Talk given at a symposium held at
Victoria University of Wellington on 21 April, 2000,
in honour of
David Vere-Jones
on the occasion of his 65th birthday
Abstract
Zhang
Heng—his
character, life and times
Zhang Heng is known in the West for his invention in the first century AD of an instrument for detecting earthquakes. This was only one of his many scientific accomplishments. But he is well-known in China not only for his work in astronomy, mathematics, seismology and technology. He was also famous as a poet, philosopher and administrator. His life and character are a reflection of the times in which he lived. This talk is an introduction to some of the aspects of history and philosophy of the period which help us to understand how such a prominent man of letters was led eventually into the field of science and technology.
Preamble
As an undergraduate, David studied under Professor Jim Campbell, who held the strong conviction that as good an all-round personality can be developed through doing mathematics as through working in any of the traditional fields of classics, literature, philosophy, history, etc. David is a good example of the validity of Professor Campbell's belief, for we all know that not only is he a mathematician, statistician, and seismologist, involved in mathematics and closely related fields; but he is also among other things: an actor, a sportsman (Rhodes scholar), a linguist fluent in Russian, and an administrator, one who has taken a prominent part in developing New Zealand education, not only in mathematical and statistical education, but also, a fact which is less well-known, in Chinese Studies, where he chaired the committee which developed the sixth-form certificate in Chinese when it was first introduced into New Zealand Schools, many years ago, long before today's fashionable interest in Chinese Studies began.
In this talk then, I would like to draw your attention to a scholar of ancient times, also with wide-ranging abilities, a Chinese scholar by the name of Zhang Heng. In works in English, almost the only thing for which he is known is the invention of an instrument for detecting earthquakes, but there is a lot more of interest in him than this. In English, detailed information about his scientific work can be found mainly in Joseph Needham's Mathematics and the sciences of the heavens and the earth. But what I want to do here is to summarise for you information about other aspects of his life, which although plentiful in Chinese, is not so easy to find in English.
Zhang Heng's is alleged to have made a number of scientific and technological inventions and discoveries which are claimed to be world firsts. These include the invention of an earthquake detector, a celestial sphere driven by a mechanical water-clock, differential gear mechanisms for a odometer, a mechanical south-pointing chariot, and some other mechanical contraptions.
People educated in the Western tradition sometimes find it hard to believe that this could have been possible in a culture which had no scientific tradition like the one which we consider to be uniquely valid, and which we tend to think, developed only in the West. This may be because most works in English present Chinese culture as being almost entirely a humanistic one, interested in literature and the arts, but showing little interest in science and technology, and even less interest in metaphysical speculation about why the physical world worked the way it did, or about who or what made human beings behave as they did.
So what I hope to do in this talk, is not to list the things that Zhang Heng is alleged to have done, but to try to give you some idea of the historical and philosophical background against which his achievements were made.
Zhang Heng was born in 78AD in the region of China near the middle reaches of the Yellow River Valley where Chinese civilisation first developed, round about BC2500.
For long periods in her history, China has been not a unified state, so much as a collection of many states, often at loggerheads with one another, and was at one period even known as the warring states. During the Zhou dynasty, founded in about BC1100, China was made up of hundreds of feudal kingdoms, which were not finally reunited into a single empire until BC221. This is the empire, famous to most westerners today for the terra-cotta warriors excavated recently from the approaches to the mausoleum of the so-called First EmperorC Qin Shihuang. But this new Qin Empire lasted only just over fifteen years, before being overthrown by the Han dynasty which was to last, for some 400 years, except for a brief interregnum between 9 and 25 AD, and so is referred to in the history books as the former and the later Han dynasties. Zhang Heng thus lived in the first century AD C just after the disturbances that brought about the fall of the former Han and led to the restoration under the later Han.
The Han period is the one in which the foundations of Chinese civilisation, laid during the Zhou dynasty in the 5th century BC, were consolidated. There were so many schools of philosophy current at this time, that they are known in Chinese as the "hundred schools", one of which being the one we know in English as "Confucianism".
