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Shen Kuo

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Shen Kuo
Public Administration
InstitutionsHanlin Academy
Shen Kuo
Sím Kuat

Shen Kuo (

Chancellor Wang Anshi

In his Dream Pool Essays or Dream Torrent Essays[3] (夢溪筆談; Mengxi Bitan) of 1088, Shen was the first to describe the magnetic needle compass, which would be used for navigation (first described in Europe by Alexander Neckam in 1187).[4][5] Shen discovered the concept of true north in terms of magnetic declination towards the north pole,[5] with experimentation of suspended magnetic needles and "the improved meridian determined by Shen's [astronomical] measurement of the distance between the pole star and true north".[6] This was the decisive step in human history to make compasses more useful for navigation, and may have been a concept unknown in Europe for another four hundred years (evidence of German sundials made circa 1450 show markings similar to Chinese geomancers' compasses in regard to declination).[7]

Alongside his colleague

Levi ben Gerson
in 1321.

Shen Kuo wrote several other books besides the Dream Pool Essays, yet much of the writing in his other books has not survived. Some of Shen's

unidentified flying objects from eyewitness testimony. He also wrote commentary on ancient Daoist and Confucian


Birth and youth

Shen Kuo was born in Qiantang (modern-day

From about 1040 AD, Shen's family moved around Sichuan province and finally to the international seaport at Xiamen, where Shen's father accepted minor provincial posts in each new location.[12] Shen Zhou also served several years in the prestigious capital judiciary, the equivalent of a national supreme court.[11] Shen Kuo took notice of the various towns and rural features of China as his family traveled, while he became interested during his youth in the diverse topography of the land.[12] He also observed the intriguing aspects of his father's engagement in administrative governance and the managerial problems involved; these experiences had a deep impact on him as he later became a government official.[12] Since he often became ill as a child, Shen Kuo also developed a natural curiosity about medicine and pharmaceutics.[12]

Shen Zhou died in the late winter of 1051 (or early 1052), when his son Shen Kuo was 21 years old. Shen Kuo grieved for his father, and following

fertilization method relied upon the effective operation of sluice gates of irrigation canals.[14]

Official career

In 1063 Shen Kuo successfully passed the Imperial examinations, the difficult national-level standard test that every high official was required to pass in order to enter the governmental system.[13] He not only passed the exam however, but was placed into the higher category of the best and brightest students.[13] While serving at Yangzhou, Shen's brilliance and dutiful character caught the attention of Zhang Chu (張蒭; 1015–1080), the Fiscal Intendant of the region. Shen made a lasting impression upon Zhang, who recommended Shen for a court appointment in the financial administration of the central court.[13] Shen would also eventually marry Zhang's daughter, who became his second wife.

In his career as a

Liao Dynasty,[15] a military commander, a director of hydraulic works, and the leading chancellor of the Hanlin Academy.[16] By 1072, Shen was appointed as the head official of the Bureau of Astronomy.[13] With his leadership position in the bureau, Shen was responsible for projects in improving calendrical science,[10] and proposed many reforms to the Chinese calendar alongside the work of his colleague Wei Pu.[8] With his impressive skills and aptitude for matters of economy and finance, Shen was appointed as the Finance Commissioner at the central court.[17]

As written by Li Zhiyi, a man married to Hu Wenrou (granddaughter of Hu Su, a famous minister of the Song Dynasty), Shen Kuo was Li's mentor while Shen served as an official.[18] According to Li's epitaph for his wife, Shen would sometimes relay questions via Li to Hu when he needed clarification for his mathematical work, as Hu Wenrou was esteemed by Shen as a remarkable female mathematician.[18] Shen lamented: "If only she were a man, Wenrou would be my friend."[18]

While employed by the central government, Shen Kuo was also sent out with others to inspect the granary system of the empire, investigating problems of illegal tax-collection, negligence, ineffective disaster relief, and inadequate water-conservancy projects.[19] While Shen was appointed as the regional inspector of Zhejiang in 1073, the Emperor requested that Shen pay a visit to the famous poet Su Shi (1037–1101), then an administrator in Hangzhou.[20] Shen took advantage of this meeting to copy some of Su's poetry, which he presented to the Emperor indicating that it expressed "abusive and hateful" speech against the Song court; these poems were later politicized by Li Ding and Shu Dan in order to level a court case against Su. (The Crow Terrace Poetry Trial, of 1079.)[20] With his demonstrations of loyalty and ability, Shen Kuo was awarded the honorary title of a State Foundation Viscount by Emperor Shenzong of Song (r. 1067–1085), who placed a great amount of trust in Shen Kuo.[17] He was even made 'companion to the heir apparent' (太子中允; 'Taizi zhongyun').[1]

