Episode 42: A Tale of Two Reforms

May 29, 2024

After Wang Mang had usurped the Imperial throne, a disastrous series of reforms led to the collapse of his dynasty. The reestablishment of the Han Dynasty called for yet another calendar reform. About a millennium later, a group of officials, including the astronomer Shen Kuo, instigated a treacherous period in court politics by pressing for a radical set of reforms called the New Policies.


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, or thereabouts. My name is Joe Antognini. To start off with, my apologies that this episode is a little later than normal. I was all set to record right on schedule, but I ended up contracting a cold the day before I was supposed to record. So I took an extra couple of days to wait for my voice to get at least somewhat back to normal. But now it is and so the show must go on.

Well, last month we looked at some of the astronomical developments that happened around the rise of the Xin dynasty in the early 1st century AD. In particular, the establishment of a new imperial dynasty demanded the promulgation of a new calendar. And the astronomer Liu Xin was up to the task and created a calendar called the Triple Concordance system that wove numerological significance into the lengths of the seasons, months, and planetary motions.

Now, the new emperor, Wang Mang, had certainly hoped that the new dynasty he inaugurated would outshine the great Han Dynasty in glory and stretch across the centuries. But it was not to be. Wang Mang had lined things up for his usurpation of the throne quite nicely in the palace. He had aligned important factions with him, in particular the Confucian court scholars. But outside the palace his standing was dicier. At first it seems to have been the minor officials who had misgivings. Wang Mang was a die-hard Confucian, and the Confucians, as a rule, tended to romanticize the Zhou Dynasty. Confucius, of course, lived during the Zhou Dynasty and scholars believed that the Zhou Dynasty most properly embodied Confucian ideals. So, as Wang Mang was setting up his dynasty and overhauling the government, he wanted things done right. He wanted them done the Confucian way. But the true Confucian way hadn’t been done for many centuries, so what exactly it was wasn’t clear. Wang Mang employed an army of scholars to scour the ancient texts for clues about the proper mechanism for deciding this or that. And, in the end, not much got decided, and what did get decided took a long time to happen. It did not help matters that Wang Mang was a quintessential micromanager. So officials out in the country were unable to do anything about the problems they had until they got an answer from the emperor himself, and the emperor was taking a long time to come to any answer at all.

Now this in itself may not have been that big of a problem for the officials. I’m sure many officials throughout history would have been quite happy to sit around doing nothing for years and protest that they were just waiting for word from the emperor before they could get to work. But one of the projects that was on Emperor Wang’s plate was to revamp the compensation scheme, and as a consequence of this, until it was completed, none of the officials got paid, and this lasted years. To support themselves, these officials started to demand bribes, and this, in turn, started to breed resentment among the common folk.

But, after a few years Wang Mang’s work restoring a Confucian system of government based on his understanding of Zhou dynasty practices started to yield fruit, and these policies began to be implemented. But unfortunately, to continue the metaphor, the fruit these policies bore was not as good as he had hoped. A representative debacle was a series of reforms that introduced a new system of coinage. During the Han Dynasty, the vast majority of coins were made of bronze and were called qian, or cash coins in English. They were round with a square hole in the middle. You could then keep your money organized by threading a string through a stack of these coins. Typically coins would be strung together in groups of a thousand, and this was a standard monetary unit that merchants would do business with. Well, based on Zhou Dynasty practices, Wang Mang introduced a rather baroque coinage system consisting of 18 different kinds of coins, with varying shapes, materials, and denominations. Some of these were made of tortoise shells and cowrie shells. And some were quite easy to forge. Use of the earlier Han Dynasty coins was outlawed. These diktats were so heavy handed that trade almost completely collapsed over the next few years.

Another even more catastrophic policy was the introduction, or reintroduction in Wang Mang’s eyes, of an old farming system called the well-field system. Under this system Wang Mang effectively nationalized all land ownership overnight. Private land ownership became forbidden. Eight families would be assigned to work on a square plot of land. The land was divided up into a 3x3 grid, and each family would get one of the eight divisions on the periphery of the grid. These divisions would be around 20 acres or so. Anything the families grew on their own land they could keep. The central plot in the middle was assigned to the state, and the eight families were to work on the middle plot collectively and hand over all produce from that plot to the state. Naturally, instituting this system was a tremendous upheaval to the commoners and the big land owning aristocracy was none too happy with losing all of their land. In the end this system survived only three years.

But this wasn’t the end of Wang Mang’s disastrous interventions into his country’s economy. He declared a state monopoly on salt, fishing, timber, and worst of all, alcohol. He imposed a so-called sloth tax which taxed the unemployed. Consequently many poor urbanites and people living in marginal lands were forced into slavery to pay the tax. He imposed the first income tax in China at a mind boggling rate of 10 percent.

All this is to say that while Wang Mang had the Confucian scholars firmly behind him, over a decade he had turned essentially everyone else in the country against him. As the years passed, revolts began to pop up in various corners of the country, usually minor officials who rallied large numbers of disaffected peasants. The first few of these did not pose a serious threat to Wang Mang’s rule, but in time the revolts grew in scale. These culminated in the Red Eyebrows movement, so called because the participants painted their eyebrows red so that they could distinguish themselves from the Emperor’s forces. Ultimately the Red Eyebrows managed to sack the capital city and beheaded Wang Mang. Apparently the peasants kicked his head around like a soccer ball and someone even cut out the late emperor’s tongue and ate it.