In uniting the feudal states of the Zhou period into a single empire, the new emperor, Qin Shihuang, strove not only for territorial unity, but also for ideological unity, and to do this banned all schools of thought, other than the legalist school, which believed that good government could only be achieved only through a system of rewards and punishments, based on a strict adherence to laws. This resulted in the setting up of an authoritarian, despotic empire, during which nearly all the classical works of history and philosophy, especially those of the Confucian school were destroyed. However, the schools such as the "Yin-yang" school, and the "five forces" school, were allowed to continue, as the Emperor wanted them to find him an elixir of life.
The first Han emperor that followed also wanted to enforce ideological as well as territorial unity. To maintain ideological unity, he had to find an alternative to the legalist philosophy, which had become too much hated because of the despotism of the Qin Empire, but he also despised the Confucian scholars C as idealists out of touch with reality. With the Confucianist and Legalist schools ruled out, the early years of the Han dynasty were dominated by a philosophical school known as the Huang-Lao school. And so, it was not until the sixth emperor Han Wudi came to the throne in BC141 that Confucian teachings were adopted as the official doctrine, and a state university was set up to teach the Confucian classics.
But this official philosophy incorporated into the basic teachings of Confucius, the religious and superstitious ideas of the Huang-Lao school, which had dominated the country during the reigns of the preceding Han rulers. The ideas of the Huang-Lao philosophy sprang from the Book of Changes, an ancient manual of divination, for telling the future on behalf of the emperor.
Divination in early Chinese history had been done by heating tortoise shells, and then interpreting the cracks that formed. The cracks were classified into two kinds, either broken lines or continuous ones, known as yin and yang lines, and it was thought that these lines were in constant movement, changing continuously from yin to yang and vice versa. From this, they developed an elaborate system for divining the future based on eight trigrams formed by all possible triples of the yin-yang lines, and of 64 hexagrams based on all possible pairings of the 8 trigrams. They developed the theory that all matter and all events in the universe arose as a result of the constant transformations of yin into yang and vice versa. How these changes work and their significance form the basis of the yin-yang theory.
But they noticed other changes as well, such as that wood supports fire, fire produces earth (in the form of ashes), earth produces metal, and metal produces water ( a bronze mirror, for example can produce dew) and that water makes possible the growth of wood. In addition to this productive cycle, they observed a destructive cycle in which water extinguishes fire, fire melts metal, metal cuts wood, wood (tree roots) penetrates earth, and earth soaks up water. And so the productive and destructive cycles in which of these five "forces" of wood, fire, earth, metal and water moved became the basis of the "five-forces" theory which was then used for analysing and controlling the behaviour of natural phenomena.
Once the divination techniques taught in the Book of Changes, and the elaborate numerology derived from the "yin-yang" and the "five forces" theories, were all incorporated into the official orthodoxy, apocryphal works were written and even forged, to prove that Confucius had supported all this mumbo-jumbo, even though, he had in fact been a rationalist of sorts, interested mainly in things like morality, how to teach it, and how to apply it, in particular to government and politics, and was not at all interested in the supernatural. Once the orthodox doctrine was established and accepted, it was spread and enforced through the education of future officials at the imperial university, and the selection and appointment of those likely to toe the line.
Zhang Heng, was born into a family of scholars. Nothing is known of his father, but his grandfather, was a child prodigy who eventually became a high official, but died leaving the family in reduced circumstances, and it is likely that Zhang Heng's early life of comparative poverty influenced his social attitudes in later life. It is recorded nevertheless that Zhang Heng, from his youth, excelled in the writing of compositions, and, in fact, his early fame rests not on his scientific and technological inventions, but on his literary ability.
In 93AD, at the age of sixteen, he left home to further his education, by visiting private teachers and noted scholars, in the region around the former capital of Chang'an and the then capital of Luoyang, arriving in Luoyang itself in 95AD at the age of 18. In Luoyang, he observed at the Imperial University, in the course of which he mastered
1. the Five Confucian Classics, and
2. the so-called six skills (of ceremonial rites, music, charioteering, archery, calligraphy, and mathematics, considered essential accomplishments for any well-bred young gentleman of the time),
both of which formed the core of the university curriculum. The fact that Zhang Heng merely observed at the University indicates that he was not high enough in rank, and/or did not have the contacts needed to qualify for entry. Nevertheless, his official biography mentions that, though he became versed in the Confucian classics and proficient in the six skills, he was not proud or arrogant, but that he did not like mixing with mediocrities, thus giving us a first glimpse of his character.
