; terminus ante quem; Warring States astronomy; Han astronomy
Introduction
In 1978, at Leigudun in Suixian, Hubei, present-day Suizhou, an archaeological team lifted a wooden box out of a Warring States tomb. The lid was taken off: on a ground of black lacquer a ring of characters had been painted in vermilion, twenty-eight of them, and in the middle a large seal-script 「斗」. Outside the ring, one at each end, a dragon was painted on the east and a tiger on the west.
The box came to be known as the twenty-eight-mansion diagram clothes box. No account of where the twenty-eight mansions came from can get around it, because it is early.
Getting around it is not the only thing that happens to it. One further sentence is habitually added: on this box there are the twenty-eight mansions, and there are also the four images.
That sentence is worth pausing over. The twenty-eight characters on the box can still be read one by one, and the dragon and the tiger are drawn plainly. But “four images” is four things, dragon, tiger, bird, turtle-and-snake, and on the lid only two are visible. The other two do not appear.
There is a further layer. The date of the box is generally put at about 433 BCE. From the sentence above, some go on to infer: the Chinese system of four images was already complete in the early Warring States.
That is a step taken a little quickly. What follows takes the sentence apart and asks how much weight it can carry.
1. What one object can pin down
In archaeological reporting there is one sentence that is often passed over: what a single object gives you is “at the latest”.
Suppose a wooden tablet is dug out of the ground with 「正月」 written on it, and it measures to two thousand three hundred years old. What can be said is: at least two thousand three hundred years ago, someone was already calling a month by this name. What cannot be said is: this way of naming began in that year. By the time the tablet was put down, the usage had most likely been going for some while. How long, the tablet does not answer.
In chronology the first of these is called the lower bound, or the latest possible date; the second is called the upper bound, or the earliest possible. A single object can usually pin down only the lower bound, never the upper.
The lower bound by itself is already valuable. It compresses the year of invention of a system from “unknown” to “no later than such-and-such”. The trouble begins at the moment the lower bound is used as an upper bound, when “at the latest there was already” is read as “only from this year was there”.
This is the third piece in the series. The first two asked whether something could be computed, and which few records ought never to be computed; this one changes direction. It asks which end of a system a physical object can pin down, and how the stretch it cannot pin down ought to be described.
2. The box
The look of the box is not described in detail here. What matters is a few details, because they decide how much the opening sentence can bear.
First, an outline. This is a wooden clothes box, lid and body each hollowed out of a single block of wood; the lid is arched, the interior red-lacquered, the exterior black-lacquered as ground with vermilion patterns. Length 71 cm, width 47 cm, overall height 40.5 cm. Five clothes boxes of similar type came out of the same tomb. The one carrying the star diagram is numbered E.66; among the others, E.61 is painted with Hou Yi shooting the suns and E.67 with Kuafu chasing the sun.
On the face of the lid, at the exact centre, is a seal-script 「斗」. Around this character runs a ring of twenty-eight characters, written in the local Chu variant forms, from 角, 亢, 氐, 房, 心, 尾, 箕 all the way round to 軫. Outside the ring, on the east and west sides, a dragon is painted on one side and a tiger on the other. The two end faces of the lid each carry a group of ornament; of the two long sides, one is painted with two beasts facing off, and the other carries only a red band.
There are several places where a reader does well to stop.
The first is the character 「斗」. Some take its strokes apart by direction: the two ends of the horizontal point to 心 and 危 respectively, and the end of the vertical points to 張, while the handle end points to 觜觿. If one follows the actual sky, the place the handle points to ought rather to fall at 畢. It points wrongly. This is often used to show that the diagram on the lid is not necessarily traced from the real sky of one particular night, and is more like a diagram drawn as a diagram.
The second is four small characters beside 亢: 「甲寅三日」. Some compare them with the old calendars and hold that this figure depicts the sky of the evening of the third day of the first month in 433 BCE, days that fell around the beginning of spring, when the ancient rites required the ploughing ceremony 【一说】. Which year and which event these four characters refer to has other readings as well.
The third is the direction of the sequence. The twenty-eight characters on the lid run clockwise, the reverse of later star charts. Guo Dewei offered an explanation: the painter took the arched lid as the round vault of heaven and the rectangular base of the box as the earth; a person standing on the earth looks up at the vault, and looking at this lid from above reverses the order. On this account the difference in direction is really the difference between looking down and looking up.
Put the three together and the identity of the object is fairly clear. It is an inscription on a vessel, not an observation log.
The date of the box itself has two values. 433 BCE is the one in general use 【通说】, and there is a further proposal of 435 BCE 【一说】. The two numbers differ by two years, which makes no difference to the judgement this piece has to make; the one in general use is taken here, and the matter is not put too firmly.
What it can pin down is this one sentence: at the latest, around 433 BCE, the twenty-eight star names together with their order, plus one 「斗」, plus a dragon to the east and a tiger to the west, were already common knowledge, painted casually on the lid of a box for clothes.
As to what it cannot pin down, the term “four images” has first to be taken apart.
3. Beneath the four images lie three layers
“Four images” on the side of the sky means the division of the twenty-eight mansions into four groups by the four directions, each paired with one animal: azure dragon in the east, white tiger in the west, vermilion bird in the south, dark warrior in the north.
This can in fact be split into three layers.
The first: twenty-eight names gathered into one closed list.
The second: the list cut by the four directions into four groups of seven.
The third: each of the four groups paired with one animal.
The three need not arrive together. They may appear one after another, or stop at the second. When the opening piece of this series discussed the four fixed stars of the 「Yaodian」, it noted that those four stars each stand within one image; that is a configuration which exists only after all three layers are in place.
Take the first layer first. The gathering of twenty-eight names into one closed list happened very late. Before that, star names in the literature are scattered: in the Yinxu divination inscriptions there is the Bird star and there is the Great Fire, stars the Shang people already knew and used for keeping records; in the Shijing and the Xia Xiaozheng there is 箕, there is 斗, there is 辰, there is 參, scattered here and there. They are all there; they simply do not form a file. The previous piece, saying that the men of Shang knew a good many stars but had no twenty-eight-mansion coordinates, was talking about exactly this stretch. The grid was drawn in later; how much later, a lower bound can be seen below.
Now search towards the earliest end.
In 1987, at Xishuipo in Puyang, Henan, in a tomb of the Yangshao culture, a dragon was laid out in clam shell to the east of the occupant, a tiger to the west, and between them a Dipper made of clam shell and human bone.
The date of this tomb requires a set of numbers here. The laboratory of the Institute of Archaeology, Chinese Academy of Social Sciences, made radiocarbon measurements on clam shell from the tomb; corrected by tree rings, the result is 6460±135 years. A second set, inferred from the Hougang type, falls between 4300 and 4100 BCE. Taking the radiocarbon set, the text writes “about six thousand five hundred years ago”, with the error recorded as ±135 years.
It has no star names, not one. What Xishuipo can say is this: the dragon and the tiger, these two images, were laid out to east and west very early, with the Dipper between them. That is the hardest single piece of evidence for directions being laid out; what it governs has nothing to do with the twenty-eight mansions.
From this tomb to Marquis Yi of Zeng is a gap of about four thousand years. Four thousand years ago there were dragon, tiger and Dipper; four thousand years later there are twenty-eight names plus dragon, tiger and Dipper. Join the two points and a very long line can be drawn: the pairing of animals with directions is very old, and was never broken.
The middle of the line is empty.
4. Afterwards: in how many steps do the four animals arrive
On the lid of Marquis Yi’s box, two can be seen at a glance. The completion of four beasts has to be sought in later material. That stretch of road is long.
Look first at the numbers in the classics. In the 「Zhouli · Chunguan」 there is an office called Fengxiang shi, whose charge is 「十有二歲，十有二月，十有二辰，十日，二十有八星之位」. This sentence was quoted in the preceding instalment; it is borrowed here to say something else. The classics have the number “twenty-eight”, and never once list the twenty-eight names. The number arrived; the list did not.
Look next at the list. In the transmitted literature the twenty-eight names appear together in a batch for the first time in the Lüshi Chunqiu · Youshi, at the end of the Warring States:
「天有九野……中央曰鈞天，其星角、亢、氐；東方曰蒼天，其星房、心、尾……」
The names are complete. But look at the division: nine parts. One central, four for the four directions, four for the four corners, together cutting the twenty-eight mansions into nine shares. The cut of seven to each of the four directions does not yet exist in this text.
One further thing is worth noticing. In the nine-field division the central share receives 角, 亢, 氐, and the eastern share receives 房, 心, 尾. Three mansions to a share, four to a share, which does not agree with the neat later cut of seven to each direction. The nine fields govern directions and field-allotments; what they divide is not the four images.
