Episode 41: Liu Xin's Theory of Everything

April 25, 2024

After Wang Mang deposed the Han Dynasty and instituted his new Xin Dynasty, he needed to promulgate a new calendar to mark the occasion. One of his court astronomers, Liu Xin, developed a new calendar that integrated the lunar and solar cycles with the planetary cycles and imbued it with numerological significance. We then talk about how Huan Tan, another astronomer of the era, would have gone about measuring the lunar mansions.


Good evening, and welcome to the Song of Urania, a podcast about the history of astronomy from antiquity to the present with new episodes every full moon. My name is Joe Antognini.

Well, last month I tried to give a fuller picture of what a calendar reform looked like in early Imperial China by chronicling the events of more than a century that led up to the calendar reform of 104 BC. In earlier episodes I had tried to emphasize the importance of setting the calendar as a symbol of Imperial authority. This month we’ll look at the subsequent calendar reform that was instituted at the start of the short-lived Xin dynasty and introduced the so-called Triple Concordance system of Liu Xin. Then we’ll turn to one of the most important features of Chinese astronomy, the system of hsiu, or lunar mansions.

As with the earlier calendar reform of 104 BC, the events that led up to the calendar reform under the Xin Dynasty began with a period of political dysfunction and fecklessness followed by a coup from a more capable leader. But in this case, the timeline of events that led to the establishment of the Triple Concordance system was accelerated relative to the earlier calendar reform. So in this episode we can begin our story just a few decades before the main event rather than a century before as we did in the last episode.

Now, in the last episode we talked about the establishment of the Han dynasty, the second imperial dynasty in China, and walked through the first few emperors until we got to Emperor Wu, who established the new calendar for the Han dynasty in 104 BC. The early Han dynasty was a relatively successful period in the history of China in part because the empire was fortunate enough to have a string of emperors who were competent administrators. This bout of good luck lasted for another half century or so, and the middle of 1st century BC under the reign of Emperor Xuan is generally considered to be the high water mark of the Earlier Han Dynasty. But all good things must come to an end, and after the death of Emperor Xuan there was a sequence of progressively less and less capable emperors. The first few of these were not exactly malevolent in the way that, say, an Emperor Nero or Caligula was in the Roman Empire. They just did not quite seem to be up to the task. They were generally indecisive and, more importantly, didn’t have strong control over their bureaucracy. So, over the decades factionalism became more pronounced, and, even worse, corruption started to get out of control. Towards the end of the 1st century BC, the Emperor Cheng died, yet another ineffectual emperor in what was by now a long line of ineffectual emperors. Emperor Cheng, however, died suddenly, and relatively young, at the age of 44, and left no obvious heirs. He had had two sons with concubines, but his consort, Zhao Hede, had had both them and their mothers killed with the Emperor’s tacit consent, one by suffocation and the other by starvation.

It’s around this time that a man named Wang Mang enters the picture. The Wang clan had been on a meteoric ascent in just a generation or two. Now, this wasn’t exactly a rags-to-riches story, the Wang clan had always been well off. But Wang Mang’s aunt was a woman named Wang Zhengjun and she had been born in 71 BC as the second daughter of the Minister of Justice. This was a high position in Chinese society, to be sure, but it was still some ways away from the top. The Minister of Justice was one of nine ministers, who in turn reported to the Three Councillors of State, who, in turn, reported to the Emperor himself.

Well, sometime around 55 BC, the consort of the Crown Prince Liu Shi died. Inconsolable, the prince wanted to have nothing to do with the other concubines in his harem. After some time, to try to get him out of his funk, his father, the Emperor Xuan, arranged for his son to meet a new set of women that he could choose from. Wang Zhengjun was one of the six women who went to meet the Crown Prince. Of these, the prince selected her to be his new consort, apparently for no other reason than that she happened to be sitting closest to him. Nevertheless, this happenstance arrangement was the breakthrough that the Wang clan needed. In time, Wang Zhengjun gave birth to a son, in fact, Liu Shi’s first son. And a few years later the Emperor died and Liu Shi ascended to the throne, taking the name Emperor Yuan, which meant that Wang Zhengjun went from being the second daughter of the Minister of Justice to an Empress of China.

Well, with this turn of events the Wang clan had an inside track in court politics. According to the histories, most of the members of the family parlayed their family position for high living. But Wang Mang was different. He didn’t seem to be attracted to wealth and dressed in the refined, but modest outfit of a Confucian scholar and used his considerable means to support a gaggle of Confucian scholars around him. Rather than living off on a grand estate out in the country, he lived within the palace complex.

