Astronomy and Mathematics

Like people of other cultures, the ancient Chinese paid close attention to the heavenly bodies and their movements, because the sun, moon, stars and their movements were the most eternal features that the ancient people could observe.
Since the ancient Chinese believed that the perceived movements of the stars were closely related to the destiny of the country and its rulers, for thousands of years they recorded their movements with great attention. From the 16th century BC to the end of the 19th century AD, almost every dynasty appointed officials charged with the sole task of observing and recording the changes in the heavens. Such observations and records have left a rich astronomical legacy.
A long time ago, people noticed that the sun and moon sometimes suddenly lost their brightness. People could not figure out the reason and feared that, once gone, the brightness would not return and would mean the end of the world. Precisely because of this, the ancient Chinese began to observe solar and lunar eclipses, recording the time and size of the coverage, and searching for the reasons for eclipses. The earliest solar eclipse record that can be verified appears in a bone inscription dating back to the Shang Dynasty. Studies have proved that the solar eclipse recorded actually took place on May 26, 1217 BC, thus also proving that it was the first reliable record of an eclipse man ever made. Records of lunar eclipses, however, date back to an even earlier time. Bone and tortoise shell inscriptions record five lunar eclipses that took place during the 14th and 13th centuries BC.
Ancient Chinese astronomers diligently observed solar eclipses, and made scrupulous records, maintaining continuity of the recording. For instance, the Spring and Autumn Annals record 37 solar eclipses during a period of 294 years -- from 770 to 476 BC. Studies have proved that most of these records are reliable. Later, recordings of solar eclipses begun in the 3rd century BC and of lunar eclipses begun in the 5th century BC continued all the way to contemporary times.
While Western astronomers of the Renaissance period were still arguing in 1615 who was the first to discover sunspots, Chinese astronomers had already accumulated a large amount of records on sunspots. Now it is known that the earliest records of sunspots were made in 28 BC by Chinese astronomers during the reign of Emperor Cheng of the Western Han Dynasty. From then until the late Ming Dynasty in the mid-17th century, Chinese history books recorded more than 100 sunspots. Furthermore, they also took note of other phenomena concerning the sun, such as solar prominences and coronas. The first record of a solar prominence has been found in a tortoise shell inscription, which describes "three suddenly bursting fires eating a chunk of the sun". According to statistics, sunspots occur in a cycle every 11.33 years on average, which is in conformity with ancient Chinese documents and once again testifies to the fact that records of sunspots made by ancient Chinese people are a very valuable astronomical legacy.
China also compiled a huge amount of records on meteoric showers. The Bamboo Annals records a meteoric shower in 2133 BC in today's Henan Province. This is the first mention in the world of a meteoric shower.
Meteorites, both of iron and of stone, often fall to the earth, and this was noticed by the ancient Chinese. Song Yingxing, a scientist of the late Ming period, once said, "When stars fall to the earth, they become stones." Shen Kuo, a scientist of the Song Dynasty, observed three meteoric explosions one evening in 1064, and described in detail an incident of meteorites falling into the garden of a farmer in Jiangsu Province in his book Dream Stream Essays.
During the Spring and Autumn Period, some 2,200 years ago, Chinese documents already had entries on what later came to be known as Halley's Comet. The record of the comet, which appeared in 613 BC, in Spring and Autumn Annals is recognized as the earliest mention of Halley's Comet in the world. Since Halley's Comet visits the earth once every 76 years, it came back to the earth 29 times during a period of 2,149 years from 240 BC (the 7th year of the reign of the First Emperor of Qin) to 1910 (the 2nd year of the reign of Emperor Xuantong of Qing). Each of these visits was clearly recorded by Chinese scholars. J. R. Hind, an astronomer from the West, once used these continuous data to calculate the orbit of Halley's Comet, and discovered that the angle of the orbit showed a narrowing trend. In the Han Dynasty, it was 170 degrees, but it narrowed down to 161 degrees in the mid-19th century.
From 1600 BC to AD 1600, China recorded comets 581 times, leaving behind valuable materials. In 635 BC, Chinese astronomers pointed out that the comet always traveled with its back to the sun. Without these repeated observations, the detailed descriptions of the comet tails could not have been made, nor could the relationship between the sun and comets have been correctly deduced.