Portrait painting of Wang Anshi

At court Shen was a political favorite of the Chancellor

Sino-Vietnamese War of 1075–1077.[23] With his reputable achievements, Shen became a trusted member of Wang Anshi's elite circle of eighteen unofficial core political loyalists to the New Policies Group.[22]

Although much of Wang Anshi's reforms outlined in the

in these battles, and in the sixteen months of Shen's military campaign, he received 273 letters from the Emperor.[17] However, Emperor Shenzong trusted an arrogant military officer who disobeyed the emperor and Shen's proposal for strategic fortifications, instead fortifying what Shen considered useless strategic locations. Furthermore, this officer expelled Shen from his commanding post at the main citadel, so as to deny him any glory in chance of victory.[17] The result of this was nearly catastrophic, as the forces of the arrogant officer were decimated;[17] Xinzhong Yao states that the death toll was 60,000.[1] Nonetheless, Shen was successful in defending his fortifications and the only possible Tangut invasion-route to Yanzhou.[17]

Impeachment and later life

Painting of a Buddhist luohan, by Liu Songnian, painted in 1207; Shen Kuo not only listed literati painting as one of his cherished pastimes, but also Buddhist meditation.[29]

The new Chancellor Cai Que (蔡確; 1036–1093) held Shen responsible for the disaster and loss of life.

geographical atlases for a state-sponsored program, Shen was rewarded by having his sentence of probation lifted, allowing him to live in a place of his choice.[17] Shen was also pardoned by the court for any previous faults or crimes that were claimed against him.[17]

In his more idle years removed from court affairs, Shen Kuo enjoyed pastimes of

Four Arts of the Chinese Scholar

According to

Yangtze River to drown himself. Although this suicide attempt failed, he would die a year later.[31]

In the 1070s, Shen had purchased a lavish garden estate on the outskirts of modern-day Zhenjiang, Jiangsu province, a place of great beauty which he named "Dream Brook" ("Mengxi") after he visited it for the first time in 1086.[17] Shen Kuo permanently moved to the Dream Brook Estate in 1088, and in that same year he completed his life's written work of the Dream Pool Essays, naming the book after his garden-estate property. It was there that Shen Kuo spent the last several years of his life in leisure, isolation, and illness, until his death in 1095.[17]

Scholarly achievements

Shen Kuo wrote extensively on a wide range of different subjects. His written work included two geographical

Gottfried Leibniz and Mikhail Lomonosov.[33]

Raised-relief map

Han Dynasty incense burner, showing artificial mountains as a lid decoration, which may have influenced the invention.[34]

Joseph Needham suggests that certain pottery vessels of the

Ma Yuan (14 BC – 49 AD) is recorded as having made a raised-relief map of valleys and mountains in a rice-constructed model of 32 AD.[35] Shen Kuo's largest atlas included twenty three maps of China and foreign regions that were drawn at a uniform scale of 1:900,000.[6] Shen also created a raised-relief map using sawdust, wood, beeswax, and wheat paste.[6][36] Zhu Xi (1130–1200) was inspired by the raised-relief map of Huang Shang and so made his own portable map made of wood and clay which could be folded up from eight hinged pieces.[37]


For pharmacology, Shen wrote of the difficulties of adequate diagnosis and therapy, as well as the proper selection, preparation, and administration of drugs.[38] He held great concern for detail and philological accuracy in identification, use and cultivation of different types of medicinal herbs, such as in which months medicinal plants should be gathered, their exact ripening times, which parts should be used for therapy; for domesticated herbs he wrote about planting times, fertilization, and other matters of horticulture.[39] In the realms of botany, zoology, and mineralogy, Shen Kuo documented and systematically described hundreds of different plants, agricultural crops, rare vegetation, animals, and minerals found in China.[40][41][42][43] For example, Shen noted that the mineral orpiment was used to quickly erase writing errors on paper.[44]

Civil engineering

pound lock
for canals, invented in China in the 10th century and described by Shen.
Five bracket arm bases and two cantilever arms, from the Yingzao Fashi
of 1103.

