Guo Shoujing

Biography

Guo Shoujing was born in 1231, the eighth year of the Zhengda era under Emperor Aizong of Jin, in Xingtai County, Xingzhou. Historical biographies do not record his father's circumstances in detail; the source states that his father may have died early. Guo was raised by his grandfather Guo Rong. Guo Rong was a respected scholar of the Jin-Yuan transition, knowledgeable in the Five Classics, astronomy, mathematics, and hydraulic technology. Under his upbringing, Guo Shoujing studied diligently from childhood and developed strong practical skills at an early age.

At about fifteen or sixteen, Guo used bamboo strips to construct an armillary instrument on the basis of an illustration in a book. He built an earthen platform for it and used it for astronomical observation. He also studied a rubbing of a stone-carved diagram of a lotus clepsydra made by the Northern Song scholar Yan Su and worked out how the device maintained a stable water level in its water vessel. These early experiments foreshadowed his later achievements in instrument construction and observation.

At the time, Liu Bingzhong, an important adviser and scholar associated with Kublai, was living in mourning for his father on Zijin Mountain southwest of Xingtai. Among his students were Zhang Wenqian, Zhang Yi, and Wang Xun. Guo Rong was friendly with Liu and sent the young Guo Shoujing to study under him. Liu Bingzhong was well versed in the Classics and astronomy, and Guo benefited greatly from his teaching while forming lasting connections with Zhang Wenqian, Zhang Yi, and Wang Xun. This period of study on Zijin Mountain had a major influence on Guo's scholarly career.

The source text states that in 1251, described there as the eighth year of Möngke Khan, Liu Bingzhong was summoned by Kublai, then in charge of Chinese territories south of the Gobi, and after leaving Xingtai introduced Guo Shoujing to Zhang Wenqian. Not long after reaching adulthood, Guo was specifically engaged to plan and design a project begun by local administrators Tuowutuo, Liu Su, and others to regulate and excavate waterways around Xingtai. Drawing on family learning and careful field surveys, Guo quickly reconstructed the system of channels damaged by warfare. The ensuing dredging restored spreading waters to their original courses, and under his direction workers uncovered a stone bridge that had lain buried in silt for nearly thirty years. The project was praised by contemporaries. The writer Yuan Haowen composed "Record of the New Stone Bridge at Xingzhou," in which the "young Master Guo" referred to Guo Shoujing.

In 1260, the first year of Zhongtong, Kublai took the throne at Kaiping, later called Shangdu, and sent Zhang Wenqian to head a pacification commission in Daming Circuit and surrounding areas. Guo accompanied him and continued learning while conducting numerous surveys of rivers and waterworks. In Daming he also assembled craftsmen to cast a version of the lotus clepsydra he had studied in youth, modifying it into what was called the Baoshan Clepsydra.

In 1262, the third year of Zhongtong, Guo Shoujing was recommended by Zhang Wenqian, then serving as a high-ranking executive official, and received by Kublai at Kaiping. He presented six proposals on hydraulic administration. Kublai reportedly nodded in approval at each one and immediately appointed him supervisor of waterways throughout the circuits, responsible for repair and management of canals and watercourses. In 1263 Guo received a silver tally and was promoted to deputy waterways commissioner.

In 1264, the first year of Zhiyuan, Guo and Suotuo Yan traveled to the former Western Xia region to inspect channels and watercourses. Several months later Zhang Wenqian was sent there as a representative of the court. Under Zhang's leadership and support, Guo was ordered to dredge the old Tanglai, Hanyan, and other canals and rebuild sluices and weirs, restoring irrigation to local farmland. The source states that local people appreciated his work and once built a shrine for him at the head of a canal. In 1265 he was promoted to vice director of the Waterways Directorate.

In 1276, the thirteenth year of Zhiyuan, the Waterways Directorate was incorporated into the Ministry of Works and Guo became a director in the ministry. That year, following a proposal Liu Bingzhong had made before his death, Kublai ordered Xu Heng to lead the Astronomical Academy, with Guo Shoujing and Wang Xun as deputies, in preparing a new calendar. Guo and his colleagues led northern and southern astronomical officials in direct observations and advanced the principle that the foundation of calendrical science lay in measurement, and that among the means of measurement none preceded precise instruments.