In the same stretch of years there are other versions. In the eleventh volume of the Tsinghua bamboo slips, published in 2021, there is a text called 「五紀」, a Chu document of the middle to late Warring States, and it too contains a full set of twenty-eight mansions. According to the editors’ transcription it is not entirely the same as the set on the lacquer box: in the western seven it writes 「濁」 rather than 「畢」; 參 and 伐 are two separate mansions and are not merged into one; in the south it uses 狼 and 弧 rather than 井 and 鬼.
By the Han the matter becomes more tangled rather than less.
The Huainanzi · Tianwenxun, in the early Western Han, sets out five directions, each with one beast:
Count them: five beasts. The centre has an extra yellow dragon.
Further on, in the Shiji · Tianguanshu, Sima Qian writes the four palaces, and begins with four sentences:
「東宮蒼龍，房、心。」「南宮朱鳥，權、衡。」「西宮咸池，曰天五潢。」「北宮玄武，虛、危。」
The eastern palace is the azure dragon, the southern palace the vermilion bird, the northern palace the dark warrior; the western palace, however, is written 「咸池」. Xianchi is the name of an asterism, not a beast. The two characters 「白虎」 occur elsewhere in the Tianguanshu, attached beneath 參; they are the image of that mansion, not the name of the western palace.
That is to say: down to the early Western Han, the western palace had still not been exchanged in writing for the name of a beast.
The four written side by side are fixed only by the Eastern Han. In Zhang Heng’s Lingxian there is a sentence:
「蒼龍連蜷於左，白虎猛據於右，朱雀奮翼於前，靈龜圈首於後。」
At this point four directions, four animals and one fixed arrangement have finally reached the written record.
5. So what is the lower bound
Set the material above into three layers and the answer comes out by itself.
Layer
Latest date
Basis
Dragon and tiger to east and west, Dipper between them
6460±135 years before present (clam-shell radiocarbon, tree-ring corrected)
The shell figures of Xishuipo tomb 45, Puyang
The twenty-eight names and their order as one set
about 433 BCE
Lacquer box E.66, tomb of Marquis Yi of Zeng
Twenty-eight mansions divided by the four directions into four groups, each with one beast
Eastern Han
Zhang Heng’s Lingxian; in the Western Han Shiji the western palace is still 「咸池」
Three dates, spanning from six and a half thousand years ago to the Eastern Han. They do not conflict, because they are talking about three different things.
Go back to the opening sentence: this box has the twenty-eight mansions, and it has the four images too. Strictly speaking, what it can support is the first half. The box gives the twenty-eight names, gives the Dipper, gives the dragon and the tiger; if “four images” is to mean four beasts complete, that must wait several centuries longer.
One reading does not accept this limitation. Huang Jianzhong and others opened the box’s six faces out flat and held that the pattern on the south face is precisely the bird representing the south, and that the north face, blackened over, represents the dark warrior. Were that reading to hold, the four images would in fact be complete on the lacquer box, only distributed over different faces instead of on the lid.
This is 【一说】, and it rests on the identification of patterns. That the south face shows a bird can be argued; whether a black face counts as the dark warrior depends even more on inference. Direct evidence in writing is not this roundabout; a pattern has to be read by eye and argued. The two kinds of evidence do not weigh the same, and in reading they must be counted separately. Where the evidence is a pattern, the reading drawn from it is 【一说】.
So the more accurate formulation is this: the lacquer box from the tomb of Marquis Yi of Zeng pins the lower bound of the twenty-eight-mansion system to the early Warring States, and at the same time supplies the dragon and the tiger, so that the line of “beast paired with direction” can be joined up from below. The step at which the four beasts are complete must wait, in objects and in texts alike.
Henceforth, whenever one meets “so-and-so proves that China had the four images as early as such-and-such a year”, three questions can be put first: which layer does it mean; does it rest on writing or on pattern; and is what it gives a latest date, or a beginning.
The twenty-eight names on the lid were put there for people to look up and identify the sky. But to fix a date by them, one thing is still missing, and that is measuring the length of the shadow each day.
Note on the text
This is a popular exposition, and it makes no claim to original research. The astronomical constants cited are standard values. This English version is issued alongside the Chinese original as the same article in another language. The author’s name is 邝楚嘉, Chujia Kuang; he writes under the pen-name 嘉言一得 (Jiayan Yide).
Declarations
Funding. This research received no external funding.
Competing interests. The author declares no competing interests.
Data availability. No new data were created or analysed in this study.
Language. The original Chinese text is deposited as a companion file to this record.
References
[1] 周禮 [Rites of Zhou]. Pre-Qin.
[2] 呂氏春秋 [Lüshi Chunqiu]. Pre-Qin.
[3] 淮南子 [Huainanzi]. Han.
[4] 史記 [Shiji]. Han.
[5] 張衡. 靈憲 [Lingxian]. Han.
[6] 湖北省博物館. 曾侯乙墓 [The Tomb of Marquis Yi of Zeng]. Beijing: Cultural Relics Press, 1989.
[7] 濮陽西水坡遺址考古隊. 河南濮陽西水坡遺址發掘簡報 [Brief report on the excavation of the Xishuipo site, Puyang, Henan]. 文物 [Cultural Relics], 1988(3).
[8] 清華大學出土文獻研究與保護中心. 清華大學藏戰國竹簡（拾壹）[The Tsinghua University Warring-States Bamboo Slips, vol. 11]. Shanghai: Zhongxi Book Company, 2021.
[9] 黃建中等. 擂鼓墩一號墓天文圖象考論 [A study of the astronomical images in Leigudun tomb no. 1]. 華中師院學報 [Journal of Central China Normal College], 1982(4).
[10] 湖北省人民政府. 《二十八宿圖》衣箱 [The lacquer box with the twenty-eight-mansion diagram]. 荊楚文物·古藏文物, 2015.
Images in this article are illustration only; they are not evidence and not a basis for any statement of fact.
This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to reprint, redistribute, or build upon it, including for commercial purposes, provided you credit the original author as 「嘉言一得（Chujia Kuang 邝楚嘉）」 and include a link to the original publication.
Copyright in the photographs of the excavated objects and in the transmitted texts quoted here remains with their respective rights holders and is not covered by this licence.
For the full terms of the licence, see: https://creativecommons.org
The words 「日有食之」, “the sun was eclipsed”, are familiar to most readers from the Chunqiu, where the entry for the third year of Duke Yin of Lu gives the earliest dated eclipse record in the transmitted literature. Earlier records, however, are incised on oracle bone. This note sorts those inscriptions into three groups and states where each group stands. The Bin-group lunar-eclipse records, five in number, are the only set that can be computed: their stem-and-branch days, their night numbers and their sequence together impose enough constraint to yield a unique solution, and they place the five eclipses between 1201 and 1181 BCE, with the reign of Wu Ding falling about 1250 to 1192 BCE. The Bin-group record known as 「三焰食日」 was once read as a total solar eclipse and the earliest such record in the world; three lines of objection — meteorological, lexical and philological — have since displaced that reading, though one later computation keeps it alive as a minority view. The Li-group records of 「日有食」 and 「日又戠」 remain unresolved even as to what they describe. The note argues that verifiability here turns on constraint: one date gives sixty days and nothing more, whereas five independent records agreeing at once can close a five-hundred-year window to a single set. The piece is descriptive and carries no prediction.
Fig. 1 A Shang dynasty oracle-bone inscription, shown for reference; it is not one of the bones carrying the “eclipse” records discussed here. Source: Wikimedia Commons, “Shang Ox Bone Oracle Bone 01.jpg” (CC0) Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Keywords: oracle bones; solar eclipses; lunar eclipses; Chinese chronology; Shang dynasty; stem-and-branch dating; source criticism
Most readers first meet the four characters 「日有食之」, “the sun was eclipsed”, in the Chunqiu. Under the third year of Duke Yin of Lu, in the second month, on the day ji-si, the sun was eclipsed — the earliest dated eclipse record in the transmitted literature.
Earlier than the Chunqiu is a group incised on oracle bone. They are scattered through the divination inscriptions from Wu Ding down to the end of the Shang, and they vary in form: some give a single stem-and-branch day, some state that it was night, and in some the character for “eat”, that is, for the eclipse itself, cannot yet be read with confidence.
These inscriptions share one feature and one problem. The shared feature is that they are written on turtle shell and ox bone, incised by the people of the time as records of questions they put. The shared problem is that only a small number of them can actually be brought to computation by modern astronomy. For the rest, the difficulty is not that they cannot be computed; it is that the prior question — whether what they record is an eclipse at all — has not been settled.
What follows separates the three heaps of material and states where each of them stands.
1. Three heaps of material, separated
The solar and lunar eclipse records in the oracle-bone inscriptions fall, by excavation group and textual character, into roughly three heaps. Their situations differ widely. The verdicts are given first; each heap is then taken in turn.