Well, after this turn of events there was a chaotic period of a few years as a number of members of the old Han family claimed the imperial throne only to be quickly deposed. But ultimately one of them, Liu Xiu, the great-great-great-great grandson of Emperor Jing, came out on top. In 25 AD he had more or less won control of the Han Kingdom and put forward his claim to rule the entire empire, and after another 12 years of hard fighting he managed to subdue the entire empire under his rule, beginning the second half of the Han Dynasty, known as the Later Han, or Eastern Han because the new emperor shifted the capital from the sacked city of Chang’an to the eastern city of Luoyang.

Well, despite the chaos of the broader political context, the astronomers seem to have kept right on doing their work throughout all of this. In 32 AD, when Liu Xiu was well on his way to gaining control over the entire empire but still had a good five years to go, astronomers began to note that their observations were not matching their predictions. They had been using the new Triple Concordance system that we talked about in the last episode, that was inaugurated by the new Xin Dynasty. But the moon’s actual position was ahead of its predicted position by about a day. The astronomers brought their concerns to the new Emperor, but understandably the Emperor felt he had more pressing matters to attend to at the moment, so the issues with the calendar were set aside for the time being.

Over the next half century the predictions from the official calendar continued to lag. During this period some of the astronomers appear to have rebelled against the official timekeeping system and unofficially developed an alternative system that was more in line with their observations, called the Quarter Remainder system. But until the emperor officially instituted a new calendar, these alternative predictions were simply for the astronomers’ private enjoyment.

The issues with the old Triple Concordance system from the defunct Xin dynasty continued to fester until 85 AD. By this point two things had happened: first, the discrepancies had become too large to sweep under the rug, and second, things had settled down in the empire. The emperor of the time, Emperor Zhang, was the third emperor of the Later Han Dynasty and his reign is regarded as being one of the high points of the era. The emperor asked his astronomers why their predictions were so poor. The astronomers protested that they knew that the predictions were poor, but the calendar was the calendar and it wasn’t in their power to change it. But if the emperor so wished, it was, of course, within his prerogative to change it. Having now reestablished the Han Dynasty on firm footing, it did seem to be an appropriate time to promulgate a new calendar, so the emperor ordered that it be done. Fortunately for the astronomers, the work involved in this calendar reform seems to have been rather limited since they had essentially already developed the new calendar years before and had just been using it unofficially. So this particular calendar reform was quite fast. Within a few months of the emperor hauling the astronomers before him to account for their errors he was giving his blessing to the new Quarter Remainder calendar.

It’s at this point, shortly after this latest calendar reform of 85 AD that reestablishes the Han Dynasty, that the astronomer Jia Kui enters the picture. Jia Kui was a respected astronomer, but he wasn’t among those tapped to lead the calendar reform. Not long after it had been promulgated, he was, however, brought in to review a peculiarity of the new calendar. In general, the months alternated between short months of 29 days and long months of 30 days. In this new calendar, the first month in the overall cycle was assigned to be a full month of 30 days rather than a short month of 29 days as had been customary. With a team of 10 astronomers Jia Kui was able to determine that the traditional practice of starting the cycle with a short month was correct.

It seems that in the course of his review, however, Jia Kui discovered some more fundamental problems with the Quarter Remainder system. The issue he discovered is that a calendar that predicts things like the solstices or phases of the moon essentially has two components: the period of the phenomenon, and then the origin, or the starting point. So, in modern terms, the calendar might specify that the time from new moon to new moon was, say, 29.53085 days as it was in the Quarter Remainder system. And then the calendar would also specify that, for example, midnight of December 25, 162 BC was a new moon. Then, to predict the date of the new moon in future, you would, in effect, just add repeatedly add 29.53085 days to the start date of December 25, 162 BC. This would then enumerate all of the full moons in your calendar. Now, this meant that your calendar could be inaccurate in two ways: the period could be off, or the origin point could be off. If the period is off, then the calendar might start out making good predictions, but over time the predictions will get worse and worse as the errors from the incorrect period accumulate. If the origin is incorrect but the period is correct, then there will always just be a systematic error in your predictions. You’ll always be off by the same amount and it won’t get any better or worse over time. What Jia Kui figured out was that although the new Quarter Remainder system was making better predictions than the old Triple Concordance system, it basically got there by accident. The new Quarter Remainder system actually had a worse estimate of the period of the moon’s orbit, but it happened to also choose a more inaccurate origin point and these two errors had essentially cancelled out in the late first century. But because the period was worse, this happy state of affairs couldn’t last, and eventually the new calendar would start making worse predictions than the old one.