In 1279, the sixteenth year of Zhiyuan, the Astronomical Bureau was expanded into the Astronomical Academy. Wang Xun became Director of the Astronomical Bureau and Guo became associate administrator of the academy. When presenting the instruments they had made, Guo explained them to Kublai in detail until evening, while Kublai reportedly remained attentive. That same year Guo directed a nationwide astronomical survey referred to in the source as the “Four Seas” survey. In his memorial he recalled that during the Kaiyuan era of Tang, Yixing had instructed Nangong Shuo to measure shadows throughout the empire and that surviving records listed thirteen places. Since the Yuan realm was even larger, he argued, remote observations were necessary because the circumstances and timing of eclipses, the lengths of day and night, and the apparent elevations of celestial bodies differed by location. Because too few observers were currently available, he proposed first erecting gnomons in the north and south and taking direct shadow measurements. Kublai approved. Fourteen observing officials were dispatched on separate routes, reaching east to Goryeo, west to Dianchi, south beyond Zhuya, and north to the Tiele lands. In all, observations were carried out at twenty-seven sites.

The Shoushi Calendar was completed in 1280, the seventeenth year of Zhiyuan. After Wang Xun died in 1281, Guo assumed responsibility for all work of the Astronomical Academy and gradually organized works including Tuibu and Licheng. In 1286 he was promoted to Director of the Astronomical Bureau.

In 1291, the twenty-eighth year of Zhiyuan, a proposal was made to use the Luan and Hun rivers as an upstream route for grain transport to Shangdu. Kublai could not decide and sent Guo Shoujing to inspect the terrain. Halfway through his survey Guo had already determined that the proposals were impractical. When reporting his findings, he presented a number of alternatives, including a new canal scheme for Dadu. Instead of relying on the old source at Yimou Spring, he proposed diverting water from Baifu Spring in the northern hills, turning west and then south through Wengshan Lake, entering the city through the western water gate and collecting in Jishuitan, then turning east and south, leaving through the southern water gate, and joining the existing grain canal. A lock would be placed about every ten li, seven in all before Tongzhou, with additional double gates about one li above each lock so that boats could pass and water levels could be controlled. Kublai was delighted by the memorial and ordered that it be implemented quickly. The Waterways Directorate was reestablished with Guo in charge.

Work began in spring 1292. On the opening day Kublai ordered officials from the Grand Councilor downward to labor personally at the site under Guo's direction. Guo led construction of the Baifu weir system for Dadu and excavation of the northernmost section of the Grand Canal from Tongzhou to Jishuitan in Dadu, present-day Shichahai in Beijing, which became the Tonghui River. He solved the canal's water-supply problem by adapting to the topography of Dadu and installed locks, dams, and regulating gates according to changes in terrain and water-level differences, controlling both the quantity and elevation of water. The Tonghui River was completed in the seventh month of 1293. When Kublai returned from Shangdu to Dadu and passed Jishuitan, he saw vessels covering the water and was greatly pleased. He personally bestowed the name "Tonghui River," awarded Guo 12,500 strings of paper currency, and ordered him to retain his astronomical office while also supervising grain transport on the canal.

In 1294 Guo became grand academician of the Zhaowen Institute and concurrently administrator of the Astronomical Academy. In 1298, the second year of Dade, someone proposed excavating a channel beneath Tiefangan Ridge northwest of Shangdu to discharge mountain floodwater. Emperor Chengzong, Temür, summoned Guo to Shangdu for consultation. On the basis of local terrain and records of past floods, Guo argued that the channel had to be fifty to seventy bu wide, approximately 80–115 meters. Those executing the project thought he was exaggerating and reduced the width by one-third. When mountain floods came the following year, the channel proved too narrow, causing inundation and nearly reaching the emperor's traveling encampment. While taking refuge from the water, Temür reportedly lamented that Grand Astronomer Guo was truly extraordinary and that it was a pity his advice had not been followed.

In 1303, the seventh year of Dade, Emperor Chengzong decreed that officials aged seventy or more could retire. Guo Shoujing alone was not allowed to do so because the court still depended on his work. This created a precedent that astronomical officials of the Astronomical Academy did not retire. After Chengzong's reign the Yuan government declined and internal conflicts within the ruling elite intensified, greatly restricting Guo's creative activity. In contrast with his rising reputation, his later years were comparatively quiet in terms of new work. He died in 1316, the third year of the Yanyou era under Emperor Renzong of Yuan, at the age of eighty-six.

Major Deeds

In addition to improvements in astronomical data, the Shoushi Calendar incorporated major innovations in computation. Its principal features included the following:

Abolition of the accumulated epoch system: The winter solstice used in 1281, the eighteenth year of Zhiyuan, became the principal starting point. For other astronomical cycles, the difference between their epochs and this solstice was calculated as a corresponding constant. This created a system of astronomical constants. The Shoushi Calendar used seven such constants, covering solar terms, revolution, intercalation, eclipse relations, cycles, conjunctions, and calendrical reckoning.