Material
Number
Reign
Verdict
Bin group, lunar eclipses
5
Wu Ding to Zu Geng
【通说】 reliability not disputed
Bin group, 「三焰食日」
1 (Jiaguwen Heji 11506)
Wu Ding
【一说】 the eclipse reading is now largely rejected
Li group, solar and lunar eclipses
5 (some count 6)
Li group (its reign attribution is itself disputed)
【待检】 not even the nature is settled
This table is the skeleton of the whole note. The difference between the three heaps lies not only in number but in the degree of scholarly grasp: the first can be computed, the second was computed and then rejected, and over the third there is still argument about whether it records a celestial event at all.
One term should be made clear first. “Bin group” and “Li group” are classificatory group names for oracle-bone inscriptions; they are not personal names and not dynasty names. The classification rests on a combined judgement of script style, diviner and excavation pit, and it is a basic piece of oracle-bone scholarship. It is itself open to discussion, but for present purposes it is enough to know that the three heaps are not one body of material from one period.
2. The heap that can be computed: five Bin-group lunar eclipses
The five records
Within the Bin group is a set of five lunar-eclipse divinations. Their stem-and-branch days and night numbers are, in order:
癸未夕、甲午夕、己未夕皿庚申、壬申夕、乙酉夕.
The character 夕 means “night”. The first, second, fourth and fifth record a single 夕; the third carries an extra character, 皿, which runs a single night across two stem-and-branch days. That one character is the only hard bone in this heap.
The character 皿
There are more than a dozen readings of 皿, and scholarship has not agreed on one. The reading with the widest support at present is Qiu Xigui’s: 皿 read as 向, so that 「己未夕皿庚申」 becomes 「己未夕向庚申」, with 向 in the same sense as in the Shijing phrase 「夜向晨」, “the night turns towards morning” — meaning that the night of ji-wei continued into the morning of geng-shen.
On that reading the eclipse occurred between the night of ji-wei and the morning of geng-shen: a record made at a junction, falling between two days. This matters for the computation that follows, because it is precisely the 向 that narrows the window of the eclipse to half a night.
This reading is 【一说】. Other scholars hold that 皿 should be read literally as 皿, or offer other readings, and the differences bear directly on which night the eclipse fell.
The result of the computation
Modern scholars have compared these five records with the lunar eclipse tables for the Shang period by astronomical back-calculation. Zhang Peiyu concluded that the five eclipses fall between 1201 and 1181 BCE.
The more important sentence is this: in the five hundred years from 1500 to 1000 BCE there is only one sequence of lunar eclipses that satisfies both the stem-and-branch correspondence and the order. That is, if these five records are used to sift all the eclipses of those five centuries, only one set fits, and there is no second.
Working upwards from that result, the reign of Wu Ding is placed between about 1250 and 1192 BCE.
This falls within the interim results of the Xia-Shang-Zhou Chronology Project, and is likewise 【通说】.
Why a unique solution is possible
There is a methodological point here that deserves separate statement.
For an eclipse three or four thousand years ago the available information is very slight: a single stem-and-branch day, a single indication of “night” or “nightfall”, and the single geographical constraint that it was visible around Anyang. Any one of these alone fixes nothing — the sixty-day cycle turns round in sixty days, and in sixty years more than one lunar eclipse is visible at Anyang.
What makes a unique solution possible is not that any one record is especially precise, but that the five records simultaneously satisfy all the constraints. Individually the precision is low; taken together, the constraint is strong. This is the real reason this heap of material can be given serious weight, and it is the watershed between it and the two heaps that follow.
One comparison
Other scholars have proposed different sets of years. Homer Dubs also placed 「己未夕皿庚申」 on 27 December 1192 BCE, in agreement with Zhang Peiyu; but for the remaining four the values diverge. Dong Zuobin, Chen Zunxian, Zhang Guangzhi, David Keightley, Fan Yuzhou and Edward Shaughnessy differ among themselves, and these results are set side by side in a comparative table in the survey by Zhu Fenghan and others.
So the phrase “unique solution” needs qualification: it holds for one particular way of combining the records, not as a claim that each eclipse has only one solution. This point is 【一说】.
3. The heap that was rejected: 「三焰食日」
The text and the weight it once carried
The Bin group contains one further inscription, far better known than the five lunar eclipses. It comes from Jiaguwen Heji 11506, a turtle plastron excavated from pit YH127 at Yinxu. The inscription reads 「乙卯允明雾，三焰食日，大星」 — though the segmentation and the reading of the characters are not entirely agreed.
This record was once taken very seriously. Dong Zuobin, in his Yinli Pu, read it as a total solar eclipse: 「三焰」 were solar prominences, and 「大星」 a planet, Mercury or Venus, visible during totality. Were that reading to hold, the record would not only be the earliest solar eclipse record in China but the earliest solar eclipse record in the world, the earliest record of solar prominences, and the earliest record of a star seen during an eclipse — three firsts at once. Liu Chaoyang dated it to 5 June 1302 BCE; Xu Zhentao computed 4 March 1250 BCE.
This is 【一说】.
The shared difficulty of both readings
Here is the most valuable sentence in the whole section. In introducing these two computations, the survey published by the Purple Mountain Observatory writes: 「此两说之困难皆在于该日是丙辰（乙卯的次日）。」 — “The difficulty of both readings lies in the fact that that day was bing-chen, the day after yi-mao.”
The meaning is this. The inscription plainly says yi-mao, while the day arrived at by both scholars was bing-chen — the next day. For either computation to work, something has to be adjusted, whether in the stem-and-branch reckoning or in the reading of the text.
The difficulty is shared, which suggests that it lies less in the details of computation than at an earlier stage: whether that day was in fact yi-mao, and whether this inscription is in fact recording an eclipse.
Three lines of objection
Later objections came from roughly three directions.
The first is Yang Shuda. In 1945, in Jiwiju Jiawen Shuo, section on the stars, he argued that the inscription actually records weather: 「大星者大晴也」, “the great star means a great clearing”, and that the three inscriptions hold together in sense, describing clear sky and not an eclipse.
The second is Yan Yiping. In 1989, in Shiri Jie, he argued that 「食日」 is in the inscriptions a term of time, denoting a part of the day, and has nothing to do with an eclipse. His explanation is that 「食日」 is 「大食」, the name of one of the divisions of the day.
The third is Li Xueqin. He wrote a study specifically on the inscription, San Yan Shiri Boci Bianwu, working through the problems of reading comprehensively and formally rejecting the eclipse interpretation.
Taken together, these three lines largely overturned the record’s claim to be an eclipse.
What the Chronology Project did with it
The Xia-Shang-Zhou Chronology Project rejected it: it is not used as a record of a total solar eclipse. Zhang Peiyu also pointed out that no total solar eclipse visible at Anyang occurred on a yi-mao day during the reign of Wu Ding. This rejection is 【通说】.
One surviving branch
The record has not been buried completely, however. Pang and others later re-read the characters 「允明」 in the inscription as 「于明」, pushing the date forward by one day and so evading the yi-mao difficulty; the result still falls on 5 June 1302 BCE, at 10:45 local time at Anyang, with totality lasting 6 minutes 20 seconds. From this they derived a value for the earth-rotation parameter ΔT: about 7.3 hours, with an uncertainty of plus or minus 0.3 hours.
This is 【一说】. It coexists with the rejection, and both must be stated; only one side cannot be written.
One further remark is needed, to avoid misunderstanding. That ΔT value is inferred backwards from the premise that this record holds. It therefore depends on the record, and cannot be used as independent evidence to establish the record. This is a circle, and in writing it must be written as a circle.
4. The heap that cannot be computed: Li-group 「日有食」 and 「日又戠」
The third heap comes from the Li-group inscriptions, and is the most complicated in situation.
How many
The Li group contains six records of 「日有食」, though the way they are combined differs and some scholars count five. The sources are roughly: Fushi Yin-Qi Zhengwen, Heaven section, 1, appearing twice; Yicun 374, which is Jiaguwen Heji 33694, appearing twice; Jingjin 3695, which is Heji 33695; Tunnan 379; Lin 1.10.5, which is Heji 11480; and Heji 11481.
There are in addition three records of 「日又戠」 and one of 「月又戠」.
The disagreement between five and six arises because different scholars treat Heji 11480 and 11481 differently, as to whether they count and whether obverse and reverse are listed separately. This point is 【待检】.
What is disputed
The first dispute concerns a character. The character below 日 is read by some as 夕, by some as 月, and by others as a combined graph read 明. There is still no agreement.
The second dispute concerns 戠. Whether 戠 is 食, “eclipse”, is also disputed. Guo Moruo first pointed out that the two were close in sound and so interchangeable; Chen Mengjia took it to refer to sunspots, an explanation that fell once the phrase 「月又戠」, “the moon again 戠”, was found.