So, how did Jia Kui know that the origin point for the new Quarter Remainder system was wrong? After all, its origin was in 162 BC and of course Jia Kui was not around then. And at any rate, any recorded observations from that time were also available to Liu Xin when he developed the previous Triple Concordance system. Jia Kui’s main innovation was that he realized that new moons and solar eclipses were not independent events. Generally speaking, determining when the new moon is is very difficult because the moon passes very close to the Sun and can’t be seen. So you have to infer it from other observations at different times. But this means that recordings of new moons in past records were not all that accurate, and in fact most of the recorded new moons were not real measurements but just dates that the calendar of the time said was a new moon. The one exception is if there happens to be a solar eclipse. If you observe a solar eclipse, total or partial, you know precisely when the new moon is. Prior to this point in Chinese astronomy there hadn’t really been any connection between eclipses and phases of the moon. In fact past records had a clear systematic bias where solar eclipses almost always were noted as happening on the last day of the month or sometimes even the day before that, which of course, was impossible. But at the time no one seemed to notice that this was an issue. As I mentioned a few episodes back, at the time there were a few different theories of eclipses floating around and the idea that the eclipse is caused by one celestial body shadowing another hadn’t become widely accepted. In more astrological theories the idea was simply that the moon would sap energy from the Sun when it shared the same lunar mansion. So observing a solar eclipse a day before the new moon wasn’t necessarily a contradictory observation in those terms. But with Jia Kui’s insight that solar eclipses could only happen on new moons, he could use the seventy recorded solar eclipses he had available to him to determine both the period of a new moon and an origin point with far higher precision than was possible previously.

Well, Jia Kui did not only work on calendrical matters. He was also very interested in the path of the moon on the sky and articulated the Nine Roads of the Moon which I mentioned briefly in a previous episode. Now, the Nine Roads of the Moon as a phrase seems to have had a long history in Chinese astronomy, but it does not seem to have meant a consistent theory of the Moon’s motion until Jia Kui’s time. Here, one of Jia Kui’s main innovations was to recognize that the Moon’s motion should be measured with respect to the ecliptic rather than the celestial equator. As I talked about at some length when I went over the system of lunar mansions, Chinese astronomy was primarily based around measurements with respect to the celestial equator. This works quite well for precision timing, but isn’t as good a system for measuring the motions of the Sun, Moon, and planets, since these bodies move closer to the ecliptic. To see the problems this creates, imagine that the Moon’s orbit were exactly on the ecliptic and perfectly circular so that the Moon moved at a constant angular speed around the Earth. If you are measuring the Moon’s position with ecliptic coordinates, you would just find that the Moon’s ecliptic longitude increases linearly with time. In this coordinate system it’s very easy to see that the Moon’s motion is constant. However, if you instead measure the Moon’s motion using right ascension, which is effectively your longitude along the celestial equator, you won’t see that it increases perfectly linearly. Instead, when the Moon is on the celestial equator, its apparent motion in right ascension will be smaller than it otherwise would be because it’s also increasing in declination. Conversely, when the Moon is at its maximum or minimum declination, its apparent motion in right ascension will be larger than average because firstly all its motion is in right ascension and not in declination, and secondly because it’s above the equator, the lines of constant right ascension are closer together. So if you plot the Moon’s right ascension as a function of time, you’ll see that it oscillates in a curve that is almost, but not quite sinusoidal. So in this coordinate system, the motion of this fictitious simple Moon looks a lot more complicated than it really is. Now, the real Moon, of course, has an orbit which is not perfectly circular, and what’s more it precesses as well, so its motion is quite a bit more complicated, even in ecliptic coordinates. But when you are measuring its position using an equatorial system and you see that its motion is complicated, it’s hard to tease apart which parts of its motion are complicated because the moon really has complicated motion, and which parts just look complicated because you used a bad coordinate system.

At any rate, Jia Kui’s innovation here was to measure the position of the Moon with respect to the ecliptic rather than the celestial equator. For this purpose he added a new ring to the official armillary sphere which was used for these kinds of measurements. However, in a tale as old as time, Jia Kui’s genius was not immediately recognized and it apparently took many years to persuade the court astronomers to make their measurements this new way.

Well, based on the name, the “Nine Roads,” Chinese astronomers had long recognized that certain features of the Moon’s motion varied in a nine-fold way. The Moon’s orbit is not exactly on the ecliptic, but is somewhat inclined to it by about five degrees. But the position of maximum declination precesses with a period of about 19 years. This means that on some months you’ll see the Moon pass right on top of a star, and then on other months you may see it pass five degrees above or below that same star. The older references to the Nine Roads seem to have divided up the path of the Moon into the ecliptic path, and then four paths above the ecliptic, and four paths below it. But the Moon’s orbit is not just inclined with respect to the ecliptic, it’s also eccentric. And this means that its speed along its orbit varies over the course of the month. Jia Kui seems to have been the first to realize that this speed varies, and the position of maximum speed precesses with a period of about nine years. Ultimately, Jia Kui was able to derive a theory of the Moon’s motion that accounted for its variable speed along its orbit. This way, when making predictions of the Moon’s position in the sky, a correction could be made to its average motion to get a more accurate prediction.

Jia Kui raised these issues late in his life, both with the calendar, and with the way that lunar and planetary positions were being measured. But his ideas were not met with immediate acclaim and he died not too long later so he was unable to defend his ideas as forcefully as he otherwise might have if he had still been around. The court astronomers seem to have understood that something was wrong with the way they were making their measurements, but didn’t seem to fully understand Jia Kui’s ideas, and, more to the point, didn’t seem to understand his solutions. So they began incorporating a series of corrections to their measurements of the position of the Moon, but these corrections were based on a gross simplification of Jia Kui’s theory and weren’t even self consistent.