This unassuming demeanor was key to his growing stature. He was quietly competent in a time when each emperor was more incompetent than the next, and, being in the heart of the Imperial machinery, he was in a position to exert some influence. With his lavish support of Confucian scholars, he brought this powerful faction of the court lockstep behind him.

So, to get back to the original thread, when Emperor Cheng died in 7 BC and left no obvious heirs, Wang Mang was in an exceptional position to influence the selection of the next emperor, and more importantly, to influence the next emperor himself if he was sufficiently pliant. Now whether or not he had conceived of any plans for ultimate power at this point isn’t really clear, and if he did, it didn’t quite work out for him in the near term. The next emperor, Emperor Ai, ascended to the throne at the age of 20, but ended up falling almost completely under the control of his step grandmother, the Empress Dowager Wang. Wang Mang clashed with the Empress Dowager on a few occasions but was soon forced to resign from his position as commander of the army.

Well, Emperor Ai had always been sickly. What exactly his illness was is not clear, but whatever it was, he died from it six years after ascending to the throne. This put his step grandmother, the Empress Dowager Wang in an awkward position. While Emperor Ai had technically been married, he was fairly open about his homosexuality, and his real partner was a minor official named Dong Xian. Later chroniclers described their relationship as the “passion of the cut sleeve,” in reference to a story in which the two had fallen asleep in each others arms. Upon waking and finding the sleeve to his Imperial robe still trapped under Dong Xian, the Emperor cut his own sleeve off rather than wake his lover. Well, over the six years of his rule, Emperor Ai lavished Dong Xian with ever higher offices, and by the time of Emperor Ai’s death, Dong Xian had become one of the most powerful men in the Chinese court and a rival to the Empress Dowager. In fact, on his deathbed Emperor Ai had pronounced Dong Xian to be his successor. So the Empress Dowager Wang put aside her differences with Wang Mang and joined forces with him to box out Dong Xian from having any role in the subsequent reign. Together, they planted an eight-year-old boy named Liu Jizi on the throne, where he adopted the name Emperor Ping. Being too young to rule in his own right, the Empress Dowager appointed Wang Mang to be regent. To further consolidate his grip on power Wang Mang then arranged for his daughter to be married to the emperor.

This was a successful strategy for a few years, but once the emperor became a teenager, Wang Mang began to worry that the boy would get thoughts of his own. To make matters worse, an awkward episode had occurred a few years earlier. Wang Mang’s son, along with several of the emperor’s uncles, had attempted a coup to wrest power away from the increasingly dominant Wang Mang. They had been discovered and Wang Mang had them all put to death, including his own son. But as Emperor Ping got older, Wang Mang worried that he might not be too happy about the fact that Wang Mang had killed all of his uncles. So he nipped this problem in the bud by poisoning the Emperor. At this point Wang Mang had become so powerful that he essentially had free reign in choosing the next emperor. The last few emperors had all died so young that they had no heirs and so the closest candidates for succession were all quite distant in the imperial line. Wang Mang settled on Ruzi Ying, who, conveniently enough, was only one year old, and so wouldn’t cause any trouble for quite some time.

At this stage, Wang Mang’s long game of bringing the court scholars and officials onto his side began to pay off. Over the next three years a series of auspicious omens started to trickle in, and a chorus of officials in court began to propose, first obliquely, and later loudly, that he assume the title of emperor. Finally, in 9 AD, Wang Mang held a formal ceremony, in which he and the four-year-old Emperor stood before the Imperial Court together. Wang Mang held the child’s hand and performatively wept before the child “for a long time.” He then explained to the child before the whole court that the Han Dynasty had been blessed by the Mandate of Heaven for many years, but that the great Han Dynasty had come to an end. Now the Mandate of Heaven had fallen to him. According to the Han Shu, he said

Oh Emperor Ying! Formerly August Heaven supported your Great Ancestor [Liu Bang, the founder of the Han], so his descendants succeeded for twelve generations, and possessed the state for two hundred and ten years, [but now] the sequence of reckonings rests on my person.

This last phrase, the “sequence of reckonings,” is “li shu,” and in essence referred to the authority to set the calendar. Shortly after taking the throne, Wang Mang created seven high ministers and associated each one with one of the planets, with the exception of Saturn, instead substituting in the Big Dipper. For example:

Jupiter has charge of conscientiousness; [under its patronage] the Grand Master of the Eastern Peak sees to it that timely rain comes about, and by its cerulean brilliance he promotes peace, examining the shadow using a gnomon.