The third dispute is the most serious: whether these inscriptions are divination texts or verification records. If they are divinations, the question asked being whether an eclipse would occur, then the statement in the text that there was no eclipse on the day gui-you does not by itself constitute counter-evidence. If they are verification records, set down after the fact as a statement of what happened, the problem is serious indeed. This step decides the issue.
Yang Shengnan’s reading
In recent years Yang Shengnan has offered another explanation in On the 「癸酉日食」. He holds that the character may indeed be read 明, but that the phrase 「明有食」 is not of a kind with the formulations used in the inscriptions for solar and lunar eclipses; and that the end of this inscription, and the whole plate on which it stands, also contain material concerning sacrifice to Shang Jia. On that basis he concludes that the group of inscriptions is in fact a divination about offering food, 「侑食」, to Shang Jia, and is not an eclipse record.
This is 【一说】. It pushes the character of the whole heap a long way towards sacrifice and away from celestial event.
What the Chronology Project did with it
The date of the Li-group inscriptions, and the question whether what they record is a solar or lunar eclipse, have long been in dispute. The expert group of the Xia-Shang-Zhou Chronology Project treated them thus: these records are for the time being not used as a basis for discussing late Shang chronology.
There is one inconsistency here that must be stated. The survey from the Purple Mountain Observatory, discussing the same matter, writes that “chronological results have also been obtained for another group of four solar and lunar eclipse records from the Li group”. One statement says the records are not used as a basis for the time being; the other says chronological results have been obtained. Both formulations exist side by side within the same discipline.
No choice between them is made here; both are simply set down.
5. So how far can verification go
Return to the table at the beginning. Three heaps of material, three situations, and together they show something more important than any single record.
First, the lunar eclipses can be computed because three constraints lie on top of one another: there is a stem-and-branch day, there is a night number, and there is an order. No one of the three suffices to fix a year; all three together close the range to a single set.
Second, solar eclipses are hard to compute because the constraint is too loose. A single stem-and-branch day for a solar eclipse locks in sixty days only; and in sixty years more than one solar eclipse is visible around Anyang. One record fewer means one layer of constraint fewer, and the solution disperses.
Third, move the reading and the conclusion changes. The three characters 皿, 戠 and 食日 have each been revised. They are not quibbles over detail: they determine directly whether the record counts at all, and which kind of celestial event it counts as.
Fourth, what can be said reliably along this whole line is mostly of the form “this cannot hold”, and seldom of the form “this certainly holds”. Among the three heaps, 「三焰食日」 belongs to the first kind, and the five Bin-group lunar eclipses are the rare computable exception. This asymmetry is not because the method is incomplete; it is because of the nature of the material — a record three thousand years old leaves only this much to hold on to.
This piece and 001 are two ends of one thing. 001 concerns a single set of numbers which, put together, yield a spread of eight thousand years. This end concerns the same heap of inscriptions, among which one must first sort out which few ought never to have been computed at all. Without the second, the first computes in vain, however precisely.
One thread is left hanging. The men of Shang knew a good many stars, and their inscriptions show attention to the Great Fire, to the Bird star, and to certain celestial events. But they had no twenty-eight-mansion coordinates — that division of the sphere into twenty-eight compartments was drawn later. When it was drawn is left to the next piece.
Note on the text
This is a popular exposition, and it makes no claim to original research. The astronomical constants cited are standard values. This English version is issued alongside the Chinese original as the same article in another language. The author’s name is 邝楚嘉, Chujia Kuang; he writes under the pen-name 嘉言一得 (Jiayan Yide).
Declarations
Funding. This research received no external funding.
Competing interests. The author declares no competing interests.
Data availability. No new data were created or analysed in this study.
Language. The original Chinese text is deposited as a companion file to this record.
References
[1] 尚书 [Book of Documents]. Pre-Qin.
[2] 诗经 [Book of Songs]. Pre-Qin.
[3] 春秋 [Spring and Autumn Annals]. Pre-Qin.
[4] 甲骨文合集 [Jiaguwen Heji]. Ed. Guo Moruo. Beijing: Zhonghua Book Company, 1978–1982.
[5] 董作宾. 殷历谱 [Yinli Pu]. 1945.
[6] 杨树达. 积微居甲文说 [Jiwiju Jiawen Shuo]. 1945.
[7] 严一萍. 食日解 [Shiri Jie]. In 甲骨古文字研究, second series. Yee Wen Publishing, 1989.
[8] 张培瑜. 甲骨文天象记录和商代历法 [Astronomical records in oracle-bone inscriptions and Shang calendrics]: concluding report of the Xia-Shang-Zhou Chronology Project. 1996–2000.
[9] 刘次沅, 马莉萍. 夏商周断代工程中的几个天文学问题 [Several astronomical questions in the Xia-Shang-Zhou Chronology Project]. Journal of Guangxi University for Nationalities, 2004, 10(1): 23–29.
[10] 杨升南. 说「癸酉日食」 [On the 「癸酉日食」]. Yindu Journal, 2019(2): 8–11.
[11] 李学勤. 三焰食日卜辞辨误 [Correcting the reading of the 「三焰食日」 inscription]. Journal name and year to be verified.
Images in this article are illustration only; they are not evidence and not a basis for any statement of fact.
This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to reprint, redistribute, or build upon it, including for commercial purposes, provided you credit the original author as 「嘉言一得（Chujia Kuang 邝楚嘉）」 and include a link to the original publication.
Copyright in the excavated Qin and Han bamboo-slip photographs and in the transmitted texts quoted here remains with their respective rights holders and is not covered by this licence.
For the full terms of the licence, see: https://creativecommons.org
Fig. 1 A chart of the twenty-eight mansions. The twenty-eight mansions laid out as a chart. A related diagram shown for reference, not an original discussed here. Source: Wikimedia Commons, “Twenty-eight mansions.jpg” (Public domain) Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Abstract
Fewer than fifty characters in the Shangshu, Canon of Yao, give four stars for the four seasons: the Bird at the spring equinox, Fire at the summer solstice, Xu at the autumn equinox, Mao at the winter solstice. Since the nineteenth century this passage has been used repeatedly to fix the date of “the age of Yao”. The results range from 8800 BCE to 1000 BCE — a spread of nearly eight thousand years from the same words and the same numbers. This note asks why the numbers will not agree. It sets out the four stars and the reading of them as dusk culminations, introduces precession as the mechanism that moves them, and examines Zhu Kezhen’s 1926 computation, in which three stars fall in the late Shang or early Zhou while Mao alone falls in the twenty-fourth century BCE. Six adjustable assumptions are then enumerated — the hour of observation, the identity of Fire, the identity of the Bird, the coordinate system used, the place of observation, and whether the text was written at one time — each of which shifts the date by centuries. A table sets the competing datings side by side. The note closes with the hypothesis that the four stars were never observational data but an institutional model of fourfold symmetry, and with an account of the scholarly dispute over the passage in early twentieth-century Japan and China. The piece is descriptive and carries no prediction.
Keywords: Canon of Yao; four fixed stars; precession; Chinese astronomy; astronomical chronology; Shang and Zhou chronology; history of science
Fig. 2 The Dengfeng observatory. Built under Guo Shoujing in the Yuan dynasty; the shadow-measuring terrace and the scale rule both survive. A related structure shown for reference, not an object discussed here. Source: Wikimedia Commons，Dengfeng Observatory.jpg（CC BY-SA 2.0） Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Introduction: one sentence, four numbers, seven millennia
The Shangshu, Canon of Yao, contains a passage of fewer than fifty characters:
日中，星鸟，以殷仲春。日永，星火，以正仲夏。宵中，星虚，以殷仲秋。日短，星昴，以正仲冬。
Four seasons — spring equinox, summer solstice, autumn equinox, winter solstice; four stars — Bird, Fire, Xu, Mao. It looks as clean as a table.
Since the nineteenth century, many have used it to compute the date of “the age of Yao”. The computers have been Chinese, Japanese and European; the instruments have included precession, ecliptic coordinates, equatorial coordinates, proper motion and horizontal-calendar simulation. The results run from 8800 BCE to 1000 BCE, a spread of nearly eight thousand years.
One sentence, one set of numbers, and answers scattered widely enough to hold a whole history of civilisation. That is what this first piece in the series is about: a set of numbers that will not agree, and why they will not.
1. Driving the four pegs in first
Translate the passage into modern terms. The ancients had no clocks and no telescopes, but they had one extremely reliable thing: each day after sunset, in the window when the sky had just gone dark — the hun, dusk — they looked up at the southern meridian to see which star stood there. That star is called the dusk culmination. Because the earth goes round the sun, the sky we face at dusk changes daily and completes one circuit in a year, so the dusk culmination is a natural hand on a calendar dial.