There is actually another example of a disconnect between what we might anachronistically call the theorists of the day with the observers. Another astronomer of the time, named Huo Rong, published another critique of the established astronomical practices, this time about the way that water clock measurements were done. It seems that in this era the water clocks would be run twice a day: once during the daytime, and another time at night. As I mentioned in the last episode, the astronomers would place a floatation device on the surface of the water with a vertical rod attached to it. Then they would measure the height of the water by comparing the gradations on the rod to a horizontal crossbar above the water clock. Because the length of day and night varied over the course of the year, you’d need a longer rod with more gradations on it during days near the summer solstice, and a shorter rod with fewer gradations on it during the night. And similarly around the winter solstice you’d need a longer rod during the night and a shorter rod during the day. According to the established practice, the court astronomers would linearly increase the length of the rod used during the day from the winter solstice to the summer solstice, and then linearly decrease the lengths of the rods they used during the night. And from the summer solstice to the winter solstice they’d do the opposite. We actually saw way back in the episodes on Babylonian and Egyptian astronomy that they had a very similar scheme. But Huo Rong pointed out that this system was not correct. In reality the change in daylight throughout the year is more sinusoidal, it’s not a zigzag. Close to the solstices it hardly changes at all, and close to the equinoxes it changes much more rapidly than you’d otherwise expect. The emperor asked his court astronomers to respond to this critique and they said that while it made sense, they had no other choice. They were simply following the established rules for making these measurements, which is precisely what the emperor required of them.

Well, a widely accepted solution for how to deal with these issues didn’t really come until Zhang Heng, who was active in the early 2nd century AD and came of age around the time of Jia Kui’s death. The essential problem in both cases, but especially for measurements of the moon and planets was that there needed to be a way to convert between equatorial coordinates and ecliptic coordinates. In modern mathematical terms, this is essentially a problem of spherical geometry, and although it’s not too hard to set it up, even in modern notation the conversion is rather ugly. But even elementary trigonometry didn’t show up in China until the 8th century AD. So in an era where trigonometric functions weren’t recognized, converting between ecliptic and equatorial coordinates was a very thorny problem indeed. Zhang Heng solved this problem in a very practical way. He simply constructed a physical sphere and carefully inscribed an equator and ecliptic, inclined at the appropriate angle, and then inscribed gradations on this sphere. Having done this he could simply measure for himself what the conversion was. He managed to do this down to a resolution in longitude of about four degrees. This meant that for the position of the Sun, every four day span would have an empirically measured conversion between its equatorial position to its ecliptic position.

Incidentally, if Zhang Heng’s solution to a problem in spherical trigonometry of literally constructing a sphere and looking at it seems to be overly simplistic, this kind of a solution was in use at the greatest telescopes in the world within living memory. One of the difficulties that telescopes have is that you oftentimes want to observe an object for a long period of time. But due to the rotation of the Earth, the objects are constantly moving in the sky, so you have to move the telescope to track them. The simplest way to do this is with what is called an equatorial mount. The idea is that you align your mount with the north celestial pole and then you have two motors: one changes the declination and the other changes the right ascension. Then it’s easy to track an object, you just have to drive your right ascension motor at a constant rate. This kind of a mount is quite simple in principle. But mechanically it starts to introduce difficulties when you’re building a very large multi-meter class telescope. The precision of the alignment has to be very high and the whole structure needs to be extremely stable, but the odd angles that you have to mount things for an equatorial mount make this very difficult to achieve. Because of this, in the second half of the twentieth century, very large telescopes started to use altazimuth mounts, where one motor would control the altitude — how high you’re pointing above the horizon — and the other would control the azimuth, the angle with respect to north. This is much simpler to build mechanically, but it presents a problem for tracking. Now, to track an object, you can’t just whirr one motor at a constant rate. Both motors will need to be going, and they’re going to have to change how fast they’re going over time. This is essentially another version of the spherical trigonometry problem that Zhang Heng was trying to solve. Before the advent of cheap computers, calculating how to drive these two motors on the fly was a very challenging task. And the solution that some telescopes used was the same as Zhang Heng. They would have a kind of “shadow telescope,” that was a much smaller physical analog of the telescope. They could then drive the shadow telescope equatorially, and then just read off the corresponding altitude and azimuth and feed those readings into the main motors of the real telescope.

Well, Zhang Heng seems to have had a knack for constructing ingenious scientific instruments. Although he was one of the greatest of China’s astronomers, he is perhaps even better known in the field of geology for having built the first seismoscope. The details that survive of this device are tantalizing. There’s enough detail to guess at how it worked with enough imagination, but the description is not quite thorough enough to allow for a definitive reconstruction. But the basic idea seems to have been that there was a large urn with a pendulum inside. The pendulum was surrounded by a ring on which sat eight balls. If there was an earthquake, it would set the pendulum swinging and it would knock one of the balls off its perch and the ball would roll out a spout. This would then indicate not only that there had been an earthquake, but also the direction had occurred in. The most famous story of Zhang Heng’s seismoscope tells of a time when the seismoscope went off but no one in the palace felt an earthquake, so it was generally believed that the device was broken. Then, two days later, messengers arrived at the capital and reported that an earthquake had occurred in Longxi, a province hundreds of miles away, in precisely the direction that the seismoscope had indicated. Although it is a good story, it is probably apocryphal because it only shows up in the later records. But Zhang Heng was certainly interested in detecting earthquakes that couldn’t be felt. After all, at the time, earthquakes were similar to solar eclipses and comets — they were indications from the Heavens that the earth had come out of harmony with the heavens, and usually this meant that there were problems with governance. And just as glancing solar eclipses, which were barely detectable, provided an important early warning sign to the emperor that he needed to change something soon, so too would a small earthquake that could barely be felt. If the emperor could course correct quickly he could stave off a bigger disaster.