By the time Zhang Heng arrived in Luoyang, opposition to the superstitious aspects of the official amalgam of Daoism and Confucianism had been developing for some time, and two schools of thought had developed known as the New Text School, and the Old Text School. The new Text School, supported the orthodox doctrines, whereas the old Text School rejected the quasi-religious and superstitious way in which the yin-yang and five forces theories were being used, emphasising instead the rationalist aspects of early Confucianism.
Among the friends that Zhang Heng made in Luoyang was one who became famous later for his commentaries on the old Texts, and so it is likely that Zhang Heng would have discussed the dispute with him in their days together as students, and that this would influence his attitudes in later life. Among the other sons of high officials was one who became his best friend. This was Cui Yuan, later a mathematician, astronomer and calendar-maker. It is possible then that his interest in mathematics and astronomy first began to develop at this time. But his first interests were literary, and were to remain so until he was well into his thirties.
It was in Luoyang that he wrote his first poems describing his feelings on his earlier visits to scenic and historic sites in the regions around the capitals of Chang'an and Luoyang, and it was in Luoyang too that he began his famous works in rhymed prose on these two capitals.
These two poems took him ten years to complete, and his official biography praises the meticulous care taken in their execution and in the development of the ideas in them. This shows an attitude to work which was to stand him in good stead in his later scientific work as well.
In the Han period and later in Chinese history, becoming an official was almost the only road to wealth and to power, and the road to becoming an official was through education. Zhang Heng, had acquired the necessary education for becoming an official first through his travels, and then through his sitting in at the state University in Luoyang, and his contacts there, and so there is no doubt that he could have obtained an official post without difficulty.
In his day, officials were appointed through the recommendation of other high officials. He had already attracted the attention of other scholars during his time in Luoyang, and had made friends with many future scholars, some of them the sons of other prominent scholars, and others with connections to the empress's family, and so he was certainly moving in the right circles if he had wanted to become an official. Zhang Heng was indeed nominated for public office a number of times during his stay in Luoyang, but refused to accept any post. Instead, in 100 AD, at the age of 23, he agreed to serve as secretary to the Prefect of his home district. His duties were not heavy, and so he found plenty of time to write and to study.
But he was also involved in administrative work. This would have made Zhang Heng familiar with the mechanical irrigation systems for drawing water that were in use, providing him with the practical experience for some of his later mechanical inventions. The devastation caused by the revolt that brought about the interregnum between the two parts of the Han dynasty, led the government to introduce many agricultural improvements, and the Prefect and Zhang Heng were put in charge of repairing the irrigation systems in their region. He was also involved together with the prefect in education, the two being responsible for the restoration of some school buildings, on the completion of which, a celebration banquet was organised for the local Confucian scholars.
In 108AD, when he was 31, the Prefect was promoted and had to return to the capital, but Zhang Heng refused to leave his village, but remained there to study. During his eight years as secretary to the prefect, his name came to the attention of a brother of the Empress Dowager, the general-in-chief, Deng Zhi, who headed an extremely powerful faction at court. Rulers in China have always found it expedient to increase their prestige by surrounding themselves with scholars, and so Deng Zhi tried to attract Zhang Heng by offering him a post in his entourage a number times, but Zhang Heng refused each time. When he fell from power in 121 AD, Deng Zhi committed suicide, dragging many of his followers down with him.
But were there other reasons for why Zhang Heng was so determined not to take the path to officialdom? We can answer this by looking at his poetry. In the Han period, the fashionable literary form was a kind of rhymed prose, known in Chinese as the fu, but often translated into English as a "rhapsody", although the subject matter was often nothing more than fulsome praise of the emperor and his works.
Zhang Heng became known as one of the "four great masters of the fu", and of the two which he began in his student days in Luoyang, one was on the former western capital Chang'an while the other was on the eastern capital of Luoyang. They had been written in imitation of a famous fu Rhapsody on two capitals, by the historian Ban Gu, who served in the entourage of a famous general. When the general fell from favour, Ban Gu was arrested, and died in prison in Luoyang, just before Zhang Heng arrived there as a student; and this would no doubt been widely talked about in the circles in which he moved. The fact that in his two early rhapsodies Zhang Heng chose to imitate Ban Gu's rhapsody, already a famous work, is an indication that he thought he could improve on Ban Gu's work. In what way did he do this?