The Yaodian gives:
Season
Length of day
Dusk culmination
Quadrant
Spring equinox
日中, equal day and night
Bird
Vermilion Bird of the south
Summer solstice
日永, longest day
Fire (the Great Fire)
Azure Dragon of the east
Autumn equinox
宵中, equal night
Xu
Dark Warrior of the north
Winter solstice
日短, shortest day
Mao (the Pleiades)
White Tiger of the west
Reading the four fixed stars as the dusk culminations of the equinoxes and solstices is the standard view 【通说】.
Note one detail: Bird, Fire, Xu and Mao each occupy the middle position of one quadrant. The middle of the Vermilion Bird is the mansion Xing; the middle of the Azure Dragon is Xin (or Fang); the middle of the Dark Warrior is Xu; the middle of the White Tiger is Mao. These are not four stars picked at random; they form a fourfold symmetrical figure. That point will come back to us.
Another sentence should be kept in mind as well: 「期三百有六旬有六日，以闰月定四时成岁」 — “the period is three hundred and sixty-six days, and by intercalary months the four seasons are fixed and the year completed”. Three hundred and sixty-six days is the second number the Yaodian supplies, and it too will not agree with observation (the tropical year is about 365.2422 days). But that is not today’s business. Today we keep our eyes on the four stars.
2. Why the numbers move: precession
The key is a term the ancients did not know at all: precession.
The earth’s axis turns slowly like a spinning top, drawing a circle in the sky with a period of about twenty-five thousand eight hundred years, though values differ slightly between authorities. Two consequences follow. First, the pole star changes office: around 3000 BCE it was Thuban; around 1000 BCE it was Kochab; in the Sui and Tang it was Polaris V; and it is only in the Ming and Qing that Kochab’s companion properly earns the name. Second, the equinoctial points recede slowly along the ecliptic, at about one degree in seventy-one years.
The implication is this: the seasons your grandfather fixed by the lunar mansions have already shifted by the time of your grandson. Not much — a single generation cannot feel it. But across a thousand years it amounts to fourteen degrees, nearly the width of thirty full moons.
The first person bruised by these numbers was Yu Xi of the Eastern Jin, around 330 CE. He compared the Yaodian with the sky of his own day and found the discrepancy: the text put the mansion Mao at the meridian at dusk on the winter solstice, but what he saw was already the mansion Bi. He did not doubt the book, and he did not doubt his eyes. He guessed a third possibility — that the sky itself moves.
His figure was “one degree in fifty years”. One detail needs to be made clear here: this “degree” is the ancient degree. The Chinese ancient degree divides the circle into 365.25 parts, and one ancient degree is about 0.9856 modern degrees; modern measurement gives about one degree of westward shift in 71.6 years. The two numbers cannot be compared directly. Yu Xi’s sentence survives in a quotation in the Songshi, Treatise on Pitch Pipes and the Calendar.
Precession was discovered earlier in the West: Hipparchus, in the second century BCE, fixed it at “one degree in a hundred years”. But the figure closer to the true value is Yu Xi’s “one degree in fifty years” — and the West went on using Hipparchus’s older value for a long time afterwards. To discover later and to compute more accurately are two different things, and should not be collapsed into one sentence. As for putting precession formally into calendrical computation, that was Zu Chongzhi’s Daming calendar of 463 CE: the first time in the history of the Chinese calendar.
Which is to say: the value of those four numbers in the Yaodian lies precisely in their being wrong. Had they agreed exactly with the sky of the Jin dynasty, Yu Xi would never have discovered precession in his life. The mismatch itself is an entry on the credit side of Chinese astronomical history.
3. Zhu Kezhen’s computation: three in 1100, one in 2400
In December 1926 the meteorologist Zhu Kezhen completed “On Dating the Four Fixed Stars of the Shangshu, Canon of Yao, by Precession”, published the following year in Science, volume 11, number 12. It was among the first modern astronomical treatments of a classical problem. The historian Xu Xusheng (also known as Xu Bingchang) later wrote in the preface to The Legendary Age of Ancient Chinese History: 「欢喜赞叹，感未曾有！余以为必须如此才能配得上说是以科学的方法整理国故！」 — “joy and admiration, such as I have never felt! I hold that only in this way does one deserve to be said to be reorganising the national heritage by scientific method.”
His conclusion was the least tidy possible:
Bird, Fire and Xu all fall in the late Shang or early Zhou, roughly the eleventh to tenth centuries BCE; Mao alone falls in the age of the legendary emperor Yao, around the twenty-fourth century BCE.
Four records, two dates, a thousand years apart.
Here the first kind of disagreement appears: the numbers do not conflict with reality; they conflict with one another. The same author, the same observation, the same instruments could not have measured the winter solstice in 2400 BCE and waited until 1100 BCE to measure the other three seasons.
Scholarship accordingly divided into two responses. One holds that this shows the Yaodian was compiled in the late Shang or early Zhou, and that “Mao” is a copied old text or a scribal error. The other holds that it shows Yao did exist, and that the other three were inserted by later hands. The same data will carry a story in either direction — and at that point, solving the problem has become choosing one.
4. Six knobs that can be turned
Why can the spread reach eight thousand years? Because the degrees of freedom in this problem are startling. Every assumption you turn shifts the date by centuries. There are at least these six knobs:
1. Dusk culmination, dawn culmination, or midnight culmination?
The text says only 「星鸟」 and 「星火」; it does not name the hour of observation. The tradition takes early dusk. Take instead the dawn culmination, before first light, and the whole celestial sphere turns through half a revolution, shifting the date by a full step at once. Recently some have argued that the four mansions refer to the sun’s station (日躔), the mansion the sun occupied, rather than to a culmination. On that reading the date moves directly to about 8800 BCE, on the ground that the four mansions form the four cardinal nodes of the ecliptic. This view is noisy online, but its price is steep: the date, the text and the archaeology of the whole Yaodian must be rewritten, and the reference list is frequently blank. It is 【待检】.
2. Which star is Fire?
The old commentaries already quarrel with one another: some say Antares (α Scorpii, the brightest, and the reading most follow today), some say the mansion Fang, some say the mansion Wei, some say between Di and Fang. Shinshin Shinnichizō took Antares; Zhu Kezhen also inclined to Antares. Change the star and the right ascension differs by a dozen degrees, with a date shift of nearly a thousand years.
3. What is the Bird?
Harder still. 「星鸟」 may mean the single star Xingxiu yi, or the seven mansions of the Vermilion Bird generally, or the stretch of Liu, Xing and Zhang. Zhu Kezhen himself reached no conclusion: he wrote that of Bird, Fire, Xu and Mao only Xu and Mao are “relatively definite”, while the Bird spans three groups — Chunshou, Chunhuo and Chunwei — a total of a hundred and twelve degrees, and cannot be precisely specified. One unsettled question, propping up half of a chronology.
4. Equatorial or ecliptic coordinates?
Ancient Chinese astronomy was equatorial — the distances of the twenty-eight mansions are equatorial distances — while Western precession theory grew on the ecliptic. Converting between the two systems introduces a systematic bias.
5. Where was the observation made?
Was it made at one place, Pingyang, the capital of Yao in what is now southern Shanxi? Or was it, as the text says, made by men sent to four places — Yanggu in the east, Nanjiao in the south, Meigu in the west, Youdu in the north? Zhu Kezhen assumed one place. In 1983 Zhao Zhuangyu computed separately for the four places using their own latitudes and longitudes and obtained about 2060 BCE, which falls squarely inside the window of the Yao-Shun age. Change the place and the date moves three hundred years.
6. Was the text written at one time?
Perhaps the most honest answer is this: the four records never belonged to one observation. They may be a compilation of material from different periods, or a supplement by later hands working from fragmentary old reports, or even a construction made to complete a fourfold scheme.
Six knobs, each worth centuries, and several thousand years between them in combination. So the conclusions that keep the interval very tight — such as the “2485 to 2478 BCE” circulating online — have a false precision: that is not the precision of measurement, it is the precision of assumption.
5. The datings side by side
Claim
Date proposed
Key assumption
Sun’s-station reading (online)
c. 8800 BCE
the four mansions are the sun’s positions at the equinoxes and solstices, not culminations
David Pankenier, He Nu and others
2300–2000 BCE
Taosi observatory and gnomon pole combined, early second millennium
Zhao Zhuangyu (1983)
c. 2060 BCE
four observers sent to the four quarters
Zhang Wenyu
c. 2000 BCE
Xia-dynasty sky
Zhu Kezhen (1926)
three in the 11th–10th centuries BCE; Mao in the 24th
dusk culmination, Antares, one place of observation
Standard textbook account
no later than the late Shang or early Zhou
the conservative form of Zhu’s view
One passage of scripture. One “scientific method”. In this table there is not a single cell that satisfies everybody’s assumptions at once.
6. Another possibility: they were never data
I want to put forward a possibility that is less popular but deserves to be taken seriously.