Each of these ministers was not only associated with a planet, but also an astronomical measurement. In this case it was measuring the shadow from a gnomon. The minister associated with Mercury was tasked with the keeping of the water clocks and the minister associated with the Sun was associated with the compass — the kind you draw circles with, not the kind you find north with.

Well, having at long last formalized his de facto rule, Wang Mang took much less time adopting the ritualistic symbols of a new dynasty than the Han dynasty had two centuries before. Now, you may recall from the last episode and the one before that, that an important feature of Chinese semiotics was the “wuxing” system in which the five fundamental elements of earth, metal, wood, water, and fire existed in various relationships to each other. Each dynasty had been associated with an element. Now, traditionally, the elements associated with subsequent dynasties had been assigned to the so-called destructive or conquest cycle. So, since the Zhou dynasty had been associated with fire, the following dynasty, the Qin dynasty, should be associated with water, since water extinguishes fire. This seems natural. But in the century leading up to this new Xin dynasty, a new line of thought started to become more popular among the scholars. As you may have intuited by this point, particularly among Confucian factions, continuity with the past was highly prized. Even when a rebel king or an ambitious official effectively seized absolute power for himself, he was very slow to formally adopt the title of Emperor and would do so only after years of laying the appropriate groundwork and at the urging of the court. In the case of the Han dynasty the first Han Emperor had to be persuaded into the role and it took about a century for the Han Emperors to formally declare themselves to be a new dynasty. With the Xin dynasty we just saw how the new Emperor stood before the court with the former emperor to emphasize this continuity with the past. Given this attitude, scholars of the time wondered whether the destructive or conquest cycle of the wuxing was really appropriate to describe dynastic successions. After all it has connotations of violence, conquest, and, well destruction. But wasn’t it really more appropriate that these dynastic successions be associated with the more peaceful generating cycle instead? There was a change, yes, from one dynasty to the next, but each dynasty grew out of the one that came before, rather than destroying it and replacing it with something new.

So, over the course of the Han dynasty, some time after the calendar reform, the idea started to become popular that the true element associated with the Han dynasty was not Earth, as had been previously assumed, but Fire. Scholars went all the way back to Shang dynasty, which had been associated with the element of metal. But in the generating cycle, metal is followed by water, since water condenses onto metal. The Zhou dynasty was thus associated with water. Then the Qin dynasty was associated with wood, since water nourishes wood. And thus the Han dynasty was associated with fire, since wood feeds fire. This meant that when Wang Mang established his new Xin dynasty, it was associated with Earth, since fire produces ash.

Well if you can remember all the way back to the beginning of this episode, my point in talking about all this was to talk about the system that Liu Xin implemented. Liu Xin was an esteemed scholar and astronomer and was a friend and staunch supporter of Wang Mang. Liu Xin had been among those who laid the political and intellectual groundwork for Wang Mang to take the imperial title. When Wang Mang finally established his new dynasty, Liu Xin was intimately involved in setting the new calendar.

Now, if you remember from the last episode, in the calendar reform of 104 BC, the idea had been to set as the starting point of the new calendar the winter solstice of 105 BC because this day happened to not only be the winter solstice, but it was also the first day of the month, or in other words, a new moon, and on top of that, it was the first day of the sexagenary cycle. And this coincidence of events only occurred every 4617 years. So much of the work in developing the calendar in this older reform in 105 BC was in setting an alignment between the yearly cycle of solstices with the monthly cycle of lunar phases along with the 60 day sexagenary cycle.

For this latest calendar reform to inaugurate the new Xin dynasty, Liu Xin’s main innovation was to introduce the motions of the planets into the cycles of the calendar. Now at this point in the history of astronomy in China the planets had been, of course, observed and recorded for some time, but their motions hadn’t been integrated into the calendar at all. Based on the past records, Liu Xin determined the periods of motion of each of the planets and then multiplied them all together to get the time it took for all five planets to end up in exactly the same spot — 138,240 years. Then, multiplying by the length of the lunar cycle, the solar cycle, and the sexagenary cycle, he ended up with the time it took the entire cosmos to return to its origin — 23,639,040 years. This was the so-called triple concordance.