Poetry in China, has never had a tradition of ''art for art's sake" as in the west. Since ancient times, it has been regarded in China as a didactic tool, particularly suitable for expressing social comment and criticism. This has been true in Chinese culture since the appearance of the Classic of Poetry, nearly three thousand years ago.
Ban Gu's Rhapsody on the two capitals appears at first sight to be little more than a long elaborate description of the construction of the splendid palaces first in the capitals of Chang'an, and in Luoyang, and of the pomp and ceremony of the events that take place within them. But in fact, the lines imply that the extravagance and ostentation of life at court was not really an appropriate way of life for the ruler and his nobles.
Zhang Heng's first fu, the xijing fu, Rhapsody on the western capital, also describes the prosperity and the power of Chang'an, the capital of the western Han dynasty. The rich luxurious life led by the emperor, nobles, officials and courtiers which he describes, can be interpreted as praise for the stability, power, and cultural splendour of the new empire founded two and a half centuries before his time, after the years of confusion during the period of the warring states, and the tyrannical rule of Qin Shihuang. But his criticism is clearer than in Ban Gu's rhapsody, for he scoffs, for instance, at the emperor's concern for finding an elixir of life, asking "if it were possible to live for ever, why such urgent building of mausoleums?"And he accuses certain inhabitants of the capital of "taking death lightly, organising cliques, forming gangs," claiming that the followers of such men were "as thick as clouds",and in describing an acrobatic display in the presence of the emperor, he accuses the emperor of "gathering precious treasure for play and amusement, mixing the rare and the beautiful with the wasteful and extravagant."
In his second fu, dongjingfu, the Eastern capital Rhapsody, his views on the social reality of his times are even more explicit. After stating quite openly that the "ostentation of the early Han Palaces was wrong" , he goes on to describe the construction of the new palaces, and the laying out of the imperial hunting domains in Luoyang, the grandeur of the imperial sacrifices, and he then goes on to describe scenes of the emperor and his courtiers relaxing after the grand ceremonies by going off in secret to the houses of courtesans. He then warns of the need for "careful behaviour", pointing out that " popular resentment can lead to enmity", quoting the well-known saying from one of the early Confucian philosophers, that "water can keep a boat afloat, but it can also overturn it." But although he realises that "veiled remonstrance brings no improvement," he warns that "a man in a dried-fish shop does not notice the stench".
There is no doubt that his distaste for the life led by the Confucians mediocrities who surrounded the Emperor was one of the reasons that kept him from accepting an official post. But, after centuries of division, the country was now a unified state covering a large area, and giving peace and stability to a large number of ethnic groups, and so, one might have expected him to have been willing to work for such a state. But the fate of scholars like Sima Qian, castrated for openly supporting a general criticised by the emperor, Ban Gu, imprisoned after the fall of the general whom he served, and the scholars brought down by the fall of the General Deng Zhi, were all comparatively recent events that would not have inspired him to aim for high office. Finally, in 111 AD, the emperor sent an imperial carriage to his home village to offer him a post as a courtier in the royal palace, and he was compelled to return to Luoyang, since he could scarcely refuse what amounted to an imperial command. By now he was 34, but it marks a turning point in his life.
In his job in the palace, he had little to do other than to fetch and carry for the officials of the history department. But this gave him access to books that he would not otherwise have seen, and it is reported in his official biography that it was at this point that he wrote to his best friend, the mathematician Cui Yuan, expressing his admiration for a philosophical work by Yang Xiong the Da Xuan Jing (The Classic of the Great Mystery)
"Xuán", meaning "mystery", is similar to the "Dao" or the "way" of traditional Chinese philosophy, whether it be Confucianism or Daoism. It was the principle which organised the behaviour of natural phenomena. For some early Confucians, it was an impersonal natural principle, but for orthodox Han Confucians, it was a kind of supernatural will or power.