Look again at the four stars: Bird, Fire, Xu and Mao, each at the middle of its quadrant. On the celestial sphere they roughly form a cross, cutting the circle into four equal parts. That is structurally too neat — too neat to look like an observational record, and more like a design.
The core task of early calendrics was to establish a frame, not to measure precisely: to fix the four quarters, the two solstices and the two equinoxes, the intercalary month, and the figure of three hundred and sixty-six days. To give an agrarian society a usable order of time, what is needed most is a model that is symmetrical, memorable, teachable and promulgable. Taking the middle star of each of the four images is the natural form of such a model. As for the actual sky differing from the model by ten or twenty degrees, that is a tolerable error in the face of the political function of “reverently bestowing the seasons upon the people” — indeed it is a puzzle that later hands were required to explain, and explaining it is exactly what Yu Xi did.
If that judgement holds, then asking “which year’s sky those four stars belonged to” is asking a question the ancients never intended to answer. It is like taking the offices in the Rites of Zhou and going to look up the headcount of the Western Zhou civil service.
But this does not make the passage a forgery. On the contrary, it may be older than any single observation: the structure of four quarters, four culminating stars, two solstices and two equinoxes, and an intercalary month very likely does come from a much earlier age in which astronomical observation served as a technology of royal power. The observatory at Taosi, where the gaps between rammed-earth columns correspond to the sunrise positions at the solstices, and the lacquered pole from a royal tomb that is thought on good grounds to have been used for gnomon shadow measurement, both indicate that such an age really existed, and that whoever could measure the shadow and fix the calendar held legitimacy. What the Yaodian preserves is the institutional memory of that age, not its observing log.
The date of an institutional memory and the date of an observation are two different kinds of date. Confusing them is the root of why these numbers will not agree.
What this section argues is my inclination, not a settled conclusion, and is recorded here as 【待检】.
7. The fight behind the numbers
One further layer cannot be left out. These numbers were never only an astronomical question.
In 1909 Shiratori Kurakichi advanced the “theory that Yao, Shun and Yu are fabricated”. It appeared in August of that year as “A Study of Ancient Chinese Legends” in Tōyō Jihō, number 131. Iijima Tadao then used astronomical methods to date the ancient texts, concluding that the Chinese calendar was established in the fourth or third century BCE, just after the eastern campaigns of Alexander — the theory of a Western origin for Chinese astronomy. Shinshin Shinnichizō entered the dispute because of the question of the date of the Yaodian raised by Kano Naoki, professor at Kyoto Imperial University, and refuted the case point by point from an astronomical background. The two sides debated for more than ten years and each produced a book (Iijima’s A Theory of Ancient Chinese History, Shinshin’s A Study of the History of Eastern Astronomy). One focus of the dispute was the astronomy of the Yaodian.
Notice: the same precession formula, turned one way, yields “fabrication”; turned the other way, it yields “trust the ancients”. Scientific method did not abolish position here; it merely provided position with a more respectable coat. Zhu Kezhen’s article provoked “joy and admiration” not only because his computation was right, but because for the first time it gave the quarrel a shared set of rules of engagement — even though victory on that field still depended on which star you took as marker.
This is something I want to keep returning to throughout the series: when a number carries both evidence and belief at once, the human mind is usually hidden somewhere inside its error bar.
8. What can be read out of it
Back to the title. From a set of numbers that will not agree, I read four things.
First, the mismatch is a source. Yu Xi’s precession grew out of the crack between the Yaodian and the Jin-dynasty sky. Data that are wrong can be more productive than data that are right, provided they are honestly wrong.
Second, precision is not accuracy. To state the interval as “2485 to 2478 BCE, within about eight years” is dangerous because it dresses the certainty of assumption as the certainty of measurement. A real answer in astronomical chronology should come with a long list of premises, and most quoters copy only the conclusion.
Third, asking the wrong question is commoner than computing the wrong number. If the four fixed stars are essentially an institutional model of four quarters, then “which year does it belong to” is a category error. A better question would be: when could this fourfold frame first have taken shape, and how many times was it rewritten in transmission?
Fourth, and the layer I care about most: when the author, or compiler, of the Yaodian wrote down these four words, he probably had no idea that he was leaving an insoluble problem for people three thousand years later. He was doing something quite plain — moving the visible order of heaven down to earth for use. And we come back to him with a precession formula and ask him for the year. He cannot answer, so we answer for him, in several dozen versions.
Perhaps we should think the other way round: a set of numbers that people are still arguing over after three thousand years is itself proof that it was looked at, used and handed down with care. The true value may not be in it, but time is.
As for that other number that will not agree — where “the period is three hundred and sixty-six days” came from, and how it fights with the tropical year, the synodic month and the intercalary month — the series will come to it later.
Appendix: firm facts and soft inferences
Reasonably secure: the text of the Yaodian; the standard reading of the four fixed stars as the dusk culminations of the equinoxes and solstices; the precession period of about 25,800 years and the shift of about one degree in 71.6 years; Yu Xi’s discovery of precession and his use of the Yaodian to reason back; Zu Chongzhi’s first inclusion of precession in a calendar; Zhu Kezhen’s conclusion of three in the late Shang and early Zhou and one in the age of Yao; the existence of the Taosi observatory and of the lacquered gnomon; the more systematic tables of dusk and dawn culminations in the Yueling and the Lüshi Chunqiu.
Contested: which star Fire and the Bird designate; whether the observation was made at one place or four; when the Yaodian was compiled (Shang, early Zhou and Warring States are all proposed); whether the four mansions may be the sun’s stations.
My own inclination, unprovable: that the four fixed stars are first of all an institutional model of fourfold symmetry, and only secondly, or partly, an observational record; so that its value for absolute dating is low.
Note on the text
This is a popular exposition, and it makes no claim to original research. The astronomical constants cited are standard values. This English version is issued alongside the Chinese original as the same article in another language. The author’s name is 邝楚嘉, Chujia Kuang; he writes under the pen-name 嘉言一得 (Jiayan Yide).
Declarations
Funding. This research received no external funding.
Competing interests. The author declares no competing interests.
Data availability. No new data were created or analysed in this study.
Language. The original Chinese text is deposited as a companion file to this record.
References
[1] 尚书 [Book of Documents]. Pre-Qin.
[2] 宋史 [History of Song]. Tuotuo 脱脱 et al. Yuan.
[3] 礼记·月令 [Liji: Yue Ling]. In 礼记 [Liji]. Pre-Qin to Western Han.
[4] 吕氏春秋 [Lüshi Chunqiu]. Lü Buwei 吕不韦 et al. Late Warring States.
[5] 竺可桢. 论以岁差定《尚书·尧典》四仲中星之年代 [On dating the four fixed stars of the 「Yaodian」 in the Shangshu by precession]. 科学 [Science], 1927, 11(12).
[6] 徐旭生. 中国古史的传说时代 [The Legendary Age of Ancient Chinese History]. 1943.
[7] 祖冲之. 大明历 [Daming calendar]. Liu-Song, 463.
[8] 新城新藏. 东洋天文学史研究 [A Study of the History of Oriental Astronomy]. Tokyo: Kobundo, 1928.
[9] 饭岛忠夫. 支那古代史论 [Essays on Ancient Chinese History]. Tokyo: Toyo Bunko, 1925.
[10] 白鸟库吉. 支那古传说之研究 [A Study of Ancient Chinese Legends]. 东洋时报 [Toyo Jiho], 1909(131).
[11] 赵庄愚. 《尧典》四仲中星与尧都平阳 [The four fixed stars of the 「Yaodian」 and the Yao capital at Pingyang]. Journal name and year to be verified.
[12] 中国社会科学院考古研究所山西队. 山西襄汾县陶寺城址祭祀区大型建筑基址2003年发掘简报 [Brief report on the 2003 excavation of a large rammed-earth foundation in the ritual area of the Taosi city site, Xiangfen, Shanxi]. 考古 [Archaeology], 2004(7).
[13] 周髀算经 [Zhoubi Suanjing]. Author unknown. Western Han (date of compilation disputed).
Images in this article are illustration only; they are not evidence and not a basis for any statement of fact.
This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to reprint, redistribute, or build upon it, including for commercial purposes, provided you credit the original author as 「嘉言一得（Chujia Kuang 邝楚嘉）」 and include a link to the original publication.
Copyright in the excavated Qin and Han bamboo-slip photographs and in the transmitted texts quoted here remains with their respective rights holders and is not covered by this licence.
For the full terms of the licence, see: https://creativecommons.org
Fig. 1 The shell mosaics of tomb M45 at Xishuipo, Puyang. An extended supine burial with a shell dragon to the east and a shell tiger to the west. The prehistoric-astronomy reading is a hypothesis and remains disputed; shown here for reference only. Source: Wikimedia Commons, “Human Burial and shell mosaics. National Museum, Beijing .JPG” (CC BY-SA 4.0) Copyright remains with the original photographer or institution; please contact this site for removal if needed.