Now, I mentioned this length of time two episodes back, but one of the things that is maybe a little unusual for the modern mind to understand about it was that it was not purely empirical. Today, when we go and measure the periods of the planets, we do so under the implicit assumption that they could be more or less anything. We just have to go out and measure them to see what they really are. But for Liu Xin and other astronomers in pre-modern China it was not generally believed that astronomical periods could be just anything. It was assumed that the numbers associated with the heavens were suffused with numerological meaning. So this meant that when Liu Xin was setting out this calendar he had a delicate dance that he needed to do. The various numbers that he defined in his calendar which represented things like the periods of the planets, the length of the year, and so forth, had to have numerological significance, so he couldn’t just do some sort of best-fit analysis on the data he had. At the same time, he couldn’t simply make up the numbers according to purely numerological methods. The periods had to be in more or less plausible agreement with the data he had. Now, fortunately for Liu Xin, the data, particularly for the planetary motions, was noisy enough that there was a fairly wide range of numbers he could pick and still be in decent agreement with past observations. Generally the planets were recorded on their first appearance, but the date of the first appearance was calculated for when the planet was 15° away from the Sun, which is usually a few days after the planet is actually visible in the sky. For the astronomers of this period, a prediction was seen to be successful as long as the planet appeared before it was predicted to. And, even setting aside any observational errors, the length of the synodic periods of the planets is intrinsically variable due to the eccentricity of the Earth’s orbit.

As an example of how this interplay of observation and numerology worked, we can look at the case of Jupiter. The basic idea was that the synodic period of each planet was, in turn, given as a multiple of the length of the year, and this multiple was given as a fraction, with a whole number in the numerator and denominator. The numerator, called the year number, had particular numerological significance and the denominator, called the appearance number, was less important numerologically. So the strategy was to use numerology to come up with the numerator and then set the denominator so that the period agreed with the observed data. In the case of Jupiter, the year number was 1,728. To arrive at this number, Liu Xin took the element that corresponded to Jupiter, which was wood, as well as the following element in the destructive cycle — metal, since metal chops wood. Each of these elements was associated with a number, 3 for wood and 4 for metal. Multiply these together and you get twelve. Then you multiply by 144, called the Chthonic reckoning, which has its origin in the I Ching. This gives you 1,728. Divide by the appearance number of 1583 and multiply by the length of the year, and you get 398.7 days for the synodic period of Jupiter, which is just five hours off from its true value of 398.9 days.

The numerological process to arrive at this number for Jupiter is fairly straightforward, but other parameters in the calendar were trickier to derive. The numerology for the lunation factor, in particular is quite involved, but in the end Liu Xin got a lunar period which was just 24 seconds off from the modern day value. And these techniques also extended to the prediction of lunar eclipses. This calendar of Liu Xin has been described as a kind of “theory of everything” from the early Imperial period. It united all the periodic phenomena observed in the heavens with numerological underpinnings.

One of the unique things that Liu Xin then did with his calendar is he went back and used it to predict the state of the heavens at different points in the past. He goes back all the way to some of the earliest events recorded in Chinese history. The first of these was the fall of the Xia Dynasty after it was conquered by the Shang. Liu Xin was able to determine that in 1751 BC Jupiter was in an auspicious position for the Shang Dynasty. Now this was not an especially rigorous test since as far as we can tell, he simply found a date that looked good for the Shang Dynasty without any independent evidence that 1751 BC was when the Xia Dynasty fell, and in any case it doesn’t seem likely from the historical record that the Xia Dynasty actually existed in the first place. He was also able to reconstruct the sky in 1122 BC, the traditional date of the fall of the Shang dynasty to the Zhou dynasty, and found the positions of Jupiter, the Moon, the Sun, and Mercury. Now, from a modern perspective the Zhou Dynasty is now known to have conquered the Shang dynasty about a century after Liu Xin thought, but nevertheless this was the first time in Chinese history that an astronomer had taken a model of the motions of the heavens and then rewound it to go back in time and see what the sky looked like during a momentous event in the past.

Liu Xin’s backdating techniques got more stringent as he approached his present day. By the Warring States Period we now start to see records which were filled with astronomical observations, and, being believed to have been authored or edited by Confucius himself, were highly regarded, and so were believed to be quite accurate. Now, fortunately for Liu Xin, over shorter time periods, any errors in his system would have had less time to build up, and at any rate, some of these observations were the very same ones he used to derive his parameters, so generally speaking he was able to reproduce various observations at different points in Chinese history. There are a couple of places where modern historians of astronomy have noted that his system disagreed with the past observations, particularly when it came to eclipses. But if he noticed these irregularities, Liu Xin said nothing about them, he simply omitted them from his descriptions.