Reading Yang Xiong's work must have re-opened Zhang Heng's mind to questions about the nature of the universe. For Yang Xiong's description of the universe laid little stress on the superstitious aspects of the Huang-Lao Daoism which formed such a large part of orthodox Han Confucianism. Because of his job in the palace, Zhang Heng would also have had access to other works, which attacked many of the current superstitious beliefs, promoted by the New Text school. These would not have been widely available outside.
Now, the court historians of ancient China were not just concerned with what we think of today as 'history'. They had another more important function. Since in Chinese the word "tian" translated as "Heaven" with a capital H in English, can also mean the physical " heavens", or the "sky", the orthodox doctrine of the day saw a close interaction between Heaven and Man. It was believed not only that human actions were affected by the movements in the heavens. It was also believed that human actions could affect the goings-on in the heavens. It was imperative therefore that the historians know what was going on in the heavens as well as what was going on earth, and so they had therefore to be astronomers, and indeed astrologers, as well as historians.
In order to be able to inform the emperor and his advisers so that they would know how and when they should act, and in particular the exact moment at which certain religious or sacrificial ceremonies had to be performed, the astronomers not only had to observe what was happening in the heavens, they also had to be able to predict what was going to happen, and so, for this purpose, they had to be able to construct accurate calendars. Thus the makers of the calendars were concerned not only with measuring the length of the years and months, and finding out the exact timing of the equinoxes and solstices, they also had to keep track of eclipses, comets, and any other celestial phenomena since these might be portents of what was going to happen on earth. All this required then that they be knowledgeable in mathematics as well. It was as a messenger-boy in an imperial history department of this kind that Zhang Heng began his career at court.
Since Heaven was thought by some to have some kind of moral power as well as physical power, observing the heavens was therefore a way of finding out the will of Heaven. The Han rulers promoted this idea of Heaven as a moral force, particularly as the ancient idea of the emperor ruling as a result of a mandate granted by Heaven helped to legitimise their authority. But Confucius had always avoided talking about the supernatural. And so, The Han Confucian scholars therefore sought support for their views of Heaven from other sources, of which the most important were the Yin-Yang theory, and the "five forces" theory.
Some of the appendices written to the Book of Changes, and some of the apocryphal writings were ascribed to Confucius himself. These elaborated on the mystical aspects of the yin-yang theory and the five forces theory, and promoted especially the idea of Heaven as not only the prime mover of everything in the universe, but also as a kind of divine will or a power in constant interaction with man. But the early Confucian, Xunzi, had opposed this idea of the moral nature of "tian", as early as the 4th century BC, while other rationalist views, like those of Wang Chong's began appearing in the first century AD. The work by Yang Xiong which attracted Zhang Heng's interest, was also rationalistic. It saw the yin and yang as simply opposite but complementary physical elements whose natural interaction, brought about the existence of everything in the universe, and the "five forces" were seen as being natural forces that needed no help from the supernatural for their interaction either.
Four years after taking up his post as a courtier in the palace, in 115AD, now in his late thirties, Zhang Heng was promoted to the post of Grand Historian or Astronomer Royal, and so was now in charge of the observation of the heavens, and the calendar making.It was while he was in this office, that he made what the Chinese sources say was his greatest achievement. From the results of his observational work, he constructed a bronze celestial globe inscribed with the stars, surrounded by armillary rings for the equator, ecliptic, horizon, and meridian. Armillary spheres have a long history, but the one constructed by Zhang Heng was driven by water dripping from a bronze vessel in order to activate a system of differential gears to drive the sphere at a speed of one rotation per day to match the observed motion of the stars. As Taishiling, Zhang Heng became personally involved in a great deal of observational work, and as a result he not only added improvements to the armillary sphere that was already in existence, but also produced a theory of the universe, based on his observational experience.
This was an elaboration of the current Huntian theory in which the universe was seen as an infinite space containing the heavens in the shape of an egg, with the earth like a yolk floating inside its shell. This was explained in his book lingxian (spiritual constitution of the universe), written in 118AD. In the course of elaborating his theory, Zhang Heng states that the moon has no light of its own, but simply reflects light that it receives from the sun, and gives a reason for the eclipse of the moon, although his explanation is is quite unscientific.As part of his observational work, he also recorded the positions of some 2500 fixed stars, which is about the maximum that can be observed with the naked eye in the region of Luoyang. In the course of refining his theory of the universe, he not only wrote the Ling xian, but also a mathematical text Suanwang lun (Discourse on mathematical networks). In this he introduced a system of grid co-ordinates for mapping the stars, which was also later used for mapping the earth, and it is from this book that later mathematicians quoted his use of the square root of ten as an approximation for pi, the closest approximation used in China or indeed anywhere else up to that time.