The writing of Shen Kuo is the only source for the date when the


If it were not for Shen Kuo's analysis and quoting in his

pagoda that burned down in 1044 and was replaced in 1049 by a brick pagoda (the 'Iron Pagoda') of similar height, but not of his design. From Shen's quotation—or perhaps Shen's own paraphrasing of Yu Hao's Timberwork Manual (木經; Mujing)—shows that already in the 10th century there was a graded system of building unit proportions, a system which Shen states had become more precise in his time but stating no one could possibly reproduce such a sound work.[48][49] However, he did not anticipate the more complex and matured system of unit proportions embodied in the extensive written work by scholar-official Li Jie (1065–1110), the Treatise on Architectural Methods (營造法式; Yingzao Fashi) of 1103.[49][50] Klaas Ruitenbeek states that the version of the Timberwork Manual quoted by Shen is most likely Shen's summarization of Yu's work or a corrupted passage of the original by Yu Hao, as Shen writes: "According to some, the work was written by Yu Hao."[48]


The Chinese had long taken an interest in examining the human body. For example, in 16 AD, the

forensic expert Song Ci (1186–1249) would promote the use of autopsy in order to solve homicide cases, as written in his Collected Cases of Injustice Rectified.[54]


Yang Hui triangle (Pascal's triangle) using rod numerals, from a book by mathematician Zhu Shijie
, 1303
An 18th-century diagram of camera obscura

In the broad field of mathematics, Shen Kuo mastered many practical mathematical problems, including many complex formulas for geometry,[55] circle packing,[56] and chords and arcs problems employing trigonometry.[57] Shen addressed problems of writing out very large numbers, as large as (104)43.[58] Shen's "technique of small increments" laid the foundation in Chinese mathematics for packing problems involving equal difference series.[58] Sal Restivo writes that Shen used summation of higher series to ascertain the number of kegs which could be piled in layers in a space shaped like the frustum of a rectangular pyramid.[59] In his formula "technique of intersecting circles", he created an approximation of the arc of a circle s given the diameter d, sagitta v, and length of the chord c subtending the arc, the length of which he approximated as s = c + 2v2/d.[58] Restivo writes that Shen's work in the lengths of arcs of circles provided the basis for spherical trigonometry developed in the 13th century by Guo Shoujing (1231–1316).[59] He also simplified the counting rods technique by outlining short cuts in algorithm procedures used on the counting board, an idea expanded on by the mathematician Yang Hui (1238–1298).[60] Victor J. Katz asserts that Shen's method of "dividing by 9, increase by 1; dividing by 8, increase by 2," was a direct forerunner to the rhyme scheme method of repeated addition "9, 1, bottom add 1; 9, 2, bottom add 2".[61]

Shen wrote extensively about what he had learned while working for the state treasury, including mathematical problems posed by computing

land tax, estimating requirements, currency issues, metrology, and so forth.[62] Shen once computed the amount of terrain space required for battle formations in military strategy,[63] and also computed the longest possible military campaign given the limits of human carriers who would bring their own food and food for other soldiers.[64] Shen wrote about the earlier Yi Xing (672–717), a Buddhist monk who applied an early escapement mechanism to a water-powered celestial globe.[65] By using mathematical permutations, Shen described Yi Xing's calculation of possible positions on a go board game. Shen calculated the total number for this using up to five rows and twenty five game pieces, which yielded the number 847,288,609,443.[66][67]


Shen Kuo experimented with the

Chinese pagoda by a seashore.[72] Chinese authors from the 12th to 17th centuries would discuss the optical observations made by Shen Kuo but not advance them further, while Leonardo da Vinci (1452–1519) would be the first in Europe to make a similar observation about the focal point and pinhole in camera obscura.[69]

Magnetic needle compass

Since the time of the engineer and inventor Ma Jun (c. 200–265), the Chinese had used the south-pointing chariot, which did not employ magnetism, as a compass. In 1044 the Collection of the Most Important Military Techniques (武經總要; Wujing Zongyao) recorded that fish-shaped objects cut from sheet iron, magnetized by thermoremanence (essentially, heating that produced weak magnetic force), and placed in a water-filled bowl enclosed by a box were used for directional pathfinding alongside the south-pointing chariot.[73][74]

, but not for navigation.