Well, in the last episode, before I got into all the details, political and astronomical, around the development of these various calendar reforms, my reason for bringing them up was to talk about one area of Chinese astronomy that we haven’t explored yet, but which I’ve referenced on a few occasions — the hsiu, or the lunar mansions.

At the most basic level, the lunar mansions were a way of identifying the positions of stars and planets in the heavens. In this way they played a similar role that the zodiac did in Greek astronomy. Just as Ptolemy recorded the positions of stars and planets with respect to the signs of the zodiac, Chinese astronomers recorded positions with respect to the 28 lunar mansions.

Now, the system of lunar mansions seems to be quite old in Chinese astronomy. The earliest artifacts that reference the lunar mansions are oracle bones which date to the 14th century BC. But there is circumstantial evidence that the system may be even a millennium older than that. As I’ll talk about in more detail in a bit, the system of lunar mansions was fundamentally an equatorial system — the 28 lunar mansions all spanned roughly even widths around the celestial equator. Each mansion was represented by a particular star or asterism. If we look at where these stars are on the sky, though, they aren’t exactly on the celestial equator. But if we go back to 2400 BC, due to the precession of the equinoxes, we find that many of the representative stars for the lunar mansions fall much closer to where the celestial equator was at the time. So it’s possible that the system may have had its origin back that far.

To get more details about the system of lunar mansions we have to go farther ahead of that in history, though. The oldest artifact with the complete system of all 28 lunar mansions is a box that was buried in a tomb in 433 BC, but this artifact simply lists their names. The first really detailed record we have of the lunar mansions was written in a book called the Huai Nan Zi in 139 BC. Each lunar mansion was given a name, a star or asterism to identify it, and its width. These widths were given in units of “du,” which is the average distance that the Sun travels on the sky in one day. The widths of all of the lunar mansions are given as whole numbers of du, except for the seventh, the “winnower,” which has a width of 11 ¼ du. So, if you add the widths of all the du up, you get 365 ¼, the number of days in the year, just as you would expect.

So, how were the widths of the various lunar mansions determined in the first place? The Huai Nan Zi doesn’t say, but if we move forward another century and a half or so we get a more detailed account by an astronomer named Huan Tan. Huan Tan was active during the tail end of the Earlier Han Dynasty and then the Xin Dynasty. He seems to have had some political acumen, or at least an instinct to keep himself out of trouble, because he managed to maintain his position in the court during the transition from the Earlier Han Dynasty to the Xin Dynasty, and then back to the Han Dynasty as it reasserted itself again in 25 AD. It perhaps helped that although he held respectable positions, he also wasn’t exactly the most powerful person around. His father had been the Director of Music and the highest position he himself ever attained was that of “lang,” which is usually translated as Court Scholar or Gentleman. In his own day he was best known for his musical talents. Apparently the greatest controversy he stirred in his career was the style of music he played on the lute which was described as “licentious.” But, among his various scholarly activities it seems that at one point in his career he was in charge of running the clepsydras, or water clocks. He wrote:

Formerly, when I served as a Court Scholar, I was in charge of the clepsydra. If [conditions varied between] dry and humid, cold or warm, then there were different [measurements]. So in order to have timings for dusk and dawn, daylight or nighttime, I checked against the solar shadow in the daytime, and in the night portion [of the clepsydra run] I checked against the stellar lodges. Thus I got the correct [measurement].

Evidently Huan Tan took his job seriously. As it happens, we have a pretty good idea of what one of Huan Tan’s water clocks may have looked like. In 1977 a clepsydra was unearthed in the Inner Mongolia region. This is a bit far flung from the capital at Chang’an which suggests that precision measuring equipment was widely dispersed across the empire, and that presumably astronomical observations took place all over. Conveniently, the clepsydra was inscribed with details about its manufacture. It says that it is a bronze clepsydra made in Qianzhang. It says that it weighs 32 “jin,” and that it was manufactured in the fourth month of the second year of the Heping period, which corresponds to the year 27 BC, so just a few decades before Huan Tan was working. Incidentally, these kinds of inscriptions are common on official equipment manufactured in Imperial China and indicated that the bureaucracy kept careful track of its inventory.

Well, this particular clepsydra was not terribly large. It had a diameter of about 20 cm and stood about half a meter tall. It had a spout at the bottom for the water to flow out. At the top there was a kind of rack. A vertical rod could be attached to the rack and it would have a floatation device at its end. The rod would have gradations on it, and based on its position relative to the horizontal bars of the rack the user could read off the water level.