Abstract
A star-chart application on a phone answers the question “what is out there”. A Tang-dynasty star chart or a Song-dynasty engraved celestial map answers a different question: “where are we, and how should we live”. This preface to a series on ancient Chinese astronomy sets out the method rather than the findings. It argues that celestial observation in early China was a matter of state: the calendar fixed the times of sowing and of taxation, and the sky supplied the observable evidence that political legitimacy required. Against that background the series adopts a narrow definition of evidence — only claims traceable to observable, checkable, comparable material are treated as such, and everything beyond that is labelled as inference. Two kinds of material are used in harness: transmitted texts, which supply the frame, and excavated material, which X-rays it. Three conventions govern the reading: no formulas, a strict separation between astronomy and astral divination, and an explicit label on every contested point. The note is methodological; it makes no original claim and no prediction.
Keywords: history of astronomy; ancient Chinese calendrics; oracle bones; transmitted texts; source criticism; astral divination; archaeology of astronomy
Fig. 2 A Chinese compass. A directional scale combined with a magnetic needle. A related instrument shown for reference; no original sinan has ever been excavated, and the modern object is a reconstruction, which this image does not stand in for. Source: Wikimedia Commons，Antic chinese Compass.jpg（Public domain） Copyright remains with the original photographer or institution; please contact this site for removal if needed.
1. Two charts: why look up at all
Load a star-chart application on a phone and point it at the night sky. Constellation lines, planetary names, satellite orbits — even the minute at which the International Space Station will pass overhead — appear on the screen at once. The chart is clean, immediate and available to anyone. Behind it lie several centuries of celestial mechanics, several generations of survey telescopes, and a globally shared coordinate system. It answers the question “what is out there”.
Set an old star chart beside it — the Dunhuang chart of the Tang dynasty (S.3326), for instance, or the celestial map engraved on stone at Suzhou in the seventh year of Chunyou in the Southern Song. The first renders more than thirteen hundred stars in fine ink, graded by brightness, with the Milky Way drawn as a washed band and the distances of the twenty-eight lunar mansions written alongside. The second places the north celestial pole at its centre: more than fourteen hundred stars between the inner and outer circles, the ecliptic and the equator crossing obliquely, and a text on the structure of heaven and earth engraved at the side.
Neither chart is immediate, and neither is convenient. They do not tell you where to look at this moment. What they do is compress an entire account of time, order and human affairs into lines and dots of ink. They answer the question “where are we, and how should we live”.
Hence the first question: why go back to a sky that modern astronomy has already explained completely?
The answer has to be sought on the ground.
For the people of early China, heaven was an institution. The calendar was the state’s public clock: when to sow, when to tax, when to promulgate the month and to announce it at the ancestral temple — all of it was settled by the calendar. The stars were the instruction manual of political legitimacy; the mandate of heaven required observable evidence to back it. Anomalies and auspicious signs were among the few soft restraints on sovereign power. A revision of the calendar therefore touched finance, ritual, imperial authority and scholarship at once; a single failed prediction of a solar eclipse could cost an astronomer his office, or give a coup its pretext.
When we look up today, we are in fact looking at the people who wrote the stars into the institutions.
There is a more practical reason as well: this sky is disappearing. Light pollution means that a child in the city may go a whole year without identifying the Dipper. Over the same period we are losing, on an unprecedented scale, the capacity to understand what the ancients experienced. When 「七月流火」 is reduced to an adjective for midsummer heat, and 「参商不相见」 survives only as a line in a dictionary of idioms, we have lost not only the poetry but the key to an entire intellectual world. So the first reason for doing empirical work is a plain one: before the memory is gone altogether, verify what can still be verified.
As for myself, the starting point was more modest. How my forebears sowed their seed, how they looked up and recognised stars, how they wrote the stars they recognised into a calendar — these have interested me for a long time. Accumulated over the years, that interest became the series that begins here: an exposition, section by section, of how the ancients observed the sky and how they made their calendars, together with the anecdotes attached to both.
2. Two legs: transmitted texts and excavated material
The word “empirical” has a precise and narrow sense in this series: only a claim that can be brought to bear on material that is observable, re-checkable and comparable counts as empirical; anything beyond that is labelled as inference without exception.
The rule comes from an uncomfortable fact. The transmitted literature of ancient Chinese astronomy and calendrics is almost entirely a layered product.
The clearest example is the Ganshi Xingjing. The title sounds like the original work of Gan De and Shi Shen in the Warring States period, but the book was long ago dispersed; what survives is largely text copied and re-copied through encyclopaedias and divination compendia of the Tang and later, supplemented by later hands and in places attributed to authors who never wrote it. To argue from it directly for a Warring States star catalogue is to hold a Qing mirror up to a Warring States face. The Kaiyuan Zhanjing, by contrast, has value precisely because it does not compose: Gautama Siddha copied out long passages from works now lost, and recorded his sources, so the text is traceable.
Transmitted texts supply the frame. Frames may have been reassembled by later hands.
The function of excavated material is to X-ray that frame. A century of archaeology has turned the field from a branch of textual criticism into a genuinely empirical discipline:
The lacquer chest from the tomb of Marquis Yi of Zeng (c. 433 BCE): the names of the twenty-eight lunar mansions are written in vermilion on the lid, with the Azure Dragon and White Tiger painted alongside. This is the earliest systematic set of mansion names yet found, and it pins the lower limit of the system firmly to the early Warring States.
The silk manuscript Wuxing Zhan and the comet chart from Mawangdui: the first gives numerical values for the synodic periods of the five planets, of surprising accuracy; the second classifies comets by shape, and is among the earliest comet-morphology charts in the world. Together they show that Han observation had a quantitative tradition, not merely divinatory formulas.
The Rishu from the Qin bamboo slips of Shuihudi and Fangmatan: these show how a local community used the calendar and selected days for its affairs — a rare sample of calendrics descending into daily life.
The calendar registers and daily logs among the Han slips from Juyan and Dunhuang: dates, weather and distances recorded day by day by frontier clerks, and thus first-hand evidence for how the Han calendar actually ran.
The Suzhou engraved celestial map and the star chart in the Liao tomb at Xuanhua: transverse coordinates of comparison for the traditions of star-drawing under different regimes and different cultures.
The point of walking on two legs is mutual correction: excavated material punctures the later embellishments of a transmitted text, and the transmitted text supplies context for fragmentary slips. A conclusion resting on one leg only is unfinished by the standard of this series.
The boundary of the empirical must be stated at the same time. Some things the material does not permit us to establish:
Silence is not absence. The absence of a record of a particular kind of omen in a period means only that none has been found so far; it does not follow that none existed. Archaeology samples; it cannot conduct a census.
The world of meaning in astral divination cannot be tested experimentally. We can check whether a given eclipse occurred and whether it was recorded; we cannot check what the ancients read into it when they wrote 「君有忧」, “the ruler has cause for concern”. That is the business of intellectual history. Astronomy cannot reach it.
Back-calculation has hard limits. To project an event three thousand years into the past by modern celestial mechanics, the accumulated error from the long-term change in the earth’s rotation (ΔT) has to be handled. For the same eclipse the computed time and zone of visibility may differ by tens of minutes and hundreds of kilometres. There is a further layer: ancient records often served political ends — good news reported and bad news suppressed, observations written up after the fact, errors of copying. A record of an omen that “came true” may have had the event first and the phenomenon attached afterwards.
Falsification is far more powerful than confirmation. This is the methodological floor of the series: we can say reliably that a given claim could not hold, but we can seldom say that a given claim certainly does.
Two examples show where the boundary lies:
The clam-shell dragon, tiger and Dipper at Xishuipo M45 in Puyang, Henan (c. 4500 BCE): the image certainly exists, and the orientation of the dragon and tiger is certainly suggestive. But to read it as a prototype of the four images or of the Dipper requires bridging a gap of six thousand years in the material. It is a hypothesis. It has not reached the point of a conclusion.
The observatory at Taosi in Xiangfen, Shanxi (c. 2100 BCE): the excavators proposed that thirteen rammed-earth columns formed observation slots from which the solstices could be determined. After publication, the scholarly response raised a series of objections concerning the formation of the column trenches, the feasibility of observation, and the chronological fit. It remains a proposal awaiting test, and should not be written into textbooks as settled.
Only by admitting the boundary does the field stand up. The argument now turns to how those positions are to be applied in reading, which requires three conventions.
3. Three conventions of reading
Convention one: no formulas.
This series will not derive calendrical procedures, will not set out spherical trigonometry, and will not give a single line of astronomical algorithm. This has nothing to do with disparaging technique. Quite the opposite: those computations are highly specialised, and I should not relay them in a half-understood form. Where computation enters, I will state three things only — what record went in, what result came out, and where the error may come from. Readers who wish to pursue it will find primary sources and specialist studies listed at the end, and it is there that the real formulas live.
