标签归档： Chinese astronomy

最后修订时间：2026年10月18日

Chujia Kuang (邝楚嘉)

Independent Researcher, Jieyang, Guangdong, China

Corresponding author: Chujia Kuang, Independent Researcher, Jieyang, Guangdong, China. Correspondence: kuangchujia.com/contact

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

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:

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

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

Related articles

• Between Looking Up and Looking Down: The Origin of an Empirical Study of Ancient Chinese Astronomy and Calendrics — the preface: two legs, three conventions of reading.
• The Verifiability of the Oracle-Bone Records of 「日有食之」 — the same heap of inscriptions, and which few of them may be computed at all.
• Three Calendars, Three Kinds of Time — the three scales, and what each is set to.

Chinese editions: 尧典四仲中星：一组对不上的数字（the original Chinese text of this essay） ｜ 抬头与低头之间：古天文历法实证研究的缘起 ｜ 甲骨文「日有食之」诸条的可核验性 ｜ 三本历法·三种时间 ｜ 立春换岁，还是正月初一换岁？ ｜ 立春不是一整天，只有一秒钟 ｜ 正月本来不是一月 ｜ 节与气：二十四节气的两半 ｜ 尧帝派人看星星，是为了种地 ｜ 古人的一天，从晚上十一点开始 ｜ 钟表上的出生时间，不等于你出生的时辰 ｜ 时间是怎么产生的？ ｜ 天上三条道：黄道、白道、赤道 ｜ 古人的星空：三垣与二十八宿 ｜ 没有指南针，古人怎么定方向 ｜ 干支：从一棵树到二十二个字 ｜ 十个字配十二个字，为什么只剩六十组

Site hubs: Glossary ｜ Calendar Reform ｜ Publications

All data in this article were collected and compiled by Chujia Kuang.

作者：嘉言一得（邝楚嘉）｜独立研究者，致力于可核验的原始文献与历法数据归档。
Author: Chujia Kuang (邝楚嘉), pen name Jiayan Yide (嘉言一得) — independent researcher devoted to archiving verifiable primary sources and calendar data.
平实记录 · 数据集 · 预印本：GitHub / WordPress / Zenodo（DOI: 10.5281/zenodo.22788686 ／ 10.5281/zenodo.23028692）
Records · Datasets · Preprints: GitHub / WordPress / Zenodo
学术身份 · Academic identity：ORCID 0009-0002-7650-833X ｜ OpenAlex A5151908354

最后修订时间：2026年10月18日

Chujia Kuang (邝楚嘉)

Independent Researcher, Jieyang, Guangdong, China

Corresponding author: Chujia Kuang, Independent Researcher, Jieyang, Guangdong, China. Correspondence: kuangchujia.com/contact

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

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:

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.

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

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• The Verifiability of the Oracle-Bone Records of 「日有食之」 — three heaps of inscriptions, three positions; only a small part can be computed at all.
• Three Calendars, Three Kinds of Time — the three scales, and what each is set to.

Chinese editions: 抬头与低头之间：古天文历法实证研究的缘起（the original Chinese text of this essay） ｜ 尧典四仲中星：一组对不上的数字 ｜ 甲骨文「日有食之」诸条的可核验性 ｜ 三本历法·三种时间 ｜ 立春换岁，还是正月初一换岁？ ｜ 立春不是一整天，只有一秒钟 ｜ 正月本来不是一月 ｜ 节与气：二十四节气的两半 ｜ 尧帝派人看星星，是为了种地 ｜ 古人的一天，从晚上十一点开始 ｜ 钟表上的出生时间，不等于你出生的时辰 ｜ 时间是怎么产生的？ ｜ 天上三条道：黄道、白道、赤道 ｜ 古人的星空：三垣与二十八宿 ｜ 没有指南针，古人怎么定方向 ｜ 干支：从一棵树到二十二个字 ｜ 十个字配十二个字，为什么只剩六十组

Site hubs: Glossary ｜ Calendar Reform ｜ Publications

All data in this article were collected and compiled by Chujia Kuang.

作者：嘉言一得（邝楚嘉）｜独立研究者，致力于可核验的原始文献与历法数据归档。
Author: Chujia Kuang (邝楚嘉), pen name Jiayan Yide (嘉言一得) — independent researcher devoted to archiving verifiable primary sources and calendar data.
平实记录 · 数据集 · 预印本：GitHub / WordPress / Zenodo（DOI: 10.5281/zenodo.22788686 ／ 10.5281/zenodo.23028692）
Records · Datasets · Preprints: GitHub / WordPress / Zenodo
学术身份 · Academic identity：ORCID 0009-0002-7650-833X ｜ OpenAlex A5151908354