In 121AD, he withdrew from his position as Taishiling, after six years in the post, and was put in charge of controlling access to the Emperor, a post that required no scientific knowledge or experience. Two years later, In 123 AD, a dispute on calendar-making broke out:
Since 104 BC, the calendar in use had been had been replaced by the sifen or quarter remainder calendar, based on a year of length 3653 days instead of 365.2502 days. Now some 200 years later, some discrepancies were found to still remain, and so some orthodox Han Confucians wanted this calendar abandoned, and the old calendar restored, on the grounds that not only did the new calendar not conform with the predictions made by their divination charts, which were derived from the Book of Changes, and deduced from the yin-yang and five forces theories in current use for foretelling good and bad fortune, but also that no sanction be found for the new calendar in the classical Confucian texts or their appendices, and that the calendar was therefore contrary to the authority of the past.
The dispute resulted in the calling of a conference of scholars, in which Zhang Heng opposed the restoration on the basis of observed facts, and a comparison with the calendars of the past. Zhang Heng was able to show that not only were divination charts not mentioned in the classical Confucian texts either, but that the superior accuracy of the sifen calendar was proved by actual observation of the heavens. He likened the astronomers who supported the divination techniques to painters who paint only ghosts and monsters, but refused to paint dogs or horses, because if they did so, their lack of skill would be obvious to anyone. In the end the new calendar was retained.
During his time away from the history department, he continued his interest in technology, and he constructed a mechanical south-pointing chariot. He also made use of a system of differential gears to invent a chariot which could keep track of distances travelled. He appears also to have invented a wooden bird that was capable of flying, for during his continuing struggle with the diviners, he was accused of not doing his job properly, and of wasting his time in useless activities. Since he could invent a wooden bird that could fly, the critics scoffed, how was it that he could not fly himself, but instead remained at the same post year after year, without receiving any increase in either rank or salary. In his reply, Zhang Heng's wrote that he was not ashamed of not receiving a sufficient salary, but would only be ashamed if his knowledge was not extensive. He was not ashamed of not having a high rank, but would be ashamed, if he did not have a high morality.
Five years after abandoning his post as Astronomer Royal, in 126 AD, he was re-instated, an event which he welcomed in a letter to a friend as a return to "Paradise" (Pénglái). Observation of celestial phenomena, seen as portents of good or evil, then led naturally to an interest in observing terrestrial portents such as earthquakes, especially since China in general, and the Luoyang region in particular, were earthquake zones, and so in 132AD, when he was already fifty-five years of age, he made the invention for which he is famous in he West, namely a directional earthquake detector. But his original construction has been lost, and what we have today are reconstructions based on the description given in his official biography and descriptions given by later writers.
The description in his official biography in he History of the Former Han Dynasty, can be translated as follows:
"In 132AD Zhang Heng also invented a 'directional earthquake detector'. It was cast in fine bronze with a diameter of eight chi, enclosed at both the top and the bottom, and shaped like wine-jar. It was ornamented with characters in the seal script, and designs of mountains, tortoises, birds and animals. Inside was a large column, and from its side ran eight tracks, fitted with mechanisms for opening and closing. Outside were eight dragons, each head holding a bronze ball, while below were eight toads with their mouths open to receive the balls. The ingenious construction of the toothed mechanisms were all hidden inside the vessel, and the cover fitted tightly around without any crack. If an earthquake occurred, the jar shook, and the dragon mechanism was set in motion and spat out a ball, which the toad caught in its mouth. The sound would spread clearly, and from this observers would be informed. Although the mechanism for one dragon was set in motion, the seven other heads did not move. By seeking its direction, the place of the earthquake was known. When examined with the reality, the agreement was like a miracle. Since records have been made in books and canons, there has been nothing like this. On one occasion, one of the dragon mechanisms was set into motion, but no earthquake was felt. The scholars of the capital were all astonished that there was no confirmation. But several days later, a messenger arrived. There had indeed been an earthquake in Longxi, whereupon all were persuaded of its marvel. From then on the officials in charge of history were ordered to record the directions from which earthquakes come."