Although the seismoscope was Zhang Heng’s most famous invention, he developed a number of other advances, too. Besides the armillary sphere he used to convert between ecliptic and equatorial coordinates, his other main astronomical innovation was an improvement to the water clocks. He realized that the problem of the flow rate slowing as the water level decreased could be solved by adding in an extra reservoir as a regulator. This could keep the main tank topped up at all times so that its flow rate was constant. Then, the amount of water that flowed out would increase linearly over time.

Well, I don’t want to give the impression that Zhang Heng was only concerned with building new equipment. He was deeply involved in what we would today consider to be more theoretical aspects of astronomy as well. Zhang Heng wrote extensively on cosmology and cosmogony. In fact, we’ve already touched on his most important theories in Episode 38 when I went over some of the estimates of the size of the heavens and the earth, so I won’t go over them again.

Well, there is much more that could be said about astronomy during the Han Dynasty. There was, for instance, in the year 175 AD, a ferocious formal debate in the court before all the officials about calendrical issues, in particular the origin point of the calendar. But in the interest of time I will have to skip over that episode and instead move forward almost a millennium, to the Song Dynasty, so that we can talk a little bit about the life of one of the other great astronomers in Chinese history, Shen Kuo.

Now, given that we’re skipping over so much time, and that Shen Kuo’s work was intimately involved with the politics of his day, I think it would be worthwhile to briefly sketch what all was going on at the time. In the intervening years the Han Dynasty had fallen and for several centuries the empire fragmented and was ruled by a variety of independent kingdoms. But in the late 7th century this chaotic period came to an end with the rise of the Sui Dynasty which managed to unite a region similar in size to the Han Dynasty at its greatest extent. The Sui Dynasty was in some ways a latter-day Qin Dynasty in that both were able to overpower the various independent kingdoms that ruled China, but were internally unstable and were quickly replaced by more stable dynasties: the Han Dynasty after the Qin Dynasty in the early Imperial period, and the Tang Dynasty after the Sui Dynasty in the middle Imperial period.

Well, the Tang Dynasty persisted for about three centuries, and much like the Han Dynasty it, too, had a brief interruption in the middle when an ambitious empress usurped the throne and declared a new dynasty. Well, to quote the way Gregory of Tours opened his own history, during this time many things happened, some of them good, and some of them bad. But for our purposes two changes during the Tang Dynasty were particularly important. The first was the development of the system of Imperial examination. Now, some form of imperial examination had existed as far back as the Han Dynasty. I mentioned in Episode 38 that during the Han Dynasty the Taixue was founded, an imperial university for aspiring scholar officials to study at. But during this period one’s pedigree mattered much more than any test results in determining who to appoint to official positions. And, at any rate, an individual needed a certain level of nobility to be eligible to take the test to begin with.

But during the Tang Dynasty the scope of the imperial examinations expanded significantly and many new categories of examination were introduced. One still needed some degree of nobility to be eligible to sit the examination, but good performance on an exam was now a factor in appointments to good positions in the bureaucracy. Then later on, during the Song Dynasty, the imperial examinations became much more democratized. In principle anyone could take an exam, and rather than being one route that could get you an official appointment, it became virtually the only way to get an appointment.

The other important change that came during this period was land reform. If you happen to know any urbanists, they will tell you that everything in economics and politics boils down to land use policy. Well, nowhere does this seem to be more true than in the history of China. Earlier I talked a little bit about how one of the many disastrous policies that led to the downfall of Wang Mang’s short lived Xin Dynasty was a land reform that introduced the so-called well-field system. Well, somewhat prior to the Tang Dynasty one of the regional emperors introduced a new land reform that was similar in spirit to the old well-field system, and after the Sui Dynasty united the various independent kingdoms, this system was exported throughout China.

This new system was called the equal field system and, like the earlier well-field system, in this system all land also belonged to the Emperor. But rather than assigning families to equal sized plots of land in a grid, the equal field system, despite the name, was somewhat more flexible as people would be assigned larger or smaller plots of land depending on their ability to work it. So a man who owned an ox would be granted more land than a man who didn’t have an ox. Well, as with the earlier well-field system, this system was intended to break the grip of the powerful land-owning nobility. And, just as an aside here, one of the things that those of us in the modern world tend not to understand about these kinds of feudal systems is that the power structures were not set up so much with the aristocracy opposing the people. There was, of course, some degree of this to ensure that the common people stayed in line. But realistically, the commoners, whether in Imperial China or medieval Europe were for the most part dirt poor, totally unorganized and weren’t a real threat to anyone. Instead the main dynamic was the monarch against the nobility. The nobles were always jealously guarding their landholdings and privileges. The monarch, meanwhile, although he had nominal allegiance of the nobility and could extract some taxes from his entire domain, was always had to be working to make sure no nobles were getting so powerful that they might become a threat. So this kind of a land reform was a perfect way to put the nobles down a peg or two. The difficulty was that these things never seemed to last long. Anytime there was a famine or flood or some other disaster there would be masses of peasants who would be reduced to penury and at the brink of starvation. The nobility would then bring them on as servants into their household, taking their land along with them. So, by the later part of the Tang Dynasty the equal field system had effectively become dead letter. And, particularly towards the end of the Tang Dynasty, the power of the Emperor was once again in decline and the country was effectively divided into a patchwork of principalities and the nobility had gained the upper hand.