Now, one of the disadvantages of a simple outflow clepsydra like the one found in Inner Mongolia is that it does not produce a constant rate of flow. When the vessel is full, the water pressure is higher and the water streams out more rapidly, so the water level falls more quickly. But towards the end of the run, once the water level is low, the water just trickles out, and the water level falls more slowly. In later Chinese history, sometime after the Han Dynasty, more sophisticated kinds of water clocks were devised similar to the ones we talked about in Egypt back in Episode 32. These would have multiple stages where one tank would continually supply water to the main chamber with an overflow gutter around it. This would keep the main chamber continually topped up so that the water pressure at the bottom of the main chamber was always constant and the outflow rate was always the same. But in Huan Tan’s time these more sophisticated clepsydras had yet to be invented and he just had a simple outflow clepsydra to work with. But given the records we have, Huan Tan was clearly a careful observer, he was accounting for things like changes in humidity and temperature when making his observations, so surely he would have been aware that the outflow rate slowed down from the beginning of the run to the end, since that’s pretty much the most basic thing you can observe about it. Although we don’t know exactly how he and other astronomers of the period dealt with this problem there are two things he could have done, depending on the size of his water clock. Now, unfortunately we also don’t know how large a water clock the imperial astronomers used. The clepsydra specimen we have is one that was discovered out in the boonies rather than one in the capital, so it’s possible that the official one in the capital was quite a bit larger. If it was quite large, so that a full run would take approximately a day, the astronomers probably would have had some assistants manually top off the clepsydra once the water level had dropped a certain level. This would have kept the outflow rate approximately constant. If the official clepsydra was smaller, more of the size of the one discovered in Inner Mongolia, then it may have taken roughly only 10 to 20 minutes to empty. In this case, the change in rate from beginning to end wouldn’t have been as much of a factor since the astronomers would be doing dozens of runs one after the other during a 24 hour period. The basic unit of time that they would be measuring would simply be time it took the vessel to empty, and they could use the graduated rod to get the fraction of the last run. The second option seems somewhat more likely since the basic unit of time in the era was the “ke,” and there were 100 ke in a day, which works out to 14 minutes and 24 seconds. Though, as an aside, one of the changes that was introduced during Wang Mang’s calendar reform when he officially established the Xia Dynasty was that he changed the value of the ke so that there were 120 ke in a day instead of 100 ke. At any rate, in either case both techniques relied on having diligent operators immediately fill the water clock back up again when it was time to do so in order to keep accurate time.

Okay, so that’s a little bit about how the astronomers of the period used to measure time, but what specifically were they measuring and how did this help them determine the lunar mansions? Now as I mentioned earlier, one of the unique things about the lunar mansions is that it was an equatorial system rather than an ecliptic system. In the West, in Babylonian and Greek astronomy, and later on in European astronomy, the positions of the planets were measured using the zodiac, and the zodiac was 12 equal divisions of the ecliptic. Now, in many ways this is a natural system for measuring the positions of the Sun, Moon, and planets, because their paths all follow the ecliptic, so you just have to measure their positions against the reference stars along the ecliptic. But if you’re doing precision measurements, in particular, using some kind of clock, an equatorial system tends to work better. In modern astronomy we use the system of right ascension and declination. You can imagine this as being basically like the system of latitude and longitude but projected out onto the celestial sphere. So the north celestial pole, near Polaris, has a declination of 90 degrees, just as the north pole on the Earth has a latitude of 90 degrees, just as the North Pole on the Earth has a latitude of 90°. And the celestial equator has a declination of zero degrees just as the Earth’s equator has a latitude of zero degrees. Then you have right ascension in a similar way as you have longitude, except instead of starting at Greenwich as you do for longitude, right ascension starts at the vernal equinox, where the celestial equator and the ecliptic meet.

Well, each star in the sky has a fixed right ascension and declination, just as each point on the Earth has a fixed latitude and longitude. Now, imagine you are standing out in a field on a clear night, facing south. Over the course of the night, you’ll see stars rising in the east to your left, climb higher in the sky moving rightward, reach their highest point as they transit the meridian in front of you, and then start to get lower in the sky, and finally set in the west to your right. If you just watch the meridian, the line going from south, to the zenith overhead, to north, and you track the right ascensions of the stars that are transiting, you’ll see that they increase in right ascension over the course of the night. In fact, traditionally, right ascension is not measured in degrees like longitude is, but in terms of time. The full circle of the celestial equator has 24 hours of right ascension. The right ascension of the stars crossing the meridian then increases at approximately one second per second. Very convenient.