The scientific and technological achievements of the Warring States Period (475-221 BC) are very impressive. The various feudal states all had their own court astronomers. The most famous among them -- Gan De of the State of Chu and Shi Shen of the State of Wei -- together wrote The Gan and Shi Book of the Stars, which accurately record the positions of 120 stars, constituting the world's earliest star chart. The lid of a lacquer chest of the Warring States Period unearthed in Suizhou, Hebei Province, has a list of the 28 constellations, China's earliest record of the entire list of the constellations.
Novas and supernovas are all variable stars created by nova outbursts. During an outburst, the brightness of a nova may increase during a matter of a few days by several thousand or even dozens of thousands of times. Then it will gradually dim, to eventually return to its original brightness after several or dozens of years. Outbursts of supernovas are on an even grander scale, increasing their brightness by up to hundreds of millions of times.
There are more than 50 reliable records of novas made in ancient China, in addition to over a dozen cases of supernovas. The first record of a nova dates from 1400 BC in China, in a tortoise shell inscription, which reads as follows: "On the 7th day of a certain month, a new star appeared next to 'Heart Constellation II'." From 1400 BC to AD 1600, China recorded 90 novas. Among them the supernova discovered in 1054 was the first to be confirmed by modern radio astronomers. In 1731, a British astronomer discovered an oblong spot of fog over China. After observation, calculation and analysis by several astronomers, it was proved that the crab-shaped nebula found in this position was the ruins of a supernova that had shot out of a dense cluster some 900 years previously, i.e., the year of 1054. This discovery was one of the most significant astronomical findings in the 1960s.
Enormous amounts of records in ancient China on happenings of the stars, comparatively, were most accurate and complete in the world. In terms of data, they held the highest rate of application. It is entirely beyond the imagination of ancient astronomers that their records could serve modern scientific studies. In future along with further developments in science, these ancient records may well prove to be of even greater values.
The period from the 3rd to the 6th centuries was an important stage in the development of culture and science in China, as many outstanding scientists emerged. Zu Chongzhi (420-589) made outstanding contributions to mathematics, astronomy and machine building. He was the first person in the world to bring the calculation of the ratio of the circumference of a circle to its diameter to the seventh decimal place, between 3.1415926 and 3.1415927. His achievement was more than a thousand years earlier than that of his European counterparts. Zu put dozens of his writings on mathematics into a book titled The Art of Mending, which represented the highest achievements in the realm of mathematics at that time. In astronomy, the Daming Calendar he worked out was China's most advanced calendar of his era. After observations and studies, he concluded that a year lasted exactly 365.24281481 days which was only 46 seconds different from the modern estimate. In machine building, records suggested that he made improvements to a compass device for carriages, built a water-mill and a "thousand-li ship". In order to commemorate Zu's outstanding contributions to science, a mountain on the moon has been named after him.
Yi Xing (683-727), a monk of the Tang Dynasty, led a large-scale project to identify the locations of the major stars, and, based on the results, concluded that the length of a degree of the meridian line was 351.27 li by Tang measurement, which meant 123.7 km. This was the first measurement of the meridian ever done in the world.
Around the year 723, Yi Xing and his colleagues constructed an armillary sphere which could move in synchronization with the movements of the heavenly bodies at night. It was installed in an observatory established in Chang'an (Xi'an), the capital of the Tang Dynasty.
Astronomical studies made impressive headway during the Song Dynasty (960-1279). During this period, five large-scale observations of the sky were undertaken, resulting in star maps. The stone planisphere kept in Suzhou today was first drawn during the reign of Emperor Yuanfeng (1078-85) and then committed to stone in 1247 by Wang Zhiyuan of the Southern Song Dynasty. On the map are 1,434 stars, the ecliptic, the equator, the Milky Way and the twenty-eight constellations. The lower part of the planisphere is occupied by explanations totaling 209 characters, which constitute a concise introduction to the astronomical knowledge man had grasped by that time. This is China's earliest and most complete star map still extant.
Shen Kuo was a noted scientist of the Northern Song Dynasty. He left behind a great store of notes and research findings in the fields of geography, geology, astronomy and mathematics. His work Dream Stream Essays contains early discussions of the compass and movable type printing. This book is of great value for the study of the history of science.
Su Song, a Northern Song Dynasty scientist, invented a new type of astronomical instrument powered by hydraulic force -- a water-driven astronomical clock tower which combined the functions of observing the stars, recording astronomical data and telling the time. His book New Design for an Armillary Clock crystallized the highest levels of astronomical science and technology of the 12th century in China.