So once the first emperor of the Song Dynasty, Emperor Taizu had conquered these various kingdoms and centralized power again, there was for good reason a sense in the court that the nobility still had too much land and too much power. Well, founding a new dynasty is always a precarious business, so Emperor Taizu was not in a position to do much about this problem. But after about a century some new and radical ideas started floating around the court. The principal driver behind these ideas was a man named Wang Anshi. Wang Anshi came from a family of imperial scholars and did very well on his own exams. In the subsequent years he was appointed to various posts throughout the empire, and rose through the ranks over time. Being out among the people over all these years, rather than holed up at the imperial palace deep in the machinations of palace intrigue, gave him a very tangible sense of which government policies were working and which weren’t. And in Wang Anshi’s estimation, almost all of them weren’t. He recognized a few fundamental problems with the social structure of his day. Most of the people were farmers, but they held only a small fraction of the arable land. To survive they had to take out extortionate loans from the few large landholders. These large landholders, in turn, generally did not pay much if any tax. And with little tax revenue, public infrastructure, particularly around irrigation and water management, had been neglected.

So, over the years, Wang Anshi had various ideas about how this situation could be improved and in 1058 he collected these thoughts and wrote a 10,000 word memorandum to the Emperor. The Emperor of the time, Emperor Renzong, gave the ideas no further thought, but the ideas attracted the attention of some members of his court.

Well, a few years later Emperor Renzong had died and was succeeded by Emperor Yingzong, but Emperor Yingzong had always been sickly and died of some illness a few years into his reign. So Emperor Yingzong was then succeeded by Emperor Shenzong. Emperor Shenzong, unlike many of the emperors who preceded him, had ambitions. He wanted to expand the size of his empire, particularly by pushing its boundaries to the north. There there had long been a tenuous peace with the Western Xia and Khitan Empires. But he recognized that this would be a significant military endeavour, and as such, it required funds, more than the imperial treasury could support when he took the throne. But fortunately for him there seemed to be a ready-made solution. Wang Anshi had spent the last ten years making the case for his reforms, called the New Policies, which would, among other things, generate substantial new tax revenue. So, after all this time, Wang Anshi had finally found the emperor’s ear. He was called to the court, promoted to Chancellor, and given the power to implement his New Policies.

For those of you more familiar with American history, some historians have drawn a parallel between Wang Anshi’s New Policies and the New Deal of the 1930s. Both were quite radical reimaginings of what the government could do in a very short period of time, both had somewhat Keynesian undertones, both had mixed results, with some policies being more successful than others, and both drew fierce opposition.

Now, enumerating all of the reforms in Wang Anshi’s New Policies program would take us too far afield, but the main highlights were a new uniform system of taxation that assessed the tax simply based on the size of the land and an assessment of its quality regardless of whether the owner was an aristocrat or not. There was also a program to provide loans to farmers for seeds at a fixed low interest rate. Another program aimed at regulating commodity prices, and in some cases instituted government monopolies on certain commodities like salt.

Well, philosophically, Wang Anshi’s reforms were most closely aligned with the school of legalism that I discussed a few episodes back. His reforms were a fairly radical break from past practices, and emphasized strong centralization and effective governance, all important pillars of legalism. But not everyone in the Song court was a legalist. To the contrary, the most popular philosophical school was Confucianism, as it had been for centuries. And the most fervent Confucians were deeply opposed to the New Policies of Wang Anshi. As Confucians, they could perhaps support slow, gradual reforms, but certainly not the abrupt, radical changes that Wang Anshi was proposing. This was a recipe for chaos. And anyway these more conservative Confucians were skeptical that the New Policies would do much good for the economy at all. Furthermore, the New Policies were plainly aimed at reducing the wealth and power of the aristocracy, but keeping the aristocracy happy was critical to maintaining social stability in the state.

Well, when Emperor Shenzong decided to back the New Policies, the fate of the conservative Confucian faction was sealed. The reformers under Wang Anshi did not play softball. When one of their ranks was appointed to some high position, they would demote anyone under them who was not with the program, and in the case of especially outspoken critics, they would appoint them to some minor post in a distant province, effectively exiling them.

One of the officials who was caught up in this purge was a man named Su Shi. Although Su Shi was nominally an official, he was best known for his poetry. In fact, today he is recognized as among the most important poets in Chinese letters, but even in his own day his poetry was wildly popular. Even the illiterate knew his poetry and would sing his poems in the streets. Well, Su Shi was not above inserting some biting political commentary into his poetry. One of his poems, for instance, criticized the salt monopoly that had been instituted as a part of the New Policies. Another had noted that whenever the money for seed loans arrived in the county seats, there was always an increase in the amount of alcohol in the town, but the peasants always seemed to go away empty-handed. These kinds of writings had gotten him exiled to Hangzhou where he was appointed to governor. This was not really too much of a punishment. They pay was good, the environs were beautiful, and he had the freedom to continue working on his poetry. But, most importantly for the reformers, out in Hangzhou he couldn’t cause any trouble at court. It’s in this period that Su Shi really came into his own as a poet.