Well, the system of lunar mansions was not quite as tidy as the modern system of right ascension and declination, but it was similar in spirit. The system of lunar mansions effectively did not have declination, this celestial latitude, but it was more or less equivalent to the system of right ascension. Each of the 28 lunar mansions were each defined by a reference star or asterism. Now, again, one of the rather unique features of the system of lunar mansions is that it does seem to have been quite deliberately designed to measure right ascension well. You might imagine that the astronomers who developed it would have picked the brightest, most prominent stars as their reference points. But actually most of the reference stars in the system are not especially notable or bright. Only two of the reference stars are of 2nd magnitude, which is about how bright Polaris is. Four of them are of 5th magnitude, which is quite faint, and one is even of 6th magnitude, which is barely visible to the naked eye. So, these stars were chosen as reference points not because they were particularly bright or easy to observe, but because they fell at roughly even intervals in right ascension around the sky.

Okay, well the documents on the system of lunar mansions that start to show up in the 2nd and 1st century BC record the width of each lunar mansion. So how was this measured? The measurement took place in three parts. The first part was to find the direction of south. This part was relatively straightforward. The precise technique the astronomers of ancient China used was not recorded, but it involved using a gnomon. So, probably what they did was one of two things. The simpler thing you could do was to just trace out the end of the gnomon’s shadow over the course of a day. Then you just draw a line from the gnomon to the point where the shadow comes closest to the gnomon. That line will be north-south. A somewhat more sophisticated technique that will be a little more accurate is to find two points on this line of equal distance to the gnomon, one on the western side and one on the eastern side. Then you draw a line between these two points and bisect it. The line from the middle point to the gnomon is also north-south.

Well, either way, once you’ve done something like this, you now have your gnomon, and you have a line that goes north-south. For the second part of your measurement, you would now introduce the clepsydra and calibrate it against the sky. To do this, you would stand on this line north of the gnomon around noon. At the moment that the Sun transited the meridian, you would set your water clock going. You’d let it run for a full day, refilling it if necessary. Then the next day you’d wait until noon and at the exact moment that the Sun transited the meridian again, you’d stop your water clock. So you’d now have some volume of water that you’ve measured from your water clock and you know that this volume of water corresponds to exactly 24 hours. And with that you’ve calibrated your water clock.

For the last part of the measurement, you would now be able to do the actual measurements of the lunar mansions. All you’d have to do is wait for a reference star to cross the meridian and then set your water clock going. After some period of time, a little less than an hour or so, the reference star of the next lunar mansion would transit. The amount of time you measured between these two transits divided by 24 hours would be the width of the lunar mansion in terms of a fraction of a circle. From there, you’d just have to multiply by 365 ¼ to convert it to a standard unit like the “du.”

Now a feature of calendars of the time is that they would also report which lunar mansions were “centered” at dusk and dawn, as well as which lunar mansion the Sun was in at various points of the year. Figuring out which lunar mansion is centered at dusk and dawn was fairly straightforward. At dusk you would just wait until the sky was dark enough that you could see the stars and observe which lunar mansion fell across the meridian at that time. And then you would do something similar at dawn. But how did astronomers of the time figure out which lunar mansion the Sun was in at different times of the year? When the Sun is up it’s day, so you can’t see any of the stars. It seems that what they did was they would observe which lunar mansion was transiting at midnight as well as at dusk and dawn. If you have a water clock going and you know when dusk and dawn are, it is not too hard to figure out when midnight was. Then they assumed that the Sun would be in that position in six month’s time. So, if you collect these measurements over the course of the year, you can determine which lunar mansion the Sun is in at any time even though you can’t actually observe it directly.

Well, with these techniques the lunar mansions could be measured relatively precisely. And because the lunar mansions were the foundation of many astronomical measurements for millennia, this allowed Chinese astronomers to detect one of the most subtle changes in the heavens, the precession of the equinoxes. I mentioned earlier how it’s plausible that when the system was first developed the reference stars were all quite close to where the celestial equator was at the time. However, due to the precession of the equinoxes, the location of the celestial equator very slowly wobbles on the sky. This meant that stars that were once close to the celestial equator over the centuries became farther and farther from the equator. And because they now started to change their positions in declination, that meant that their positions in right ascension were also changing. So even if the reference stars started out as being equally spaced in right ascension, due to the precession of the equinoxes they didn’t stay that way over the centuries. So every few centuries when the astronomers went to measure the widths of the lunar mansions, they would find that it did not quite agree with the measurements of astronomers in the past. In fact, by the 13th century, precession had changed the position of the celestial equator so much that in one case one of the stars that had traditionally been listed after another started to transit before, so the order of the mansions got switched. To deal with this, from time to time astronomers would make new measurements of the widths of the lunar mansions, and more infrequently, when things really got bad, they would drop one of the reference stars and replace it with one that was better suited.