About 4,000 years ago, the oldest astronomical instrument known to man up to date appeared. It was merely a bamboo pole planted in the ground so that the movement of the sun could be observed from the direction and length of the shadow of the pole. This primitive instrument had two other important functions: One was to judge the time according to the direction of the shadow during the day and the other was to tell the summer and winter solstice by watching the length of the shadow at the noontime of the given day. By adding a disc carved with radiating lines, it became a sundial. The shadows of the bamboo pole happened to be the shortest at the summer solstice and longest at the winter solstice. Experience told people that when the sun began to move northward from the southernmost point, the weather would gradually become warmer, with all things coming back to life. It also meant that famine would soon be ended. In the same fashion, when the sun moved from its northernmost position toward the south, the weather would turn cold, and living things would wither. People then had to store food for the long winter. As a result, the summer and winter solstices were very important to ancient people. To identify the summer and winter solstices thus became one of the most essential purposes of astronomical studies in ancient China.
Guo Shoujing (1231-1316), a noted scientist of the Yuan Dynasty, made major improvements to the sundial. First he created a tower sundial, raising its height from the original 2.66 meters to 13.33 meters, which drastically increased its accuracy. Based on his research, the calendar was revised. His calendar had 365.2425 days in a year, which was only 26 seconds different from the time it takes the earth to go around the sun. His achievement was 300 years earlier than the finalization of the modern calendar. Xing Yunlu, an astronomer of the Ming Dynasty (1368-1644), further raised the height of the sundial by erecting a twenty-meter-tall one and his statistics derived from this sundial enabled him to calculate that there were 365.2417 days in a tropical year, which constituted the most accurate figure at the time in the world, with a difference of only 2.3 seconds from the modern calculation.
Guo Shoujing made great contributions in the areas of astronomy, the calendar and water conservation. He made or improved 13 kinds of astronomical instruments. In 1296, he improved the armillary sphere into an astronomical observation apparatus, in which he discarded the ecliptic ring, and combined the azimuth, equatorial torquetum and sundial into one, which not only simplified the structure but also made the armillary sphere more accurate. It overcame the shortages of the armillary sphere in having too many rings, being difficult to operate and having limited measuring capacity. The equator device in Guo's new instrument was an important invention in astronomical apparatus making and very similar to that in modern astronomical telescopes. Occupying an important position in the world's history of astronomy, Guo's torquetum was 300 years earlier than a similar instrument produced by Danish astronomers.
The water-driven astronomical clock tower was produced by Su Song and Han Gonglian in 1088 in the Northern Song capital of Bianliang, now called Kaifeng. The wooden tower consisted of three levels. The top level housed an armillary sphere to measure the location of the sun, moon and stars; the middle level was reserved for a globe and a mechanical installation which allowed the revolving globe to move in synchronization with that of the natural celestial sphere. The lower level was a wooden cabin divided into five stories, with a door in each story. A wooden puppet would emerge and tell the time by beating a drum every quarter of an hour, waving a bell every hour and beating the bell every two hours.
Counting-rods were used for arithmetical calculations in China for about 1,000 years. During the Song Dynasty (960-1279), the abacus appeared, and gradually replaced the counting-rods.
The earliest calculation tools -- counting-rods--appeared some time in the Western Zhou period (11th century-771 BC). The rods were small sticks of various lengths made of bamboo, bone, bronze, iron or lead. According to the History of the Han Dynasty, the rods were about six Chinese inches or 13.86 centimeters long.
The rods could be placed either upright or horizontally. In the upright position, they represented units of one, one hundred, 100 thousand, million, etc., while horizontally, they represented units of ten, one thousand, 100 thousand, 10 million?. A blank space represented zero. The counting-rods could be used for addition, subtraction, multiplication, division and extraction. And the system used was decimal.
The water clock was an ancient timing device in China, which calculated time according the constant flow of water. A sinking-arrow type bronze water clock of the Han Dynasty (202 BC-AD 220) unearthed in Hanggin Banner, Inner Mongolia, in 1976 is 47.9 centimeters high, 24.2 centimeters deep inside and with a volume of 3,684 cubic centimeters. Wooden arrows carved with scales were fixed to the handle, lid and body of the pot. When water flowed out, the arrows gradually sank, and from their position the time could be determined. This was an early form of water clock. Later, people invented water clocks of multiple containers with floating arrows, which were more accurate.