Well, in the mid 1070s, Su Shi was visited at his outpost by Shen Kuo, who is the main subject of this segment of the narrative. To back up somewhat and introduce Shen Kuo, Shen Kuo was born in the south in 1031. He was a real beneficiary of the reforms of the imperial examination system. His father had been a fairly low level official, and his mother was from a similar social status. In older times, Shen Kuo, too, would have simply been a low-level official in an out of the way province. But he had done so well in his exams that he earned the attention of the imperial court and was appointed to the bureau of the treasury. But he seems to have had a particular knack for engineering and mathematics, so he was soon promoted to be the director of hydraulic works, and he had distinguished himself so well that within a decade he had been appointed to be the head of the astronomical bureau.

Well, not long after his appointment to astronomer royale, the Emperor sent him on a mission to check up on Su Shi and see how the great poet was faring out in the boondocks. Now, in his time at Court, Shen Kuo had ended up becoming a close ally of Wang Anshi. Shen Kuo’s engineering skills were put to good use in dredging an important canal near the capital, which was a component of the New Policies. And Shen Kuo further impressed by showing that the silt he recovered could be used as a fertilizer. Eventually, Wang Anshi had moved Shen Kuo into his closest circle of allies.

Well, during his visit with Su Shi, Shen Kuo copied down a number of the poet’s poems. When he got back to court, he read them aloud and declared that the poems insulted the Imperial Court and that the “expressions were all abusive and hateful.” Despite Shen Kuo’s snitching, nothing seems to have happened immediately. But a few years later, two other members of Wang Anshi’s faction seem to have become alarmed at the growing popularity of Su Shi’s poetry and they brought the matter back up and formally charged him with “denouncing the imperial chariot with great irreverence,” essentially treason. This was a very serious charge, in fact, one of the so-called “10 abominations,” for which the punishment was immediate execution and which was hardly ever commuted by the Emperor. The resulting trial, called the Crow Terrace Poetry Trial, was one of the most important events in the history of China in establishing the scope of artistic freedom and speech.

The trial seems to have been something like a graduate seminar in literary criticism, but with much higher stakes. The evidence in question was simply the corpus of poems that Su Shi had written over the years and it was up to the prosecution and defense to argue that the poems should be interpreted this way or that, either as an insult to the emperor, or simply a suggestion of how policies could be improved. After all, as a great poet, Su Shi did not exactly come right out and say precisely what he thought, so what were the implications of his poems and just how far did those implications go? Another facet of Su Shi’s defense was a legendary oath that Emperor Taizu, the first emperor of the Song Dynasty, had taken. Supposedly he had inscribed on a pillar the order to not kill the scholars of his court. During their coronation, the Song Emperors would ritually swear this oath. And to raise the stakes even higher, it was not merely Su Shi arguing in his own defense, although he was the central figure. There were thirty other people charged as accessories to his alleged crimes. If his poetry was treasonous, anyone who aided him in publishing or disseminating his work was also guilty of conspiracy and would be subject to similarly harsh punishment.

Well, in the end Su Shi was judged to be guilty of his crimes, but his popular fame as a poet did at least help him to get his punishment of decapitation commuted, which was very lucky for him. Instead he was once again sent into political exile. This exile was much more severe than his earlier exile. Previously he had been appointed the governor of a nice province, had a good salary and lived on a beautiful estate. This time around he was sent to a much more remote location and placed under house arrest, and while he was appointed to some minor office, he was given no salary and essentially lived in poverty during this time. But, for what it is worth, the poetry that Su Shi produced during this time is generally considered to be the best of his career.

Well, all this is to say that the factional politics in the Song Court were no joke and the political winds could quickly shift. While Shen Kuo had clearly chosen the right faction to join early in his career, his own good fortune was not to last. By the late 1070s the consequences of Wang Anshi’s New Policies were starting to make themselves felt, and this was not all for the good. Part of this was certainly flaws in the reforms or in their execution, but bad luck also played a role. In the middle of the decade there had been a major drought which resulted in a famine, and to make matters worse in 1075 a comet appeared in the skies, which was an omen that things were going very badly indeed. As a consequence of this Wang Anshi retired from public life around this time and the energy around the reform project was diminished. From the Emperor’s perspective this outcome was acceptable. His main interest had always been in increasing tax revenue so that he could attack the kingdoms to his north. By 1081 he felt that the New Policies, whatever their shortcomings, had at least produced enough revenue and raised a large enough army that he could begin his attack.

At this point, Shen Kuo’s career had taken him into the military and he had been given command of a force in Inner Mongolia. The first year and a half of his command was a resounding success. Shen Kuo successfully fended off attacks from the Western Xia, which was his primary objective, and captured a few military targets to boot. But then he had some differences of opinion with another officer in the area, and at least according to the accounts this other officer made a number of strategic blunders and in an ensuing attack, some 60,000 men under Shen Kuo’s command were killed.