And it seems to be thanks to the precision of this system that an astronomer named Yu Xi was able to discover the precession of the equinoxes in the 4th century AD. He noted that the position of the winter solstice seemed to move by one degree every 50 years, which is not too far off from the correct value of one degree every 72 years. It’s also possible that the precision of Chinese astronomical measurements, along with the many centuries that they were conducted over, allowed them to detect another phenomenon that took until the 18th century to definitively discover, that of proper motion. In basic spherical astronomy we tend to use an idealized model of the heavens where the stars are imagined to be fixed to a great sphere that rotates around us. This model works quite well for many observations, but today, modern astronomy tells us that the stars are not points of light fixed to an enormous sphere, but are distant objects freely floating in space. As such, they are constantly moving relative to each other and to us, but because the distances are so large, we on the Earth don’t perceive these motions over a human lifespan. But over the centuries these motions build up and, at least for the closer stars, can eventually become quite noticeable. Over the millennia, the shapes of the constellations themselves change and after long enough times, they will become unrecognizable. In the 9th century AD, an astronomer named Yi Xing observed that a group of stars in Taurus was on the ecliptic. But in the past records, this group of stars was noted as being 4° south of the ecliptic. Now, your position relative to the celestial equator can change over time due to the precession of the equinoxes, but your position relative to the ecliptic cannot. This change in position was in fact due to the proper motion of this group of stars.

Well, before leaving the subject of the hsiu I should say at least a few more words about its origin. I’ve been using the common term “lunar mansion” to describe this system, but it is admittedly a bit of an odd translation since you may have noticed that I didn’t mention the moon at all when talking about the lunar mansions. That said, its origins are undoubtedly lunar. The moon advances by roughly one lunar mansion every night. Now, the fact that there were 28 lunar mansions in this system needs a bit of explaining because if the idea was that the moon would advance by exactly one mansion per night, there really should be 27 since the sidereal period of the moon is 27.3 days. But astronomers were also interested in the synodic period of the moon, the time from new moon to new moon, and this is 29 and a half days. So it’s possible that they settled upon 28 lunar mansions as a kind of average between these two lunar numbers. But this is, at least to me, a somewhat unsatisfying explanation.

Now you may recall from Episode 35 that there was a similar system in India called the nakshatras. The relationship between the Indian system and the Chinese system has engendered no small amount of debate, much of which has produced more heat than light. Partisans of either side have argued that their own system is the older of the two and that it later influenced the other. What is clear is that the two systems are not totally independent. Nine out of the twenty-eight reference stars are identical, which is fairly remarkable since as I mentioned earlier, many of these reference stars are otherwise not especially notable. Eleven of the 28 are reference stars are very close to each other in the two systems, which, again, is fairly remarkable since the stars could in principle be chosen quite far from the equator. So even if they were constrained to be nearby in right ascension, there was no reason for them to be nearby in declination as well. Only eight of the 28 references stars are truly distinct between the two systems, and of these, two are very bright stars, Vega and Altair, and these were very likely part of the Chinese system in its infancy. But all this tells us is that the two systems were not independent of each other, not which one came first. The first really detailed descriptions of the systems appear in the literary record at about the same time in both China and India. But both locations also have more oblique references or evidence that indicate that the system was a lot older in both places, which makes it very hard to adjudicate which of the two had precedence. It’s also possible that some version of the two systems initially developed independently, but that the two systems converged as contacts between India and China increased. So, given the contentiousness of the topic I will not wade into this debate and pollute it with my own ill-informed opinions.

Well, I think I will leave it here for this month. I hope you are as relieved as I am that I have at long last gotten around to talking about the system of lunar mansions. Next month we’ll talk about a couple of the other great astronomers in Chinese history, Zhang Heng, who worked in the later Han Dynasty, and Shen Kuo, who worked during the Song Dynasty. I hope you’ll join me then. Until the next full moon, good night and clear skies.

Additional references

  • Cullen, Christopher, Heavenly Numbers
  • Needham, Science and Civilisation in China, Vol. 3