Using ten-thousandths as the daily denominator: Earlier astronomical data were expressed as fractions, making comparison difficult and requiring complex conversion to common denominators. From the Tang onward some calendrical specialists tried to break with this practice. Nangong Shuo's Shenlong Calendar of 705, the first year of the Shenlong era under Emperor Zhongzong of Tang, used a decimal-like hundred-based system, and Cao Shiwei's Futian Calendar of the Jianzhong era under Emperor Dezong of Tang (780–783) more explicitly proposed dividing the day into ten thousand parts. The Shenlong Calendar was not promulgated, and the Futian Calendar circulated only privately and was disparaged by official astronomers as a "minor calendar." The Shoushi Calendar decisively adopted the ten-thousand-part system, making astronomical data simpler and more rational to express.

A correct method for third-difference interpolation: Since Liu Zhuo of the Sui dynasty, astronomers had used second-difference interpolation to calculate non-uniform motions of the sun, moon, and other celestial bodies. Tang astronomers found that second differences were not accurate enough for many motions and that third differences were needed, but no satisfactory third-difference interpolation formula had been established. The Shoushi Calendar introduced a method called zhaochafa, solving a problem that had remained unresolved for more than three centuries. In principle, the method could be generalized to interpolation of arbitrary higher differences.

Use of a geometric arc-chord method: Guo employed a method described in the source as similar to modern spherical-trigonometric calculation to convert between ecliptic and equatorial coordinates.

Determination of precise data: The calendar used 29.530593 days for a month and 365.2425 days for a year. It formally discarded accumulated discrepancies from older calendars in favor of direct observation. It defined each solar term as one twenty-fourth of a year and treated a month lacking a principal term as an intercalary month, a principle the source states continued in later use.

For the calendrical revision, Guo Shoujing redesigned or invented twelve instruments, including the Simplified Armilla and tall gnomon. He emphasized that the foundation of calendrical science lay in measurement and that precise instruments came first among the tools of observation. Wang Xun, Guo Shoujing, and others worked with the Nepalese architect Araniko to build a new observatory in Dadu (Beijing). It housed astronomical instruments designed by Guo and was described in the source as one of the best-equipped observatories in the world at the time. The surviving observatory at Mount Song in Henan, associated with Guo Shoujing, was built for astronomical research.

Dredging the Xingtai waterways: Soon after reaching adulthood, Guo was commissioned to plan and design the dredging of waterways around Xingtai. The work restored spreading waters to their courses and uncovered a stone bridge buried in silt for nearly thirty years.

Waterworks in the former Western Xia region: In 1264 Guo was ordered to dredge the Tanglai, Hanyan, and other old canals and reconstruct their sluices and weirs, restoring irrigation. The source states that twelve main canals and sixty-eight branch channels in Xingzhou, Lingzhou, Yinglizhou, and Mingshazhou were repaired, restoring irrigation to more than ninety thousand qing of land on the Ningxia Plain. Guo proposed overflow dams to reduce current velocity, weirs at diversion points to raise water levels, intake gates at canal heads to ensure adequate water, and drainage gates to regulate flow. These were presented as hydraulic innovations, and the repaired canal structures were reportedly still in use into the mid-Ming.

Tonghui River project: In 1291 Guo proposed a new grain-transport canal for Dadu, bringing water from Baifu Spring into the city, collecting it in Jishuitan, and placing a lock roughly every ten li. Construction began in spring 1292 and was completed in the seventh month of 1293. Kublai named it the Tonghui River. The canal improved north-south transport and the grain-shipping system.

Tiefangan drainage channel: In 1298 Guo recommended a width of fifty to seventy bu. The recommendation was not followed, and mountain floods caused disaster the following year.

In 1279 Guo proposed a realm-wide astronomical survey, described in the source as the “Four Seas” survey, which was carried out by imperial order. Following his recommendation, Kublai dispatched fourteen astronomers beyond Dadu to twenty-six other sites in the realm for major observations. The scale was unusual in the history of astronomy. At six locations they specifically measured the length of gnomon shadows at the summer solstice and the lengths of day and night. The observations supplied scientific data for a calendar intended to apply across the empire. Guo also organized measurements of stellar positions, the winter-solstice point, perigee, and intersections of the ecliptic and lunar path, compiled a table of lunar motion, and measured latitudes at twenty-seven observing sites.