No details are given of the column, tracks and toothed mechanisms hidden inside the detector. Although later Chinese writers gave more details of the mechanisms, by the thirteenth century, the principles of Zhang Heng's earthquake-detector had been lost. The structure of the instrument reflects the huntian theory in that:C the outer body symbolises the heavens (egg-shell), the inner pendulum the earth; the dragons symbolise the yang forces, and the toads the yin forces, bearing witness to the dialectical relationship between yin and yang, above and below, movement and stillness.
In 133AD, Zhang Heng was moved from the history department to a post giving him personal access to the Emperor, and whose duties were to advise the Emperor on state affairs and report his decisions. As a result of further disputes with the orthodox Confucians, Zhang Heng called for the banning of the apocryphal writings, but when this was rejected, he asked for a transfer to the imperial library to re-edit the classics, and to correct their mistakes. But this was also refused. He also made many enemies when he became caught up in the factional rivalries at court, and wrote a Rhapsody on contemplating the Mystery in which he wonders whether in the face of a corrupt world of slander and hostility he should escape far from home or remain, in spite of adversity, to persist in the cultivation of his character.
Ultimately, his rationalistic view of the universe derived from Yang Xiong's Daxuan jing, gives him little comfort, and he wishes to return home to continue his study of the ancient classics, write poetry, and lead the life of a country scholar, but permission to do this is also refused. Instead, he was sent as Prime Minister to the state of Hejian, a minor state within the Han Empire. The ruler of Hejian was corrupt and debauched, bending the law in collusion with the local landlords and bullies. Once he took up his post, Zheng Heng, was able enforce the laws and stop the activities of the landlords and other local despots, who thereupon fled to exercise their skills elsewhere. This did little for the people it was intended to help. Instead his courts were now filled with insignificant people involved in petty crimes, the big fish having all escaped.
He fell into a deep depression over the inefficacy of his reforms, expressing this in a number of his later poems . In his last poem he adopted a new poetical form made up of a series 7-syllable couplets, and so helped to develop a poetic form which eventually replaced the rhapsody to become the most widely used form of Chinese poetry during the Tang dynasty six centuries later, and during subsequent dynasties, right up to today. His request to retire was refused, and he was recalled to the capital instead and given another position in the history department, where he died at his post in 139AD at the age of 62.
Conclusion
Zhang Heng's invention of the water driven armillary sphere came as a result of his interest in the Huntian theory
The Huntian theory and his theory of the evolution of the cosmos arose from his interest in the rational aspects of the Yin-Yang and the Five forces theories. The observations made with the armillary sphere for constructing the calendar led to his early approximation to pi, and to his development of co-ordinate grids in both celestial and geographical mapping. A career in the foretelling the future from heavenly portents, led to his becoming interested in how to foretell other portents of disaster such as earthquakes. His study of the Yin-yang, five elements theories laid the basis for his fight against superstition in attacking the divination theories of other scholars of his time.
This attitude no doubt also affected his administrative actions such as the encouragement of water conservancy; and influenced his political actions, such as his long refusal to take part in official life; while the social attitudes reflected in his poems, such as his disillusionment with the life led by those who governed, and his sympathy for the governed, contributed to his extreme depression in the later years of his life.
Thus he was not just a seismologist, inventor, astronomer, and mathematician, but also a poet, a painter, philosopher and administrator C a man of letters as well as a man of science: in fact a kind of early Chinese "renaissance man". What I have tried to show is that Zhang Heng was not only a man skilled in so many different fields, but a man with principles and ideals which are reflected in all that he accomplished or tried to accomplish. As such, he is just one mathematician in a long tradition of mathematicians who did not confine themselves to mathematics.
David is certainly another mathematician in this tradition, and I am grateful to have been given this opportunity to show my esteem by giving this talk in his honour, and at the same time in honour of Mary, whose heritage he and his children, and indeed all of us, share.
J. Hoe
A printed version of this talk with endnotes and Chinese characters, is available form the Centre
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This page last revised: 24th July, 2002