A copper clepsydra cast in 1316 is the earliest multiple-container water clock extant in China today. Its four component parts, namely, the sun pot, moon pot, star pot and receiving pot, are arranged on a terraced frame next to each other. The four pots resemble cylinders in outside appearance. Their tops, covered with lids, are larger in diameter than their bases. The sun pot, carved with the image of the sun, was the largest. A tube for letting the water flow was fixed to the bottom. The moon pot is carved with the image of the moon, while the star pot is carved with the seven stars of the Big Dipper. To tell the time, water was first poured into the sun pot, which then dripped at a constant rate into the next pot through the tube, until it finally reached the receiving pot. Here there is a copper ruler in the center, bearing 12 marks, each representing a two-hour period. In front of the ruler is a narrow rectangular hole to which is fixed a wooden arrow. Underneath the arrow is a floating boat. As the water level rose, the boat pushed up the arrow. By matching the arrow with the markings on the ruler, one could tell the time of day. Originally, this copper clepsydra was placed on the rostrum of the North Gate Tower in Guangzhou. It was damaged by fire in the 18th century, but was repaired later.
The Arithmetical Classic of the Gnomon and the Circular Paths, written during the Han Dynasty, is an ancient work on mathematics. The book not only summarizes the mathematical achievements made up to that time, such as the multiplication and division of fractions, the application of fractions and the use of right-angled triangles for astronomical calculations, but also records scientific knowledge in many other areas, including the movement of the heavenly bodies, and the fact that the moon reflects the sun's light. Nine Chapters on the Mathematical Art, written during the Eastern Han Dynasty, introduces mathematical achievements up until Eastern Han. The book contains 246 solutions to mathematical problems, arranged in nine chapters. The book touches upon the rules of the four basic operations of fractions, calculation of the area of plane figures, simultaneous linear equations, square and cubic roots, and the rules of addition and subtraction of positive and negative numbers, exerting a great impact on mathematical development in China and the East, and leaving a glorious chapter in the history of mathematics of the world.
Social and economic development as well as the introduction of scientific and technological knowledge from the West during the Qing Dynasty (1644-1911) gave a boost to studies in the natural sciences. In mathematics, Ming Antu, of the Mongolian ethnic group, was a pioneer in examining the ratio of the circumference of a circle to its diameter in his book An Express Way to Solve the Ratio of the Circumference of a Circle to Its Diameter. Mei Wending, another noted mathematician of the same period, made a comparative study of European and traditional Chinese mathematics in an effort to promote the study of mathematics in China. A prolific writer, he wrote A Comprehensive Study of Chinese and Western Mathematics, which included almost all the current knowledge of mathematics worldwide. Wang Xichan, an astronomer, wrote the New Methods of Xiao An, in which he calculated the transits of Venus and Mercury, based on his in-depth studies of Chinese and Western astronomy.
China was also one of the first countries in the world to apply astronomical knowledge to navigation. How does one determine the location of a ship in a boundless ocean? Before the invention of modern navigation technology, the only solution was to rely on observation of the stars.
The Book of the Prince of Huai Nan, which was compiled during the Han Dynasty, describes how locating the polar star can help ships navigate. This is the earliest written work on sea navigation in China, indicating that terrestrial observation was widely applied to sea navigation as early as the initial years of the Han Dynasty.
Zhu Yu of the Song Dynasty wrote in his Pingzhou Table Talks, "The ship's captain, well-armed with knowledge of geography, observed the stars at night and the sun during the day. When it was gloomy, he consulted his compass." Thus, we know that the stars, the sun and the compass were all used to tell directions at sea.
Zheng He, a famous navigator of the Ming Dynasty, undertook several epic sea voyages as commander of the then largest fleet in the world. Apart from the advanced compass, invented in China, he and his fleet also benefited from the method of terrestrial observation to find their way. His fleet cruised through the South China Sea and the Strait of Malacca, to reach the Indian Ocean and the eastern coast of Africa. The book Charts of Zheng He's Voyages presents the entire course of his voyages in the form of charts, from which we learn that different positioning methods were used in three stages: First from Suzhou, China, to the northern tip of Sumatra in Indonesia, compasses were enough, since the fleet sailed with the coast on its right. The second stage was from Sumatra to Sri Lanka, when the fleet went westward without much change of latitude. In addition, the distance between the two places was relatively short. Compass was the major means of positioning, and terrestrial observation was employed as an auxiliary method. The third stage was from Sri Lanka to the eastern coast of Africa across the Indian Ocean. A slight digression of the fleet would take it far away from its destination. As a result, terrestrial observation became the only means of positioning. The book also contains a supplement titled Charts of Relying on the Stars to Cross the Sea. These charts are marked with, in great detail, the locations of the stars and the levels of the horizons when the fleet sailed through the Indian Ocean.