Convention two: astronomy and astral divination are strictly separated.
Modern Chinese tends to run the two together; in antiquity they were two distinct operations:
Astronomy
Astral divination
Object
Observable positions, periods, moments
Correspondences between celestial phenomena and human affairs
Method
Measurement, record, computation, verification
Drawing images, analogy, interpretation
Testability
Recomputable, re-checkable
Not falsifiable (interpretations are always adjustable)
Stance of this series
Treated as history of science
Treated as intellectual and political history
That is to say: I will discuss the star-officer system of the Shiji, Treatise on the Celestial Offices, and its observational basis seriously; I will also discuss its underlying logic of power seriously. But I will not use today’s astronomy to “prove” that a divinatory formula worked, nor will I dismiss the whole thing with the word “superstition”. To prove a divination formula by modern astronomy is pseudoscience; to dismiss it in one word is laziness.
Convention three: every contested point is labelled.
This is the most tightly fixed convention of the series. Wherever scholarship has not reached agreement, an explicit label is attached, and no single scholar’s view is written up as fact. There are three levels:
【通说】 tongshuo: accepted by most researchers, on a fairly complete chain of evidence.
【一说】 yishuo: maintained by a substantial number of scholars, but on insufficient evidence or with competing explanations.
【待检】 daijian: a hypothesis only, with no key evidence yet available to test it.
For example: “Of the solar eclipses recorded in the Chunqiu, most can be matched by modern back-calculation 【通说】”; “The event recorded as 「天再旦于郑」, ‘the sky dawned twice at Zheng’, is the eclipse of 899 BCE and can serve as a chronological anchor 【一说】”; “The Xishuipo clam-shell figures represent a prototype of the Dipper and the four images 【待检】”.
Believe what you will, but you can always find out which of them you are believing.
4. So this is where it begins
In 1054 the Song astronomical office recorded a “guest star”. The Songshi, Treatise on Astronomy, notes: 「至和元年五月己丑，出天关东南可数寸，岁余稍没」 — “on the ji-chou day of the fifth month of the first year of Zhihe it appeared a few inches southeast of the celestial gate, and faded after more than a year”. The Song Huiyao, chapter 52, adds that it 「昼见如太白，芒角四出，色赤白，凡见二十三日」 — “was visible by day like Venus, with rays spreading in four directions, of a reddish-white colour, and was seen for twenty-three days in all”.
Nine hundred years later astronomers identified that region as the “celestial gate” of the Song record, which is the Crab Nebula. But when they used the expansion rate to run the clock backwards, the date they obtained was eighty to a hundred and twenty years later than 1054. The mismatch forced a new recognition: the nebula is expanding at an accelerating rate.
To my mind, this is what empirical work looks like at its most moving: a sentence copied for nine hundred years, and an instrument invented nine hundred years later, addressed to the same question. Even when the first number failed to agree, it was an encounter. In that moment the ancients’ act of looking up and our act of looking down met.
The aim of this series is to find as many such points of contact as possible. Where none can be found, that too will be marked honestly.
As for where the first contact point lies, the next piece will show. Four thousand years ago a tribal leader had to decide when to sow. He had neither clock nor calendar.
5. Where the series is going
The structure first. The series is arranged chronologically: the pre-Qin period first, then Qin and Han, then down to Ming and Qing. The first collection, “Sources of Pre-Qin Calendrics”, begins with qualitative observation — a time when there were no coordinates and no degrees, and the only instruments were the stars overhead and the changing length of day and night.
No.
Title
Status
Preface
Between Looking Up and Looking Down: The Origin of an Empirical Study of Ancient Chinese Astronomy and Calendrics
this piece
001
The Four Fixed Stars of the Yaodian: A Set of Numbers That Will Not Agree
forthcoming
002
The Verifiability of the Oracle-Bone Records of 「日有食之」
forthcoming
003
The Twenty-Eight Mansion Chart on the Lacquer Chest of Marquis Yi of Zeng: A Lower Limit for the Four-Image System
forthcoming
004
Gnomon Shadow Measurement and 「日至」: The Observational Tradition before the Dengfeng Observatory
forthcoming
005
The 「Zhuanxu Calendar」 and the Archaeological Evidence for Qin and Early Han Calendrics
forthcoming
006
The Taichu and Santong Calendars: Errors in the Synodic and Intercalation Cycles
forthcoming
007
The Gnomon Data in the Zhoubi Suanjing and the Twelve-Month Deity Chart on the Chu Silk Manuscript (one of the two)
to be selected
008
Closing Piece: Where the Verifiable and the Unverifiable Divide
forthcoming
What the collection sets out to answer can be put in one sentence: in a time without clocks and without coordinate systems, on what basis did people fix their days.
Note on the text
This is a popular exposition, and it makes no claim to original research. The astronomical constants cited are standard values. This English version is issued alongside the Chinese original as the same article in another language. The author’s name is 邝楚嘉, Chujia Kuang; he writes under the pen-name 嘉言一得 (Jiayan Yide).
Declarations
Funding. This research received no external funding.
Competing interests. The author declares no competing interests.
Data availability. No new data were created or analysed in this study.
Language. The original Chinese text is deposited as a companion file to this record.
References
[1] 尚书 [Book of Documents]. Pre-Qin.
[2] 史记 [Records of the Grand Historian]. Sima Qian 司马迁. Western Han.
[3] 春秋 [Spring and Autumn Annals]. Pre-Qin.
[4] 宋史 [History of Song]. Tuotuo 脱脱 et al. Yuan.
[5] 宋会要辑稿 [Song Huiyao Jigao]. Compiled by Xu Song 徐松. Qing.
[6] 甘石星经 [Ganshi Xingjing]. Attributed to Gan De 甘德 and Shi Shen 石申. Warring States (the present text is a later reconstruction, attributed to Tang–Song and after).
[7] 瞿昙悉达. 开元占经 [Kaiyuan Zhanjing]. Tang.
[8] 长沙马王堆汉墓帛书整理小组. 五星占 [Wuxing Zhan]. In 马王堆汉墓帛书: 肆. Beijing: Wenwu Press, 1985.
[9] 睡虎地秦墓竹简整理小组. 睡虎地秦墓竹简 [Shuihudi Qinmu Zhujian]. Beijing: Wenwu Press, 1990.
[10] 甘肃省文物考古研究所. 居延新简 [Juyan Xinjian]. Beijing: Wenwu Press, 1990.
[11] 敦煌星图（S.3326）[Dunhuang star chart, S.3326]. Tang manuscript. London: British Library.
[12] 苏州石刻天文图 [Suzhou stone-carved star map]. Engraved in the seventh year of Chunyou, Southern Song (1247). Suzhou: Suzhou Stele Museum.
[13] 湖北省博物馆. 曾侯乙墓 [Tomb of Marquis Yi of Zeng]. Beijing: Wenwu Press, 1989.
[14] 河南省文物考古研究所. 濮阳西水坡遗址发掘报告 [Excavation report of the Xishuipo site, Puyang]. 文物 [Cultural Relics], 1988(3).
[15] 中国社会科学院考古研究所山西队. 山西襄汾县陶寺城址祭祀区大型建筑基址2003年发掘简报 [Brief report on the 2003 excavation of a large rammed-earth foundation in the ritual area of the Taosi city site, Xiangfen, Shanxi]. 考古 [Archaeology], 2004(7).
[16] 太初历 [Taichu calendar]. In 汉书·律历志 [Book of Han: Treatise on Pitch Pipes and the Calendar]. Ban Gu 班固. Eastern Han.
[17] 三统历 [Santong calendar]. In 汉书·律历志 [Book of Han: Treatise on Pitch Pipes and the Calendar]. Ban Gu 班固. Eastern Han.
[18] 周髀算经 [Zhoubi Suanjing]. Author unknown. Western Han (date of compilation disputed).
Images in this article are illustration only; they are not evidence and not a basis for any statement of fact.
This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to reprint, redistribute, or build upon it, including for commercial purposes, provided you credit the original author as 「嘉言一得（Chujia Kuang 邝楚嘉）」 and include a link to the original publication.
Copyright in the excavated Qin and Han bamboo-slip photographs and in the transmitted texts quoted here remains with their respective rights holders and is not covered by this licence.
For the full terms of the licence, see: https://creativecommons.org
答：目前主流的判断是「不是」。董作宾等人曾把它释为日全食，刘朝阳、徐振韬各给出过具体年份，但两家的推算都卡在同一个困难上——卜辞写的是乙卯，他们算出的日子干支是丙辰。后来杨树达、严一萍、李学勤分别从气象、时间辞、释读三个方向提出质疑，夏商周断代工程最终否定了日食说。不过 Pang 等人近年仍有新算，这条恐怕不算彻底定案。