That same year, the Emperor’s forces suffered an even more catastrophic defeat at Yongle. This battle, in effect, determined the outcome of the war. The Emperor Shenzong was crest stricken upon learning of this defeat and felt that his entire life’s purpose had been for nothing. The reforms he had implemented hadn’t turned out all that well, and their primary purpose, funding this war effort, had also failed. He nominally kept the war going for another few years, but his heart wasn’t in it, or anything else for that matter, and he died shortly thereafter.

The death of Emperor Shenzong saw the pendulum of reform start to swing back hard in the other direction. The first priority of the subsequent emperor, Emperor Zhezong, was to roll back the New Policies of Wang Anshi. Everyone who was in in the previous court was now out, and everyone who was out was now in. Shen Kuo, of course, was in the innermost circle of the reformers, and the military disaster that occurred under his watch was as good an excuse as any to get rid of him. Shen Kuo was stripped of his titles and official positions and sent to live in the countryside for six years. He managed to get his sentence reduced to two years by creating an atlas for the Emperor, at which point he was given the freedom to choose the place he wanted to live.

So, for the last decade of his life, Shen Kuo moved to an estate he had purchased at the height of his career. Now, I went into all this detail about Shen Kuo’s life because it’s really thanks to this exile in the final years of his life that we are able to know so much about him. To pass the time, he wrote a long autobiographical book, which he called Brush Talks from a Dream Brook. The name came from the name of his estate, which was Dream Brook, and he wrote that “Because I only had my writing brush and ink slab to converse with, I call it my Brush Talks.” The book is a series of essays, largely on the things that Shen Kuo had worked on in his long career. And we can see from this work that he was a remarkable polymath.

In addition to his innovations in civil engineering and, of course, astronomy, Shen Kuo made major advances in medicine, geology, meteorology, optics, and mathematics, among other disciplines. Relevant to his astronomical work he made advances in spherical geometry, and like Archimedes he also came up with a notation to specify extremely large numbers, in his case a number as large as 10 to the power of 172. Like Xenophanes, Shen Kuo had observed sea shells high up in mountains, and in one location where erosion had stripped away the side of a mountain, he had even observed that the shells formed a band at roughly the same level across the mountain. From this he proposed that geographical features must change gradually over time, and that in the distant past the mountains must have been lower and the sea closer.

Well, in terms of his astronomy, one discovery of his in particular is indicative of his exacting nature as an astronomer. At the time, the pole star was believed to be a star called Chi Hsing, or, the Summit Star, appropriately enough. When Shen Kuo was installed as the head of the Astronomical Bureau he decided to check to see whether this star was indeed at the north celestial pole. To do this, he constructed a sighting tube and then oriented it towards this star. He then observed it over the course of the night and found that the star moved out of the sight of the tube. Based on this he concluded that this star must not be the true pole star, because if the star really was at the north celestial pole it would not move at all and would stay within the sight of the tube all night long. But he didn’t stop there. He then constructed a slightly wider sighting tube and repeated the experiment. Once again, the supposed pole star drifted out of the line of sight of the tube. So, he repeated the process again, he constructed a new, slightly wider sighting tube and did the experiment all over again. Over the course of three months he continued constructing slightly wider sighting tubes until, at last, he had constructed a tube that was just wide enough that the pole star circled around the edge of the field of view over the course of the night. Based on the width of this sighting tube, he concluded that the pole star was slightly more than 3° away from the true pole. This episode is a good illustration of his engineering skill in being able to design precision instruments for the job at hand, his perseverance in carrying the experiment out, and the skepticism he had to apply in the first place to even think to test the idea that the pole star might not be exactly at the pole.

Another, somewhat less successful, program that Shen Kuo attempted was a project to precisely measure the positions of the Moon and planets at dusk, midnight, and dawn for five years. As I mentioned a few episodes back, around this time in Chinese history there was some, shall we say, talent issues in the Astronomical Bureau. Although the astronomers were supposed to record the positions of the Moon and planets, in practice they would simply use a simplified version of an old planetary model to predict where the planets should be and mark that down rather than observe where the planets actually were. And at this point the model that they had been using was more than three centuries old and had become extremely inaccurate. Nevertheless, even as head of the Astronomical Bureau, Shen Kuo was not able to get his underlings to make real observations on a consistent basis.

Although Shen Kuo’s greatest achievements were in areas that he could put his engineering abilities to use, constructing instruments to make observations, he was adept at the more theoretical side of astronomy as well. In his day it was still an open question whether the Moon and Sun were flat disks or spherical. Proponents of the flat disk or fan theory argued that if the Moon and Sun were spherical, they would crash into each other when they met on the sky as during a solar eclipse. For his part, Shen Kuo argued in favor of the spherical theory. He devised a demonstration where he painted one side of a ball a light color and the other dark. Then by rotating the ball through various angles you could observe that the light portion would form a crescent, just as you see with the phases of the moon. Furthermore, he seems to have been the first one to argue that the reason that we don’t see an eclipse every month at the new moon is because the orbits of the Sun and Moon were slightly inclined to each other, so most months they did not overlap on the sky.

Well, this episode is late enough as it is, so I think that is all I will say about Shen Kuo. Next month will be the last episode in our series on the astronomy of pre-modern China. In the next episode we’ll skip ahead to the late Ming Dynasty and explore the arrival of the Jesuits to China, and how the astronomy they brought with them helped them to get access deep inside the Imperial Court. 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